Construction and initialization of a temperature dependent
magnetorelaxometry measurement system for the quantitative
detection of magnetic nanoparticles in biological samples
vorgelegt von
Dipl.-Ing. Christian Knopke
aus Meerane
von der Fakultät V - Verkehrs- und Maschinensysteme
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. phil. Dietrich Manzey
Gutachter: Prof. Dr.-Ing. Marc Kraft
Gutachter: Jun.-Prof. Dr.-Ing. Daniel Baumgarten
Tag der wissenschaftlichen Aussprache: 21. Dezember 2016
Berlin, 2017
D 83
Eidesstattliche Erklärung
Der Autor versichert, dass er über die urheberrechtlichen Nutzungsrechte an allen Teilen des
Werkes verfügt und Rechte Dritter, insbesondere Urheber- und Persönlichkeitsrechte Dritter, mit
der Veröffentlichung nicht verletzt werden.
Hiermit versichert der Autor, dass der Autor die vorliegende Arbeit selbstständig verfasst und keine
anderen als die angegebenen Quellen und Hilfsmittel benutzt wurden. Alle Ausführungen, die
anderen veröffentlichten oder nicht veröffentlichten Schriften wörtlich oder sinngemäß entnommen
wurden, wurden kenntlich gemacht.
Die Arbeit hat in gleicher oder ähnlicher Fassung noch keiner anderen Prüfungsbehörde vorgelegen.
Ort, Datum Unterschrift
Abstract
The unique physical properties of magnetic nanoparticles (MNPs) have attracted increasing interest
from researchers around the world. In particular, biomedical applications of MNPs are currently
a growing research topic in medical science. However, all biomedical applications of MNPs
crucially depend on reliable quantification methods that determine the concentration of MNPs
in biological tissues. While well-established photometric iron quantification methods exist, they
generally do not differentiate between iron originating from MNPs and other natural iron deposits
in the body. In contrast, magnetorelaxometry (MRX), an analysis method based on the detection
of the specific magnetic signals originating from MNPs, is capable of determining the particle
content in biological tissues. However, MRX quantification is limited to MNPs with a magnetic
core diameter of approximately
15 nm
to
25 nm
. The relaxation times for MNPs with smaller core
diameters are too short to be determined at room temperature.
In the course of this thesis, MRX measurements were performed at various temperatures well below
room temperature to investigate MNPs with core diameters <
15 nm
. This analysis of the relaxation
amplitude as a function of temperature is referred to as temperature dependent magnetorelaxometry
(TMRX). In addition to quantification of MNPs, TMRX analyses can be performed to investigate
changes in the relaxation signal of the particles, which can be caused by in vivo concentration
effects, dipole–dipole interactions between the particles, and interactions of the MNPs with the
surrounding media.
This thesis was aimed to establish TMRX as an in vitro quantification method for MNPs in
biological tissue samples. To do so, an existing measurement device (MPMS-XL, Quantum Design)
was employed to perform TMRX analyses. With this device, the influence of the core size and size
distribution of particles on their TMRX signals was investigated, and a quantification method for
particles with diameters <
15 nm
was developed. In addition, TMRX analyses were performed to
investigate dipole–dipole interactions between the particles. However, TMRX analyses with this
device were very time consuming and a single relaxation measurement took up to
40 min
, which
in turn limited the sampling rate of the measured TMRX spectra. Therefore, only particularly
long relaxations could be detected in this so-called long time regime of the Magnetic Property
Measurement System (MPMS).
To perform TMRX analyses in the short time regime of only a few seconds, a custom instrument
was designed. For this purpose, an existing, magnetically shielded MRX system was extended
using a helium flow cryostat as a temperature-controlled sample holder and magnetizing unit. The
highly sensitive magnetic sensors of this system required only non-magnetic and non-metallic
materials for its construction. In addition, a magnetizing coil had to be designed and characterized
for magnetizing the tissue samples. Therefore, the construction and initialization of this temperature
controlled sample holder with a magnetizing unit was one of the key aspects of this thesis.
To conclude, the in vitro quantification of MNPs in biological tissues was established using TMRX
analyses in the long and short time regime. In addition, dipole–dipole interaction was investigated
using TMRX analyses, which led to the development of a novel empirical model describing
the interaction energy in MNP samples. Therefore, the performed analyses exhibited the strong
potential of TMRX as an investigation method to quantify and characterize MNP in biological
tissues.
Zusammenfassung
Die einzigartigen physikalischen Eigenschaften magnetischer Nanopartikel (MNP) haben in den
vergangenen Jahren das Interesse von Wissenschaftlern aus aller Welt geweckt. Insbesondere die
biomedizinischen Anwendungsmöglichkeiten der MNP sind aktuell ein wachsendes Forschungsfeld.
Allerdings hängen die biomedizinischen Anwendungen der MNP entscheidend von verlässlichen
Quantifizierungsmethoden ab, welche die MNP-Konzentration in biologischen Geweben bestimmen
können. Die etablierten photometrischen Eisenquantifizierungsmethoden können nicht zwischen
Eisen, welches von Nanopartikeln stammt, und körpereigenem Eisen unterscheiden. Im Gegensatz
zu diesen Methoden kann die Magnetrelaxometrie (MRX) die Menge an MNP in biologischen
Geweben bestimmen, basierend auf dem spezifischen magnetischen Signal der MNP. Dennoch ist
die MRX-Quantifizierung nur für MNP mit Kerndurchmesssern von
15 nm
bis
25 nm
möglich, da
die Relaxationszeiten kleinerer MNP zu kurz sind, um bei Raumtemperatur detektiert zu werden.
Im Zuge dieser Arbeit wurden MRX-Messungen bei verschiedenen Temperaturen unterhalb der
Raumtemperatur durchgeführt, um MNP mit Kerndurchmessern von <
15 nm
zu untersuchen. Diese
Untersuchung der Relaxationsamplitude als Funktion der Temperatur wird auch als temperat-
urabhängige Magnetrelaxometrie (TMRX) bezeichnet. Zusätzlich zur Quantifizierung der MNP
kann die TMRX auch genutzt werden, um Änderungen im Relaxationssignal der Partikel zu
untersuchen. Diese Änderungen können dabei von in vivo Konzentrationseffekten, der Dipol–Dipol-
Wechselwirkung zwischen den MNP und von Wechselwirkungen der MNP mit dem umgebenden
Medien stammen.
Das Ziel dieser Arbeit war es, TMRX als in vitro Qantifizierungsmethode für MNP in biologischen
Gewebeproben zu etablieren. Um dieses Ziel zu erreichen, wurde zunächst ein existierendes Mess-
gerät (MPMS-XL, Quantum Design) für TMRX-Messungen verwendet. Mit diesem Messgerät
konnte der Einfluss der Kerngröße und Größenverteilung der Nanopartikel auf das TMRX Signal
untersucht, sowie eine Quantifizierungsmethode für MNP <
15 nm
entwickelt werden. Zusätzlich
wurde das TMRX-Messverfahren genutzt, um die Dipol–Dipol-Wechselwirkung zwischen Partikeln
zu untersuchen. Die TMRX-Messungen mit diesem Messgerät sind sehr zeitaufwendig, da schon
eine einzelne Relaxationsmessung bis zu
40 min
braucht. Die lange Messzeit senkt zusätzlich die
Auflösung der TMRX-Spektren. Mit dem Magnetic Property Measurement System (MPMS) kön-
nen daher nur besonders lange Relaxationen gemessen werden im sogenannten langen Zeitregime.
Um TMRX Messungen im kurzen Zeitregime mit einer Messzeit von wenigen Sekunden durch-
zuführen, wurde daher ein eigenes Messinstrument konstruiert. Zu diesem Zweck wurde ein
bereits vorhandenes, magnetisch-geschirmtes MRX-System mit Hilfe eines Helium-Durchfluss-
Kryostanten um einen temperierbaren Probenhalter und eine Magnetisierungseinheit erweitert.
Die hoch-sensiblen magnetischen Sensoren des Systems erlaubten dabei nur unmagnetische und
nichtmetalische Werkstoffe als Konstruktionsmaterial. Zusätzlich wurde eine Magnetisierungsspule
für die Charakterisierung und Magnetisierung der Gewebeproben entworfen. Die Konstruktion
und Inbetriebnahme des temperierbaren Probenhalters mit Magnetisierungseinheit stellt daher ein
Schwerpunkt dieser Dissertation dar.
Zusammenfassend lässt sich sagen, dass die in vitro Quantifizierung von MNP in biologischem
Gewebe mittels TMRX im kurzen und langen Zeitregime erfolgreich etabliert wurde. Zusätzlich
wurde die Dipol–Dipol-Wechselwirkung mit Hilfe der TMRX untersucht und ein neues empirisches
Model zur Beschreibung der Wechselwirkungsenergie in MNP-Proben entwickelt. Die durchge-
führten Untersuchungen zeigen daher das starke Potential der TMRX als Untersuchungsmethode
zur Quantifizierung und Charakterisierung von MNP in biologischem Gewebe.
Danksagung
Diese Arbeit ist im Rahmen meiner wissenschaftlichen Tätigkeit an der Physikalisch–Technischen
Bundesanstalt (PTB) in Kooperation mit der SocraTec R&D GmbH entstanden. Ich bedanke mich
daher bei Arbeitsgruppenleiter Lutz Trahms dafür, dass er diese Gelegenheit an der PTB ermöglicht
hat und bei dem gesamten Team von SocraTec, dass sich für mich eingesetzten hat. Mein höchster
Dank gilt Frank Wiekhorst für seine konsequente Unterstützung, Geduld und wissenschaftliche
Betreuung während der gesamten Promotionsphase.
Für die Unterstützung beim Entwerfen und Konstruieren des Kryostaten möchte ich mich bei Dirk
Gutkelch und Götz Klaukin bedanken und die hervorragende Arbeit der gesamten Institutswerkstatt
der PTB loben. Bei Jens Voigt, Rainer Körber und Allard Schnabel möchte ich mich dafür bedanken,
dass sie mir mit ihrem einmaligen Erfahrungschatz über die Inbetriebnahme von Helium-Kryostaten
besonders in den kritischen Phasen der Doktorarbeit mit Rat und Tat beistanden.
Ohne die professionelle Unterstützung von Maik Liebl und Nora Höfner beim Betreiben der MRX-
Messtechnik wäre die Arbeit in dieser Form nicht möglich gewesen. Für ihre Hilfe möchte ich mich
besonders bedanken. Für ihre selbstlose Hilfsbereitschaft bedanke ich mich bei Patricia Radon. Das
erfolgreiche Betreiben der Sensortechnik ist ihrer professionellen Unterstützung zu verdanken. Bei
Dietmar Eberbeck möchte ich mich für die vielen Gespräche über die Wechselwirkung der Nanopar-
tikel bedanken, die entscheidend zur Entwicklung des neun Wechselwirkungsmodells beigetragen
haben. Ebenso bedanke ich mich bei Norbert Löwa und Uwe Steinhoff für ihre Anregungen und
ihre Unterstützung bei meinem wissenschaftlichen Werdegang. Natürlich möchte ich mich auch
bei Olaf Kosch bedanken, welcher mich 2007 im Rahmen meiner studentischen Tätigkeit mit der
PTB und SocraTec in Kontakt brachte und mir die Welt der Wissenschaft eröffnete.
Besonderen Dank auch an den gesamten Fachbereich 8.2 für die stets freundschaftliche Arbeit-
satmosphäre und stete Hilfsbereitschaft, die wesentlich zum Gelingen dieser Arbeit beigetragen
haben.
Contents
IBackground
1Introduction .................................................. 23
1.1 Magnetic Nanoparticles in Medical Science 24
1.2 Aim of the Thesis 25
1.3 Way of Proceeding 25
1.4 Clinical Applications of Magnetic Nanoparticles 27
1.4.1 Drug Targeting 27
1.4.2 Hyperthermia 28
2Theoretical Background ....................................... 31
2.1 Magnetism in Nanoparticles 32
2.1.1 Superparamagnetic Single-Domain Particles 32
2.1.2 Néel and Brownian Relaxation of Magnetic Nanoparticles 33
2.1.3 Particle Distribution 35
2.1.4 Dipole–Dipole Interactions 36
3Measuring Principles ......................................... 39
3.1 Magnetorelaxometry (MRX) 40
3.1.1 Basic Principles 40
3.1.2 Magnetorelaxometry Measurement Setup 41
3.2 Temperature Dependent Magnetorelaxometry (TMRX) 43
3.2.1 Basic Principles 43
3.2.2 Creation of the TMRX Spectrum 44
3.2.3 Influence of the Particle Core Size on the TMRX Spectrum 44
3.2.4 Influence of the Particle Core Size Distribution on the TMRX Spectrum 45
3.2.5 TMRX using a Magnetic Property Measurement System 45
3.2.6 TMRX using the 6-Channel SQUID System 47
II Results
4TMRX Analyses in the Long Time Regime ...................... 51
4.1 Data Analysis for the Magnetic Property Measurement System 52
4.1.1 Uncertainty of the Measurement Results 52
4.1.2 Fitting the Exponential Decay of the Measured Relaxation Signal 54
4.1.3 Analysis of the Switch-Off Time of the Superconducting Magnet 55
4.1.4 Communication with a Magnetic Property Measurement System 56
4.2 Influence of Magnetic Nanoparticle Amount on the TMRX Spectrum 58
4.2.1 Analysis of a Magnetic Nanoparticle Dilution Series 59
4.2.2 Quantification of the Iron Content via Peak Comparison 60
4.2.3 Analysis of Magnetic Nanoparticles in Cell Samples 62
4.3 Influence of the Magnetizing Field Strength on the TMRX Spectrum 65
4.3.1 Magnetizing Field Strength dependent Changes in the Relaxation Signal 66
4.4 Influence of Particle Aggregation on the TMRX Spectrum 68
4.4.1 Influence of Dipole–Dipole Interactions on the TMRX Spectrum 69
4.4.2 Quantification of Aggregated and Unaggregated Particles 70
4.5 Multicore Particle Analysis via TMRX of Underlying Fractions 72
4.5.1 TMRX Analysis of Multicore and Precursor Particles 73
4.5.2 TMRX Analysis of Separated Particles 74
5Numerical Simulation of TMRX Spectra ......................... 77
5.1 Influence of Dipole–Dipole Interactions on the TMRX Spectrum 78
5.2 Simulation of TMRX Spectra of Non–Interacting Particles 80
5.3 Simulation of TMRX Spectra Including Dipole–Dipole Interactions 84
6Development of a TMRX System for the Short Time Regime ..... 89
6.1 Custom TMRX Measurement System 90
6.1.1 Description of the Temperature Controlled Sample Holder 90
6.1.2 Description of the 6-Channel TMRX Measurement Setup 93
6.2 Characterization of the GRP Cryostat with Magnetizing Coil 94
6.2.1 Characterization of the Magnetizing Coil 94
6.2.2 Magnetic Characterization of the System 96
6.2.3 Determination of the Sample Position 98
6.2.4 Temperature Calibration at the Sample Position within the Cryostat 100
6.3 Quantification of Magnetic Nanoparticles using TMRX in the Short Time
Regime 103
6.3.1 TMRX Analysis of the Resovist Dilution Series 104
6.3.2 Magnetic Nanoparticle Quantification Using the 6-Channel SQUID System 107
6.4 Quantification of Magnetic Nanoparticles in Biological Tissues using TMRX
in the Short Time Regime 109
7Conclusion .................................................. 113
7.1 Summary and Conclusion 114
III Appendices
8Magnetic Property Measurement System (MPMS) .............. 119
8.1 Description of the Magnetic Property Measurement System 120
9Construction ................................................ 125
9.1 6-Channel SQUID System for TMRX 126
9.2 6-Channel SQUID System: Additional Graphics and Pictures 127
9.3 Technical Drawings of the GRP Cryostat 129
9.3.1 MPMS measurements from Chapter 6.4 134
9.3.2 Measurement and Fit Data from Chapter 5.3 135
List of Figures
1.1 Illustration of a magnetic nanoparticle with a
a
Superparamagnetic core,
b
Dextran
coating, cPolyethylene glycol (PEG) layer, and dAntibody. 24
1.2 Picture of the TMRX measurement setup. The GRP Cryostat, which was designed
and constructed in the course of this thesis, is inserted into the 6-channel SQUID system.
The cryostat is cooled by liquid helium via the controllable helium transfer tube. The
read out of the temperature sensor and control of the helium flow is established via the
temperature control system. 26
1.3
a)
Application of magnetic nanoparticles in a tumor supplying artery. The particles
are magnetically guided into the malign tissue using an external high gradient DC magnet.
b)
Once the particles have reached the tumor, an external AC coil exposes the particles to
an alternating magnetic field. Because of physical loss processes, the particles heat the
surrounding tissue. 29
2.1 Illustration of the magnetic moments in a single domain MNP solution. Each particle
consists only of one magnetic domain, which can be described through its magnetic
moment and orientation. (A) Without an external magnetic field, the magnetic moments
randomly orient into an equilibrium state. (B) With an external magnetic field, the single
particles change their orientation in the direction of the external field. 32
2.2 Magnetization patterns of aferromagnetic and bsuperparamagnetic materials. 33
2.3 Influence of the particle distance (
D
) on the Néel relaxation time (
τ
). With decreasing
distance, the MNP relaxation time increases exponentially. The relaxation time of a
20 nm
particle at 290 K is displayed. 37
12 LIST OF FIGURES
3.1 Procedure for MRX analyses: Prior to the magnetizing phase, the particles are
randomly oriented and no net magnetic moment is detectable. When the external magnetic
field is applied, the magnetic moments of the particles align in the direction of the field
when it is applied, and then after a short delay time following switch-off of the field, the
relaxation is measured. During this measurement phase, the single magnetic moments of
the MNP sample realign into a random equilibrium. The magnetic moments colored in red
are aligned in the direction of the external magnetic field while the opposing moments are
colored in blue. 40
3.2 Typical MRX setup: The magnetization coil creates a homogeneous magnetic field
in the sample space during the magnetization phase (blue arrows). After switching off
the coil, the SQUID detects the decaying net magnetic moment of the MNP sample. The
magnetic field of the sample is illustrated in red. The superconducting, low–temperature
SQUID sensors require liquid helium as coolant in order to operate inside the insulating
Dewar vessel. 42
3.3 Measurement ranges for the MPMS and MRX 6-channel SQUID systems for particles
of different sizes at
5 K
,
100 K
, and
300 K
. The Néel relaxation time (
τ
) was determined for
monodisperse particles with an effective anisotropy of
1·104J/m3
that are not affected by
dipole-dipole interaction (Equation 2.4) 43
3.4 Left: A typical TMRX plot where the amplitude change (
∆M
) is displayed as a function
of temperature. The maximum relaxation amplitude was observed at
30 K
, indicating that
the investigated MNPs had a magnetic core size of
7 nm
to
10 nm
. Right: Single relaxation
curves at selected temperatures. The amplitude change is more or less pronounced
depending on the temperature. 44
3.5 TMRX signals of two similar MNP samples differing only in their magnetic core
diameters. Sample
A
(blue), with a core diameter of
6 nm
, had a maximum relaxation
amplitude at
15 K
, whereas sample
B
(orange), with a core diameter of
7 nm
, exhibited its
maximum relaxation amplitude at
25 K
. The different peak temperatures are indicated by
the arrow. Because of the similar size distributions of the two particle samples, the shapes
of the two curves resembled each other, even though the peak temperatures for the two
particle systems were different. 46
4.1 In RSO mode the sample is periodically moved through a second order gradiometer.
The SQUID response depends on the sample position within the gradiometer (Picture
from Manual [
1
]). The samples magnetic moment and fit quality are determined through
comparison of the SQUID response with a previously defined response curve of a reference
sample. 52
4.2 Relative magnetic moments of different RSO measurements and their corresponding
fit qualities. A lower fit quality resulted in a decreased accuracy for a given magnetic
moment. A confidence interval of 95% was obtained. 53
4.3 Left: Exponential least squares fit (red line) of relaxation measurements, each
consisting of 100 single RSO scans. The RSO measurements in the first five minutes
experienced more variation because they only consisted of single RSO scans while the
latter scans were repeated three times. Right: Residual of the fitted exponential function.
The upper maximum deviation from the fit was approximately ±3·10−8Am253
4.4 TMRX graph with error bars determined from the residuals of the fitted relaxation
curves. The error bars are more or less pronounced depending on the signal strength at
each temperature. The fit quality varied from a good average of 0.8 at room temperature
to a low quality of 0.2 below 100 K. 54
LIST OF FIGURES 13
4.5 Switch–off and switch–on times of the MPMS superconducting magnet for set fields
ranging from 0,1 mT to 5 T. 55
4.6 Dilution series of the CD021110 magnetic nanoparticle solution in PCR tubes. 58
4.7 Relaxation curves for the CD021110 solution at different temperatures (10 of 17
curves are displayed). In the first 7 minutes, each data point was determined from a single
RSO scan while the subsequent points obtained by averaging 3 RSO scans. 59
4.8 TMRX spectra of the different CD021110 dilution samples. The amplitude change
(
∆
m) of each relaxation curve is displayed at the measured temperature. The maximum
amplitude for each sample was observed at approximately
20 K
. The detection limit for
this dilution series was determined with approximately
5·10−8Am2
. Due to the logarithmic
display negative data points are not shown. At temperatures above
200 K
no relaxation
was observed within the measurement time window. 60
4.9 Total Iron Contents in the CD021110 dilution samples versus their relaxation ampli-
tudes (∆m) at their peak temperatures. 61
4.10 Relaxation amplitude (
∆
m) as a function of temperature for CD021110 and Feraheme
R
.
Even small differences in the particle characteristics resulted in noticeable changes in the
relaxation amplitude curves. 62
4.11 MRX analysis of the control sample. No relaxation was observed. The background
signal was
0,3 µAm2
for the first
7 min
of detection and, then decreased to approximately
0,1 µAm2because of the change in the number of averaged RSO measurements. 63
4.12 Temperature dependent magnetorelaxometry spectra for HeLa tumor cell lines and
the initial CD021110-MNP solution as a reference. The TMRX spectra indicate that the
MNP signals mainly differed in their relaxation signal strengths. The shapes of the curves
remained the same for the incubated and non–incubated MNP samples. 63
4.13 TMRX signals for the Resovist precursor DDM 128 at different magnetization field
strengths. The TMRX signal for DDM 128 exhibited two distinct peaks at
15 K
and
150 K
that were attributed to the bimodal distribution of the particle core size. Changes in the
field strength had varying impacts on the particles of different sizes. The larger particles
were less affected by higher field strengths because they were already saturated. 66
4.14 Left: Magnetization curves for small (blue line) and large (red line) superpara–
magnetic particles. The larger MNPs exhibited a steeper slope than the smaller particles.
Right: Magnetization and relaxation processes during an MRX procedure. The larger par-
ticles required a lower magnetization field strength to reach their saturation magnetization.
Therefore, the larger particles were less magnetized than their smaller counterparts when
exposed to the same magnetic field
Hmag
. This leading to a smaller amplitude change
during the relaxation process. 67
4.15 Left:
30µL
of the original particle solution in distilled water. Right: Visible aggregation
and sedimentation
30 min
after addition of a sodium chloride solution (
cNaCl =1 mol/L
). 68
4.16 Changes in the TMRX signal through enforced aggregation. Both the stable and
aggregated MNP samples exhibited relaxation signals at nearly every investigated temper-
ature, with peak temperatures at 130 K and 210 K, respectively. 69
4.17 TMRX signals of original (left) and aggregated (right) particles at different concen-
trations. The overall amplitude declined with increasing dilution. The peak temperatures at
130 K
for the original and
210 K
for the aggregated MNP samples remained unchanged for
the different dilution steps. 70
14 LIST OF FIGURES
4.18 Nominal total iron content versus relaxation amplitude at the maximum tempera-
ture for aggregated and unaggregated particles. While the samples had different peak
temperatures, the ratio of the amplitude to the iron content was the same for both. 71
4.19 (Left) Transmission Electron Microscopy (TEM) image of the DMSA–coated precur-
sor and (right) Gum Arabica multicore particles. (Picture from [67]) 72
4.20 TMRX Spectra of precursor and GA-coated MNPs. The precursor particles (gray
squares) exhibited the largest relaxation amplitude at
60 K
and a secondary shoulder at
120 K
. The GA–covered multicore particles (red squares) only exhibited one maximum at
130 K. 73
4.21 The eluate (blue diamonds) exhibited a peak amplitude at
110 K
whereas the
discharge (orange circles) displayed a maximum at
70 K
to
80 K
. The amplitude strength
per mg of iron for both fractions was slightly higher than that of the original precursor. 74
4.22 TMRX results for the aggregated precursor (stars) compared to the signals shown
in Figure 4.20 and 4.21. The peak temperature for the aggregate was
175 K
, and its
amplitude per gram iron was only 30 % of that of the precursor. 75
5.1 TMRX spectra of the investigated MNP dilution series normalized to the iron content.
The spectra were well described by a log-normal distribution of temperatures, from which
the median temperature Tmed was extracted. 79
5.2 Median temperature obtained from the log-normal fit of the TMRX spectra for the
Endorem dilution series. The medium temperature was plotted as a function of the
corresponding concentration. 79
5.3 Discretized core diameters (
di
) with corresponding probability densities (
Pi
) when
˜
d=10 nm
and
σd=0,3
. In order to illustrate the discretization of
¯
d
, a particular large
discretization step size was chosen. Highlighted respectively in green, red, and orange
are the discrete values for the
8 nm
,
8,5 nm
, and
9 nm
sized particles in the simulated
distribution. In Figures 5.4 and Figure 5.5, their influence on the magnetization process
and relaxation signal at a specific temperature are displayed. 80
5.4 Simulation of the magnetization process at
10 K
based on the
10 nm
particle dis-
tribution displayed in Figure 5.3. The time dependency of the magnetizing phase was
calculated using Equation 5.6. The net magnetization of the sample was calculated by
summing up the magnetizations of the discretized particle sizes according to their proba-
bility densities. In the MPMS magnetization process, the magnetization time (
tmag
) was set
to
480 s
and the external field to
1 mT
. Although the particle distribution exhibited a median
at
10 nm
, the particles that were active at
10 K
were in the
8 nm
(green) to
9 nm
(orange)
range. Most prominent was the influence of the
8,5 nm
particles (red) on the magnetization
curve. 81
5.5 Relaxation process for the
10 nm
particle distribution shown in Figure 5.3 simulated
using the discretized Néel formula (Equation 5.8). The relaxation signal is the summation
of the individual decaying moments of the discretized particles. At
10 K
, particle cores with
a diameter of
8,5 nm
(red) relaxed mainly in the first few minutes. Smaller particles (e.g.,
8 nm
, green, see Figure 5.4) relaxed in the microsecond range and are therefore not seen
here. Only larger particles with diameters near
9 nm
relaxed over the entire measurement
time of
45 min
. A dead time of
90 s
, which is typical for MPMS analyses, is indicated with
a red dashed line. The amplitude change (
∆m
) is the difference between the magnetic
moment at the end of the dead time and the remaining magnetic moment at the end of the
measurement phase. 82
LIST OF FIGURES 15
5.6 Simulated TMRX spectra of four different simulated samples displayed as a function
of temperature. The spectrum for a monodisperse sample consisting only of
10 nm
particles is illustrated in blue while the spectrum for a simulated MNP sample with a core
size distribution of
˜
d=10 nm
and
σ=0,3
is presented in red. Distributions with
σ=0,2
(orange) and σ=0,1(brown) are also shown. 83
5.7 TMRX simulations of a log-normal distributed particle system with a mean diameter
of
8 nm
and a size distribution with
σ=0,25
. Different interaction energy terms (
Ed
) for the
approaches A, B, C, and D were implemented. With a decreasing inter–particle distance
(
D
), the maximum temperatures and shapes of the TMRX spectra changed. The arrows
indicate how the increasing interaction energy changes the value of
Tmax
in the TMRX
spectra. 85
5.8 TMRX results for dilution step C2 (red squares). Simulation of approaches A, C, and
D for a log-normal distributed particle system with a mean diameter of
8 nm
and a size
distribution of
σ=0,25
. The interaction energy for each approach caused a shift of
Tmax
from 15 K to 28 K. In approach A, the spectrum was shifted as a whole and not stretched
like in approaches C and D. 86
5.9 Relationship between the experimentally determined nominal iron contents of the
Endorem dilution series and the iron contents quantified using the approaches A, C, and
D and the peak comparison method. 87
6.1 Experimental Setup: The data acquisition system (DAQ) reports the relaxation
signal (
a
) obtained using the SQUID system and controls the magnetization coil (
b
).
The temperature controller reports the data for the temperature sensor (
c
) in the glass
reinforced plastic (GRP) cryostat and controls the needle valve (
d
) in the helium transfer
tube. The measured temperature is then transmitted to the DAQ System (a). 90
6.2 One layer of (left) aluminum-coated fabric and (right) slit Mylar film. The aluminum-
coated fabric is used as insulation in the Dewar. 91
6.3 Arrangement of the temperature diodes around the sample space. During MRX
analyses, the permanently installed temperature diode can only measure the system
temperature
4 cm
from the sample. In order to calibrate the system, a second (calibration)
sensor is installed in a sample dummy. 92
6.4 Transversal field at the center of the magnetizing coil at
356 mA
for different longitudi-
nal offsets. The longitudinal center of the
6,9 cm
long coil is marked as zero on the X-axis.
The direction toward the helium transfer tube is negatively notated. The curve reveals that
the coil produces a small transversal field that is strongest at its longitudinal boundaries.
The maxima are therefore at
−4,25 cm
and
4,0 cm
. The transversal field strength at
356 mA
ranges from 30 µT to 40 µT at these maxima. 94
6.5 Longitudinal field in the center of the magnetizing coil at
356 mA
for different axial
offsets. The center of the
6,9 cm
long coil is marked as zero on the X-axis. The direction
toward the helium transfer tube is negatively notated. The curve reveals a maximum
plateau ranging from −2 cm to 2 cm with a field strength of approximately 1 mT. 95
6.6 Switch-off procedure for the magnetizing coil measured with a Digital Storage Oscil-
loscope (Agilent Technologies, DSO-X 2004A). After the switch-off impulse is initiated at
t=0 s
, the voltage in the coil drastically decreases. After
20 µs
, the overshooting oscillation
ceases as well. 96
16 LIST OF FIGURES
6.7 MRX relaxation amplitude changes for the silica diode at different longitudinal po-
sitions in the 6-channel SQUID system are displayed for one SQUID sensor. The tem-
perature sensor generates a dipole moment similar to that of an MNP sample because
of its magnetic elements. The MRX analysis of the sensor was performed at different
longitudinal positions from
−40 mm
to
40 mm
relative to the center of the magnetizing coil.
A typical MRX sequence (
Bmag =1 mT
,
tmag =1 s
,
tmeas =1 s
) was performed at each position,
and the sensor was operating during the MRX analysis. Therefore, the wires connected to
the sensor conducted a 10 µA current. 98
6.8 Illustration of the sample position relative to magnetizing coil and SQUID. The sample
is not positioned directly under the SQUID because the sensor can only detect transversal
magnetic fields. Instead, it is placed with a longitudinal offset of approximately
4 cm
in
order to optimize the transversal magnetic field relative to the SQUID. The magnetizing coil
and the permanent temperature sensor are placed directly beneath the SQUID. Through
this arrangement, the sensor is less affected by the magnetic dipole fields because they
are mainly longitudinal at the center position. 99
6.9 Arrangement of the temperature diodes around the sample space. The helium flow is
illustrated in blue. The permanent sensor (red) can only measure the sample temperature
indirectly. The calibration sensor (green) is installed in a sample dummy. During calibration
measurements, both sensor signals are stored in a look-up table. 100
6.10 Typical temperature cool down sequence of the GRP cryostat for the calibration
of the temperature at the sample position. The temperature of the diode which is four
centimeter away from the sample space is displayed in black, while the sample temperature
is displayed in red. In this sequence the system temperature falls from
290 K
to
5 K
in less
than 20 minutes. During that time an offset between the sensor and the sample is visible.
101
6.11 (Left): Relaxation measurement at
275 K
for the most concentrated Resovist sam-
ples obtained using MPMS. The relaxation process in the long time regime took
40 min
.
(Right): Relaxation measurement performed using the GRP Cryostat in the 6-channel
SQUID system. The measurement time in the short time regime only required
1 s
. In
both plots, a relationship between the amplitude change and the MNP concentration was
observed. However, the decay of the relaxation after switching off the external field was
significantly more pronounced in the short time regime. 104
6.12 (Left) TMRX results for the Resovist dilution series performed using MPMS. (Right)
TMRX results obtained using the GRP cryostat in the 6-channel SQUID system. The
investigated temperature ranged from
5 K
to room temperature for both systems. Both
spectra were bimodal, with one peak at
25 K
and a second peak at
200 K
to
300 K
. Notably,
while the second peak was between
200 K
and
250 K
in the spectrum obtained via MPMS
(left), it appeared near room temperature in the spectrum obtained using the 6-channel
SQUID system (right). 105
6.13 Peak temperatures for Resovist samples of different concentrations observed in the
MPMS long time regime and 6-channel SQUID system short time regime. Each TMRX
spectrum exhibited two distinct peak temperatures. The constant offset between the
measured peak temperatures was attributed to the different time regimes. 106
LIST OF FIGURES 17
6.14 Nominal iron content in the different Resovist samples versus the iron content
determined using three different methods. The concentration of iron in the samples
varied by several orders of magnitude. The axis in the figure are therefore displayed
logarithmically. The methods included phenanthroline staining [
78
], quantification via
MPS [
51
], and quantification via TMRX peak comparison. While all three methods were
generally capable of determining the iron content, they differed in their overall accuracy.
107
6.15 TMRX spectra of five different mice liver samples and a freeze–dried reference
sample. The measurements were performed using the 6-channel SQUID system with
a GRP Cryostat. The amplitude changes at each temperature for temperatures ranging
from
5 K
to
290 K
are displayed. All of the mice liver samples with administered MNPs
exhibited temperature depending relaxation signals. The highly concentrated samples and
the reference sample exhibited a signal peak at
150 K
to
170 K
. The liver from the control
mouse (black line) was not exposed to nanoparticles and did not exhibit a significant TMRX
signal. 110
6.16 Quantification results for an MPS analysis (orange) compared to those obtained
via TMRX (blue) and MRX (gray) at room temperature. The peak comparison method
described in chapter 4.2 was used for the TMRX analysis. The iron contents determined
using MPS and TMRX matched, although their confidence intervals did not always overlap.
The deviation is attributed to the different sample volumes (see Table 6.4). Quantification
via MRX at room temperature overestimated the MNP amount. 111
8.1 Quantum Design Magnetic Property Measurement System (MPMS) 120
8.2 Above: A dilution series of freeze–dried nanoparticle solution in poly carbonate
capsules. Below: A sample straw with an installed PC capsule. 121
8.3 Sample rod and Sample straw setup (Picture from Manual [1]) 121
8.4 Example of a typical MultiVu sequence: A measurement file was defined, different
temperatures were set, and other sequences were called. 122
9.1 6-channel SQUID system: A magnetically shielded Dewar vessel containing six
SQUID sensors. On the front of the cylindrical Dewar the
27 mm
wide opening of the warm
bore can be seen. In the course of the dissertation a helium flow cryostat was designed to
fit in the warm bore and to cool a biological sample for TMRX analyses. 126
9.2 Illustration of the 6-channel SQUID system: The outer vacuum vessel surrounds the
inner helium vessel. The warm bore is magnetically shielded by a niobium tube. The six
SQUID sensors are operated with flux-locked-loop (FLL) electronics. 126
9.3 Experimental Setup: The data acquisition system (DAQ) reads out the relaxation
signals (
a
) measured with the 6-channel SQUID system and controls the magnetizing
coil(
b
). The temperature controller reads out the temperature sensor and controls the
heating coil (
c
) in the glass reinforced plastics (GRP) Cryostat. In order to reach a certain
temperature in the cryostat the temperature controller may open or close the needle
valve(
d
) in the helium transfer tube. The measured temperature, the voltage of the heating
coil, and the opening percentage of the needle valve are continuously transmitted to the
DAQ System (a). 127
18 LIST OF FIGURES
9.4 Oxford Instruments low loss transfer tube (LLT): The helium coolant is taken up over
the Dewar leg, which fits into our helium transport vessels. The GRP Cryostat is attached
at the tip of the flexible section. At the tip, the helium cryostat inlet cools the GRP Cryostat
and retrieves the warm helium gas. The returning helium is released over an outlet at
the knee of the transfer tube. The stepper motor off the automated needle valve and its
corresponding serial interface also located at the knee. 127
9.5 Close-up picture of the sample holder with an installed sample during the cooling
process. 128
9.6 The virtual interface (VI) for the Mercury ITC gives the user an easy method for
sending commands and receiving data. The VI constantly measures the temperature of
the permanent sensor with the option to save the data to an ASCII text file. The commands
that can be sent to the ITC include manual opening of the helium needle valve to a defined
percentage. In addition, an ASCII text file can be loaded in order to perform temperature
sweeps. The VI allows to initiation of both cool–down and warm–up sweep procedures.
128
9.7 General assembly drawing of the cryostat 129
9.8 Rear end cover 129
9.9 Front end flange 130
9.10 Vacuum valve housing 130
9.11 Vacuum valve plug 131
9.12 Outer vaccum tube 131
9.13 Inner vaccum tube 132
9.14 Sample rod 132
9.15 Sample holding 133
9.16 TMRX analyses of MNP samples presented in Chapter 6.4. The analyses were
performed in the long time regime of the MPMS at
Bmag =1 mT
. The resulting TMRX
spectra were not usable for quantification. 134
9.17 Relaxation data for the MNP samples (m82,
T=290 K
) presented in Chapter 6.4.
The analyses were performed in the long time regime of the MPMS at
Bmag =1 mT
. Except
for the reference sample, the signal to noise ratios in the relaxation curves were too low
for interpretation. 134
List of Tables
4.1 Iron amount in CD021110 dilution series. 60
4.2 Iron amount in CD021110–exposed tumor cells. 64
9.1 Given parameters of the Endorem dilution series. 135
9.2 Fit parameters obtained by simulation without interaction energy. Iron amount
estimated via peak comparison. 135
9.3 Fit parameters obtained by simulation with approach A. Iron amount estimated
comparison of the amplitude factor. 135
9.4 Fit parameters obtained by simulation with approach C. Iron amount estimated
comparison of the amplitude factor. 136
9.5 Fit parameters obtained by simulation with approach D. Iron amount estimated
comparison of the amplitude factor. 136
I
1Introduction ......................... 23
1.1 Magnetic Nanoparticles in Medical Science
1.2 Aim of the Thesis
1.3 Way of Proceeding
1.4 Clinical Applications of Magnetic Nanoparticles
2Theoretical Background .............. 31
2.1 Magnetism in Nanoparticles
3Measuring Principles ................ 39
3.1 Magnetorelaxometry (MRX)
3.2
Temperature Dependent Magnetorelaxometry
(TMRX)
Background
1. Introduction
24 Chapter 1. Introduction
1.1 Magnetic Nanoparticles in Medical Science
The term nanotechnology is used to describe materials with structural features having at least
one dimension in the nanometer range (
1·10−9m
-
1·10−7m
). The unique physical properties
of these nanometer scale materials have attracted an increasing interest from researchers around
the world. A very promising class of nanotechnology is known as nanoparticles, i.e., ultrafine
particles, often stabilized in a liquid suspension. The use of nanoparticles in biomedical applications
is currently a growing research topic in medicine: their small size and unique properties enable
these particles to be used in a whole new range of applications. For instance, nanoparticles may
cross the blood-brain barrier [
45
] or even overcome the placental barrier [
93
] while carrying a
medically active ingredient. The characteristics of these particles are significantly determined by
their core materials and coatings. In most cases, the coating consists of a polymer or monomer
to which proteins can be attached for functionalization of the nanoparticle. The core consists of
metallic (e.g., gold) or non-metallic (e.g., silicon) materials (Figure 1.1) and affects the toxicity,
visualization capabilities, and magnetic behavior of the nanoparticle. The core material of magnetic
nanoparticles often consists of magnetic elements such as iron, nickel or cobalt and their oxides.
Figure 1.1: Illustration of a magnetic nanoparticle with a
a
Superparamagnetic core,
b
Dextran
coating, cPolyethylene glycol (PEG) layer, and dAntibody.
Their magnetic properties make these particles particularly interesting for biomedical applications
because they can be remotely moved, heated, and/or detected using an external magnetic field
[68]. In the present study, only magnetic nanoparticles with iron oxide cores were investigated. A
prominent biomedical application of magnetic nanoparticles (MNPs) is the treatment of cancer
via the induction of heat into the malignant tissue, i.e., hyperthermia [
40
]. Other applications
include the use of MNPs as contrast enhancement agents in existing imaging methods such as
magnetic resonance imaging (MRI) [
81
] and magnetic particle imaging (MPI), a novel particle-
based imaging method [
28
]. In magnetic drug targeting for cancer therapy, a chemotherapeutic
substance is bound to the MNPs [
100
] and the particles are remotely delivered to the tumor region
using an external magnetic gradient. Notably, the coating on the MNPs can be formulated with
specific ligands that bind to cancer cells [79].
In all the applications mentioned above, the ability to quantify the amount of MNPs in the biological
system is crucial. Achieving the appropriate concentration and distribution of the MNPs within
the tissue is a decisive factor for the success of these biomedical applications. Well-established
photometric techniques used for the quantification of the iron content in cells include Perls’ Prussian
blue staining method [
70
], phenanthroline staining [
78
], and atomic absorption spectroscopy (AAS).
However, these methods generally do not differentiate between iron originating from MNPs and
other natural iron deposits in the body.
1.2 Aim of the Thesis 25
In contrast magnetic measurements are capable of determining the iron oxide nanoparticle content
in biological samples [
96
]. Superconducting quantum interference device (SQUID) magnetometry
[
92
] and magnetic particle spectroscopy [
51
] are magnetic methods for in vitro quantification of
the MNP contents in tissues. Magnetorelaxometry (MRX) has also been applied as quantification
method [
97
]. In MRX, the magnetic relaxation of the MNPs is measured. This relaxation is a
delayed magnetic response to an external magnetization impulse. Through the temporal separation
of the magnetization impulse and the measurement process, only the MNP signal is detected
because biological iron deposits do not contribute to the relaxation signal. In addition, the MRX
analysis of MNPs can be conducted in vitro or in vivo [
97
]. Because the relaxation time depends
on the sizes of the magnetic particle’s core, the obtained signals can also be used to characterize
the MNPs. Furthermore, if the rotation of the particles is blocked because of binding to biological
tissue, alteration of the relaxation process occurs and can be detected [
46
]. However, when MNPs
are applied in vivo, their signals may also change because of concentration effects, dipole–dipole
interactions, and interactions with the surrounding media.
Notably, the particle size detectable using MRX ranges from
25 nm
to approximately
15 nm
[
97
].
The relaxation times for MNPs with smaller core diameters are too short to be detected at room
temperature. One way to investigate MNPs with smaller magnetic cores is to slow down their
relaxation processes by lowering the sample temperature. This analytical technique is referred to as
temperature dependent magnetorelaxometry (TMRX) and can be performed in vitro. The display
of the relaxation spectrum as function of temperature provides a detailed view of the magnetic
behavior of the MNPs, their concentration, and how the relaxation is altered by the biological
environment. TMRX analyses have been performed earlier mainly to investigate the distribution of
energy barriers within MNPs [75].
1.2 Aim of the Thesis
The aim of this thesis is to establish TMRX as a quantification method for magnetic nanoparticles
in biological tissue samples and for the detection of alterations in the magnetic behavior of MNPs
within biological tissues.
In order to establish TMRX analyses several milestones need to be fulfilled in the course of
this dissertation. These include the implementation of a consistent data analysis method, the
development of the MNP quantification procedure and the measurement of exemplary MNP
samples in order to investigate the signal alterations of MNPs in biological tissues. Another main
emphasis of this work is the reduction of the TMRX measurement time. To accomplish this
milestone the TMRX procedure of an existing measurement system will be revised. If necessary a
custom TMRX measurement system should be build in order to reduce the measurement time to a
minimum.
1.3 Way of Proceeding
In a first step, an existing measurement device (MPMS-XL, Quantum Design) was employed to
perform TMRX analyses, which is described in Chapter 4. With the MPMS, the influence of
the core size and size distribution of particles on their TMRX signals was investigated, and a
quantification method for particles with diameters <
15 nm
developed (Section 4.2). In addition,
alterations of the TMRX spectra because of changes in the MNP concentration were investigated
(Section 4.4). The MPMS is attractive because it provides precise control of the sample temperature
and has a convenient measurement procedure. However, TMRX analyses with this device are very
time consuming; a single relaxation measurement takes up to
40 min
. This long measurement time
also limits the sampling rate of the TMRX spectra measured with the MPMS. In the course of this
study, therefore, an alternative magnetization procedure was implemented using the MPMS and
investigated to determine if faster TMRX analyses were feasible (Section 4.1.4).
26 Chapter 1. Introduction
Furthermore, a numerical simulation of the TMRX process is introduced in Chapter 5. The
simulation results were used to describe the influence of the core diameters and size distributions of
particles on their TMRX spectra (Section 5.2). Moreover, an interaction energy term was introduced
to describe alterations of the MNP signal because of dipole–dipole interactions (Section 5.3). The
numerical simulation results were then used to develop phenomenological models to assist the
quantification of MNPs via TMRX.
A custom instrument with a reduced overall TMRX measurement time and switch-off time was
also developed, as can be seen in Chapter 6. For this purpose, an existing magnetically shielded
SQUID system (see Section 9.1 in the Appendix) capable of MRX was extended using a helium
flow cryostat as a temperature-controlled sample holder and magnetizing unit. In order to perform
fast relaxation measurements, the switch-off process of the magnetizing unit was also optimized.
Along with to the manufacturing, which was performed by the Institute’s workshop, the temper-
ature control software for the cryostat was programmed and a reliable cool down procedure was
developed. The final measurement setup with the glass reinforced plastic cryostat (GRP cryostat) is
displayed in Figure 1.2.
Figure 1.2: Picture of the TMRX measurement setup. The GRP Cryostat, which was designed and
constructed in the course of this thesis, is inserted into the 6-channel SQUID system. The cryostat
is cooled by liquid helium via the controllable helium transfer tube. The read out of the temperature
sensor and control of the helium flow is established via the temperature control system.
TMRX analyses with this new 6-channel system are faster with a higher sampling rate than those
performed with the MPMS. Through the optimized switch-off process of the coil and its non-
magnetic design, the new measurement system is capable of performing MRX analyses within
seconds. Therefore, the TMRX spectra obtained with the new system belong to a different, faster
time regime than the spectra obtained using MPMS (Section 6.3). Quantitative TMRX analyses of
MNPs in biological samples that could not be performed in the long time regime using the MPMS
were successfully conducted using the 6-channel SQUID system (Section 6.4). In addition, poten-
tial alterations of the TMRX spectra because of interaction with the biological tissue were evaluated.
1.4 Clinical Applications of Magnetic Nanoparticles 27
1.4 Clinical Applications of Magnetic Nanoparticles
1.4.1 Drug Targeting
Since the earliest days, drugs have been a cornerstone of traditional medicine. Their formulation
and administration are both important factors in determining the success any treatment. From orally
administered pills to parenterally injected liquids and inhaled aerosols, a broad variety of dosage
forms have been invented to provide a full spectrum of treatment options. However, regardless of
their route of administration, the distribution of drugs within the body was not controllable until the
recent development of antibody-drug conjugates.
Depending on the location of administration the drugs either diffuse into neighboring tissues or are
absorbed by the bloodstream for systemic dispersion. Systemic delivery often makes it necessary to
administer a higher overall dose in order to attain and maintain a certain local drug concentration.
As a result, healthy cells are also exposed to a potential harmful drug and filtering organs such as
the liver and spleen can be overly stressed. Chemotherapy treatments for cancer provide prominent
examples of the devastating effects of nonspecific drug distribution. It is also noteworthy that
some areas of the body are difficult to reach with traditional injection methods because local tissue
barriers (e.g. the blood–brain barrier and blood–retina barrier) need to be damaged in order for
the therapeutics to pass through [
102
]. As a consequence, potential treatable diseases such as
retinal degeneration are practically untreatable with traditional methods. These two problems, i.e.,
uncontrolled drug dispersion and inaccessibility of certain areas within the body, clearly support
the need for and potential of an in vivo drug manipulation mechanism.
With the first magnetic nanoparticle solutions patented in 1965 by NASA engineer Steve Papell [
87
],
a new tool was available for controlling fluids through the forces of magnetism. Papell’s Ferrorfluid
was a kerosene-based dispersion containing micro- and nanometer scale iron oxides originally
designed as a magnetically controllable liquid rocket fuel. In the late 1970s, Widder [
94
] [
95
]
and Senyi [
82
] adapted Papell’s invention so that a magnetic fluid could transport therapeutics to
specific target sites within the body. In this first medical application of a ferrofluid as a drug carrier,
the researchers used magnetic microspheres to encase the drug. Later, research teams bound the
therapeutic molecules directly to the coatings on the iron oxide nanoparticles [54].
When a high gradient magnetic field is applied to free magnetic nanoparticles, they experience a
dragging force toward the center of the magnetic field. If the surface of the particles is additionally
combined with a therapeutic molecule, the particles can be used for so-called drug targeting, i.e., the
magnetic guiding of therapeutics to the intended target site within the organism. While nanoparticle
fluids can be prepared using a variety of liquid media, only aqueous suspensions are relevant for
medical applications. The drug-carrying nanoparticle solution is injected into the vascular system
and then, exposed to high gradient magnetic fields that guide the particles to the intended target
site. When the particles reach their target, they are held in position long enough to release the
therapeutic agents into the surrounding tissue. The release can be supported through changes in the
surrounding pH, enzymatic activity or temperature [
3
]. Finally, the external magnet is switched off
so that the particles can move freely and be filtered out by the macrophage system.
For successful and safe clinical application, different requirements for the particle coating and
magnetic core, the external magnetization mechanism, and the entire process must be fulfilled [
65
].
The particle core often consists of the iron oxides maghemite, or magnetite which offer good
magnetic characteristics while being well tolerated and generally biocompatible. However, there is
potential for optimization of the core shape and diameter because these parameters influence the
cellular uptake of nanoparticles [
14
] and their magnetic properties. The choice of coating for the
particles is significant because it determines their hydrodynamic diameters and surface structure,
and both of these parameters influence the cellular uptake, clustering potential, and hydrodynamic
flow velocity of the particles. Thus, the particle core and coating must be specifically designed for
the particular task because the physical environment and operating conditions may vary. In addition,
the particles must be sufficiently small to move freely through the capillaries but at the same time
sufficiently large to be affected by the magnetic field and overcome the opposing hydrodynamic
28 Chapter 1. Introduction
forces of the bloodstream. Furthermore, the applied particle concentration must not be too dense in
order to avoid agglomeration and thromboses. Finally, the MNPs must be completely biodegradable
and biocompatible in order to avoid long-term accumulation within the tissues.
Because the magnetic forces decrease cubically with distance, strong, high-gradient permanent
magnets are required to create a sufficient dragging force to move the particles that are farthest from
the surface of the body. In fact, it has been shown that drug targeting for chemotherapy works best
for superficial tumors [
30
]. To overcome the depth limitations, however, it is possible to temporarily
implant small magnets close to the tumor region [103].
Different mechanisms for the release of the active agent at the target site are beeing investigated.
External triggers, such as, ultrasound [
74
], light [
104
], heat [
105
], electricity [
26
], and magnetic
AC fields [
10
] allow the technician to determine the point at which the active therapeutic agents
should be released. These mechanisms tent to offer greater reliability than physiologically triggered
release mechanisms because the physiology may vary from patient to patient.
Currently, the most promising biomedical applications for magnetic drug targeting include chemother-
apeutic treatment of brain [
72
], liver [
98
], and breast [
53
] cancers. However, other prominent
applications for magnetic drug targeting also exist in the fields of cardio- and endovascular dis-
eases, e.g., stenosis and thrombosis. Here, nanoparticles assist the delivery of therapeutic drugs to
endothelial cells, which are located along the inner walls of the blood vessels [
76
] [
77
]. In addition,
magnetic nanoparticles also have the capability to deliver therapeutic genes to specific targets in
vivo [
19
]. In so-called magnetofection the MNPs enhance traditional gene therapy by allowing
gene delivery to otherwise non-permissive cells. Magnetic nanoparticles for magnetofection may
drastically reduce the incubation time and lower the gene dose required to achieve a high transfec-
tion rate [80].
At present, there are only a few applications of magnetic drug targeting of which clinical trials have
been successfully completed, the most prominent ones of them being the Phase I studies of Lübbe’s
group [
54
], Phase I & II trials of Wilson et al. [
98
], and the preclinical studies with animal models
performed by Alexiou et al. [
4
]. These trials demonstrated the virtues of cell-specific targeting
while also revealing several problems that must be resolved before drug targeting reaches clinical
marketability. A challenge that researchers must consider is the scaling problem of animal models.
While control of nanoparticles may be practical in a small organism such as a mouse, it may be
more difficult in a human because the distance between the particles and the magnet is likely greater.
Simply doubling the distance between the magnet and the particles reduces the magnetic field
strength at the particles by approximately a factor of eight. Although stronger magnets could be
built, they would quickly exceed economic and safety requirements. A closely related issue is the
ongoing need for optimization of the properties of the magnetic cores of the nanoparticles. While
it is possible to achieve better magnetic behavior with materials other than pure iron oxide [
13
],
the biocompatibility of these materials, including their potential to negatively impact organs such
as the spleen and liver, must be evaluated. The design of coating materials is likewise important
because certain coatings may lead to particle agglomerations and thromboses [
73
]. In summary, the
current challenges in magnetic drug targeting are to create effective and biocompatible particles
that are suitable for use with a safe and economical application method.
1.4.2 Hyperthermia
Another promising field for magnetic nanoparticles is hyperthermia, i.e., heat treatment of cancer
cells. In hyperthermia, malign cells are exposed to high temperatures over a defined period of
time. The applied heat damages proteins within the cells and triggers apoptosis [
56
], i.e., controlled
cell death. This heat treatment is particularly interesting for cancer therapy; studies indicate that
the heat does only minor damage to normal cells but kills the cancer cells [
91
]. This behavior
can be explained through the poorly developed nervous and unresponsive vascular systems of the
malign tissue, which leads to inferior temperature regulation for the fast growing cancer cells.
However, hyperthermia is nearly always used to enhance other forms of therapy such as radiation
1.4 Clinical Applications of Magnetic Nanoparticles 29
and chemotherapy [
101
]. Hyperthermia treatments are classified as local,regional or whole
body depending on the area they tend to affect. In local applications, two therapy modalities are
differentiated: actual hyperthermia is heat treatment of tissue with temperatures only slightly above
the body temperature (
42 ◦C
–
45 ◦C
). For this therapy, application times of
30 min
to several hours
are required to kill the malign cells. Alternatively, a more radical approach is the application of
high temperatures (
>50 ◦C
) for a short period of time. However, so-called thermoablation suffers
from side effects because of the sudden death of the tumor cells, which leads to the generation
of a large quantity of necrotic material and results in an inflammatory response [
62
]. Different
methods and devices for hyperthermia and thermoablation treatments have been developed that are
mainly distinguished by the manner in which the thermal energy is created: capacitive coupling,
microwave radiation, ultrasound, laser photoagulation, and radiofrequency phased arrays. When
Figure 1.3:
a)
Application of magnetic nanoparticles in a tumor supplying artery. The particles are
magnetically guided into the malign tissue using an external high gradient DC magnet.
b)
Once
the particles have reached the tumor, an external AC coil exposes the particles to an alternating
magnetic field. Because of physical loss processes, the particles heat the surrounding tissue.
magnetic nanoparticles are used for hyperthermia, they are first injected or magnetically guided into
the tumor region and then exposed to an external AC magnetic field. The different particle types are
classified based on their specific absorption rate (SAR). This value is an expression of their ability
to transduce the energy of the AC field into thermal energy and can be described by a combination
of different physical loss processes [
21
]. These processes include the so-called hysteresis loss,
the loss because of Néel and Brownian relaxation, and frictional losses. The hysteresis loss is
caused by displacement of magnetic domain walls within the multidomain particles but can deviate
from the hysteresis loop of the magnetization curve for the particles. The second loss process,
so-called Néel relaxation, describes the internal reorientation of the magnetic moments within the
particles. In addition to the internal friction of the Néel relaxation, there is also mechanical friction
because of rotation of the particles themselves, which is referred to as Brownian relaxation. Thus, a
current focus of several research groups is improvement of the specific absorption rate of magnetic
nanoparticles used in combination with AC field generators, which must be in compliance with
medical regulations and meet both therapeutic and economic requirements.
Surgeon Richard K. Gilchrist was the first to apply magnetic nanoparticles for the treatment of cancer
cells [
27
]. While Gilchrist injected the particles directly into the malign tissue, researchers have
since then demonstrated that magnetic particles can be delivered through the body to the targeted site
of action using an external magnet [
60
]. Research has thus focused on the optimization of treatment
methods [
34
] [
55
] and the design of the magnetic particles [
40
]. The first clinical trials with
magnetic nanoparticles for hyperthermia were conduced by the research group of Andreas Jordan
at Charité, Berlin [
89
]. In a feasibility study, a small group of patients suffering from malign brain
tumor glioblastoma multiforme was treated with aminosilane-coated iron oxide nanoparticles [
59
].
30 Chapter 1. Introduction
These first clinical studies demonstrated that hyperthermia treatment with magnetic nanoparticles is
a viable therapy that may complement other established therapies. However, this first hands-on
experience emphasized many unsolved challenges of the method.
One major problem is the application of the nanoparticles in the tumor and their homogeneous
distribution within the tissue. Without uniform distribution of the MNPs within the tissue, consistent
heat production cannot be guaranteed. The application method must also ensure selective delivery
of the magnetic nanoparticles only to the tumor site. The method used by Gilchrist, i.e., direct
injection, has the disadvantage that multiple injections are necessary to achieve a homogenous
distribution. While this method offers good control over the local quantity of particles in the
tissue, it also increases the risk of spreading the tumorous cells through the puncture wounds.
A more promising approach is the coating of MNPs with cancer-specific antibody proteins [
18
].
Through this specific docking mechanism, the thermal damage of healthy cells is reduced, and even
undetected small tumors can be treated. However, the local distribution of the particles is difficult
to control, and thus, it is not always possible to guarantee that the quantity of particles bound to the
tumor tissue is sufficient to successfully damage the malign cells.
This problem leads to another unsolved challenge in magnetic nanoparticle hyperthermia: the need
for a quantitative in vivo detection method for magnetic nanoparticles. To date, different imaging
methods such as magnetic resonance and x-ray imaging have been investigated for determination
of MNP concentrations in tumor tissues. However, while these methods are capable of detecting a
certain number of particles, they are not reliably quantitative. Alternatively, the use of the magnetic
relaxation signal of the particles to generate a spatially resolved quantitative image appears to be
promising [50] [5].
To conclude, hyperthermia using magnetic nanoparticles has high potential to assist established
cancer treatments in the near future. Nevertheless, a number of serious problems in different
interdisciplinary fields must first be overcome.
2. Theoretical Background
32 Chapter 2. Theoretical Background
2.1 Magnetism in Nanoparticles
Introduction
Magnetic nanoparticles for clinical applications consist of magnetic iron oxide cores covered by
nonmagnetic coatings. The nonmagnetic coatings prevent single particles from aggregating by
stabilizing them in solution and serve as carriers for drug and imaging molecules. The size and
structure of the coating influence the viscosity of the MNP solution and also its bio-compatibility.
In contrast, the magnetic behaviors of nanoparticles are mainly defined by their magnetic cores.
Although, numerous types of iron oxides particles exist, only maghemite and magnetite are relevant
for biomedical applications [
48
]. The magnetism of these materials is generally defined by their
magnetic domain structures. However, the MNPs investigated in the present study were assumed to
be the so-called single-domain particles, i.e., particles that can be described using a single magnetic
moment.
Figure 2.1: Illustration of the magnetic moments in a single domain MNP solution. Each particle
consists only of one magnetic domain, which can be described through its magnetic moment and
orientation. (A) Without an external magnetic field, the magnetic moments randomly orient into an
equilibrium state. (B) With an external magnetic field, the single particles change their orientation
in the direction of the external field.
2.1.1 Superparamagnetic Single-Domain Particles
Because the particles are always separated by their nonmagnetic coatings, their single domains
are randomly oriented when no external field is applied (Figure 2.1 A). When an external field is
applied, the magnetic moments of the particles readily align in the direction of the external field
(Figure 2.1 B).
The magnetic moments inside the particles are organized as single domains only for particles with
diameters below a critical core diameter [
12
]. The dimension of this critical diameter depends on
the material. In the literature, the values for iron oxides range from
60 nm
[
66
] to
80 nm
[
36
]. The
magnetic moment of such a single domain particle depends on the magnetization of the material
(Mp) and the particle volume (Vp):
m=MpVp.(2.1)
In contrast to bulk materials, for which the magnetic domains interact strongly with one another,
the single domain in a nanoparticle can change its orientation more freely. Similar to the bulk
material, the magnetic domains in a group of nanoparticles will oppose and try to cancel one
another out in the absence of an external field. However, freely moving single-domain particles can
oppose each other more effectively and are less affected by interaction effects resulting from the
increased inter-particle distance. The remaining net magnetization will therefore be zero [
6
]. If a
2.1 Magnetism in Nanoparticles 33
ferrimagnetic material exhibits no remanent magnetization, it is superparamagnetic.
Thermal fluctuations generally affect the magnetic behavior of a material because they can be
strong enough to change the orientation of a magnetic domain. The temperature can be seen as an
opposing force to the ordering trends of the magnetic domains. Temperature strongly influences
both the in-field magnetization process and the loss of the magnetic moment in the absence of an
external magnetic field. The magnetization process can be described by the Langevin equation [
47
],
which relates the magnetic energy (µ0H) and the thermal energy (kBT).
M(H,T) = Mpcothmµ0H
kBT−kBT
mµ0H(2.2)
The magnetization (
Mp
) and the magnetic moment (
m
) depend on the core material and the particle
design. Note that
Mp
is closely related to the saturation magnetization of the bulk material (
MS
) but
is typically much smaller than the latter because of surface effects [
61
]. The physical constant
kB
denotes Boltzmann’s constant and
µ0
represents the permeability in free space. Equation 2.2 suc-
cessfully predict the magnetization patterns observed for typical M(H)-curves of superparamagnetic
nanoparticles. In contrast to ferrimagnetic bulk materials, there is no hysteresis in superparamag-
netic materials (Figure 2.2 b). In the absence of an external field, the magnetic moments within the
Figure 2.2: Magnetization patterns of aferromagnetic and bsuperparamagnetic materials.
superparamagnetic particles reorient themselves into an equilibrium state without net magnetization.
This exponential decay of the magnetization amplitude (
A
) does not occur immediately but after a
characteristic time (τ):
M=A·exp(−t
τ).(2.3)
For a more detailed description of the magnetic behavior of MNPs, the relaxation process can be
separated into two different processes: Néel relaxation and Brownian relaxation.
2.1.2 Néel and Brownian Relaxation of Magnetic Nanoparticles
The first observation of superparamagnetic relaxation was documented by the French geophysicist
Emile Thellier in 1941 [
88
]. He measured the magnetization of ancient rocks and pottery, thus
performing pioneering work in the new field of paleomagnetism. While investigating the temper-
ature dependence of a sample’s magnetism, he observed an unexpected decay of the magnetism
over time, a phenomenon today known as relaxation. The origin of this magnetic effect can
be explained by considering the collective magnetic moments within the material. If the single
34 Chapter 2. Theoretical Background
magnetic moments are all facing in the same direction, a net magnetization can be measured.
However, no magnetization is detectable if the magnetic moments are randomly oriented. On an
atomic scale, thermal vibration causes random changes in the orientations of the single magnetic
moments [
11
], thus provoking the decline of the net magnetization. The strength and frequency
of these changes therefore defines the time during which the entire system dephases into random
orientations. In 1949, Louis Néel published the first theoretical model of this particular magnetic
behavior of superparamagnetic particles [
64
]. He showed that magnetic relaxation can be expressed
as an exponential decay with a characteristic decay time, the Néel relaxation time (τN):
τN=τ0expKVc
kBT.(2.4)
The Néel relaxation time of a particle is strongly influenced by its anisotropy (
K
) and core volume
(
Vc
). The anisotropy describes the directionality of the particle, which is determined by its shape
(shape anisotropy) and crystalline structure (crystal anisotropy). Because of this directionality,
magnetization process for a particle depends on the direction from which the external magnetic
field originates. The direction that requires the least energy is referred to as the easy axis, and if the
material has only one easy axis, then it has uniaxial anisotropy. The so-called attempt time (
τ0
) in
equation 2.4 is a time span characteristic of the material, with typical values ranging from
10−9s
to
10−11 s
. The reciprocal of the attempt time is referred to as the attempt frequency. William Fuller
Brown, Jr. developed a model for calculating the relaxation time of a ferromagnetic particle using
the Langevin equation [11]:
τ0=1+(ηγ0Ms)2
ηγ2
0
√π
4KkBT
KV 1/2
.(2.5)
Although
τ0
can have different values because it is temperature dependent, it is often assumed
to be a constant. This approximation is in most cases reasonable because the temperature depen-
dent changes in the relaxation time, as defined in Equation 2.4, overshadow the relatively small
alterations in
τ0
. During 1994–95, the theory for magnetic nanoparticle relaxation with uniaxial
anisotropy was developed further by Coffey et al. [
16
], and the influence of a constant magnetic
field transverse to the easy axis of the particles was simulated [15].
Néel relaxation plays an important role in the magnetic behavior of superparamagnetic nanoparticles
and an understanding of this phenomenon is crucial for their use in different clinical applications, in-
cluding hyperthermia and magnetic particle imaging. However, the Néel relaxation in nanoparticles
is often overshadowed by Brownian relaxation. In 1929, Peter Debye described the random changes
in the orientation of a free floating particle because of collisions with other particles. In this type
of relaxation, a single particle can change its orientation by turning its whole body. Naturally, the
Brownian relaxation time (
τB
) is significantly influenced by
η
, the viscosity of the fluid surrounding
the particle:
τB=3ηVh
kBT.(2.6)
In general, the hydrodynamic volume (
Vh
) includes of the iron oxide core volume (
Vc
) together with
a non-magnetic coating with thickness
δ
. However, if the particles aggregate and form clusters,
their hydrodynamic volume can reach much larger values. In combination with the Boltzmann
constant (
kB
) the temperature (
T
) in Equation 2.6 has an accelerating or retarding effect on the
relaxation process. Both, the Brownian relaxation time (Equation 2.6) and the Néel relaxation time
(2.4), are highly sensitive to the particle size and system temperature. However, while
τB
only
grows linearly with particle size,
τN
increases exponentially. Since the two relaxation types may
occur simultaneously, the effective relaxation is a combination of both processes:
τeff =τNτB
τN+τB.(2.7)
2.1 Magnetism in Nanoparticles 35
The overall relaxation time of magnetic nanoparticles may vary by several orders of magnitude
depending not only on the particle properties (e.g., anisotropy) but also on the system parameters
(e.g., temperature and magnetization time). In addition, the measuring time plays an important
role in relaxation measurements. In order to observe a relaxation signal at a defined temperature,
the timescale of the applied measurement technique must be carefully adjusted for each given
sample such that both the relaxation and measuring times are of the same order. If the relaxation
is fast compared to the measuring time, no relaxation will be observed and only the sample’s
magnetization at zero field is detected. If the relaxation is too slow for the measurement timescale,
only a value similar to that of the in-field magnetization of the sample is obtained. The relaxation
can be perceived only if the relaxation time and measuring time are of the same order. In typical
investigations, the measuring time is often held constant while the temperature is varied. The
temperature at which the superparamagnetic relaxation time is equal to the measuring time is
referred to as the blocking temperature (TB).
2.1.3 Particle Distribution
Magnetic nanoparticle samples typically do not consist of particles with uniform core sizes, but a
distribution of variably sized particles. In 1976, Granqvist et al. [
29
] reported that the particles they
investigated exhibited a log-normal distribution. Although the origin of the log-normal distribution
in MNP systems is still disputed, it is a general consensus that most particle suspensions have
log-normal core size distributions. This distribution is described by Equation 2.8:
Pd(d,µd,σd) = 1
√2πσddexp−ln2(d/µd)
2σ2
d.(2.8)
Assuming a spherical particle core, the diameter (
d
) can also be expressed as the core volume (
V
).
The volume for a single particle may also be expressed as a function of its magnetic moment (
m
)
and saturation magnetization (MS) as given in Equation 2.9:
m=MsV.(2.9)
Inserting equation 2.9 into 2.8 leads to the log-normal distribution of the magnetic moments within
an MNP sample:
Pm(m,µm,σm) = 1
√2πσm/3mexp−ln2(mµm)
2(σm/3)2.(2.10)
36 Chapter 2. Theoretical Background
2.1.4 Dipole–Dipole Interactions
A great number of models describing the dynamics of nanoparticles have been developed for
non-interacting nanoparticles. However, experimental data often differs from the predicted results,
indicating that interactions between the particles may play an important role. This deviation from
the experimental data often appears as a difference in the relaxation time (τ).
There are different types of interactions known to influence MNP and define their characteristic
behaviors and relaxation times, ranging from more physical interactions such as thermal vibrations,
streaming turbulence around the particles, and even binding of particles to one another or to larger
structures to elemental interactions on a molecular level that define the magnetism of the substance.
On the molecular level, the exchange interaction between electrons plays a major role in connecting
the electron spins to a macroscopic magnetic moment providing an explanation for the existence
of magnetic domains [
36
]. However, the exchange interaction is too short-ranged to influence
single domain particles that are separated by a nanometer-thick coating. Compared to the exchange
interaction energy, long–range dipole–dipole interactions are weak; despite this fact, they play
an important role for ferro- and ferrimagnetic nanoparticles with sufficiently small inter–particle
distances, such as in high-concentration solutions or samples in which the particles are unevenly
distributed because of sedimentation or aggregation. In such samples, dipole–dipole interactions
can lead to the formation of a collective state of the magnetic moments. In this collective state,
the MNP sample often displays a longer relaxation time. This behavior is also referred to as
spin glasses. In addition the close proximity of the magnetic cores can lead to the formation of
chain–like superstructures and alignment of the magnetic moments.
In order to investigate the influence of dipole–dipole interactions for ferrimagnetic nanoparticles,
Zang et al. [
106
] performed AC-susceptibility analyses of frozen suspensions of magnetite particles
in kerosene. When trying to describe the measurements using Néel relaxation (Equation 2.4), they
experienced problems fitting the measured values for
τ
to the different concentration steps. In the
Néel relaxation equation, the parameters for anisotropy and particle volume should not change
with concentration, and thus the only variable parameter is the attempt time (
τ0
). However, the
fitted values for
τ0
fell in an atypical range for magnetite. In this instance, the Néel relaxation
equation apparently lacked a parameter that expressed the influence of the MNP concentration. The
temperature dependence of the samples appeared to be better phenomenologically described using
the empirical Vogel–Fulcher law, which includes the critical temperature (T0):
τ=τ0exp∆E
kB(T−T0).(2.11)
Subsequent studies of nanoparticle interactions [
32
] have shown that, in most cases, the critical
temperature (T0) in the Vogel–Fulcher law can be related to the dipole interaction energy:
T0≈Edipole
kB
.(2.12)
The interaction energy (
Edipole
) may in turn be described as a function of the magnetic dipole–dipole
interactions between two ideal magnetic dipoles (~miand ~mj) [37]:
Edipole =µ0
4π"~mi·~mj
r3
i j −3(~mi·~ri j)(~mj·~ri j)
r5
i j #,(2.13)
where
~ri j
is the distance vector between the centers of the two magnetic dipoles. However, in an
ensemble of nanoparticles with an average magnetic moment and an average distance (
D
), the
dipole interaction energy is often simplified to [69]:
Edipole ≈µ0
4π
m2
D3.(2.14)
If
D
in an MNP solution decreases, for instance when the particles aggregate, the relaxation time of
2.1 Magnetism in Nanoparticles 37
Figure 2.3: Influence of the particle distance (
D
) on the Néel relaxation time (
τ
). With decreasing
distance, the MNP relaxation time increases exponentially. The relaxation time of a
20 nm
particle
at 290 K is displayed.
the sample increases (see Equation 2.3). Through this variable parameter
D
and the Vogel–Fulcher
law (Equation 2.11), the deviation of the experimentally determined relaxation signals and the
values calculated using the Néel relaxation equation can be explained. Most studies of the dipole–
dipole interactions of MNPs have been performed on immobilized samples with a narrow size
distribution. The broad distribution of their blocking temperatures would cover possible interaction
effects and make them difficult to detect. This specific problem is discussed in Chapter 5.3, where
a method is introduced for including the size distribution into dipole interaction equations.
These dipole–dipole interactions must be taken into account for ferro- and ferrimagnetic nanoparti-
cles. For anitferromagnetic particles, however, dipole interactions are negligible. The majority of
studies on dipole–dipole interactions have shown an increase in the relaxation times and blocking
temperatures of such samples. However, Mössbauer studies of maghemite nanoparticles have
revealed that weak particle interactions result in a decrease in the relaxation time [
71
] [
63
], which
has been explained by a lowering of the average value of the energy barriers separating the minima
of the magnetic energies [38] [32] [7] [8].
3. Measuring Principles
40 Chapter 3. Measuring Principles
3.1 Magnetorelaxometry (MRX)
3.1.1 Basic Principles
One way to characterize the magnetic performance of small magnetic nanoparticles is to investigate
their ability to react to a rapidly changing magnetic field. A typical technique involves the
application of an alternating external magnetic field at a defined frequency. In contrast to direct
current (DC) analyses, which measure the equilibrium value of the magnetization in a sample,
alternating current susceptometry (ACS) provides information about the magnetization dynamics
of the MNPs [17], i.e., how rapidly the magnetization can change.
Another method for investigating the dynamic performance of MNPs is magnetorelaxometry
(MRX). A typical MRX analysis consists of two phases: a magnetizing phase, in which the sample
is exposed to a defined external magnetic field
B
for a time
tmag
, followed by a measurement phase
during which the external field is turned off and the declining net magnetic moment of the sample is
measured (Figure 3.1). Unlike in ACS, no external field is applied during the actual measurement.
Figure 3.1: Procedure for MRX analyses: Prior to the magnetizing phase, the particles are randomly
oriented and no net magnetic moment is detectable. When the external magnetic field is applied,
the magnetic moments of the particles align in the direction of the field when it is applied, and
then after a short delay time following switch-off of the field, the relaxation is measured. During
this measurement phase, the single magnetic moments of the MNP sample realign into a random
equilibrium. The magnetic moments colored in red are aligned in the direction of the external
magnetic field while the opposing moments are colored in blue.
The detected signal can therefore be assigned to the decaying net magnetic moment of the sample.
At the beginning of a measurement, it is assumed that the sample has no remanent magnetization
and the single magnetic moments of the MNPs are randomly oriented. During the magnetization
phase, the single magnetic moments in the sample align in the direction of the external DC field
and create a macroscopic magnetic moment. When the external field is turned off, they seek to
reach their equilibrium state once again. In this equilibrium, the magnetic moments are randomly
oriented and oppose each other so that there is no remaining macroscopic moment. This decay of
the magnetic moment is called relaxation. Relaxation because of the physical rotation of entire
particles is referred to as Brownian relaxation, whereas relaxation because of reorientation of the
3.1 Magnetorelaxometry (MRX) 41
magnetic moments of MNPs is considered to be Néel relaxation. The relaxation of a sample’s
net magnetic moment is detected over a specified measurement time (
tmeas
) using SQUIDs, i.e.,
sensitive magnetic field sensors. The control electronics of the SQUID require a certain delay time
between the magnetization and measurement phases. This delay time (
tdead
) is typically in the range
of microseconds but can extend to several seconds depending on the behavior of the measurement
system.
The relaxation time of a particle sample is determined by both its particle characteristics and
the predominant relaxation type. Whether the relaxation mechanism for MNPs is dominated by
Brownian or Néel relaxation depends on their particle sizes and mobilities. Brownian relaxation
only occurs when the particles are freely moving in a solution; immobilized particles may only
relax via Néel relaxation. Although both relaxation types may occur in a sample simultaneously,
according to Equation 2.7, the resulting relaxation time will be dictated by the faster relaxation.
For nano scale particles, Brownian relaxation is several orders of magnitude faster than Néel
relaxation and therefore clearly distinguishable. In addition, the magnetic core sizes, anisotropies
and hydrodynamic diameters of MNPs determine how fast they undergo magnetic relaxation. In
this dissertation, only immobilized particles were investigated. Therefore, Brownian relaxation was
neglected. The Néel relaxation of the investigated samples, however, provided information about
the magnetic core sizes, anisotropies, and aggregation states of the MNPs.
3.1.2 Magnetorelaxometry Measurement Setup
In a typical MRX setup for conducting analyses at room temperature, a small MNP sample
(a few
µL
) is placed in the center of the magnetization coil (Figure 3.2). The magnetization units
typically consist of Helmholtz coils [
58
] that create a homogeneous magnetic field in the sample
space. Depending on the coils, the applied field strength can reach several millitesla. The sample
magnetization is typically of the order of seconds. A longer magnetization time is necessary only
for relaxation measurements using magnetic property measurement systems and similar devices,
which have long switch-off times (see also 4.1.3). The length of the measurement phase depends
on the relaxation behavior being investigated.
Larger particles typically display a longer relaxation than MNPs with smaller diameters. In these
larger particles, Brownian relaxation is often the predominant relaxation type, whereas smaller
MNPs relax mainly via Néel relaxation. If MNPs that display Brownian relaxation are immobilized,
their relaxation times increase by several orders of magnitude. In general, the measurement time is
of the same order as the magnetization time.
The relaxation signal of a particle sample is typically measured using sensitive magnetometers such
as SQUIDs, fluxgates [
57
], and optical magnetometers [
41
]. To reduce magnetic far field distortions,
these sensors are often arranged in a gradiometer setting. SQUID–based MRX systems are often
preferred because highly sensitive SQUIDs excel with respect to their measurement accuracy,
and they can detect magnetic fields in the picotesla range. They do, however, require special
magnetically shielded environments such as the BMSR-2 [
9
] because the magnetic background
signal is in the microtesla range. In addition, superconducting SQUIDs come with high operational
costs because they require excessive cooling. While low–temperature SQUID systems require
liquid helium as the coolant, high–temperature SQUIDs may be operated using liquid nitrogen,
which is cheaper. Furthermore, the thermal insulation needed between the SQUID sensor and the
nanoparticle sample also reduces the overall detection limit of the system because the magnetic
signal of the sample decays cubically with distance. In all MRX systems, it is therefore desirable
to place the sample as close as possible to the magnetic sensor. Finally, because of their high
sensitivity to magnetic field changes, SQUID sensors must be switched off during the magnetization
phase because they may otherwise be driven to saturation and overload. Switching off of the
magnetization coil results in the need for a short dead time because the coil’s magnetic field does
not instantaneously cease. Depending on the switch–off process of the coil and the possible flux
creep in the Dewar the necessary dead time of the SQUID can range from
10 µs
to minutes (see
42 Chapter 3. Measuring Principles
also Chapter 4.1.3). A shorter delay time is generally desirable because the detection limit of a
system increases exponentially as the delay time decreases.
Figure 3.2: Typical MRX setup: The magnetization coil creates a homogeneous magnetic field in
the sample space during the magnetization phase (blue arrows). After switching off the coil, the
SQUID detects the decaying net magnetic moment of the MNP sample. The magnetic field of the
sample is illustrated in red. The superconducting, low–temperature SQUID sensors require liquid
helium as coolant in order to operate inside the insulating Dewar vessel.
3.2 Temperature Dependent Magnetorelaxometry (TMRX) 43
3.2 Temperature Dependent Magnetorelaxometry (TMRX)
3.2.1 Basic Principles
Measurement of the magnetic relaxation signal allows investigation of the dynamic magnetic
behavior of MNPs. This relaxation behavior strongly depends on the particle core size, anal-
ysis temperature, and measurement time window. At room temperature, only particle core
sizes of approximately
15 nm
–
25 nm
[
97
] are detectable with typical MRX systems.
1
In ad-
dition, in order to detect a certain particle type, its relaxation time constant (
τ
) must be of
the same order as the measurement time. Within a fixed time window, particles above a crit-
ical diameter will relax too slowly to contribute significantly to the amplitude change during
the measurement phase. In addition, the net magnetic moment for small particles below a
certain diameter will have already decayed prior to initiation of the measurement phase. Ac-
cording to the equation for Néel relaxation (Equation 2.4), reducing the temperature of an
MNP sample should lead to a longer relaxation time and therefore a slower relaxation process.
Figure 3.3: Measurement ranges for the MPMS and MRX 6-channel SQUID systems for particles
of different sizes at
5 K
,
100 K
, and
300 K
. The Néel relaxation time (
τ
) was determined for
monodisperse particles with an effective anisotropy of 1·104J/m3that are not affected by dipole-
dipole interaction (Equation 2.4)
During the measurement phase, after the single magnetic moments have been aligned by the external
magnetic field, thermal vibrations of the single magnetic domains have a certain probability for
changing the orientation of the net magnetic moment. This probability increases with increasing
temperature. In order to investigate particles with core sizes <
15 nm
, it is worthwhile to slow down
their relaxation processes by lowering the analysis temperature. Previously, Romanus and Berkov et
al. showed that temperature dependent magnetorelaxometry is a valuable, complementary method
for the analysis of magnetic nanoparticles. However, they focused on the energy barrier distribution
[
75
] of the MNPs and not on the biomedical applications. The MPMS offers great capabilities for
performing different magnetic measurements at temperatures as low as
5 K
. However, because
of the design of the instrument, the time between switching off the magnet and measuring the
first data point is rather long at
1,5 min
(see also 4.1.3). This long dead time requires extended
magnetization and measurement phases in order to detect particles. The MPMS is therefore only
capable of measuring long relaxations in a measurement time window of
40 min
, which restricts
the spectrum of detectable particles to those whith core diameters ranging from
26 nm
to
28 nm
at room temperature. The measurement range of the MPMS is indicated in Figure 3.3 by dashed
1
The measuring range of
15 nm
to
25 nm
applies to particles with moderate dipole-dipole interaction. MNPs with
core diameters of less than
15 nm
can also be measured at room temperature if they are influenced by strong dipole-dipole
interaction.
44 Chapter 3. Measuring Principles
red lines. Néel relaxation times at
300 K
for particles of different sizes as determined according to
the interaction-free Néel relaxation equation (Equation 2.4) are indicated by the orange line in the
figure. At a sample temperature of
100 K
(blue line), the Néel relaxation of MNPs with
17 nm
to
19 nm
magnetic cores is observable while at
5 K
, only very small MNPs with core diameters of
approximately 7 nm relax within the time window of the MPMS (black line).
3.2.2 Creation of the TMRX Spectrum
By measuring the relaxation times at different temperatures using the MPMS, it is possible to
screen the relaxation spectrum of a sample. In a typical TMRX plot, the amplitude change of the
sample’s relaxation is plotted as a function of temperature (Figure 3.4 left). This information can
be used to determine the core size of the MNPs and the sample concentration (4.2). In addition,
the temperature dependent relaxation signal is a sensitive indicator of dipole–dipole interactions
between the particles (4.4).
Figure 3.4: Left: A typical TMRX plot where the amplitude change (
∆M
) is displayed as a function
of temperature. The maximum relaxation amplitude was observed at
30 K
, indicating that the
investigated MNPs had a magnetic core size of
7 nm
to
10 nm
. Right: Single relaxation curves
at selected temperatures. The amplitude change is more or less pronounced depending on the
temperature.
3.2.3 Influence of the Particle Core Size on the TMRX Spectrum
The relaxation behavior of an MNP is described by its relaxation time (
τ
). Néel showed that this
relaxation time depends on the system temperature (
T
) and the magnetic moment of the particle
(m):
τN=τ0expKm
MskBT.(3.1)
Parameters such as the attempt time (
τ0
), the anisotropy (
K
), and the magnetization saturation (
Ms
)
are constants that are directly related to the properties of the magnetic nanoparticle. In contrast,
Boltzmann’s constant (
kB
) is a natural constant. The system temperature (
T
) in Equation 3.1 has a
strong influence on the relaxation time; a change in this temperature not only changes the value of
the entire fraction but also has exponential influence on
τ
. The numerator is mainly determined by
the magnetic moment (
m
) of the particle and is in turn connected to the magnetized volume through
the relationship
m=MsV
. The relaxation time is thus influenced by the relationship between the
particle’s core size and temperature. By defining a constant measurement time (
tmeas
), a fixed time
window is created wherein the relaxation amplitude change (
∆B
) can be measured. The amplitude
change that occurs during
tmeas
is displayed for different measurement temperatures. If
τ
is too
small, no relaxation will be detected in the time window because the particles will have already
relaxed during the switch-off time. Similarly, no relaxation will be detected in the time window
3.2 Temperature Dependent Magnetorelaxometry (TMRX) 45
if the relaxation time is too long. A particle of a certain size will only reach its highest
∆B
for a
fixed timeframe at a defined temperature. When
∆B
is plotted as a function of
T
, a peak at a certain
temperature is observed that is directly related to the MNP core size (Equation 3.5) if interactions
can be neglected.
Thus, TMRX spectra may be used to determine the characteristics of MNPs. This analytical method
was introduced by Berkov and Romanus et al. [
75
], who coined the term TMRX. They explained
the different relaxation amplitudes in terms of energy barriers. They also demonstrated that the
magnetic particle core size distribution can be determined if the anisotropy of the sample is known.
Alternatively, if the magnetic particle core size distribution is known from other analyses, TMRX
can be used to determine the anisotropy distribution. The impact of dipole–dipole interactions on
the relationship between the peak temperature and particle size is discussed in Chapter 4.4.
3.2.4 Influence of the Particle Core Size Distribution on the TMRX Spectrum
If a particle sample contains only one specific particle size or has a sufficiently narrow size
distribution, it is considered to be monodisperse. Depending on the particle size, there will be a
range of temperatures at which the relaxation can be detected within a constant time window. As
explained in Chapter 3.2.3, the temperature dependency of the relaxation will lead to a defined
peak temperature at which the relaxation amplitude change is the most pronounced. Even for a
monodisperse sample, the TMRX spectrum will be a peak shaped function. If the particle sample
also contains MNPs with other core diameters, the resulting signal will be a combination of the
individual relaxations. If the second particle type is much larger or smaller in diameter, the TMRX
spectrum will exhibit a second peak. However, if the two particle types have similar particle
diameters, the TMRX spectrum will broaden, i.e., the temperature range at which the relaxation is
measured will be increased.
Most particle samples have a relatively broad log-normal distribution of different particle sizes.
This distribution can be expressed using the median diameter (
˜
d
) and a variance (
σ
) according
to Equation 2.8. Therefore, the variance directly influences the temperature range of the TMRX
signal, and a broader particle distribution results in a broader TMRX peak.
The peak temperature indicates the median core diameter in the MNP sample while the broadness
of the TMRX spectra indicates the diversity of the core diameters in the sample. However, particle
interactions may alter the peak temperature, which makes interpretation of TMRX spectra more
difficult.
3.2.5 TMRX using a Magnetic Property Measurement System
Because one relaxation measurement using the MPMS takes approximately
40 min
, the overall
analysis time for one sample can be
10 h
to
12 h
. Therefore, only a limited number of relaxation
measurements are typically performed for a given sample; a typical TMRX analysis using the
MPMS only consists of approximately 20 single relaxation measurements. It would be advan-
tageous to reduce the measurement time in order to increase the sampling rate and obtain more
detailed TMRX spectra. The TMRX measurements performed in the present study using the MPMS
are presented in Chapter 4. Additional information about the MPMS, its programming, and a
typical analysis procedure can be found in Appendix 8.1.
Analysis Procedure for TMRX using a Magnetic Property Measurement System
Using an MPMS, temperature dependent relaxation measurements were conducted at
5 K
–
300 K
.
The different temperatures and magnetic fields were set using Multi-VU sequence commands
(see Appendix 8.1). For each temperature, a magnetizing field of
1 mT
was applied for
8 min
in
order to magnetize the MNPs in the sample, followed by recording of the relaxation signals for
approximately
40 min
. In the recording phase, the magnetic moment of the sample was detected
100 times in a row. The switch–off time of the
1 mT
field from the superconducting magnet was
46 Chapter 3. Measuring Principles
Figure 3.5: TMRX signals of two similar MNP samples differing only in their magnetic core
diameters. Sample
A
(blue), with a core diameter of
6 nm
, had a maximum relaxation amplitude at
15 K
, whereas sample
B
(orange), with a core diameter of
7 nm
, exhibited its maximum relaxation
amplitude at
25 K
. The different peak temperatures are indicated by the arrow. Because of the
similar size distributions of the two particle samples, the shapes of the two curves resembled each
other, even though the peak temperatures for the two particle systems were different.
approximately
1,5 min
, during which the SQUID could not be turned on to detect the magnetic
moment. To determine the magnetic moment from the measurement data, the reciprocating sample
option (RSO) mode was used. During the first
5 min
of the relaxation measurement phase, the
MPMS only performed single RSO scans; in the latter portion of the measurement phase, three
repetitions of each RSO scan were performed. The RSO scans with one repetition had a shorter
measurement time and a lower accuracy than those obtained using three repetitions.
Measurements in the Reciprocating Sample Option (RSO) Mode
In the RSO mode, the sample was moved stepwise through the second-order gradiometer supercon-
ducting pick up loop. During the analysis, the SQUID voltage and sample position were measured,
and the results were fitted to a model to determine the magnetic moment of the sample.
In a typical RSO measurement the sample is positioned in the sample holder at the end of the
sample rod which is then placed in the sample chamber through the airlock. The sample rod is held
at the top by the RSO-Motor. The motor then moves the sample sinusoidally through the pick up
coils. A change of the sample’s position comes along with a change of the flux in the system. The
pick up coils induce a current into the superconducting circuit depending on the flux to which they
are exposed. The position of the sample rod is tracked by a shaft encoder on the servo motor. To
lower the signal to noise ratio, the sample is moved several times through the pick up coils and the
measurements are averaged. The final RSO measurement therefore consists of the absolute SQUID
voltage at each position of the sample rod within the sample chamber. The incline of this bell
shaped curve is then fitted and compared to the calibration curve of a palladium standard sample.
This standard sample imitates a point dipole with an accuracy up to
0,1 %
. For an exact fit the
unknown sample should therefore have small spacial proportions of about
3 mm
in diameter and
3 mm to 5 mm in height.
3.2 Temperature Dependent Magnetorelaxometry (TMRX) 47
3.2.6 TMRX using the 6-Channel SQUID System
The 6-channel SQUID system is an alternative device capable of MRX measurements [
2
]. The
crucial advantage of this instrument is the reduced dead time because of its optimized, non–magnetic
design. The short delay time allows measurement of the relaxation to begin within
100 µs
–
1 s
after switch–off of the magnetizing coil.
The faster measurement window results in the detection of different particle spectra at room
temperature. The measurement time window of the system is illustrated as dashed blue lines in
Figure 3.3. Compared to the MPMS, the 6-channel SQUID system detects a broader range of
particle sizes at a defined temperature because of the different measurement time window. For
instance, at
300 K
particles with core diameters of
22 nm
to
26 nm
are detectable. The 6-channel
SQUID system does not, however, have a sample cooling option installed and is therefore only
capable of analyses at room temperature.
In Figure 3.3, the range of detectable particles would also be increased if the fast measurement time
window was combined with low-temperature analysis. At
5 K
, even small particles with a
5 nm
core would be detectable with the 6-channel MRX system. In addition, the faster magnetization and
measurement times would significantly reduce the overall measurement time. For a single sample,
the overall measurement time would mainly be determined by the cooling time. Furthermore,
because one relaxation measurement could be performed every three seconds, the sampling rate
for TMRX analysis could be significantly increased. With a higher sampling rate, more detailed
information about the particle distribution could be obtained. In particular, small sub–maxima next
to the main temperature peak that are hidden at lower sampling rates may become visible. Because
the magnetic relaxation moment of the sample decays exponentially with time, the delay after
switching off the magnetization coil also has a significant effect on the relaxation signal strength.
The shorter dead time of the 6-channel SQUID system would therefore increase the relaxation
signal strength, which could in turn be used to reduce the necessary magnetization time. Thus, the
detection limit of the system could be increased because of the gain in the relaxation amplitude.
The above mentioned advantages make the expansion of the 6-channel SQUID system for TMRX
desirable. In order to do so, a helium flow cryostat must be designed as a sample cooling unit. The
design and implementation of the cryostat is discussed in Chapter 6.
II
4TMRX Analyses in the Long Time Regime
51
4.1
Data Analysis for the Magnetic Property Measure-
ment System
4.2
Influence of Magnetic Nanoparticle Amount on the
TMRX Spectrum
4.3
Influence of the Magnetizing Field Strength on the
TMRX Spectrum
4.4
Influence of Particle Aggregation on the TMRX
Spectrum
4.5
Multicore Particle Analysis via TMRX of Underlying
Fractions
5Numerical Simulation of TMRX Spectra 77
5.1
Influence of Dipole–Dipole Interactions on the
TMRX Spectrum
5.2
Simulation of TMRX Spectra of Non–Interacting
Particles
5.3
Simulation of TMRX Spectra Including Dipole–
Dipole Interactions
6Development of a TMRX System for the
Short Time Regime .................. 89
6.1 Custom TMRX Measurement System
6.2 Characterization of the GRP Cryostat with Magne-
tizing Coil
6.3
Quantification of Magnetic Nanoparticles using
TMRX in the Short Time Regime
6.4
Quantification of Magnetic Nanoparticles in Biologi-
cal Tissues using TMRX in the Short Time Regime
7Conclusion ......................... 113
7.1 Summary and Conclusion
Results
4. TMRX Analyses in the Long Time Regime
52 Chapter 4. TMRX Analyses in the Long Time Regime
4.1 Data Analysis for the Magnetic Property Measurement System
Abstract 4.1
The process for analyzing the TMRX data obtained with the MPMS is briefly
introduced. A typical TMRX spectrum comprises a series of MRX measurements. Therefore, in
the first step, these single relaxation measurements must be processed. The uncertainty in the
measurements is then determined and a curve–fitting process is used. As the TMRX measure-
ments with the MPMS take up to
12 h
, an alternative magnetizing procedure is implemented
and investigated to determine if faster TMRX analyses are feasible. In order to implement the
alternative magnetizing procedure different methods for controlling and accelerating the MPMS
analyses are also discussed (Section 4.1.4).
4.1.1 Uncertainty of the Measurement Results
The MPMS output file for an RSO measurement (see also Chapter 8.1) is an ASCII table that
contains, among other things, information about the measurement time, field, temperature, and
the measured magnetic moment. An important value for each RSO measurement is the fit quality.
This value shows how well the measured SQUID response (see Figure 4.1) fits a previously defined
response curve that represents the signal of an ideal point–like source. The quality of the fit is given
as a value between
1
and
0
, with
1
representing a very good match and
0
representing a failed fit. A
lower fit quality results in a higher uncertainty for the sample’s determined magnetic moment.
Figure 4.1: In RSO mode the sample is periodically moved through a second order gradiometer. The
SQUID response depends on the sample position within the gradiometer (Picture from Manual [
1
]).
The samples magnetic moment and fit quality are determined through comparison of the SQUID
response with a previously defined response curve of a reference sample.
As described in Section 3.2.5, a relaxation measurement obtained using an MPMS consists of 100
single RSO measurements, each of which provides a value for the net magnetic moment of the
sample. In this work the accuracy of these RSO measurements was investigated. To determine
the influence of a low fit quality on the accuracy, the magnetic moment of an MNP sample was
analyzed using different magnetic fields. When the field was sufficiently strong (
B>10 mT
), a
fit quality greater than
0.9
was obtained. At lower applied fields the fit quality decreased and the
4.1 Data Analysis for the Magnetic Property Measurement System 53
uncertainty of the determined magnetic moment increased. The relative magnetic moments and
their corresponding fit quality are displayed in Figure 4.2.
Figure 4.2: Relative magnetic moments of different RSO measurements and their corresponding
fit qualities. A lower fit quality resulted in a decreased accuracy for a given magnetic moment. A
confidence interval of 95% was obtained.
Using these results, a phenomenological function (
ferr
) for the confidence interval was generated
in the course of this dissertation. A determined magnetic moment with a certain fit quality
gfit
is
covered by this interval in 95% of cases:
ferr =1−q−ln(gf it ∗√2∗π∗0.42)2∗0.42
6.6.(4.1)
This confidence interval was then used to determine the uncertainty of each RSO measurement in a
magnetic relaxation scan (Figure 4.3, left frame).
Figure 4.3: Left: Exponential least squares fit (red line) of relaxation measurements, each consisting
of 100 single RSO scans. The RSO measurements in the first five minutes experienced more
variation because they only consisted of single RSO scans while the latter scans were repeated three
times. Right: Residual of the fitted exponential function. The upper maximum deviation from the
fit was approximately ±3·10−8Am2
54 Chapter 4. TMRX Analyses in the Long Time Regime
4.1.2 Fitting the Exponential Decay of the Measured Relaxation Signal
The relaxation measurements obtained using the MPMS comprised up to 100 single RSO mea-
surements. For TMRX analyses, the amplitude change for each single relaxation curve had to be
determined for a constant time window. For TMRX analyses using the MPMS, a time window of
40 min
was used in this work. It was essential that this time window remained constant for all the
relaxation measurements in order to be able to compare the different amplitudes. However, because
of deviations in the switch–off time, the start time for the first RSO measurement varied slightly. It
was therefore useful to compare the different relaxations over the time period from
tbegin =1,5 min
to
tend =40 min
. In order to determine the net magnetic moment at
tbegin =1,5 min
an exponential
decay function was fitted to the relaxation data.
As described earlier in Section 3.2.5, during the first
5 min
, the MPMS only performed single RSO
scans and later switched to RSO scans with three repetitions. The first RSO scans therefore tended
to have higher measurement uncertainties than the RSO scans with three repetitions. Therefore, the
measurement quality was also taken into account in the form of a weighted least squares fit using
weight matrix
W
, as shown in Equation 4.2. The obtained RSO data was inserted in vector
X
while
the exponential fitting function was Y=Aexp(−t/τα), with Aand ταas free fitting parameters:
PFit = (XTWX)−1XTWY.(4.2)
Because of the weighting factors, data points with low fit qualities influenced the relaxation fit
less than the data points with high accuracies. In addition, an option to remove outliers based on
their measurement quality was included. When performing the data analysis a threshold for the fit
quality could be chosen so that RSO measurements below that value (e.g. fit quality < 0.2) would
be excluded. In Figure 4.3 (left frame), a fitted relaxation curve and the corresponding RSO data
points with individual error bars are shown.
Finally, the fitted relaxation curve was subtracted from the original data points in order to determine
the residual. The maxima of the residual (Figure 4.3, right frame) were then used to determine
the upper and lower limits of the error bars for the amplitude changes. In a typical TMRX graph,
the amplitude changes with their associated error bars are displayed as a function of temperature
(Figure 4.4). The TMRX spectrum of a highly diluted MNP sample (
mFe=0,2 µg
) is shown in
Figure 4.4. The error bars are therefore particularly large.
Figure 4.4: TMRX graph with error bars determined from the residuals of the fitted relaxation
curves. The error bars are more or less pronounced depending on the signal strength at each
temperature. The fit quality varied from a good average of 0.8 at room temperature to a low quality
of 0.2 below 100 K.
4.1 Data Analysis for the Magnetic Property Measurement System 55
4.1.3 Analysis of the Switch-Off Time of the Superconducting Magnet
The switch–off time of the superconducting magnet is an important factor for determining the
measurement uncertainty. As described in Section 8.1 of the Appendix, the persistent–current
switch must be heated prior to changing of the current in the coil. Because of the increase in
temperature, a small portion of the circuit loses its superconductivity, and the current in the coil is
reduced. If the magnet is in persistent mode, the magnitude of the power supply’s current must
be matched with the current flowing in the magnet. The higher the active current in the coil, the
more time this process takes. Furthermore, if the current in the superconducting coil is changed,
a current is also generated in the detection coil via induction. To prevent the detection coil from
charging, a small section of this coil is also heated.
Figure 4.5: Switch–off and switch–on times of the MPMS superconducting magnet for set fields
ranging from 0,1 mT to 5 T.
In order to switch the magnet back on, the persistent switch must be heated to induce a current in
a similar manner. Using the attached current source on the switch, a current can be brought into
the superconducting magnet. After setting the required field, the switch must then be cooled again
in order to achieve persistent mode; because an active switch would increase the noise level. A
side effect of the magnetization of the coil is the so–called flux creep, a relaxation effect of the
magnetic field in the system. This effect causes a slight field change in the superconducting magnet,
which again induces a current in the detection coil and therefore leads to a SQUID drift. While
the linear portion of the SQUID drift is compensated by the MPMS control system, the non-linear
portion cannot be compensated. A short delay is thus added after the field has been changed. For
higher magnetic fields, the flux creep is more pronounced, and hence the wait time is longer. This
field dependency can be seen in Figure 4.5. The average switch–off time for fields below
1 T
is approximately
75 s
. For fields above
1 T
, the delay increases exponentially up to
250 s
. The
switch–on time is approximately
20 s
to
30 s
longer than the switch–off time for all changed fields.
Based on this data, the relaxation measurements performed in the present study were executed with
fields ranging from 1 mT to 10 mT because the switch–off times of these fields are fairly short.
56 Chapter 4. TMRX Analyses in the Long Time Regime
4.1.4 Communication with a Magnetic Property Measurement System
In general, communication with the MPMS is achieved via the sequence manager of the MultiVu
software (see also 8.1). However, other more direct forms of communication with the MPMS
are also possible. The command–system in the background of the MultiVu software is the EDC
language (see also Section 8.1). While single EDC commands can be sent directly via the MultiVu
software, an additional (script-)language is needed to perform a sequence of measurements. In
order to avoid the switch–off time of the MPMS, magnetization of the sample was attempted using
the AC–coil in the system, rather than the superconducting magnet. This normal conducting coil
is designed to perform AC measurements in the MPMS. Even though the maximum generated
field of the coil is only
0,1 mT
, it would be sufficient to magnetize a sample for TMRX analysis.
Because the sequence manager of the MultiVu software does not include a DC setting for this coil,
its activation was achieved using EDC commands that were initially sent directly over a LabVIEW
interface. For the communication via LabVIEW, the GPIB port of the MPMS was utilized. The
GPIB port enables a user to send any three–letter EDC command string to a specific address in the
MPMS (e.g., the RSO–motor). Ultimately, the EDC commands were sent via a Delfi script because
the LabVIEW interface was found to be insufficient for the intended task.
LabVIEW
In order to send direct EDC commands to the MPMS, LabVIEW software from National Instruments
was utilized. This software was installed on a second computer connected to the MPMS over a
USB to a GPIB cable. When operating in general mode, the MultiVu software frequently sends
EDC commands to check the status of the system. If one of those EDC commands is sent at the
same time as one of the EDC commands from LabVIEW, complications with the MPMS may occur.
Thus, although running LabVIEW and MultiVu at the same time is possible, it is not recommended.
The main part of the LabVIEW program consists of predefined EDC command strings. These
strings include specific tasks that are required for the TMRX sequence, i.e., temperature and field
settings. As is the case for the MultiVu software, there are also frequently repeating EDC commands
in the LabVIEW program, such as the temperature read-out and a vigilance command for the MPMS
to confirm that the operating PC is still operational. If this vigilance command is not received
by the MPMS regularly, the system shuts down in safe mode. Eventually, a stable LabVIEW
communication system for sending direct commands to the MPMS was developed. However,
complete replacement of the MultiVu software with the modified LabVIEW program suffered from
complications because of the need for replacement frequent background EDC commands from the
MultiVu software. Even though long delays between the single EDC commands were included, the
MPMS missed some commands, and as a result the entire communication system was unreliable.
The decision was thus made to halt work on the LabVIEW–based communication system and
switch to the Delfi script expansion package.
Delfi
The Delfi expansion package was offered as an add-on to the existing Multivu software. It proved
more reliable than LabVIEW–based communication. The script expansion package enabled the
inclusion and execution of user designed EDC–based scripts via the MultiVu sequence manager. Use
of the MultiVu software in combination with written Delfi scripts was advantageous compared to
the LabVIEW communication approach because it was not necessary to replace the entire MultiVu
system; Delfi scrips were only required for the new program elements. The new commands included
in particular, use of the AC coil for DC magnetization. Ordinary tasks such as temperature settings
were retained in the MultiVu sequence manager. Quantum Design offered various example scripts
for their Delfi expansion package, which was an added perk. Using these examples, the AC coil
in the MPMS was successfully utilized for DC magnetization of the sample space. In contrast to
the large superconducting magnet, the AC coil in the MPMS is not superconducting and can only
generate very small fields of
0,1 mT
. However, the AC coil has a very short switch–off time of less
than a second. Consequently, a single RSO measurement takes a long time, which is a limiting
4.1 Data Analysis for the Magnetic Property Measurement System 57
factor when using the MPMS for fast TMRX analyses. Thus, although the switch–off time with the
AC coil was set to less than a second, the first RSO measurement point still took
30 s
, eliminating
the time gain that was achieved by using the AC coil. A second attempt to accelerate the analysis
was then made by directly reading the MPMS SQUID signal. The read-out was realized over
the J-C10 serial–port on the rear side of the MPMS using a digital storage oscilloscope (Agilent
Technologies, DSO-X 2004A). Unfortunately, the oscilloscope measurements revealed a strong
drift in the first
30 s
, even without a sample. This background signal exceeded the relaxation signal
of a typical MNP sample by a factor of 100. Therefore, the AC coil not only magnetized the MNP
sample but also parts of the MPMS sample chamber. The background signal is most likely because
of magnetization of the superconducting magnet and the pickup coil and additional flux creep. In
ordinary RSO measurements, the long wait time and offset corrections adjust for this background
relaxation so that it does not interfere with the analyses. In addition, use of RSO measurements in
combination with the AC coil would still result in a delay of approximately
5 s
because of the RSO
measurement time. In combination with the small magnetization field of
0,1 mT
, this delay would
result in a severe signal loss.
It was therefore not possible to significantly accelerate the relaxation analyses using the MPMS.
Hence, the development of a custom TMRX device looked more promising.
Conclusion
In the first part of this chapter an analysis method for relaxation data obtained with the MPMS was
introduced. In order to consistently determine the relaxation amplitude change an exponential curve
was fitted via least squares. The measurement quality value of standard RSO data files was used to
create a weighted exponential fit and further optimize the fit accuracy. In addition, the residue of
each relaxation curve could be determined by subtracting the exponential fit. The residue was then
displayed as error bars in a typical TMRX plot.
In the second part an alternative magnetizing procedure was implemented in the MPMS with the
intention of accelerating the TMRX measurement procedure. In order to do so an AC coil in
the MPMS had to be utilized for DC magnetization of the sample. This could be achieved by
sending direct commands to the MPMS via a LabView or Delfi interface. However, it turned out
that a significant acceleration was not possible with the MPMS because of interfering background
relaxation signals which are probably caused by flux creep. This led to the decision to design
a custom measurement system for faster TMRX measurements which is explained in detail in
chapter 6.
58 Chapter 4. TMRX Analyses in the Long Time Regime
4.2 Influence of Magnetic Nanoparticle Amount on the TMRX Spectrum
Abstract 4.2
In this chapter the influence of the total amount of magnetic nanoparticle on the
TMRX signal is discussed. To do so, a dilution series of very small non–interacting particles
with known iron content was investigated. In the course of this thesis a novel MNP quantification
method was developed based on the correlation between the TMRX amplitude and the total
amount of magnetic iron in the sample. The quantification of MNPs in tissue or cell samples
plays an important role for different biomedical applications of MNPs. To demonstrate the
applicability of the introduced MNP quantification method, the MNP uptake in two different
cancer cell lines was determined.a
aThe content of this chapter was published in 2013 [43]
Figure 4.6: Dilution series of the CD021110 magnetic nanoparticle solution in PCR tubes.
Investigated Particles
Feraheme
R
is a commercial drug product with the active drug substance ferumoxytol (AMAG
Pharmaceuticals Inc., formerly Code 7228). Feraheme
R
is indicated for the treatment of iron
deficiency anemia [
86
]. It is also being developed as a diagnostic agent for first–pass contrast–
enhanced magnetic resonance angiography to assess peripheral arterial disease [
49
]. The iron
oxide Feraheme
R
is surrounded by a carbohydrate coating composed of polyglucose sorbitol
carboxymethyl ether.
CD021110 consists of carboxydextran–coated superparamagnetic iron oxide particles for pre-
clinical use and synthesized based on patent US 5,424,419.
Preparation of Dilution Series Samples
In this work a dilution series of immobilized reference samples of the CD021110 MNP solution
was prepared using an automated pipetting robot (epMotion 5070, Eppendorf). Each subsequent
dilution step involved dilution with aqua dest. by a factor of three, starting with the original MNP
suspension (iron concentration
=0,1 mol/L
). A mannitol solution containing
15 %
mannitol was
then added to each dilution, and the resultant MNP solutions were stabilized in polycarbonate
capsules via freeze drying to obtain immobilized samples. Thus, the nominal iron content in
the dilution series varied from several micrograms (1:3) to a few nanograms (1:2187) (see also
Table 4.1).
TMRX Measurement Procedure
The analyses were performed using a Quantum Design SQUID magnetometer (MPMS) via RSO
measurement following the procedure described in Chapter 3.2.5.
4.2 Influence of Magnetic Nanoparticle Amount on the TMRX Spectrum 59
4.2.1 Analysis of a Magnetic Nanoparticle Dilution Series
In a first step, the relaxation of the magnetic moment for the CD021110–nanoparticle preparation
was recorded at various temperatures (see Figure 4.7). For a better graphical representation, the
magnetic moment obtained at the end of each recording period was subtracted from the relaxation
curve such that the last data points coincided for each temperature. In addition, only 10 out of
17 relaxation curves are displayed. The magnetic moment of each RSO scan is represented as a
single data point. Two different measurement modalities of the MPMS SQUID magnetometer were
used in a single relaxation measurement: the single RSO scan and three RSO scan average. The
single RSO scan offers a faster determination of the magnetic moment at the price of a higher
measurement uncertainty compared to that of the three RSO scan average. Hence, during the first
7 min
of the analysis, when the relaxation signal was strongest, the single scan technique was used.
Averaging of three scans was subsequently employed for the remainder of each analysis.
Figure 4.7: Relaxation curves for the CD021110 solution at different temperatures (10 of 17 curves
are displayed). In the first 7 minutes, each data point was determined from a single RSO scan while
the subsequent points obtained by averaging 3 RSO scans.
For MNP signals within the time window
∆
t=
1,5 min
–
40 min
typical relaxation behavior was
observed, i.e., the magnetic moments decayed in curves described as stretched exponentials. While
the relaxation curve amplitudes varied considerably with temperature, the shapes of these curves
remained identical within the measurement uncertainty. Above
200 K
, no magnetization signal
was detected; a measurable relaxation amplitude within this window appeared only below
100 K
.
When displaying only the amplitude change (
∆
m) at each temperature, the amplitude increased
dramatically as the temperatures decreased and reached a maximum at approximately
20 K
(see
Figure 4.8).
At room temperature, virtually all of the particles in the MNP distribution were too small to generate
a relaxation signal within the measurement time window. When the maximum was observed, the
majority of the particles relaxed within the measurement time window while at lower temperatures,
the amplitude decreased again because increasing numbers of particles relaxed too slowly to be
detected in the constant time window.
60 Chapter 4. TMRX Analyses in the Long Time Regime
Figure 4.8: TMRX spectra of the different CD021110 dilution samples. The amplitude change (
∆
m)
of each relaxation curve is displayed at the measured temperature. The maximum amplitude for
each sample was observed at approximately
20 K
. The detection limit for this dilution series was
determined with approximately
5·10−8Am2
. Due to the logarithmic display negative data points
are not shown. At temperatures above
200 K
no relaxation was observed within the measurement
time window.
In Figure 4.8, the amplitude change (
∆
m) is displayed as a function of temperature for the different
dilution samples. The iron amount in these samples varied from
55,8 µg
to
0,23 µg
. Interestingly, it
can be seen in Figure 4.8 that each TMRX spectrum had the same peak temperature at approximately
20 K
, and all of the spectra had a similar shape. However, it can be clearly seen that the amplitude
change scaled with the iron content, implying that for this dilution series, the Néel relaxation time
(
τN
) was not affected by the amount, and only the amplitude (
A
) of the magnetic moment changed:
M(t) = A·exp−t
τN(4.3)
These findings revealed that the amplitude at the peak temperature could be correlated to the known
total iron content.
4.2.2 Quantification of the Iron Content via Peak Comparison
In order to use TMRX analysis for quantification, the measured amplitude change must be correlated
to the iron content in the sample. For the CD021110 samples, the nominal iron contents were
Dilution Step Nominal Iron µgFe Quantified iron µgFe
1/3 55.8 54.6
1/9 18.6 54.6
1/27 6.2 5.2
1/81 2.0 1.4
1/243 0.69 0.36
1/729 0.23 0.19
Table 4.1: Iron amount in CD021110 dilution series.
4.2 Influence of Magnetic Nanoparticle Amount on the TMRX Spectrum 61
determined via M(H) analyses performed using the MPMS. A linear relationship was revealed by
comparing the amplitudes at the peak temperature with the known iron contents in the samples.
All of the TMRX spectra exhibited maximum amplitudes near the same peak temperature (
Tmax
,
approximately
20 K
). The linear correlation between the amplitude change (
∆
m) and the nominal
iron content is displayed in Figure 4.9. For this type of MNP analysis, the detection limit was
estimated to be approximately 250 ng iron.
[H]
Figure 4.9: Total Iron Contents in the CD021110 dilution samples versus their relaxation amplitudes
(∆m) at their peak temperatures.
Because a linear correlation between the total iron content and amplitude at the peak temperature
was demonstrated, the new method was applied to in vitro quantification.
62 Chapter 4. TMRX Analyses in the Long Time Regime
4.2.3 Analysis of Magnetic Nanoparticles in Cell Samples
For this in vitro experiment, HeLa and Jurkat tumor cell lines were incubated by colleagues at the
Charité
1
using Feraheme
R
and CD021110 iron oxide MNPs. After
30 h
, approximately
106
cells of
each type were harvested. The cell samples were incubated with different quantities of CD021110
or Feraheme
R
. As a control, one cell sample was incubated without exposure to an MNP solution.
In Figure 4.10, the relaxation amplitudes (
∆
m) of the initial MNP solutions are plotted as a function
of temperature. The different shapes of the two TMRX spectral curves reflect the different size
distributions of the two MNP systems. The maximum amplitude for CD021110 occurred at a
slightly higher peak temperature than that for Feraheme
R
. This result is attributed to the different
core diameters of the particles. These observations illustrated that TMRX spectral shapes can be
utilized to characterize the magnetic properties of MNP preparations, and, in particular, to identify
changes in the particle size distribution.
Figure 4.10: Relaxation amplitude (
∆
m) as a function of temperature for CD021110 and Feraheme
R
.
Even small differences in the particle characteristics resulted in noticeable changes in the relaxation
amplitude curves.
In addition, the MNP specificity of the relaxation curves was be illustrated using the control data
obtained for the cell sample that was not exposed to MNPs, as shown in Figure 4.11. Absolute
magnetic background moments of approximately
0,3 µAm2
were determined for a tissue sample
without MNPs using single and averaged RSO scans, respectively.
1Ines Gemeinhardt, Monika Ebert, Jörg Schnorr, Susanne Wagner, Matthias Taupitz
4.2 Influence of Magnetic Nanoparticle Amount on the TMRX Spectrum 63
Figure 4.11: MRX analysis of the control sample. No relaxation was observed. The background
signal was
0,3 µAm2
for the first
7 min
of detection and, then decreased to approximately
0,1 µAm2
because of the change in the number of averaged RSO measurements.
Subsequently, TMRX analyses of the different incubated cell samples were performed. Figure 4.12
presents the TMRX spectra of HeLa cell samples with low and high MNP concentration and a
CD021110 reference sample (
mFe
=
55,84 µg
). Using a reference sample with known iron amount,
it was possibleto apply the peak comparison method for quantification of the cell samples.
Figure 4.12: Temperature dependent magnetorelaxometry spectra for HeLa tumor cell lines and the
initial CD021110-MNP solution as a reference. The TMRX spectra indicate that the MNP signals
mainly differed in their relaxation signal strengths. The shapes of the curves remained the same for
the incubated and non–incubated MNP samples.
Again, all of the spectra exhibited a similar shape, and their maxima occured roughly at the same
peak temperature (
Tmax
). Although the amplitudes of the peaks in the spectra of the tumor cell
64 Chapter 4. TMRX Analyses in the Long Time Regime
Name Exposure M(H)µgFe TMRX µgFe
Hela-5 Low 15(1)16(1)
Hela-8 High 111(5)107(6)
Jurkat 16 Low 15(1)13(1)
Jurkat 18 High 178(9)177(10)
Table 4.2: Iron amount in CD021110–exposed tumor cells.
lines were considerably reduced, they remained above the detection limit. Without additional
MNP interaction, the relaxation moment is directly proportional to the iron content. Therefore,
the iron content of the cell samples was determined from the ratio of the peak amplitude in the
reference MNP solution spectrum and the amplitudes at the peak temperature in the spectra of the
cell samples. The results for the dilution series and control indicated an accuracy of approximately
250 ng
for the CD021110 particles and the current setup. The last sample of the mannitol dilution
series that could be analyzed had a total iron content of
200 ng
. A slight shift in
Tmax
and very small
but systematic deviations in the shape of
∆
mwere be noticed in the spectra of the HeLa (Fig. 4.12)
and Jurkat cell samples. These results may be because of areas of high, local MNP concentrations
in the cell samples that altered the relaxation behavior with respect to the reference sample via
dipole–dipole interactions [
24
]. The shift in the relaxation amplitude curve may also be attributed
to size–selective MNP uptake. Shifts in the peak temperature of up to
10 %
were also observed and
resulted in a quantification uncertainty of approximately
6 %
. These two phenomena have also been
shown to influence other properties, such as the M(H) signal, by several percent [
25
]. The M(H)
measurement uncertainty was estimated to be approximately
5 %
. Hence, both methods provide
similar results within the limits of uncertainty.
Conclusion
In this chapter a dilution series of non-interaction MNPs were analyzed via TMRX in order to
investigate the influence of the MNP amount on the relaxation signal. The measurements revealed
a linear correlation of the total particle amount to the peak amplitude of the TMRX curves. The
method was furthermore used to successfully quantify the MNP uptake in HeLa and Jurkat tumor
cell lines. The determined iron contents were in accordance with other established quantification
methods. In addition, it was shown that it is possible to distinguish different MNP types based on
their TMRX spectra. The measurements performed in the course of this thesis therefore expanded
the field of application of the TMRX method.
4.3 Influence of the Magnetizing Field Strength on the TMRX Spectrum 65
4.3 Influence of the Magnetizing Field Strength on the TMRX Spectrum
Abstract 4.3
The influence of the magnetization field on the TMRX signal was investigated. A
DDM 128 sample was evaluated at magnetization field strengths of
1 mT
,
10 mT
,
50 mT
and
100 mT
. DDM 128 is a precursor of the contrast agent Resovist and, like Resovist, is bimodally
distributed. Because of the size dependence of the saturation magnetization, the field strength
affected the particles in the distribution differently depending on their core sizes. Variation of the
magnetization field strength was found to be a facile method for visualizing the dispersity of a
particle system, i.e., to determine whether the particle core sizes are more mono- or polydisperse.
Investigated Particles
MNPs of the precursor of Resovist (Bayer Schering Pharma AG) were investigated. Resovist
is a commercial contrast agent for MRI that is used to detect malign liver tumors. The contrast
agent consists of superparamagnetic iron oxide nanoparticles (SPION) coated with carboxydextran.
Resovist and its precursor particles are known to have bimodal size distributions with particle core
diameters ranging from 8 nm to 26 nm [90][23].
Preparation of Dilution Series Samples
The highly concentrated original DDM 128 solution (
500 mmol
) was diluted to create a solution
with a defined iron content. Specifically, the original solution was diluted with distilled water in
order to achieve an iron concentration of
1 mol/L
which was assumed to be sufficiently dilute to
prevent particle interaction. A
15 %
mannitol solution was then added to
30 µL
of the dilute MNP
solution, which was then immobilized in a polycarbonate capsule via freeze drying.
TMRX Measurement Procedure
The measurements were performed using a Quantum Design SQUID magnetometer (MPMS-
XL) with RSO measurements following the previously described procedure (3.2.5). In order
to investigate the influence of the field strength, the TMRX sequence was performed using a
magnetization field strengths of
1 mT
,
10 mT
,
50 mT
and
100 mT
. The switch–off time of the
magnetization field varied for the different fields from approximately
1,3 min
to
1,5 min
(see 4.1.3),
and was therefore considered constant. Both the magnetization and the measurement times were
left unchanged.
66 Chapter 4. TMRX Analyses in the Long Time Regime
4.3.1 Magnetizing Field Strength dependent Changes in the Relaxation Signal
TMRX analysis was first performed using the diluted DDM 128 sample. The same sample was
measured repeatedly using TMRX sequences with different magnetization field strengths, and the
absolute relaxation amplitude change (
∆m
) is plotted as a function of
T
in Figure 4.13. When
BMag =1 mT
, two distinct peaks were observed in the TMRX spectrum at
15 K
and approximately
150 K
. The peaks differed in both width and absolute height, or signal strength with the
150 K
peak
nearly twice as high as the 15 K peak.
Figure 4.13: TMRX signals for the Resovist precursor DDM 128 at different magnetization field
strengths. The TMRX signal for DDM 128 exhibited two distinct peaks at
15 K
and
150 K
that
were attributed to the bimodal distribution of the particle core size. Changes in the field strength
had varying impacts on the particles of different sizes. The larger particles were less affected by
higher field strengths because they were already saturated.
When
BMag =10 mT
, the TMRX signal increased at all temperatures, and the two peaks became
even more pronounced. In addition, while the temperatures at which the peaks occurred remained
nearly unchanged, the ratio of the intensities of the two maxima was drastically altered with the
15 K
peak exhibiting a similar relaxation amplitude to that of the
150 K
peak. This trend continued
for the
50 mT
and
100 mT
measurements. The change from
50 mT
to
100 mT
had a significant
effect on the amplitude of the
15 K
peak but negligible effect on the
150 K
peak. A slight shift
in the
150 K
peak to lower temperatures also occurred at higher magnetization field strengths; at
100 mT, the second peak was observed at 100 K rather than 150 K.
It is known from previous studies [
90
][
23
] that Resovist and its precursor DDM 128 have a
bimodal size distribution, i.e., there is a small fraction with core diameters of approximately 5 nm
and a large fraction with core diameters ranging from
15 nm
to
20 nm
. The two distinct peaks seen
in Figure 4.13 are attributed to these two size distributions within the MNP sample. As described in
Chapter 3.2.3, the two magnetic core volumes have different relaxation times and corresponding
energy barriers. Hence, their relaxation amplitude changes peak at different temperatures.
Using the Langevin equation (Equation 2.2), the magnetization behavior of the differently sized
4.3 Influence of the Magnetizing Field Strength on the TMRX Spectrum 67
Figure 4.14: Left: Magnetization curves for small (blue line) and large (red line) superpara–
magnetic particles. The larger MNPs exhibited a steeper slope than the smaller particles. Right:
Magnetization and relaxation processes during an MRX procedure. The larger particles required a
lower magnetization field strength to reach their saturation magnetization. Therefore, the larger
particles were less magnetized than their smaller counterparts when exposed to the same magnetic
field Hmag. This leading to a smaller amplitude change during the relaxation process.
particles can be visualized. In Figure 4.14, the idealized magnetization curves for the small and
large particles are displayed on the left. These magnetization curves illustrate, that the larger
particles require a lower magnetization field strength (
H
) to reach saturation magnetization, which
directly affects the relaxation process (Figure 4.14, right) and leads to different relaxation amplitude
changes for the differently sized particles.
Therefore, when
H
increased from
1 mT
to
10 mT
, both particle distributions within the sample
increased their magnetic moments. However, when the field strength was increased further to
50 mT
and
100 mT
, the fraction of larger particles reached saturation, whereas the signal strength of the
smaller particles continued to grow. The saturation effect for the large particles also explains the
temperature shift for the relaxation peak from
150 K
to
100 K
as the magnetization field increased.
The fraction of larger particles itself consisted of log-normal distributed (2.1.3) smaller and larger
particles. The change in the magnetization field affected these diverse MNPs differently. While the
larger particles within the log-normal distribution were already saturated, the smaller continue to
experience gains in their magnetic moments. As a result the peak for the entire fraction of larger
particles shifted to lower temperatures.
Finally, the question remained as to why the maximum amplitude change for the fraction of smaller
particles at
15 K
was nearly three times as pronounced as the maximum amplitude change for
the fraction of larger particles at
100 mT
. As introduced in Chapter 4.2, the amplitude change is
linearly dependent on the MNP concentration. The different pronounced peaks can therefore be
attributed to the total quantities of small and large MNPs in the sample. However, to determine the
nominal MNP concentrations of the different fractions, a reference sample with known quantities
of each fraction is needed.
Conclusion
The performed experiment can be used to visualize the dispersity of a particle distribution. For the
DDM 128 sample, the fraction of smaller particles with a peak at
15 K
appeared to be much less
affected in terms of peak-shifting. This result indicated that this fraction was actually monodisperse.
The peak shift of the fraction of larger particles, in contrast, indicated a larger variance in the
log-normal distribution of the particle core diameters. In addition, the field dependence can be used
to determine the ratio of two fractions within one sample. For exact determination of the nominal
iron concentration, however, reference samples for each fraction are needed.
68 Chapter 4. TMRX Analyses in the Long Time Regime
4.4 Influence of Particle Aggregation on the TMRX Spectrum
Abstract 4.4
The influence of particle interactions on the relaxation signal was investigated. In
order to provoke dipole–dipole interactions, citrate–coated MNPs were deliberately aggregated
via the addition of a sodium chloride solution. A stable dilution series of MNPs was prepared and
subsequently aggregated. The magnetic properties of both the stable and aggregated solutions
were then examined using temperature dependent magnetorelaxometry. The previously presented
quantification method (Section 4.2) was employed in this case because the underlying interaction
process was independent of the macroscopic concentration. a
aThe content of this chapter was published in 2014 [42]
Figure 4.15: Left:
30µL
of the original particle solution in distilled water. Right: Visible aggregation
and sedimentation 30 min after addition of a sodium chloride solution (cNaCl =1 mol/L).
Investigated Particles
For the quantification experiment, a solution of citrate–coated small iron oxide MNPs manufactured
by Charite Berlin was used. Two dilution series of the original particle system (
cFe =0.1mol/L
)
were prepared. One was prepared by diluting with distilled water, and the other by diluting with a
sodium chloride solution (
cNaCl =1 mol/L
) in order to force aggregation. The addition of sodium
chloride led to visible aggregation after
30 min
(see Figure 4.15). Subsequently, the samples were
immobilized by freeze drying after addition of
30 µL
mannitol (
cmannit =50 mmol/L
) solution over
night.
TMRX Measurement Procedure
The measurements were performed using a Quantum Design SQUID magnetometer (MPMS-XL)
and RSO measurements as described in Section 3.2.5.
4.4 Influence of Particle Aggregation on the TMRX Spectrum 69
4.4.1 Influence of Dipole–Dipole Interactions on the TMRX Spectrum
For both the aggregated and unaggregated MNP samples, the peak temperature of the amplitude
(
Tmax
) was observed well below room temperature. Forced aggregation via the addition of sodium
chloride led to a change in the shape of the relaxation curve. The peak temperature of the amplitude
increased from
130 K
for the unaggregated particles to
210 K
for the aggregated system, as can be
seen in Figure 4.16. This shift resulted from a change in the relaxation time (
τ
) for the aggregated
particles, which required more time to fully relax than the unaggregated particles.
Figure 4.16: Changes in the TMRX signal through enforced aggregation. Both the stable and
aggregated MNP samples exhibited relaxation signals at nearly every investigated temperature,
with peak temperatures at 130 K and 210 K, respectively.
Investigation via TMRX revealed that each sample exhibited a broad relaxation spectrum, i.e.,
the samples displayed relaxation signals from
5 K
to ambient temperature. This width can be
explained by broad distributions of the magnetic core sizes within the samples. In addition, the
small shoulder at
20 K
in the spectra for both samples indicated the presence of a second smaller
fraction of particles within the sample.
While aggregation led to an increase in the peak temperature of approximately
80 K
, it affected
the relaxation at temperatures other than the peak temperature significantly less, resulting in more
of a stretched deformation of the curve to higher temperatures than an equal shift. In addition,
comparison of the peak temperatures revealed an amplitude loss of more than
50 %
, with a decrease
in the overall amplitude per milligram iron. This change can be explained by an elongation of the
Néel relaxation time (τN) because of the dipole–dipole interaction energy E, as in Equation 4.4:
τN=τ0expKV
kBT+E.(4.4)
With a longer
τN
, relaxation of the aggregated particles at most temperatures was too long to be
detected within the constant measurement window (
tstart =1,5 min
to
tend =40 min
). However,
aggregation did lead to an increase in the amplitude at temperatures ranging from
200 K
to
310 K
.
In this temperature range, the particles relaxed very rapidly prior to aggregation and lost a portion
of their relaxation amplitude in the first
1,5 min
, i.e., prior to initiation of the measurement window
started. Their relaxation behavior at these temperatures then slowed down because of aggregation,
resulting in an increase in the relaxation amplitude.
70 Chapter 4. TMRX Analyses in the Long Time Regime
Signal alterations at temperatures near
300 K
are particularly relevant because nanoparticles for
biomedical applications are applied at ambient temperatures. Signal changes caused by concen-
tration effects, aggregation, and immobilization are therefore important for applications such as
imaging and hyperthermia.
4.4.2 Quantification of Aggregated and Unaggregated Particles
TMRX analyses of the aggregated and unaggregated samples revealed that their curve shapes and
maximum temperatures (Figure 4.17) did not change with concentration. These results indicated a
constant relaxation time for each dilution series, which is contrary to previous results in which the
peak temperature (
Tmax
) was observed to scale with the concentration (see also Chapter 5.1) [
106
].
In addition, the decrease in amplitude was directly proportional to the nominal iron content within
the samples, as can be seen in Figure 4.18.
Figure 4.17: TMRX signals of original (left) and aggregated (right) particles at different concentra-
tions. The overall amplitude declined with increasing dilution. The peak temperatures at
130 K
for the original and
210 K
for the aggregated MNP samples remained unchanged for the different
dilution steps.
Thus, the iron content of a sample may be determined via peak comparison (see also Chapter 4.2)
using a known reference sample [
43
]. Quantification via TMRX peak comparison is, however, only
reliable if the curve shapes of the TMRX spectra remain unchanged. The known reference sample
must therefore have a similar TMRX spectrum as the sample to be quantified.
Dissolution Total Iron Amount [g] ∆m[Am2]at TMax =200K
1 6.9·10−43.93·10−5
1 to 3 2.3·10−49.53·10−6
1 to 10 6.9·10−53.22·10−6
1 to 30 2.3·10−51.29·10−6
1 to 100 6.9·10−64.06·10−7
1 to 300 2.3·10−61.56·10−7
1 to 1000 6.9·10−7−
4.4 Influence of Particle Aggregation on the TMRX Spectrum 71
Figure 4.18: Nominal total iron content versus relaxation amplitude at the maximum temperature
for aggregated and unaggregated particles. While the samples had different peak temperatures, the
ratio of the amplitude to the iron content was the same for both.
Conclusion
TMRX reveals detailed information about the magnetic behavior of MNPs. In the present study,
aggregation led to an increase in the temperature of the amplitude maximum because of dipole–
dipole interactions. The aggregated particles had a smaller average core–to–core distance, which
increased the interaction energy and slowed down particle relaxation. Notably, the dilution series
revealed that the magnetic relaxation signals scaled linearly with concentration, implying that the
underlying interaction process was independent of concentration. Hence, dipole–dipole interactions
are attributed to the formation of a local MNP superstructure consisting MNP clusters or aggregates.
The dipole–dipole interactions within the superstructure predominate over interactions caused by
concentration effects.
72 Chapter 4. TMRX Analyses in the Long Time Regime
4.5 Multicore Particle Analysis via TMRX of Underlying Fractions
Abstract 4.5
The applicability of TMRX for the investigation of Multicore Particles was
illustrated. An MNP solution was separated into two fractions via static separation and the
separation products analyzed via TMRX. Gum Arabica–covered multicore particles [
67
]
designed for MRI use and their precursor particles were used for this study. A static separation
process was performed on the precursor particles in order to determine whether or not only
certain fractions were integrated into the multicore particles.
Introduction
All biomedical applications of magnetic nanoparticles depend on the particular magnetic properties
of the MNPs. How suitable a particle type is for a specific application is amongst, other things,
determined by its magnetic characteristics, size, and surface properties. One method for improving
these characteristics is to develop advanced chemical processes that produce MNPs tailored for a
desired task. Another approach is to improve existing particle solutions through specific filtering
procedures, i.e., the separation of desired particles. MNP separation is a currently developing
research field within the nanoparticle community with growing impact. Unlike purely mechanical
filtration, magnetic separation divides the particles based of their magnetic properties, and not just
their geometric sizes. In biomedical applications, magnetic separation is used to improve the quality
of magnetic tracer particles for magnetic particle imaging and magnetic resonance imaging.
Investigated Particles
The precursor particles were produced by thermal decomposition of Fe(acac)3 in organic solvent
and then coated with meso-
2,3
-dimercaptosuccinic acid (DMSA). The DMSA coated MNPs were
then reacted with Gum Arabica (GA), leading to the formation of covalent bonds between the
DMSA and GA, and thus multicore particles. GA is a hydrophilic, composite polysaccharide
harvested from the exudates of Acacia senegal and Acacia seyal trees. To solutions of the DMSA-
coated precursor and GA–containing multicure particles,
30 µL
mannitol solution (containing
15 %
mannitol) was added. Each solution was then immobilized in a polycarbonate capsule via freeze
drying to obtain stable samples. A solution of the precursor was also forcefully aggregated via
dehydration. The iron concentrations of the original precursor and GA–coated multicore particle
solutions were
1,37 mg
iron per
mL
and
1,2 mg
iron per
mL
, respectively. Transmission Electron
Microscopy (TEM) using a 100-kV JEOL JEM1010 microscope was performed to characterize the
particle size of the DMSA particles (Figure 4.19).
Figure 4.19: (Left) Transmission Electron Microscopy (TEM) image of the DMSA–coated precursor
and (right) Gum Arabica multicore particles. (Picture from [67])
4.5 Multicore Particle Analysis via TMRX of Underlying Fractions 73
TMRX Measurement Procedure
The measurements were performed using a Quantum Design SQUID magnetometer (MPMS-XL)
and RSO measurements following the procedure described in Section 3.2.5.
Separation Procedure
The original precursor solution was diluted with distilled water to an iron concentration of
0,1 mg
iron per liter. The diluted sample was then separated using commercial cell separation columns
(Miltenyi Biotec MACS) in combination with a permanent magnet (Miltenyi Biotec MiniMACS
Separator). The strong magnetic gradient in the column led to retention of the larger MNPs and
passage of the smaller particles. The retained and collected fractions are referred to as the eluate
and discharge, respectively.
4.5.1 TMRX Analysis of Multicore and Precursor Particles
First, samples of the immobilized precursor and multicore particles were analyzed using the de-
scribed TMRX sequence. Notably, even though the magnetic cores within the precursor MNPs and
MCNP were the same, their magnetic relaxation behaviors were unequal. The TMRX measurements
displayed in Figure 4.20 show the amplitude changes as a function of temperature for the two MNP
samples. The DMSA–coated single core particles exhibited the largest relaxation amplitude at
60 K
Figure 4.20: TMRX Spectra of precursor and GA-coated MNPs. The precursor particles (gray
squares) exhibited the largest relaxation amplitude at
60 K
and a secondary shoulder at
120 K
. The
GA–covered multicore particles (red squares) only exhibited one maximum at 130 K.
and a secondary maximum at
120 K
. However, the GA–covered, multicore particles only showed a
single maximum at
130 K
. In addition, the overall amplitude per milligram of iron was reduced
to approximately
50 %
for the latter sample. The TEM analyses (see Figure 4.19) indicated that
the precursor consisted of MNPs with a narrow core size distribution of
7,1 nm ±1,4 nm
. While
the multicore particles consisted of these cores, the cores were combined into larger structures.
The TMRX signal of the GA–covered multicore particles reflected the magnetic characteristics of
particles with larger cores. A temperature peak at
130 K
is typically obtained for particles with
magnetic iron oxide cores of
15 nm
to
18 nm
. It was uncertain, however, whether the results of
these TMRX measurements indicated that the multicore particles included a fraction of particles
74 Chapter 4. TMRX Analyses in the Long Time Regime
larger than the median precursor particles or whether these unusual TMRX signals were because of
dipole-dipole interactions.
4.5.2 TMRX Analysis of Separated Particles
In order to investigate the single core MNPs in more detail, a static separation was performed
because the TMRX signal of the sample indicated the presence of two fractions with different size
distributions. The subsequent static separation divided the solution into discharge, i.e., smaller
particle fraction, and eluate, or larger particle fraction. The TMRX analyses (Figure 4.21) of the
eluate exhibited a peak amplitude at
110 K
, whereas the peak amplitude of the discharge appeared
at
70 K
to
80 K
. The amplitude strength per mg iron was slightly higher than that of the original
precursor for both fractions. Separated fractions typically have higher signal per gram iron ratios
than original solutions because the relaxation spectra are narrower for separated particles. The
Figure 4.21: The eluate (blue diamonds) exhibited a peak amplitude at
110 K
whereas the discharge
(orange circles) displayed a maximum at
70 K
to
80 K
. The amplitude strength per mg of iron for
both fractions was slightly higher than that of the original precursor.
presented results indicated that the static separation of the precursor particles was successful, and
that fractions of larger and smaller particles were separated. It was, however, still unknown whether
the large fraction contained
20 nm
–sized particles or if it consisted of agglomerates of
7 nm
single
core particles that interacted with one another. Analysis of the TEM images did not indicate the
presence of
20 nm
–sized particle cores. In order to obtain a sample with dipole–dipole interactions,
the precursor solution was aggregated via drying. The TMRX signals for this aggregated sample,
the multicore particles, the two separated fractions, and the original precursor are displayed in
Figure 4.22. It can be seen in the figure that the amplitude per gram iron steadily declined with
rising peak temperature. The discharged particles had the highest amplitude and the lowest peak
temperature of
70 K
while the eluate particles had a peak temperature at
110 K
and a slightly lower
amplitude. The Gum Arabica covered multicore particles and aggregated precursor followed the
latter trend.
This tendency can be attributed to increasing dipole–dipole interactions between the single parti-
cle cores. The discharged solution contained only freely moving single core particles with core
diameters of
7 nm
that experienced almost no interactions. The eluate, however, already contained
4.5 Multicore Particle Analysis via TMRX of Underlying Fractions 75
Figure 4.22: TMRX results for the aggregated precursor (stars) compared to the signals shown in
Figure 4.20 and 4.21. The peak temperature for the aggregate was
175 K
, and its amplitude per
gram iron was only 30% of that of the precursor.
agglomerates of these single core particles. The particles therefore came close enough to each other
to allow interaction of their magnetic moments. In the Gum Arabica–coated multicore particles,
the single cores were densely packed and experienced even more pronounced dipole–dipole interac-
tions. Finally, in the aggregated form, the single magnetic cores were even closer to one another
because their coatings were dehydrated. The magnetic behavior of these MNPs was attributed to
the retarding effects of dipole–dipole interactions, as described in Chapter 4.4.
Conclusion
To conclude, the magnetic behavior of the Gum Arabica covered multicore particles was strongly
influenced by dipole–dipole interactions and they exhibited the magnetic characteristics of particles
15 nm
to
18 nm
in size. The precursor, in contrast, showed a predisposition to form these multicore
structures even without the Gum Arabica as connector. The magnetic signal of the precursor
therefore consisted of a mixture of interacting and non-interacting particles. For this MNP system,
the combination of magnetic separation and TMRX analysis enabled further understanding of the
underlying magnetism of the multicore particles and their precursor.
5. Numerical Simulation of TMRX Spectra
78 Chapter 5. Numerical Simulation of TMRX Spectra
5.1 Influence of Dipole–Dipole Interactions on the TMRX Spectrum
Abstract 5.1
Dipole–dipole interactions play an important role in relaxation measurements
because these interactions can easily alter the MRX or TMRX signals. In order to investigate the
influence of dipole–dipole interaction on the TMRX spectrum we analyzed a dilution series of
the clinical contrast agent Endorem. TMRX analysis of the series revealed changes in the peak
signal temperature and curve shape that correlated with sample concentration, clearly indicating
the degree of dipole–dipole interactions at each concentration step. Next, TMRX spectra were
simulated using various equations (Langevin equation for MNP magnetization, Néel formula
for particle relaxation, ect.) in combination with information about the size distribution of the
particles. While the simulated results reproduced the relaxation behavior of the most dilute
samples, they were not in agreement with the data for the samples with higher concentrations.
In order to slow down the relaxation for the highly concentrated samples, a dipole–dipole
interaction term was included. Specifically, an interaction energy term was numerically adapted
because conventional approaches for dipole–dipole interactions were not sufficient to describe
the experimental data. The different simulations were evaluated based on their quantification
accuracy and plausibility. Notably, introduction of the novel numerical interaction term enabled
accurate simulation of the TMRX spectra of the investigated dilution series and quantification
of the individual samples.
Magnetic Nanoparticle Samples
The contrast agent Endorem contains dextran–coated superparamagnetic magnetite nanoparti-
cles with core size diameters ranging from
5 nm
to
10 nm
. The MNP stock suspension with
cFe =11,2 mg/mL
was diluted using distilled water (Milli-Q, Millipore Corporation) to six dif-
ferent iron concentrations, and subsequently
100 µL
volume samples were immobilized by freeze
drying. The concentration of the freeze dried stock suspension
S
was
106 mg
iron per gram sample.
The resulting solid dilution samples
C1
–
C6
had concentrations of
58,9 mg
, to
0,16 mg
iron per
gram sample, respectively. These samples were the same as those recently used in an AC suscepti-
bility study [
52
]. In that study, the Endorem dilution series was analyzed and used as references for
the quantification of MNPs in the liver and spleen tissues of rats. Here, the same dilution series was
investigated using TMRX in order to compare the experimental data with simulated results. The
given iron contents from [52] are listed in Appendix 9.1.
TMRX Measurement Procedure
The measurements were performed using a Quantum Design SQUID magnetometer (MPMS-XL)
according to the procedure described in Chapter 3.2.5.
TMRX Measurement of the Dilution Series
The effect of decreasing dipole–dipole interactions as a consequence of the increasing inter–
particle distance between the MNPs in more dilute solutions was apparent, as can be seen in the
TMRX spectra shown in Figure 5.2, where the relaxation amplitude is plotted as a function of
temperature. Here, a decrease in the amplitude and a shift in the maximum temperature toward
higher temperatures were observed. These signal changes are similar to previously published
data concerning dipole–dipole interactions [
39
]. The different dilution steps for the MNP solution
exhibited distinct relaxation maxima at different temperatures well below the room temperature.
The increasing dipole–dipole interactions led to a decrease of
50 %
in the amplitude and a shift of
the relaxation maximum toward higher temperatures by approximately
15 K
. While the maximum
for the original Endorem solution appeared at
30 K
, that for the most diluted fraction C6 was
observed at 15K.
5.1 Influence of Dipole–Dipole Interactions on the TMRX Spectrum 79
Figure 5.1: TMRX spectra of the investigated MNP dilution series normalized to the iron content.
The spectra were well described by a log-normal distribution of temperatures, from which the
median temperature Tmed was extracted.
Figure 5.2: Median temperature obtained from the log-normal fit of the TMRX spectra for the
Endorem dilution series. The medium temperature was plotted as a function of the corresponding
concentration.
The TMRX spectra shape was well–described by fitting a log–normal distribution, which also
provided the position of the maximum and the width of each individual TMRX spectrum. The
log–normal fit parameters displayed in Figure 5.2 revealed that the median temperature (
Tmed
) of
the original Endorem solution was twice as high as
Tmed
for the diluted solutions. Importantly, the
median temperature remained nearly the same for the three least–concentrated fractions. Therefore,
C6 can be assumed to be interaction free.
80 Chapter 5. Numerical Simulation of TMRX Spectra
5.2 Simulation of TMRX Spectra of Non–Interacting Particles
Abstract 5.2
TMRX spectra of non-interacting particles were simulated based on the Néel
relaxation process. A log-normal distribution of the sample core diameters was assumed. In
order to include this distribution, a numerical discretization of the Néel equation was performed.
The sample’s relaxation behavior at a specific temperature was assumed to be the sum of the
underlying relaxations of the discretized magnetic moments.
The magnetic relaxation signal of single MNPs can in general be described through the equations
given in Chapter 2.1. However, real magnetic nanoparticle samples normally exhibit a distribution
of core diameters, which commonly is described by a log-normal distribution with median core
diameter
˜
d
and variance
σd
(see also Chapter 2.1.3). The size distribution must be considered in
the relaxation time because
τ
is dependent on the core volume of the particles. Analogously, the
magnetization amplitude is also dependent on the particle core diameter d.
The probability density function (Equation 2.8) must therefore be discretized in order to obtain the
individual probabilities of the different core diameters in the sample. Here, the discrete probability
function (P(di)) is defined over i=1,2,3...Nas
P(di) = Pi=1
√2πσddi
exp−ln2(di/˜
d)
2σ2
d,(5.1)
with
ZP(¯
d)(d)¯
d≈
N
∑
i
P(di)∆d=
N
∑
i
Pi∆d=1.(5.2)
The vector
¯
d
contains the possible discrete core diameters
di
from
d0=0 nm
to
dN=100 nm
. The
discretization step size is defined as
∆d= (dN−d0)/N
. In order to display the discretization of the
probability density function, the core diameters of vector
¯
d
were plotted over their probability (see
Figure 5.3) assuming a median diameter ( ˜
d) of 10 nm and variance (σd) of 0,3.
Figure 5.3: Discretized core diameters (
di
) with corresponding probability densities (
Pi
) when
˜
d=10 nm
and
σd=0,3
. In order to illustrate the discretization of
¯
d
, a particular large discretization
step size was chosen. Highlighted respectively in green, red, and orange are the discrete values for
the
8 nm
,
8,5 nm
, and
9 nm
sized particles in the simulated distribution. In Figures 5.4 and Figure
5.5, their influence on the magnetization process and relaxation signal at a specific temperature are
displayed.
5.2 Simulation of TMRX Spectra of Non–Interacting Particles 81
The relaxation of a sample’s magnetic moment toward its equilibrium state is generally described by
Equation 2.3:
M(t) = Aexp(−t/τN)
, with the Néel relaxation time
τN
, and an initial magnetization
amplitude
A
. Assuming the net magnetic relaxation signal of the sample is a combination of the
single relaxations of individual particles according to their probabilities, the time dependency of
the sample’s magnetic moment may be written as
M(t) = ZP(d)A(d)exp−t
τN(d)dd≈
N
∑
i
PiAiexp−t
τNi∆d.(5.3)
The magnetization behavior of the discretized core diameters can then be calculated according to
the Langevin equation (Equation 2.2). In the present cases, for each diameter
di
, a correspond-
ing magnetic moment
mi
was calculated using
Vi=1/6πd3
i=miMS
, and a constant saturation
magnetization of 379400 Am2/kg, which is typical for magnetite MNPs, was assumed:
M0(di) = M0i=NPπd3
iMS
6cothπd3
iMSB
6kBT−6kBT
πd3
iMSB.(5.4)
Figure 5.4: Simulation of the magnetization process at
10 K
based on the
10 nm
particle distribution
displayed in Figure 5.3. The time dependency of the magnetizing phase was calculated using Equa-
tion 5.6. The net magnetization of the sample was calculated by summing up the magnetizations of
the discretized particle sizes according to their probability densities. In the MPMS magnetization
process, the magnetization time (
tmag
) was set to
480 s
and the external field to
1 mT
. Although
the particle distribution exhibited a median at
10 nm
, the particles that were active at
10 K
were in
the
8 nm
(green) to
9 nm
(orange) range. Most prominent was the influence of the
8,5 nm
particles
(red) on the magnetization curve.
82 Chapter 5. Numerical Simulation of TMRX Spectra
Here,
B
represents the external magnetic field and
T
represents the sample temperature. Boltz-
mann’s constant (
kB
) is defined as
1,38·10−23 J/K
, and the number of particles
NP
is defined as
an adjustable scaling factor. During the magnetization interval (
tmag
) the sample’s net magnetic
moment exponentially converges toward the magnetization-value
M0
. The discretized amplitude
A(di) = Aiof this initial magnetization is given by
A(di) = Ai=M0i 1−exp −tmag
τfield
i!!.(5.5)
The magnetization of the sample is the sum of the magnetic moments of the discretized single
particles and their corresponding probability densities. The magnetization process for a distribution
of MNPs is illustrated in Figure 5.4.
A(t) =
N
∑
i
PiM0i 1−exp −tmag
τfield
i!! (5.6)
Similar to the Néel relaxation process the magnetization process, can be described through a
magnetization time constant (τfield ) which is field dependent [22]:
τfield (di) = τfield
i=τ0expKV
kBT1−0.82Bµ0MS
2K.(5.7)
A typical fixed value of
1·104J/m3
for magnetite MNP was used as the value of the magnetocrys-
talline anisotropy constant (K). The relaxation time constant τ0was assumed to be 1·10−11 s.
The Néel relaxation time (τN) was then calculated for each discretized core diameter di:
τN(di) = τNi=τ0expKπd3
i
6kBT.(5.8)
Figure 5.5: Relaxation process for the
10 nm
particle distribution shown in Figure 5.3 simulated
using the discretized Néel formula (Equation 5.8). The relaxation signal is the summation of the
individual decaying moments of the discretized particles. At
10 K
, particle cores with a diameter
of
8,5 nm
(red) relaxed mainly in the first few minutes. Smaller particles (e.g.,
8 nm
, green, see
Figure 5.4) relaxed in the microsecond range and are therefore not seen here. Only larger particles
with diameters near
9 nm
relaxed over the entire measurement time of
45 min
. A dead time of
90 s
,
which is typical for MPMS analyses, is indicated with a red dashed line. The amplitude change
(
∆m
) is the difference between the magnetic moment at the end of the dead time and the remaining
magnetic moment at the end of the measurement phase.
5.2 Simulation of TMRX Spectra of Non–Interacting Particles 83
Using Equations 5.3 – 5.8, it was then possible to simulate the relaxation processes of MNP
samples with distributions of the core diameters. The final relaxation moment is a summation of
the individual moments of the discretized particles based their probability densities. The relaxation
of a
10 nm
particle distribution (see Figures 5.3 and 5.4) is shown in Figure 5.5. In the simulation,
the time parameters were the same as those used for the MPMS analyses, i.e., a delay time of
90 s
and a measurement time of 45 min.
In Figure 5.5, the relaxation process is displayed for
T=10 K
. In particular, particle cores
with diameters of
8 nm
–
9 nm
contribute to the relaxation signal at this temperature. In the
temperature dependent MRX simulation, the relaxation process for a sample is therefore calculated
at temperatures ranging from
5 K
to
300 K
. In the TMRX plot, the amplitude change (
∆m
) is
displayed as a function of temperature. In Figure 5.6, the simulated TMRX spectrum is plotted for
the
10 nm
particle distribution shown in Figure 5.3, which had a core diameter variance of
σd=0,3
.
For comparison, a 10nm particle sample with no size distribution is also displayed (blue line).
Figure 5.6: Simulated TMRX spectra of four different simulated samples displayed as a function
of temperature. The spectrum for a monodisperse sample consisting only of
10 nm
particles is
illustrated in blue while the spectrum for a simulated MNP sample with a core size distribution
of
˜
d=10 nm
and
σ=0,3
is presented in red. Distributions with
σ=0,2
(orange) and
σ=0,1
(brown) are also shown.
The influence of the size distribution width can be clearly seen in the figure. The maximum temper-
ature slightly decreased from
16 K
for the distributed particles (red) to
14 K
for the monodisperse
sample (blue). Even more pronounced was the change in the width of the TMRX spectrum for the
samples with a particle size distribution. The sample with a variance (
σ
) of
0,3
yielded a relaxation
over the temperature range
6 K
to
34 K
while the non–distributed particles (blue) only generated a
narrow relaxation signal from 12 K to 16 K.
Using this simulation approach, the experimentally obtained TMRX spectra for the Endorem
samples were further analyzed in order to extract information about the particle’s core size and
distribution width. However, this simulation did not include an interaction energy term. Therefore,
any signal alterations because of dipole–dipole interactions were expected to falsify the analyses.
In the Endorem dilution series, only the most diluted sample was assumed to be interaction free
(Figure 5.2, sample C6).
84 Chapter 5. Numerical Simulation of TMRX Spectra
5.3 Simulation of TMRX Spectra Including Dipole–Dipole Interactions
Equation 2.4 for the Néel relaxation time is valid for non–interacting particle systems. As described
in Chapter 2.1.4, the Vogel–Fulcher equation is one approach for including dipole–dipole interac-
tions in the Néel equation in order to slow down the relaxation time such as in spin glasses. In the
Vogel–Fulcher law (Equation 2.11) a critical temperature (
T0
) is introduced to compensate for the
difference in the measured and calculated blocking temperatures. The Vogel–Fulcher law may be
discretized based on the core diameters in the distribution diwith i=1,2,3...N:
τi=τ0exp∆E
kB(T−T0i)=τ0expKπd3
i
6kB(T−T0i).(5.9)
As introduced in Chapter 2.1.4, one method for estimating
T0
for an ensemble of nanoparticles is
by using simplified dipole–dipole interaction equation (Equation 2.14):
T0≈Edipole
kB≈µ0m2
4πkBD3.(5.10)
For the equations that were discretized in the previous chapter, it was sufficient to calculate the
independent behavior of a single particle and summarize the resulting magnetic moments according
to their probabilities. However, the dipole interaction term for a discrete particle diameter in a
distribution can not be calculated without information about the particles it interacts with. Therefore,
the interaction energy term must include information about all the particles in the sample and their
probabilities.
Discussed below are four different possible numerical implementations of the dipole energy term
and a comparison of the calculated results obtained for each of the quantitative data presented in
Figure 5.2.
Approach A
One way to include dipole–dipole interactions is to calculate the critical temperature using the
median magnetic moment ( ˜m=˜
VMS):
T0(˜m)≈Edipole
kB=µ0˜m2
kB4πD3(5.11)
This approach implies that the interaction energy (
Edipole
) affects each discretized relaxation time
(τi) with the exact same value T0(˜m).
Approach B
The interaction energy term can also be calculated using only the discretized magnetic moment
(mi). This approach implies that only particles of the same size are interacting.
T0(mi)≈Edipole
kB=µ0m2
i
kB4πD3(5.12)
In this implementation, each discretized relaxation time (
τi=τ(mi)
) is affected by a corresponding
discretized critical temperature.
Approach C
In approach C, the interaction energy term is the product of the current discretized magnetic
moment (
mi
) and every other magnetic moment (
mj
) and their probabilities (
Pj=P(mj)
), with
j=1,2,3...N:
T0(mi)≈Edipole
kB=µ0mi∑jPjmj
kB4πD3.(5.13)
The critical temperature
T0(mi)
in this approach therefore combines information not only about the
simulated single particle but also about the entire particle distribution in the sample.
5.3 Simulation of TMRX Spectra Including Dipole–Dipole Interactions 85
Approach D
Although different concepts have been proposed regarding the origin of the Vogel–Fulcher law
[
85
] [
99
], it remains an empirical equation. It is therefore reasonable to discuss other empirical
approaches for describing the inclusion of dipole interactions in the Néel relaxation time. Thus,
instead of reducing
T
by a critical temperature
T0
, it is possible to directly add the interaction
energy term (Edipole) to the anisotropy energy, as in approach D:
τN=τ0expKmi/Ms+Ed(mi)
kBT.(5.14)
Edipole here is calculated in a manner similar to that used in approach C:
Ed(mi) = µ0mi∑jPjmj
4πD3.(5.15)
Approaches A – D serve the purpose of slowing down the relaxation time as the dipole–dipole
interaction energy increases. This retardation of the relaxation process can be attributed to the
increasing geometrical frustration of the MNP system [
20
]. The influence of the particle distribution
is, however, different for each approach. Approaches A, B, and C are expansions of the Vogel–
Fulcher model, whereas approach D represents a different empirical model. In order to visualize
the different influences of approaches A to D on the TMRX signal, simulations were performed,
and the results are presented in Figure 5.7. In these simulations, the particle distribution was
constant (
˜
d=8 nm
,
σ=0,25
), and only the interaction energy term was changed by decreasing the
interparticle distance (D).
Figure 5.7: TMRX simulations of a log-normal distributed particle system with a mean diameter
of
8 nm
and a size distribution with
σ=0,25
. Different interaction energy terms (
Ed
) for the
approaches A, B, C, and D were implemented. With a decreasing inter–particle distance (
D
), the
maximum temperatures and shapes of the TMRX spectra changed. The arrows indicate how the
increasing interaction energy changes the value of Tmax in the TMRX spectra.
Starting from a non–interacting distance of
100 nm
, the inter particle distance
D
was decreased in
10 nm
steps with logarithmic decreasing step size. As can be seen in the resulting TMRX spectra
in Figure 5.7, at the largest simulated distance (
D=100 nm
), the signal reached a maximum at
86 Chapter 5. Numerical Simulation of TMRX Spectra
15 K
. In addition, for all of the approaches (Equations 5.11, 5.12, 5.13 and 5.15) the interaction
energy increased as the distance
D
decreased, resulting in a lengthening of the relaxation time. In
all four approaches, this slow–down led to an overall decrease in the amplitude change, i.e., the
absolute relaxation signal intensity was reduced. Simultaneously, the peak temperatures changed
with increasing interaction energy (indicated by arrows in Figure 5.8). For approaches A, C,
and D,
Tmax
increased as the interaction energy increased while for approach B, it surprisingly
decreased. Approach B was therefore no longer considered because it was unable to describe the
experimentally observed increase in Tmax with increasing interaction energy (see Figure 5.2).
Furthermore, the decline in the relaxation amplitude accompanying the change in maximum
temperature was different for each approach shown in Figure 5.7, and in most cases nonlinear.
Specifically, an increase in
Tmax
from
15 K
to
20 K
was predicted result in amplitude losses of
17 %
,
46 %
, and
23 %
for approach A,C, and D, respectively. This alteration of the TMRX spectra is of
utmost importance for quantification because the process involves scaling of the simulated spectra
to the experimentally obtained results. The introduction of the interaction energy terms not only
change the maximum temperatures but also the shapes of the TMRX spectra. Previous analyses
indicated that that the interaction energy often has a broadening effect on TMRX spectra (see also
Chapter 4.4, Figure 4.16). The TMRX spectra of interacting samples therefore have the same
appearance as those of non-interacting particles but with a broader size distribution
σ
. In approach
A, the entire TMRX spectrum was shifted to higher temperatures with increasing interaction energy
(Figure 5.8, A). On the contrary, the TMRX spectra obtained using approaches C and D appeared
to be more stretched (Fig. 5.8, B and C).
Figure 5.8: TMRX results for dilution step C2 (red squares). Simulation of approaches A, C, and D
for a log-normal distributed particle system with a mean diameter of
8 nm
and a size distribution of
σ=0,25
. The interaction energy for each approach caused a shift of
Tmax
from
15 K
to
28 K
. In
approach A, the spectrum was shifted as a whole and not stretched like in approaches C and D.
A comparison of the simulated and experimentally obtained TMRX spectra revealed that approaches
C and D have a better correlation with the actual data for dilution step C2 (Figure 5.8). In contrast,
the simulated spectrum obtained using approach A exhibited a significant lack of TMRX signals at
temperatures below
28 K
. One criterion for evaluating the different approaches was to calculate the
residuals between the simulated and measured relaxation spectra. A large residual was determined
for approach A for the experimental spectrum of the highly concentrated sample.
5.3 Simulation of TMRX Spectra Including Dipole–Dipole Interactions 87
The quantification accuracy of the different approaches was a second criterion for evaluating their
applicability. For non-interacting particles, a valid method for determining the iron content in
an unknown sample involves comparison of the peak amplitude at
Tmax
in its TMRX spectrum
to the peak amplitude at
Tmax
in the spectrum of a known sample [
43
]. This method is referred
to as quantification by
peak comparison
. However, the relative amplitude per gram iron can be
significantly lowered because of the interaction energy (Figure 5.2). For the Endorem dilution
series, this quantification method worked well for
Tmax
from
15 K
to
20 K
. However, the three
most concentrated fractions were underestimated by
35 %
,
45 %
, and
62 %
when using the peak
comparison method (Figure 5.9 and Table 9.2 in the Appendix).
Figure 5.9: Relationship between the experimentally determined nominal iron contents of the
Endorem dilution series and the iron contents quantified using the approaches A, C, and D and the
peak comparison method.
A comparison of the nominal iron content with the iron content calculated using approach A
revealed a similar underestimation as that obtained using the peak comparison method (Figure
5.9). For the low–concentrated dilution steps, the calculated iron content equaled the nominal
iron content. For the samples with high levels of interactions, however, the iron content was
underestimated by
20 %
to
58 %
(see Table 9.3 in the Appendix). The quantification accuracy
of approach C was similar to that of approach A, although the iron content was overestimated
for the highly concentrated particle suspensions (
150 %
–
190 %
, see Table 9.4 in the Appendix).
However, using approach D, the quantified iron content was in good agreement with the nominal
iron concentration for most samples (see Table 9.5 in the Appendix). Only the content in the most
concentrated dilution step was underestimated by
27 %
; the concentrations in the other samples
were calculated with an accuracy of approximately ±10% (Figure 5.9, Model D).
Thus, compared to the other three approaches, model D had the highest quantification accuracy.
Finally, a comparison of the estimated interparticle distances (
D
) for the four approaches was
performed. In the original dipole interaction equation for two ideal spheres (Equation 2.13),
D
describes the center–center distance. In Equation 5.10 used for these simulations, however,
D
represents the average distance between the particles. The particles in the distribution have a
median core diameter
˜
d
and an additional coating with a thickness of several
nm
(
rcoating
), and
therefore
D
should not be less than
˜
d+2rcoating
. For the Endorem dilution series, the Dextran
coating thickness was approximately
3 nm
. Unlike for approaches A and C, the center–center
88 Chapter 5. Numerical Simulation of TMRX Spectra
distance was found to be less than
˜
d+2rcoating
when fitted using Approach D for the more highly
concentrated suspensions, and was therefore unrealistic.
Conclusion
Simulation of TMRX spectra was performed by employing a novel mathematical model that
describes the dipole–dipole interaction within an MNP sample. The calculated spectra were
compared with experimental obtained data for an MNP dilution series. The simulated spectra
revealed changes in the maximum amplitude
Tmax
and also the decline in the amplitude strength
because of dipole–dipole interactions.
A homogenous distribution of the particles in the sample without local clusters or specific bindings
was assumed. Some of the interparticle distances fitted using the novel model fell in an unrealistic
range. Therefore, they cannot be interpreted as absolute values. The introduction of an additional
factor may, however, enable their adjustment to real values. The determination of this factor would
require further experiments and knowledge of the actual interparticle distances in the MNP samples.
6. Development of a TMRX System for the Short Time Regime
90 Chapter 6. Development of a TMRX System for the Short Time Regime
6.1 Custom TMRX Measurement System
Abstract 6.1
A non–magnetic, cryogenic system that provides a variable sample temperature
environment from
5 K
to
290 K
was constructed. The helium cryostat was intended to hold
standard PCR sample tubes and to fit into the warm bore of the 6-channel MRX system [
2
] (see
also Appendix 9.1). The cryostat was designed to be combined with an Oxford Instruments
low loss transfer tube (LLT 600) with a needle valve for helium transfer regulation. The most
prominent difference from commercially available cryogenic systems was the use of a glass
fiber–reinforced material for construction of the cryostat walls. The non-magnetic cryogenic
system is suitable for magnetic measurements with fast changing fields because disruptive
eddy currents do not occur. The cryostat is also connected to an external copper coil and is
thus capable of performing temperature dependent MRX analyses in combination with the
multichannel SQUID system. The coil was designed to magnetize an MNP sample in the center
of the magnetizing coil at
1 mT
to
5 mT
. Although this cryostat was designed to fit into the
6-channel MRX system, it can be moved freely and be used as a temperature–controlled sample
holder for other analytical systems.
6.1.1 Description of the Temperature Controlled Sample Holder
The cryogenic system comprises an evacuated, double-walled glass fiber–reinforced plastic (GRP)
Dewar vessel combined with a commercial liquid helium transfer tube. In order to fit into the
warm bore of the 6-channel MRX system, the insulating outer tube is
25 mm
in diameter and
97,5 cm
long. The sample space within the double-walled tube is
14,5 mm
in diameter. It bears
a single-walled,
57 cm
long and
7 mm
thin GRP tube that transfers liquid helium from the outlet
of the helium transfer tube to the sample holder. The outer tube’s rear flange has a thread suitable
for fitting the helium transfer tube. A commercial
12 V
heating coil and a cryogenic temperature
sensor (Omega/Newport CY670) are also located inside the Dewar. Their connectors are installed
at the rear flange of the transfer tube. In order to minimize heat transfer via thermal radiation, the
evacuated GRP double wall contains eight layers of an aluminum–coated polyester fabric [
83
]. In
contrast to the often utilized reflective BoPET film Mylar, the aluminum–coated fabric does not
produce eddy currents when exposed to changing magnetic fields. In addition to the fabric, a small
amount of granulated activated carbon was placed inside the evacuated double wall. When cooled
down, the activated carbon works as a high-capacity adsorbent because of its huge surface area. It
therefore removed any remaining or leaking helium particles from the vacuum.
Figure 6.1: Experimental Setup: The data acquisition system (DAQ) reports the relaxation signal
(
a
) obtained using the SQUID system and controls the magnetization coil (
b
). The temperature
controller reports the data for the temperature sensor (
c
) in the glass reinforced plastic (GRP)
cryostat and controls the needle valve (
d
) in the helium transfer tube. The measured temperature is
then transmitted to the DAQ System (a).
6.1 Custom TMRX Measurement System 91
Insulation Fabric
The insulating fabric, previously presented by Seton et al., is made of woven polyester fibers and
coated on both sides with
25 nm
of aluminum [
84
]. The single strings consist of 24
10 µm
polyester
threads and are woven to a pitch of
300 µm
. Where the strings touch each other, the metallization
on each string is interrupted. The aluminum coating offers excellent reflecting properties while the
interrupting thread structure prevents eddy currents. Because the evacuated area between the inner
and outer tubes is only
2,5 mm
wide, there are currently only 8 layers of the aluminum–coated
fabric installed. Prior to the final construction, the materials were tested for magnetic impurities and
eddy currents, and the performance of the fabric was compared to that of the conventional Mylar
film. Both materials were found to be sufficient for the intended MRX analyses (see Chapter 6.2.2).
Figure 6.2: One layer of (left) aluminum-coated fabric and (right) slit Mylar film. The aluminum-
coated fabric is used as insulation in the Dewar.
Magnetizing Coil
The magnetizing coil is located around the outer GRP tube and directly below the SQUIDs in the
multichannel system. Because of the orientation of the coil, the SQUIDs are not disturbed by its
magnetic field. The coil consists of 170 windings of a
0,4 mm
diameter copper wire. The entire
coil is 6,9 cm long and approximately 25 mm in diameter.
Temperature Sensor
In this TMRX setup, a silica temperature diode (Omega/Newport CY670) was used. The voltage
of the diode changed with temperature while applying a constant current of
10 mA
over the
ITC. It was possible to upload a voltage–to–temperature conversion table on the ITC in order to
directly monitor the temperature. Because all CY670 silica diodes have a standardized calibration
curve, each individual diode does not require a separate calibration, which is advantageous when
comparing the signals of two different CY670 diodes during the sample calibration process (see
Chapter 6.2.4). The small dimensions of the diode (
1 mm ×1 mm ×2 mm
) make it ideal for taking
measurements inside the GRP cryostat. These temperature sensors cover a temperature range of
1 K to 400 K.
92 Chapter 6. Development of a TMRX System for the Short Time Regime
Figure 6.3: Arrangement of the temperature diodes around the sample space. During MRX analyses,
the permanently installed temperature diode can only measure the system temperature
4 cm
from
the sample. In order to calibrate the system, a second (calibration) sensor is installed in a sample
dummy.
Glass Reinforced Plastic Tubes
To prevent the generation of induced eddy currents because of magnetic field changes, a non-
magnetic and electrical insulating material was required for the cryostat walls. Researchers at
the Friedrich-Schiller-Universität in Jena [
44
] demonstrated that glass fiber–reinforced plastic is
a suitable alternative to steel. In particular, researchers found that a thin glass-textured wall with
a thick lacquer film (>
0,1 mm
) can reduce the permeability of the GRP. However, because of its
internal structure, the GRP has a higher helium permeability than stainless steel, which leads to
overall restriction of the lifetime of the insulating vacuum. Considering this data, glass reinforced
plastic tubes from Erhard Hippe KG (EP GC 22.15) were chosen because they have a high density
and a lacquer film suitable for vacuum and helium applications.
Resistance Heating Coil
The temperature control unit (Mercury ITC) controls a resistance heater in order to regulate the
temperature in the flow cryostat. In conventional cryostats, the heater is installed directly at
the sample holder. Typically, this sample holder is a massive copper block with good thermal
conductivity. For the intended MRX setup, however, the use of such a copper block was not
possible because it would result in the formation of eddy currents that would interfere with the
measurements. The resistance heater was therefore installed
6 cm
away from the sample holder in
order to avoid interference with the measurements. Therefore, the heater cannot be used to directly
heat the sample or to warm up the incoming gas. It is, never–the–less, possible to heat the entire
system during the warm up sequence. This feature is advantageous it reduces the total measurement
time. The dimensions of the foil are
400 mm ×45 mm
, with a thickness of just
1 mm
(see also
Figure 6.2 in the Appendix).
6.1 Custom TMRX Measurement System 93
6.1.2 Description of the 6-Channel TMRX Measurement Setup
The constructed GRP cryostat can be utilized as a temperature controlled sample holder and
magnetization unit. However, for TMRX analyses, additional components are required. Thus,
a helium transfer tube with an automated needle valve is attached to the cryostat. The transfer
tube is capable of reducing the gas flow via the automated needle valve, which is controlled by
the temperature and gas flow control unit. In addition, a temperature diode is integrated in the
cryostat to determine the sample temperature. This temperature sensor data is also recorded by the
temperature and gas flow control unit. Finally, a data acquisition system (DAQ) was developed to
store the temperature data and perform the cool down procedure for the cryostat. Magnetic SQUID
TMRX analyses are performed using the 6-channel MRX system [
2
] that existed prior to this work
and is therefore not a part of this dissertation. An illustration of the entire setup can be found in the
Appendix (Section 9.5).
Temperature Controller (Oxford Instruments Mercury ITC)
A commercial temperature and gas flow control unit (Oxford Instruments Mercury ITC) was used to
regulate the temperature within the GRP cryostat. In its stock version, the Mercury ITC is capable
of reading out one temperature sensor, controlling one heating resistor, and operating one needle
valve. By adding additional plug–and–play expansion cards, the capabilities of the system can be
expanded to record data from up to 9 temperature sensors. One of the main features of the system
is that it can independently regulate and hold the temperature of the cryostat and run predefined
temperature curves and temperature sweeps. The mercury ITC can be operated manually over the
build–in touch screen or remotely over the LabVIEW interface.
Helium Transfer Tube (Oxford Instruments LLT 600)
The Oxford Instruments low loss transfer tube (LLT) is designed to transfer liquid helium to
horizontally fed cryostats. It has been developed to supply continuous flow (CF) cryostats similar
to the temperature controlled sample holder designed in the course of this dissertation. It is ideally
suited for the TMRX setup because it can transport gas bidirectionally. The cold gas that exits
the cryostat is therefore used to cool the insulation surrounding the incoming liquid within the
transfer tube. The transfer tube consists of a
1,3 m
long Dewar leg, that fits into the helium vessel,
and a
1,2 m
long flexible section. The flexible part enables easy adjustment of the GRP cryostat
position in the 6-channel system. Its most essential feature is the automated needle valve, which
enables regulation of the helium flow used to cool the cryostat. The stepper motor at the valve can
be controlled using the mercury ITC, which itself can be programmed via the designed LabVIEW
interface. In addition, helium can be transported at temperatures as low as
2,5 K
. Consequently,
the LLT 600 is ideal for the intended application. A descriptive graphic of the transfer tube can be
found in the Appendix (Section 9.4).
The Data Acquisition System (DAQ)
The data acquisition system (DAQ) controls the Mercury ITC and all the MRX–related components
and collects the incoming measurement data. Data transfer from the Mercury ITC to the DAQ
system occurs via USB. In order to display and save the transferred data in the DAQ, a virtual
user interface (VI, see Appendix, Figure 9.6) was designed using LabVIEW (V.12.0.1f5). The
required commands for interacting with the ITC using the LabVIEW software and some example
applications were provided by Oxford Instruments. All control of and data acquisition from the
Mercury ITC and the connected LLT 600 helium transfer tube were achieved using the virtual
interface (see Figure 9.6 in the Appendix). The interface was developed and implemented in the
course of the dissertation. The implemented commands include readout of the system temperature,
opening and closing of the needle valve, and activation of the resistance heating coil. The VI offers
the possibility to read in ASCII files in order to perform specific temperature sweeps. Information
about the measurement time and date, the temperature, and the percentage opening of the needle
valve are also saved in an ASCII text file.
94 Chapter 6. Development of a TMRX System for the Short Time Regime
6.2 Characterization of the GRP Cryostat with Magnetizing Coil
Abstract 6.2
Different elements of the cryostat were characterized, including properties and
switch-off timing of the magnetizing coil. The magnetic impurities in the raw materials used for
construction of the cryostat were also examined. In addition, the optimal position of the sample
relative to the magnetizing coil and the appropriate cool down procedure for the cryostat were
determined.
6.2.1 Characterization of the Magnetizing Coil
An essential part of the MRX setup is the magnetizing coil which had to be specifically designed
for the purpose of performing TMRX analyses using the 6-channel SQUID system. The size of the
warm bore of the multichannel system restricted the outer diameter of the coil to
26 mm
while the
size of the outer GRP tube of the cryostat required that the inner diameter of the magnetizing coil
be 25 mm.
Figure 6.4: Transversal field at the center of the magnetizing coil at
356 mA
for different longi-
tudinal offsets. The longitudinal center of the
6,9 cm
long coil is marked as zero on the X-axis.
The direction toward the helium transfer tube is negatively notated. The curve reveals that the coil
produces a small transversal field that is strongest at its longitudinal boundaries. The maxima are
therefore at
−4,25 cm
and
4,0 cm
. The transversal field strength at
356 mA
ranges from
30 µT
to
40 µT at these maxima.
A
0,4 mm
copper wire was used for the solenoid magnetizing coil. The single spooled solenoid
required a retracting wire that, unfortunately, could only be placed unsymmetrically. Because of
its position and orientation, the wire was expected to cause interference for the SQUID sensors.
The coil had 170 windings, a total length of 69 mm, and could safely conduct a maximum current
of approximately
2,2 A
(as determined by its diameter). The measured resistance and inductivity
of the coil were
2,2Ω
and
20 µH
, respectively. The longitudinal field strength for
356 mA
, which
is used to magnetize MNP samples, was
1 mT
(Figure 6.5) while the maximum transversal field
strength ranged from
30 µT
to
40 µT
(Figure 6.4) because of the small inhomogeneities created by
the retaining wire.
The relaxation amplitude strength is directly related to the magnetic moment of the magnetized
6.2 Characterization of the GRP Cryostat with Magnetizing Coil 95
sample. A higher magnetization field increases the magnetic moment of the sample, as described
by the Langevin equation (Equation 2.2). A strong magnetization field therefore improves the
detection limit of the system. Although the coil supports currents up to
2,2 A
a small current of
only
356 mA
was chosen for creating a magnetization field that is comparable to the
1 mT
used in
the MPMS. With an applied field strength of
1 mT
, it is feasible to perform the intended MRX and
TMRX analyses. In addition, the relaxation signal of small MNPs is strongest at lower temperatures,
which also improves the detection limit.
Figure 6.5: Longitudinal field in the center of the magnetizing coil at
356 mA
for different axial
offsets. The center of the
6,9 cm
long coil is marked as zero on the X-axis. The direction toward
the helium transfer tube is negatively notated. The curve reveals a maximum plateau ranging from
−2 cm to 2 cm with a field strength of approximately 1 mT.
Coil Switch-Off Timing
An important parameter for MRX analyses is the delay time between the end of the magnetization
phase and the beginning of the measurement phase. In general, it is favorable to minimize the delay
time as much as possible. A long offset between switch-off of the magnetizing coil and the start
of the actual measurement results in a high loss of relaxation signal strength. This loss can be
compensated for by using longer magnetization and measurement times, which is why the time
setting in the MPMS is particularly long. To improve the measurement modalities compared to the
MPMS, the dead time in the 6-channel SQUID system was therefore reduced to a minimum.
The necessary length of the delay time in a SQUID-based measurement system is essentially
determined by the SQUID’s control electronics. In measurement mode, these control electronics
compensate gradual shifts. However, during switch-off of the magnetizing coil they must be in
reset mode. The time when the SQUID sensors may operate again depends on the lingering of the
coil and possible flux creep in the Dewar.
In order to reduce the noise level and accelerate the switch-off process, the magnetizing coil is
not directly connected to the current source
1
. Instead, a metal-oxide semiconductor field-effect
1
The different devices required to perform the MRX analyses except the magnetizing coil were preexisting [
33
][
35
]
and are therefore not part of this dissertation. These devices include, in particular, the MRX current source, the
MOSFET-switch unit with Zener diodes, and the SQUID measurement system.
96 Chapter 6. Development of a TMRX System for the Short Time Regime
transistor (MOSFET)-switch manages the connection and separation of the circuit. A
10 kΩ
resistor
is connected in series to the solenoid in order to accelerate the switch-off process. Several Zener
diodes with a breakdown voltage of
150 V
are located parallel to the magnetizing coil. Below
150 V
, the Zener diodes essentially prevent any current flow and therefore reduce the thermal noise
of the 10 kΩresistor.
Using an oscilloscope, the lingering behavior of the magnetizing coil after the switch-off was
measured (Figure 6.6).
Figure 6.6: Switch-off procedure for the magnetizing coil measured with a Digital Storage Oscillo-
scope (Agilent Technologies, DSO-X 2004A). After the switch-off impulse is initiated at
t=0 s
,
the voltage in the coil drastically decreases. After
20 µs
, the overshooting oscillation ceases as well.
It was found that although the magnetizing coil was deactivated within
20 µs
in the existing system,
the SQUIDs only began measuring again after
100 µs
. The additional interfering signal was
attributed to magnetic after–effects in the 6-channel MRX system.
6.2.2 Magnetic Characterization of the System
Magnetic Impurities of GRP Parts
When working with highly sensitive SQUID sensors in a magnetic shielded environment even
small magnetic moments in the femtotesla range can be detected. It was therefore crucial to
carefully investigate all parts and materials before they were permanently incorporated into the
new instrument; even the smallest impurities in otherwise nonmagnetic materials can influence the
analytical results. All construction methods, such as cutting and drilling, must be executed with
special nonmagnetic tools in a dust–free environment. In addition, all materials must be checked
for magnetic contamination after each construction step.
In order to create a magnetically clean cryostat, larger numbers of important parts, such as the
GRP tubes, were ordered to ensure that only parts with low magnetic noise were included in the
device. The different GRP parts were investigated using the 304-channel SQUID system in the
Berlin Magnetically Shielded Room (BMSR-2) at the PTB [9].
6.2 Characterization of the GRP Cryostat with Magnetizing Coil 97
Part: Magnetic Field [pT] at 3cm distance
Outer Vacuum Tube before cleaning 20
Outer Vacuum Tube after cleaning 10−15
Inner Vacuum Tube before cleaning 30
Inner Vacuum Tube after cleaning 5−10
Inner Helium Transport Tube 10−12
Sample Holder <2
Cap <2
Flange <2
Investigation of the GRP tubes revealed some magnetic contaminants that could be traced back to
the manufacturing process. During the production process, the GRP matting is wound along an
iron rod in order to form the tube. The contamination was therefore assumed to be primarily on
the inside of the tubes and potentially removable. The interiors of the GRP tubes were therefore
cleaned using hydrochloric acid (10%) and their subsequent magnetic moments were found to have
decreased.
Magnetic Moment of the Insulation Material and its Influence on MRX Analyses
Similar to the GRP parts, the insulation material in the cryostat was also evaluated for magnetic
contamination. It is however important to keep in mind that insulation materials such as Mylar film
are coated with a reflective metal in order to block thermal radiation. Conducting materials placed
close to the MRX magnetizing coil cause eddy currents that can interfere with the measurement.
The insulation materials were therefore not only revealed for magnetic impurities but also for their
behavior when performing MRX analyses. In order to identify the insulation material with the least
interference, both a conventional Mylar film and the aluminum–coated fabric (see Chapter 6.1.1)
were investigated. It should be noted that the Mylar film was slit in order to reduce potential eddy
currents. The investigation was performed using the magnetizing coil and the 6-channel SQUID
system at ambient temperature. A typical MRX sequence with a magnetizing time of
1 s
and a
measurement time of
1 s
was performed for a
30 µL
Resovist sample using sample chambers covered
in either Mylar film or aluminum–coated fabric. An MRX analysis was also performed for the
same sample in a non-insulated sample chamber. In all three spectra, the resulting amplitudes of the
peaks appearing at the maximum temperature were identical within the range of the measurement
accuracy. This result indicated that no detectable eddy currents were present because the insulation
had no disturbing influence on the measurement.
The Mylar film and aluminum–coated fabric were also evaluated for magnetic impurities using
the 6-channel SQUID system. Several layers of each insulation material were placed around a
sample rod and moved to different longitudinal positions relative to the center of the coil. The
amplitude changes (
∆B
) for both materials did not exceed
±5 pT
, which was within the range of
the background noise.
Magnetic Signal of the Temperature Sensor Diode
The influence of the temperature sensor on the TMRX signal was also a very important factor
considered during the design of the GRP cryostat. In general, it is preferable to place the temperature
sensor as close as possible to the sample in order to more accurately measure its temperature.
However, because the sensor is made partially of metal, it is not possible to do so. Because
the distance that the sensor needed to be placed from the sample depended on the strength of
the interfering signal, the sensor signal was measured at different positions within the 6-channel
SQUID system. Specifically, the temperature diode was placed at different longitudinal positions
within the 6-channel SQUID system, and the changes in the amplitude of the peak appearing at the
maximum temperature in the MRX spectra were detected.
98 Chapter 6. Development of a TMRX System for the Short Time Regime
Figure 6.7: MRX relaxation amplitude changes for the silica diode at different longitudinal
positions in the 6-channel SQUID system are displayed for one SQUID sensor. The temperature
sensor generates a dipole moment similar to that of an MNP sample because of its magnetic
elements. The MRX analysis of the sensor was performed at different longitudinal positions
from
−40 mm
to
40 mm
relative to the center of the magnetizing coil. A typical MRX sequence
(
Bmag =1 mT
,
tmag =1 s
,
tmeas =1 s
) was performed at each position, and the sensor was operating
during the MRX analysis. Therefore, the wires connected to the sensor conducted a
10 µA
current.
As can be seen in Figure 6.7, the silica diode caused two distinct maxima at
−15 mm
and
15 mm
respectively. The maximum relaxation signal created by the sensor was about
75 pT
. The magnetic
moment generated by the sensor can be attributed to impurities in the braze joints of the diode.
Therefore, in order to minimize the interference of the temperature sensor on the TMRX analyses,
it was determined that the sensor be placed more than
40 mm
from the center. Alternatively, the
sensor could be positioned at the center of the coil.
Magnetic Signals of other Materials
Additionally the influence of the activated carbon was investigated as it is placed at the rear end of
the GRP cryostat and therefore close to the sensors. It did however not produce any interfering
relaxation signal. Another concern was the influence of the stainless steel helium transfer tube tip.
The tip does produce disruptive eddy currents when placed closed to the magnetizing coil. Due to
the design of the GRP cryostat the transfer tube is placed
50 cm
away from the sensor and therefore
outside of the 6-Channel SQUID system and far enough away from the sensor. The transfer tube
therefore produced no detectable signal at that position.
6.2.3 Determination of the Sample Position
During the magnetization phase of a TMRX analysis, the sample must be magnetized by the longi-
tudinal field of the coil. During the measurement phase, the SQUID sensors detect the decaying
net magnetic moment of the sample. The orientation of the magnetizing coil is transversal to the
measurement direction of the SQUID sensor. Therefore, the longitudinal field of the coil will not
be detected by the SQUID sensors. An MNP sample in the center of the coil will create a dipole
field when magnetized. If the sample is placed acentrically under the SQUID sensor, the transversal
component of the dipole field becomes detectable for the SQUID. This design feature is illustrated
6.2 Characterization of the GRP Cryostat with Magnetizing Coil 99
in Figure 6.8. The optimal position for the sample was found to lie between
1 cm
and
4 cm
from
the center. At
3,5 cm
, the SQUIDs receive the highest transversal response from the MNP sample.
Similar to the magnetizing coil, the sample creates a magnetic dipole field with the poles along the
long axis of the coil. If the sample is placed directly beneath the SQUID, the sensor is only affected
by the longitudinal field. However, our SQUID system is designed to measure the transversal field.
The sample must therefore be placed beneath the SQUID with a longitudinal offset, for the sensor
to face the transversal magnetic field of the dipole.
Figure 6.8: Illustration of the sample position relative to magnetizing coil and SQUID. The sample
is not positioned directly under the SQUID because the sensor can only detect transversal magnetic
fields. Instead, it is placed with a longitudinal offset of approximately
4 cm
in order to optimize
the transversal magnetic field relative to the SQUID. The magnetizing coil and the permanent
temperature sensor are placed directly beneath the SQUID. Through this arrangement, the sensor
is less affected by the magnetic dipole fields because they are mainly longitudinal at the center
position.
The sample holder was designed in such a way that the permanent temperature sensor is located
4 cm
from the sample position. Depending on the position the temperature sensor itself can create a
magnetic response that would disturb the measurement. As is shown in Figure 6.7, however, the
sensor does not interfere with the measurement when it is placed sufficiently far away from the coil
or directly at the center. The permanent temperature sensor was therefore positioned at the center
of the coil while the sample was placed at a distance of
4 cm
, where it was magnetized by a
1 mT
field.
Influence of Thermal Expansion
The sample position within the instrument is important because it determines how the MNPs will
be magnetized and the strength of the transversal field received by the SQUID sensors. Any change
in its position can therefore result in a signal change and in inaccurate analysis results. The MNP
sample is placed in the sample holder, which is located on the inner helium tube. The inner helium
tube is a
58 cm
long GRP pipe that is mounted on the tip of the stainless steel helium transfer tube.
During the cool-down procedure, the stainless steel pipe is
44 cm
deep in the installed GRP cryostat.
When performing TMRX analyses, the inner GRP tube and the steel tip experience temperature
changes of approximately
285 K
. Depending on the material, such a thermal change can result
100 Chapter 6. Development of a TMRX System for the Short Time Regime
in expansion or contraction. Stainless steel, for example, has a coefficient of thermal expansion
(
αsteel
) of
17 ·10−6K−1
, which results in a length change (
∆LSteel
) of approximately
2 mm
for the
given temperature change. The coefficient of thermal expansion for GRP (
αGRP
) depends on the
preferred direction of the material. The given values vary from
7·10−6K−1
to
27 ·10−6K−1
, which
can result in length changes (
∆LGRP
) of
1 mm
to
4 mm
, respectively. Therefore, the sample position
may change between 3 mm and 5 mm in total.
∆L
L0=α·∆T(6.1)
In order to determine the exact influence of changes in the sample position on the signal the
thermal expansion coefficient of the GRP tube was determined. A
25 cm
long GRP tube was
therefore cooled with liquid nitrogen (boiling point
77 K
). Using the measured length change
(
∆L=0,05 mm
) and Equation 6.1, a thermal expansion coefficient for
αGRP
of
10 ·10−6K−1
was
determined. Therefore, the GRP tube in the cryostat is expected to contract by approximately
1,5 mm
when cooled from ambient temperature to
5 K
. For the stainless steel, a length change
of
2 mm
was assumed. The total position change of the sample was therefore determined to be
3,5 mm
for a temperature change of
285 K
. According to the positioning tests performed at ambient
temperature, such a change in the sample position was determined to lead to a signal loss of
3 %
.
In order to compensate for this signal change, it is possible to introduce a linear correction term.
However, the embedding of such a linear correction term into the analysis software exceeded the
scope of this dissertation.
6.2.4 Temperature Calibration at the Sample Position within the Cryostat
The main function of the GRP cryostat is to provide a defined sample temperature from
5 K
to
290 K
in order to perform TMRX analyses. It is therefore crucial to know the exact temperature of
the sample at the time of the measurement. However, the temperature sensor can not be located
directly at the sample position because it would interfere with the MRX analyses. The temperature
of the sample must therefore be calibrated prior to each analysis.
An MRX analysis using the 6-channel system takes
1 s
for magnetization and
1 s
for measurement
of the relaxation of the sample. Therefore, a temperature sweep procedure was performed using the
cryostat to cool the sample at less than
0,5 K/s
. This cooling rate is sufficiently slow to assume a
constant temperature for individual MRX analyses. During the predefined temperature sweep, the
system lowers the temperature continuously. After the intended temperature is reached, the helium
inlet is closed and the system heats up again. In order to perform a temperature sweep, a defined
temperature alteration rate is mandatory.
Figure 6.9: Arrangement of the temperature diodes around the sample space. The helium flow is
illustrated in blue. The permanent sensor (red) can only measure the sample temperature indirectly.
The calibration sensor (green) is installed in a sample dummy. During calibration measurements,
both sensor signals are stored in a look-up table.
6.2 Characterization of the GRP Cryostat with Magnetizing Coil 101
One of the challenges when designing the GRP cryostat was temperature measurement at the
sample space. In other commercial systems, the sample holder is made of a highly heat–conducting
material such as copper or sapphire. Typically, the temperature sensor is directly integrated into the
copper block of the sample holder. Because of the high conductivity, the temperature at the sensor
is very close to that of the sample and can be easily calibrated. However, to use the cryostat for
fast MRX analyses, this type of sample holder is not possible. Because of the rapidly changing
magnetic field at the end of the magnetization time, eddy currents can be induced in the copper
that can then produce disruptive magnetic signals. In addition, the temperature sensor must be at
least
4 cm
from the sample in order to prevent interference with the analyses results. Hence, it is
necessary to calibrate the temperature at the sample position prior to the actual MRX procedure
in order to determine the temperature offset between the sample and the actual sensor position.
In Figure 6.9, the positions of the permanent temperature sensor (red) and the calibration sensor
(green) are shown. The calibration sensor is installed in an empty PCR tube used to house MNP
samples. The permanent sensor is placed above a
1 mm
diameter hole. Through this hole, the sensor
receives a constant supply of helium coolant that also cools the sample. This setup allows direct
detection of temperature changes because of changes in the helium flow. Without the connection
hole, the permanent sensor would only measure the back-flowing helium gas, which is already
partly heated at that point.
Figure 6.10: Typical temperature cool down sequence of the GRP cryostat for the calibration of the
temperature at the sample position. The temperature of the diode which is four centimeter away
from the sample space is displayed in black, while the sample temperature is displayed in red. In
this sequence the system temperature falls from
290 K
to
5 K
in less than 20 minutes. During that
time an offset between the sensor and the sample is visible.
Temperature Sweep
In order to cool the cryostat, the connected transfer tube (LLT) has an integrated needle valve to
control the helium flow. The valve can be activated and set to a defined opening percentage by
the temperature controller (Oxford Mercury ITC). The opening percentage in combination with
the pressure in the helium vessel influences the cooling rate of the system. The temperature of
the system increases after closing of the valve. Although the cryostat has an installed reflecting
102 Chapter 6. Development of a TMRX System for the Short Time Regime
film, the thermal radiation of the outer tube is still sufficient enough to heat the system when the
helium valve is closed. Therefore, after closing the valve, the system temperature slowly rises to
approximately 250 K. To warm the system to ambient temperature, an additional heating coil was
installed close to the sample chamber which can also be activated and controlled by the Mercury
ITC. For the TMRX measurements a cool-down sweep with
7 %
opening of the needle valve was
used. The opening percentage was increased every time the system temperature falls below a
predefined value. The resulting change in the slope of the temperature curve can be seen in Figure
6.10 below
30 K
. The temperature at which the opening percentage is changed is defined in a text
file that can be read by the LabVIEW interface.
Calibration Look-up Table and Repeatability
Because the sample temperature cannot be measured directly during MRX analyses, a calibration
look-up table was implemented. This table links the temperature from the permanent sensor
to the samples temperature. Each look-up table must be designed for a specific temperature
sweep because changes in the helium valve opening only have a delayed effect on the sample and
system temperature. In the course of the dissertation, look-up tables were created for a cool-down
procedure from
290 K
to
5 K
and the reverse warm-up process. The temperature sweeps were
repeated several times and the average temperature course was determined. The relationship
between the temperature of the permanent sensor and the temperature at the sample space was
saved in an ASCII–file. This file was accessed by the Mercury ITC LabVIEW interface and
used to estimate the sample temperature. A comparison of the measured and estimated sample
temperature allowed determination of the accuracy of the temperature estimation. Subtracting the
real temperature data points from the estimated values provided the temperature residual function.
According to this function, the difference in the estimated and real temperature values was of the
order of
±1 K
. This temperature deviation is acceptable for the TMRX analyses performed in the
present study. To improve the accuracy, it may be possible to install a sapphire sample holder that
would conduct the temperature to the permanent sensor. Sapphire is often used in cryostat designs
because it has a relatively high thermal conductivity of
42 W/mK 2
but does not produce eddy
currents. Another option for improving the thermal accuracy would involve installation of a second
permanent temperature sensor for measurement of the temperature of the returning helium gas. This
approach would provide an improved temperature determination because the sample temperature
could be narrowed down to the range between the temperatures of the incoming returning gases.
Lastly, the sweep procedure could be improved; slower temperature changes have been shown to
generally lead to a more accurate determination of the sample temperature.
2The thermal conductivity of copper for example is about 400W/mK and of GRP it is about 0,3 W/mK.
6.3 Quantification of Magnetic Nanoparticles using TMRX in the Short Time Regime103
6.3 Quantification of Magnetic Nanoparticles using TMRX in the Short Time
Regime
Abstract 6.3
An example analysis using the GRP cryostat was performed to demonstrate its
potential for the quantification of MNPs in biological samples. A Resovist dilution series
previously analyzed using the MPMS (see also Chapter 4.3) was selected in order to be able
to compare the results obtained with the two systems. Based on the differences in the spectra,
the effects of the two time regimes on the TMRX analyses were considered. The detection
limit of the short time regime was also investigated, and quantification of the dilution series was
conducted.
Investigated Particles
DDM128, the precursor of the commercial contrast agent Resovist (Bayer Schering Pharma AG)
was investigated. The MRI contrast agent consists of superparamagnetic iron oxide nanoparticles
coated with carboxydextran. Resovist and its precursor particles are known to have a bimodal size
distribution with particle core diameters ranging from 8 nm to 26 nm [90][23].
Preparation of Dilution Series Samples
The highly concentrated original DDM 128 solution (
500 mmol
) was diluted to prepare a series of
solutions with defined iron contents. The original solution was diluted with distilled water in order
to achieve the dilution steps with different concentrations. Finally, to
30 µL
of the dilution
30 µL
mannitol solution (containing 15 % mannitol) were added and then each sample was immobilized
in a polycarbonate capsule via freeze drying.
MPMS TMRX Measurement Procedures
The measurements were performed using a Quantum Design SQUID magnetometer (MPMS-XL)
with RSO measurements following the procedure described in Chapter 3.2.5.
6-Channel TMRX Measurement Procedures
The cool-down of the GRP cryostat was performed using the temperature sweep method described in
Chapter 6.2.4. By constantly cooling the sample at approximately
0,1 K/s
, the sample temperature
changed from
290 K
to
5 K
within
30 min
. During that time, the data acquisition system of the
6-channel SQUID system performed a continuous series of MRX analyses. The MRX procedure
consisted of a magnetization time of
1 s
, a delay time of
100 µs
, and a measurement time of
1 s
.
Between each individual MRX analysis, a waiting time of
1 s
was implemented to ensure complete
relaxation of the sample. In total, 600 single MRX analyses were performed during the cool-down
period.
104 Chapter 6. Development of a TMRX System for the Short Time Regime
6.3.1 TMRX Analysis of the Resovist Dilution Series
Both devices, the MPMS and the 6-channel SQUID system with the GRP cryostat, were used to
perform temperature dependent relaxometry analyses on the same Resovist dilution series. The
6-channel SQUID system recorded the foremost magnetic field strength at the individual SQUID
sensors in
pT
. First, the magnetic moment of the sample was calculated from the recorded field
strength. To estimate the magnetic moment of the sample, the magnetic point dipole formula
[
31
] was used. The SQUID sensor position (
rs
), the sample position relative to the center oft the
magnetization coil (
rd
), and the orientation vector of the SQUID sensor (
n
) were inserted into
Equation 6.2:
B=µ0
4π 3n((rs−rd)(rs−rd)T)
|rs−rd|5−nT
|rs−rd|3!m.(6.2)
After rearranging Equation 6.2, the estimated dipole moment (
m
) in
Am2
was obtained by inserting
the measured magnetic field (B).
Figure 6.11: (Left): Relaxation measurement at
275 K
for the most concentrated Resovist samples
obtained using MPMS. The relaxation process in the long time regime took
40 min
. (Right):
Relaxation measurement performed using the GRP Cryostat in the 6-channel SQUID system.
The measurement time in the short time regime only required
1 s
. In both plots, a relationship
between the amplitude change and the MNP concentration was observed. However, the decay of
the relaxation after switching off the external field was significantly more pronounced in the short
time regime.
A comparison of the relaxation signals obtained for each system is presented in Figure 6.11 for
the short time regime of the 6-channel (right) and the long time regime of the MPMS (left). In
both plots, the relaxation signals at
275 K
for the Resovist samples of different concentration are
displayed. From a technical point of view, the most prominent differences concerned the time scale
and the sampling rate of the two systems. The MPMS measures in a long time regime of
40 min
per relaxation, whereas the 6-channel SQUID system measures in the short time regime of
1 s
per
relaxation. In addition, the 6-channel system exhibited a higher sampling rate of 10000 data points
per relaxation compared to 100 single RSO measurements for the MPMS.
Regarding the results for the Resovist samples shown in Figure 6.11, one feature was foremost
apparent. The relaxation decay in the long time regime was slower than the decay in the short time
regime. This difference could be attributed to the unequal measurement times of the two systems;
at a defined temperature the measurement time window defines which core diameters of the particle
distribution contribute to the relaxation signal. Despite these differences, the concentration was still
6.3 Quantification of Magnetic Nanoparticles using TMRX in the Short Time Regime105
related to the signal amplitude in both types of spectra. This means that more concentrated samples
exhibited stronger net magnetic moments.
In Figure 6.12, TMRX spectra from
5 K
to room temperature obtained using both measurement
systems are shown. On the right side of the Figure the influence of the higher sampling rate of the
6-channel SQUID system is illustrated with 600 single relaxation measurements equally distributed
over the temperature spectrum. In contrast, the MPMS spectra shown on the left side of the figure
consist of MRX analyses at 19 discrete temperatures and are therefore less smooth. The influence
of the different sampling rates is particularly obvious for the most concentrated Resovist sample
(red curve).
Figure 6.12: (Left) TMRX results for the Resovist dilution series performed using MPMS. (Right)
TMRX results obtained using the GRP cryostat in the 6-channel SQUID system. The investigated
temperature ranged from
5 K
to room temperature for both systems. Both spectra were bimodal,
with one peak at
25 K
and a second peak at
200 K
to
300 K
. Notably, while the second peak
was between
200 K
and
250 K
in the spectrum obtained via MPMS (left), it appeared near room
temperature in the spectrum obtained using the 6-channel SQUID system (right).
The shape of the curves for the two sets of TMRX analyses are also clearly different. The MPMS
spectra exhibit distinct signal peaks near
200 K
–
250 K
while the spectra obtained using the
6-channel SQUID system all display a constantly increasing signal as the temperature increased
to room temperature. These different behaviors are attributed to the different measurement time
regimes of the two systems. For TMRX analyses the measurement time window in combination
with the relaxation time (τ) determines particle sizes that are detectable at a specific temperature.
An MNP sample analyzed in the two different time regimes will therefore exhibit its strongest
signal (
Tmax
) at different temperatures (see also Figure 3.3 in Chapter 3.2). The signal maximum in
the 6-channel spectra is assumed to be at or above room temperature. A comparison of the signal
peaks obtained using the two systems is displayed in Figure 6.13. A constant offset can be seen for
the signal peak of the MPMS spectra at approximately 200 K.
A second peak was also apparent at
25 K
in the TMRX spectra obtained using both measuring
systems. This second peak is attributed to the underlying fraction of the bimodal MNP sample
with smaller diameters. In contrast to the quite obvious changes in the peak temperature for the
fraction of the larger particles, the peak temperature for the fraction of smaller particles shifted only
slightly (
5 K
) for the spectra obtained using the two measurement systems. The
5 K
temperature
difference is also attributed to the different time windows of the measurements. It should be noted
that the overall TMRX spectra obtained using the 6-channel SQUID system (Figure 6.12, right) are
less pronounced than the spectra obtained using the MPMS. This difference can also be attributed
106 Chapter 6. Development of a TMRX System for the Short Time Regime
to the different time regimes and the associated detectable particle spectrum at each temperature.
At a defined temperature, only the relaxations of a very distinct group of particles are detected in
the long time regime of the MPMS. In the short measuring regime of the 6-channel system, on
the other hand a broader range of particle sizes is detected at the same temperature, leading to an
overall broader and less pronounced TMRX spectrum.
The changes in the peak intensities of the magnetic moments (m) are also generally smaller in the
spectra obtained using the 6-channel system than those in the spectra obtained using the MPMS.
This can be explained by the short magnetization time of only
1 s
in the 6-channel system, during
which specific types of MNPs are not fully magnetized. However, it is important to note that
although the amplitude changes are generally smaller in the spectra obtained using the 6-channel
system, the overall proportions of the peak amplitudes in the spectra for the different samples are
the same, regardless of the analytical instrument. As was shown in Chapter 4.2, the signal ratio for
the spectra of an unknown sample and a reference sample with known iron content can be used to
quantify of the MNP content in the sample.
Figure 6.13: Peak temperatures for Resovist samples of different concentrations observed in
the MPMS long time regime and 6-channel SQUID system short time regime. Each TMRX
spectrum exhibited two distinct peak temperatures. The constant offset between the measured peak
temperatures was attributed to the different time regimes.
6.3 Quantification of Magnetic Nanoparticles using TMRX in the Short Time Regime107
6.3.2 Magnetic Nanoparticle Quantification Using the 6-Channel SQUID System
Quantification of the Resovist dilution series via TMRX in the short time regime of the 6-channel
system was performed. To do so, the peak comparison method described in Chapter 4.2 was applied.
The iron contents in the samples were also quantified via MPS analysis[
51
] and phenanthroline
staining [
78
], and the results were compared to the estimated iron contents. The determined total
iron content of the individual samples are plotted in Figure 6.14 as a function of the nominal iron
content.
Figure 6.14: Nominal iron content in the different Resovist samples versus the iron content
determined using three different methods. The concentration of iron in the samples varied by
several orders of magnitude. The axis in the figure are therefore displayed logarithmically. The
methods included phenanthroline staining [
78
], quantification via MPS [
51
], and quantification via
TMRX peak comparison. While all three methods were generally capable of determining the iron
content, they differed in their overall accuracy.
Figure 6.14 illustrates that the MNP concentration in the samples were successfully determined
using all three methods. The quantification accuracy of the different methods did vary, however. The
highest correlation with the nominal iron content was achieved using the MPS quantification method
for this particular dilution series. The quantification analyses performed using the phenanthroline
and TMRX methods suffered from slightly higher deviations. The detection limit for the TMRX
quantification with the 6-channel system was estimated to be approximately
1 µg
iron for the
investigated Resovist samples. Below that iron concentration, the changes in the peak amplitude in
the TMRX spectra were on the order of the background signal (∆Bnoise) of 4·10−10 Am2.
Next, the possible cause of the deviation of the TMRX quantification method was investigated. The
applied peak comparison method requires that the maximum amplitude change in the TMRX spectra
for all of the samples occurs at the same temperature. If the peak temperature changes because
of particle interactions, this change must be describable and predictable using a mathematical
model. For the presently investigated Resovist dilution series, it was assumed that the peak
temperature was constant at room temperature in the TMRX spectra obtained in the short time
108 Chapter 6. Development of a TMRX System for the Short Time Regime
regime (Figure 6.12, right). However, it is possible that the maximum temperature changes actually
occurred above room temperature and therefore not in the field of view. In addition, the TMRX
spectra obtained using the MPMS in the slow time regime (Figure 6.12, left) revealed that the peak
temperatures were not identical for all of the samples due to particle interactions. Although this
effect would be less pronounced in the short time regime, it may have had an influence on the
results.
Conclusion
TMRX measurements in the short time regime were demonstrated by measuring a dilution series of
the known MRI contrast agent Resovist. The GRP cryostat was capable of cooling the samples in
the temperature range from
5 K
to room temperature. Compared to the long delay time of
1,5 min
for the MPMS, the 6-channel SQUID system demonstrated a severely reduced delay of only
100 µs
.
The shorter delay time led to an overall reduced analysis time of
40 min
to
60 min
per sample,
which is faster than the average MPMS measurement by a factor of ten. Due to the faster analysis
time, more highly resolved TMRX spectra were obtained during the TMRX temperature sweeps.
The short analysis time for a single MRX measurement of
1 s
for the 6-channel SQUID system also
affected the shape of the obtained TMRX spectra compared to that of spectra obtained in the long
time regime of the MPMS. A comparison of spectra obtained over for the same samples over the
two time regimes revealed that the position of the peak temperature within the temperature spectrum
was mainly affected. On the other hand, the linear relationship between the signal amplitude and the
iron content remained the same and thus could be used to demonstrate the quantification capabilities
of the measurement system.
Quantification of the MNP contents in samples with different concentrations was performed using
the TMRX peak comparison method, and the results were compared to those obtained using other
established methods. The TMRX quantification results were found to be valid, although there were
slight deviations for the given samples. The deviations were within the accuracy range of the other
methods and attributed to the specific behavior of the particles. The TMRX setup was capable of
detecting up to 1 µg nanoparticle iron in the investigated Resovist samples.
The new measurement system therefore offered improvements in the measurement time and sample
rate in combination with a solid quantification method. Hence, the potential applicability of the
6-channel SQUID system with the GRP cryostat for the determination of MNP concentrations in
biological samples was successfully demonstrated.
6.4 Quantification of Magnetic Nanoparticles in Biological Tissues using TMRX in the
Short Time Regime 109
6.4 Quantification of Magnetic Nanoparticles in Biological Tissues using TMRX
in the Short Time Regime
Abstract 6.4
TMRX analysis and quantification of biological samples containing MNPs were
investigated. The analyses were performed using the 6-channel SQUID system with the GRP
Cryostat. Five different samples of mice liver tissue were investigated. The mice were injected
with an aqueous iron oxide MNP contrast agent. Twenty-four hours after injection, the MNPs
were accumulated in the livers of the mice. In order to quantify the MNP uptake, a small sample
of tissue from each mouse was analyzed via magnetic particle spectroscopy (MPS) and TMRX.
TMRX analysis using the 6-channel SQUID system was found to be suitable for determining
the MNP content in the tissue samples; the results obtained via TMRX were in good agreement
with those obtained via MPS. The TMRX spectra further revealed that the particle relaxation
did not change when the MNPs were incorporated into the tissue. Therefore, it was concluded
that no particle interactions or aggregation occurred during uptake.
Investigated MNP System
The rodents were given
50 µL
of the MRI agent precursor containing iron oxide MNPs covered with
a dextran coating (
cFe =445 mmol/L
). The magnetic core sizes of the particles ranged from
15 nm
to
20 nm
. In order to obtain a sample with an iron concentration comparable to the concentration
in the tissue samples, the original solution was diluted with distilled water to
cFe =4,5 mmol/L
.
Finally, to
100 µL
of the dilution
50 µL
mannitol solution (containing
15 %
mannitol) were added,
and the resultant solution was immobilized in a PCR capsule via freeze drying.
Preparation of biological Samples
Twenty–four hours after intravenous administration of
50 µL
of the MRI contrast agent (
445 mmol/L
),
four mice were sacrificed and their liver tissue harvested. For comparison, a single mouse that
had not been exposed to magnetic nanoparticles was sacrificed and its liver harvested. The total
quantities of liver tissue in the sample tubes used for the MPS and TMRX analyses are listed in
Table 6.4.
Mouse ID MPS tissue mass [g] TMRX tissue mass [g]
Control 0.072 0.17
M79 0.027 0.12
M80 0.028 0.21
M82 0.043 0.12
M83 0.030 0.17
MPS Measurement Procedures
The samples were analyzed at
25 kHz
using a drive field of
25 mT
. The measurement time for each
sample was
10 s
at
300 K
. Quantification of the MNP content was performed using the method of
Löwa et al. [51].
6-Channel TMRX Measurement Procedures
Similar to the sequence described in Section 6.3, a temperature sweep was performed to cool
down the samples. For this study, a faster cooling rate of
0,25 K/s
was used, and the samples
were cooled from
290 K
to
5 K
within
20 min
. During that time, the data acquisition system of the
6-channel SQUID system continuously performed MRX analyses. The MRX procedure consisted
of a magnetization time of
1 s
, a delay time of
100 µs
, and a measurement time of
1 s
with a waiting
time of
1 s
between each individual MRX analysis to ensure complete relaxation of the sample.
In total, 400 single MRX analyses were performed during the cool-down period. In order to
increase the sensitivity of the system, a magnetization current of
1,5 A
was applied, resulting in a
magnetizing field of 4 mT.
110 Chapter 6. Development of a TMRX System for the Short Time Regime
TMRX Measurement of the biological samples
At room-temperature, the MNP reference sample already exhibited a relaxation behavior within
the measurement time of one second. During the cool-down process, the relaxation amplitude in
the spectra of the MNPs changed due to the longer relaxaton times of the particles. The amplitude
changes for the spectra of the reference MNP sample are displayed in Figure 6.15 (pink line) for
each temperature. The peak temperature, which exhibited the strongest relaxation amplitude (
∆m
),
was observed at
160 K
. Unlike the previously described samples (e.g., Resovist, see Chapter 6.3)
the TMRX spectrum of the MNPs contained only a single peak temperature, indicating that the
particle sample consisted of a monomodal size distribution. For this sample, the noise level was in
the range of 1·10−9Am2.
Subsequently, the 5 mice liver tissue samples were analyzed via TMRX. Four of the samples
exhibited relaxation signals at room temperature. The fifth sample (Control, black line), however,
showed no relaxation behavior. This result was expected because the mouse was not injected with
the MNP contrast agent. The highest relaxation amplitude was exhibited by sample m80 (turquoise
Figure 6.15: TMRX spectra of five different mice liver samples and a freeze–dried reference sample.
The measurements were performed using the 6-channel SQUID system with a GRP Cryostat. The
amplitude changes at each temperature for temperatures ranging from
5 K
to
290 K
are displayed.
All of the mice liver samples with administered MNPs exhibited temperature depending relaxation
signals. The highly concentrated samples and the reference sample exhibited a signal peak at
150 K
to
170 K
. The liver from the control mouse (black line) was not exposed to nanoparticles and did
not exhibit a significant TMRX signal.
line in Figure 6.15). Like the spectrum of the reference sample, the spectrum of this sample exhib-
ited a pronounced temperature peak near
160 K
with an amplitude (
∆m
) of
1,35·10−8Am2
. The
TMRX spectra for samples m79, m82, and m83, on the other hand, only contained less–pronounced
temperature peaks at
160 K
. Nevertheless, a decrease in the amplitude change was clearly visible
below
150 K
for all of the analyzed MNP samples. Similar to the reference sample, the TMRX
spectra of the biosamples exhibited a noise level in the range of
1·10−9Am2
or less. However, a
comparison of the noise levels of the individual samples revealed that sample m80, had a signifi-
cantly lower noise level than the others. This difference can be attributed to external sources of
6.4 Quantification of Magnetic Nanoparticles in Biological Tissues using TMRX in the
Short Time Regime 111
disturbance that affect the sensitive SQUID sensors. The measurement setup was shielded against
most high frequency electromagnetic waves that are typically emitted from different power supply
units, e.g., the power supply unit for the laptop used with the system. It was, however, not possible
to completely remove the physical vibrations of the vacuum pump, which was directly connected
to the GRP Cryostat. The quality of the vibration decoupling was different for each sample. It is
assumed that this difference is the main source of the different noise levels observed in the spectra
of the individual samples.
TMRX Quantification compared to MPS and MRX
Next, the TMRX analysis results obtained using the 6-channel system were used to determine the
iron contents in the biosamples by employing the peak comparison method described in Chapter
4.2. While the more highly concentrated samples (m83, reference) had a clear peak temperature
near
160 K
, the samples with lower concentrations of MNPs exhibited a plateau above
150 K
. The
total iron content in the biosamples was determined by comparing their amplitude change at
160 K
with the amplitude change of the reference sample. The relative iron concentration per gram tissue
was obtained by normalizing the total iron content to the mass of each individual sample. The
results are displayed in Figure 6.16. The quantification error was defined by the variance in the
TMRX spectrum for each sample and the variance in the TMRX spectrum of the reference sample.
These quantification errors are displayed as error bars on the TMRX values in Figure 6.16 (blue
bars).
Figure 6.16: Quantification results for an MPS analysis (orange) compared to those obtained via
TMRX (blue) and MRX (gray) at room temperature. The peak comparison method described in
chapter 4.2 was used for the TMRX analysis. The iron contents determined using MPS and TMRX
matched, although their confidence intervals did not always overlap. The deviation is attributed
to the different sample volumes (see Table 6.4). Quantification via MRX at room temperature
overestimated the MNP amount.
A comparison of the values determined for the relative iron contents via TMRX and MPS reveal that
they were in good agreement. The biosamples used for the TMRX analyses where obtained from
the same rodents as the biosamples used for the MPS analyses. However, the sample tubes used
for the MPS analyses contained less tissue than the tubes used for TMRX analyses (see Table 6.4).
112 Chapter 6. Development of a TMRX System for the Short Time Regime
The deviations in the determined iron contents are assumed to be attributed to the different sample
volumes.
In addition to the MPS analyses, quantification via room temperature MRX [
96
] was also performed.
Particularly for the highly concentrated samples, the amplitude change at room temperature was
different from the
∆m
value at
160 K
. It can be seen in the TMRX spectrum shown in Figure
6.15, that the
∆m
values of the reference sample at room temperature and the peak temperature
were approximately
1,1·10−8Am2
and
1,9·10−8Am2
, respectively. It can be seen in Figure 6.15
that this difference between the
∆m
values at
160 K
and
290 K
was not visible for the samples
with lower concentrations (m82, m83, and m79). Quantification based on the
∆m
value at room
temperature therefore leads to a severe overestimation of the MNP concent in the samples (see
Figure 6.16).
Finally, quantification via TMRX with the MPMS was attempted. Due to the limited sample volume
and the long delay time, the resulting TMRX spectra where very close to the detection limit, and
quantification was not possible (see Figure 9.16 in the Appendix).
Conclusion
Quantification via TMRX using the 6-channel SQUID system was presented, and the results were
compared to those obtained using established quantification methods. The TMRX spectra of the
biosamples revealed that the strongest amplitude change occurred at a peak temperature of
160 K
.
Therefore, quantification using the peak comparison method (see Chapter 4.2) was performed.
The determined iron concentrations were in accordance with the values obtained via MPS analyses.
The quantification via room temperature MRX, on the other hand, led to overestimation of the iron
concentrations in the liver samples. This result is attributed to the position of the peak temperature
at
160 K
for this particular type of MNP. For particles that have a peak temperature close to room
temperature, e.g., Resovist (see Chapter 6.3), MRX quantification at room temperature is sufficient.
TMRX analyses via MPMS were not sufficient to perform quantification because the overall signal
quality of the biosamples was too low (see Figure 9.16 in the Appendix).
Thus, the new measurement setup with the GRP Cryostat in the 6-channel SQUID system offers a
feasible method for quantification of MNP concentrations via TMRX. This method is attractive
because it enables the analysis of larger biosamples, requires shorter delay times, provides overall
faster TMRX results, and has the ability to depict changes in MNP signals due to particle interactions
and aggregation. It is therefore a viable extension to existing measurement devices.
7. Conclusion
114 Chapter 7. Conclusion
7.1 Summary and Conclusion
Summary
The scope of this work was to establish temperature dependent magnetorelaxometry (TMRX)
measurements as quantification and characterization method for magnetic nanoparticles in biological
tissue. This could be achieved by reaching several key milestones in the course of this dissertation.
A commercial magnetic susceptometer (MPMS) was utilized to complete the first milestones, the
development of a novel MNP quantification method, and the implementation of a consistent data
analysis method.
With the MPMS, different MNP characteristics, like core diameter, size distribution and particle
concentration were investigated via TMRX. Based on these measurements, a quantification method
was developed for MNP in biological samples and the uptake of small MNP in cancer cells
determined. The TMRX spectra measured with the MPMS also exhibited distinct alterations
because of dipole–dipole interaction of the magnetic particles. With the measurement data that was
collected, a simulation of the TMRX spectra could be performed. These measurements also formed
the basis of the phenomenological dipole–dipole interaction model, which was developed in the
course of the dissertation.
Another key milestone of this thesis was the optimization of the TMRX measurement time. Because
of the magnetizing and measuring procedure TMRX measurements with the MPMS were only
possible in a long time regime, i.e., the measurement of relaxations in the minute range. A single
relaxation measurement took up to 40 minutes and a whole TMRX sequence took between 12 hours
to 20 hours. In order to change the measurement procedure to the short time regime, a different
magnetizing procedure was implemented in the MPMS. Nevertheless, a significant acceleration
of the MPMS measurement was not possible, as internal background signals overshadowed the
relaxation signal.
Therefore a measurement device was developed, capable of measuring relaxations in the micro-
second range, i.e., the short time regime. For that purpose, an existing SQUID system was extended
by a temperature controlled sample holder with magnetizing unit. The sample holder was therefore
implemented in a helium flow cryostat, which was designed in the course of the thesis. With
the cryostat TMRX spectra could be measured on a temperature range from room temperature
down to
5 K
. In addition, a LabVIEW interface was developed to control and measure the sample
temperature. Finally, the uptake of MNP in biological samples that could not be quantified with the
MPMS was quantified with the new TMRX device.
7.1 Summary and Conclusion 115
Conclusion
With the successfully established TMRX analysis a robust and reliable investigation method is now
available. The developed measurement techniques offer not just a way to quantify MNP uptake in
cells, but also to investigate alterations of the MNP signal in more detail. These signal alterations
are of increasing importance for the current MNP development as they often occur in a biological
environment. It is crucial for biomedical MNP applications that the particle’s performance does
not decrease when the MNP are exposed to biological tissue, which may happens because of
aggregation, interaction or immobilization of the MNP. With the developed TMRX device a reliable
and fast way to get a detailed view on the state of the MNP within the biological tissue is now
available.
In addition, with the custom build measurement system, investigating larger series of biological
samples with TMRX is now also feasible. This is important for the practical application of TMRX
as MNP characterization method. Previously, TMRX analyses were only reasonable for a few,
chosen MNP samples because of the long measurement time. The new system is now capable
of providing a valuable contribution to the project related particle characterization procedures. It
complements other established methods, like Magnetic Particle Spectroscopy or room temperature
MRX, which do currently provide the main proportion of the standard particle characterization.
Lastly, the numerical simulation which was developed in the course of the thesis completes the
TMRX analyses. Now, a more detailed analysis of the TMRX spectra is possible that also reveals
information about the dipole–dipole interaction of the MNP sample. Furthermore, the novel dipole
energy term is potentially applicable for other numerical simulations as well. This includes room
temperature MRX but also alternating current (AC) field measurements like in Magnetic Particle
Spectroscopy or Magnetic Particle Imaging.
Outlook
Our main suggestion for improvement of the TMRX measuring system concerns the cryostat
itself. Through a redesign of the cryostat an important improvement concerning the sample change
could be performed. Currently the design of the cryostat resembles a Dewar flask with only one
single–sided opening. Hence, the cryostat has to be detached from the liquid helium transfer tube
for every sample change. We therefore suggest a tube like cryostat design that provides a second
opening with a retrievable sample rod. This would significantly decrease the delay time between
the different sample measurements. In addition, it would increase the positioning accuracy of the
magnetization coil beneath the SQUIDs.
Another improvement would be the additional installation of a thermally conducting sapphire heat
bridge between the sample and temperature sensor. The heat bridge would reduce the thermal offset
between the temperature sensor and sample, and therefore, increase the accuracy of the temperature
measurement.
Although the fundamental principles of MNP interaction are already known nanoparticle interaction
remains a research topic that attracts growing interest in the research community. The MNP
performance for specific biomedical tasks crucially depends on the sensitive interaction between
particles with each other or with the surrounding media. As biomedical applications are becoming
more and more complex, these alterations of MNP within biological tissue become a relevant
research question that needs to be addressed. Temperature dependent measurements, like the
TMRX, will therefore become of increasing importance, as they are capable of presenting a detailed
insight into particle interaction through in vitro experiments. In the future temperature dependent
measurements will remain an essential tool to validate interaction models like the one presented
here.
III
8Magnetic Property Measurement System
(MPMS) ............................ 119
8.1
Description of the Magnetic Property Measurement
System
9Construction ....................... 125
9.1 6-Channel SQUID System for TMRX
9.2
6-Channel SQUID System: Additional Graphics
and Pictures
9.3 Technical Drawings of the GRP Cryostat
Appendices
8. Magnetic Property Measurement System (MPMS)
120 Chapter 8. Magnetic Property Measurement System (MPMS)
8.1 Description of the Magnetic Property Measurement System
TMRX measurement devices
For the measurements displayed in Section 4 a conventional SQUID magnetometer (MPMS-XL,
Quantum Design, 8.1) was used. The Magnetic Property Measurement System (MPMS) excels
through a temperature control system which is capable of reaching a holding temperature from
5 K
to 350 K.
Figure 8.1: Quantum Design Magnetic Property Measurement System (MPMS)
SQUID
A superconducting quantum interference device (SQUID) is a very sensitive magnetometer used
to determine smallest changes in the magnetic field. However, in the MPMS the SQUID does not
detect the magnetic field from the sample directly. The sample rather moves through a system of
superconducting detection coils which are connected to the SQUID. With this setup the current
flowing in the detection coils is induced to the SQUID sensor. When a DC-current is introduced in
the SQUID a detectable voltage can be measured. This voltage is strictly proportional to the current
flowing in the SQUID pick up coil.
Second-Order Gradiometer
The particular alignment of the superconducting detection coils around the sample space is called a
second order gradiometer. When SQUID pick up coils are aligned as a gradiometer a significant
reduction in background drifts and signal noise caused by the relaxation of the superconducting
magnet can be achieved. In a three coil gradiometer the upper coil and the bottom coil are bound
clockwise with one turn whereas the center coil has two counter-clockwise turns. In this setup the
flux change through relaxation of the superconducting magnet in the center coil will be canceled by
the other two coils which experience the same flux change. However the signal produced by the
sample will still be detectable as it is not constant on all three coils.
8.1 Description of the Magnetic Property Measurement System 121
The magnetization unit
The sample chamber is surrounded by a superconducting five Tesla magnet which is constructed as
a closed loop. As there is no electrical resistance in superconducting material, this setup allows
running the magnet in a persistent mode. Once it has been set in this mode the magnet simply holds
the magnetic field without the need of a constant external current. In order to change the current
within the superconducting magnet the loop needs to be electrically opened. Therefore a small part
of the magnets wire is wrapped around a heater. This is called the persistent-current switch. When
the persistent switch is heated it loses its superconductivity and becomes normal again. In this state
an electrical current may be induced. After the desired magnetic field is set, the heater is turned off
and the persistent-current switch becomes superconducting again.
The RSO-Transport
The sample is positioned in the sample holder at the end of the sample rod which is then placed in
the sample chamber through the airlock. The sample rod is held at the top by the RSO (Reciprocat-
ing Sample Option)-Motor. The RSO-Motor moves the sample sinusoidally through the pick up
coils while measuring. A change of the sample’s position comes along with a change of the flux in
the system. The pick up coils induce a current into the superconducting circuit depending on the
flux to which they are exposed. The position of the sample rod is tracked by a shaft encoder on the
servo motor. To lower the signal to noise ratio, the sample is moved several times through the pick
up coils and the measurements are averaged. The final RSO-measurement therefore consists of
the absolute SQUID voltage at each position of the sample rod within the sample chamber. The
incline of this bell shaped curve is then fitted and compared to the calibration curve of a palladium
standard sample. This standard sample imitates a point dipole with an accuracy up to
0,1 %
. For
an exact fit the unknown sample should therefore have small spacial proportions of about
3 mm
in
diameter and 3 mm to 5 mm in height.
The Sample Rod
The MPMS sample rod is designed to carry standard polycarbonate capsules (PC capsules) with
a capacity of
150 µL
to
200 µL
. The capsules are placed into a nonmagnetic straw at the end
of the sample rod. The PC capsules may contain liquid or immobilized materials. For TMRX
measurements only immobilized (freeze dried) nanoparticle samples were used.
Figure 8.2: Above: A dilution series of freeze–dried nanoparticle solution in poly carbonate
capsules. Below: A sample straw with an installed PC capsule.
122 Chapter 8. Magnetic Property Measurement System (MPMS)
Figure 8.3: Sample rod and Sample straw setup (Picture from Manual [1])
After subtracting SQUID offset and drift the amplitude is determined by fitting a magnetic
point dipole to the response curve. The signal to noise ratio can be improved through repeated
RSO scanning. In the first
7 min
the MPMS only performed single RSO scans (
32 s
per data point),
after which RSO scans with three repetitions (
140 s
per data point) have been performed. Each
relaxation measurement was executed at selected temperatures. The overall measurement time for
one sample added up to about 12 h in total.
MultiVu Sequences
The MPMS MultiVu software is a Windows application to communicate with the MPMS. The
software is capable of monitoring and calibration task and may perform different measurement
procedures. Information about the instruments status may be displayed or logged in measurement
files. SQUID measurements can be performed manually or through sequenced commands. These
commands include a variety of system functions such as setting a certain magnetic field or changing
the samples temperature.
Figure 8.4: Example of a typical MultiVu sequence: A measurement file was defined, different
temperatures were set, and other sequences were called.
While working with the predefined measurement modi is quite easy with the MultiVu sequences
other measurements require the usage of the External Device Control (EDC) Commands.
External Device Control
The External Device Control (EDC) language allows the user to communicate with the MPMS
through a variate of short commands send through its General Purpose Interface Bus (GPIB).
EDC commands are addressed directly to a device or sensor (e.g. the temperature sensor) in the
system. This gives the user a more direct control over the magnetometer than it would be possible
through the MultiVu sequences. Each EDC command triggers a specific task in the device it is send
to. These tasks include sending and receiving data or changing the status of a component. It is
important to understand that the MultiVu Sequence commands consists of EDC commands. While
some of the MultiVu commands only consists of one EDC command, others may involve up to
10 or 20 different types. The current EDC activity of the MPMS can be watched in the MultiVu
8.1 Description of the Magnetic Property Measurement System 123
software under "Utilities
>
Diagnostics
>
GPIB
>
View GPIB Activity". With "GPIB
>
Send EDC
commands" is also possible to send single EDC commands. If more complex command sequences
are needed it is possible to include .dll files compiled by Borland Delphi. These .dll files can then
be executed though the MultiVu script sequence. Another way to communicate with the MPMS
magnetometer is to send the EDC commands directly through a Virtuall Intervace (LabVIEW).
Syntax: SMP (code)
where code = 0turns the magnet power supply OFF
where code = 1turns the magnet power supply ON
Initial: The power supply is OFF when
the MPMS Controller is initially started.
Purpose: Turns the magnet power ON and OFF
An example EDC Code is given above. The description is taken from the Quantum Design MPMS
XL User Manual.
9. Construction
126 Chapter 9. Construction
9.1 6-Channel SQUID System for TMRX
For TMRX analysis in the short time regime a magnetically shielded Dewar vessel was used. The
vessel contained six SQUID (Superconducting QUantum Interference Device) sensors arranged
around the center of the warm bore of the system. The horizontal warm bore of the 6-channel
SQUID System measures
27 mm
in diameter and
700 mm
in length and is made out of a glass
reinforced plastic. In order to reduce the magnetic background noise in the system a niobium shield
is installed around the sample space. The superconducting niobium tube is
500 mm
in length and
50 mm in diameter. The cold–warm distance between SQUID sensor and warm bore is 10 mm.
Figure 9.1: 6-channel SQUID system: A magnetically shielded Dewar vessel containing six SQUID
sensors. On the front of the cylindrical Dewar the
27 mm
wide opening of the warm bore can be
seen. In the course of the dissertation a helium flow cryostat was designed to fit in the warm bore
and to cool a biological sample for TMRX analyses.
Figure 9.2: Illustration of the 6-channel SQUID system: The outer vacuum vessel surrounds the
inner helium vessel. The warm bore is magnetically shielded by a niobium tube. The six SQUID
sensors are operated with flux-locked-loop (FLL) electronics.
The 6-channel SQUID System was cooled down in the magnetically shielded room BMSR-2 at the
PTB in order to minimize the residual field within the Dewar vessel. At the center of the warm bore
a residual field of
100 nT
was achieved. The Dewar vessel was manufactured by Fujihira Inc. in
cooperation with the Kanawazawa Institute of Technology.
9.2 6-Channel SQUID System: Additional Graphics and Pictures 127
9.2 6-Channel SQUID System: Additional Graphics and Pictures
Figure 9.3: Experimental Setup: The data acquisition system (DAQ) reads out the relaxation
signals (
a
) measured with the 6-channel SQUID system and controls the magnetizing coil(
b
). The
temperature controller reads out the temperature sensor and controls the heating coil (
c
) in the
glass reinforced plastics (GRP) Cryostat. In order to reach a certain temperature in the cryostat
the temperature controller may open or close the needle valve(
d
) in the helium transfer tube. The
measured temperature, the voltage of the heating coil, and the opening percentage of the needle
valve are continuously transmitted to the DAQ System (a).
128 Chapter 9. Construction
Figure 9.4: Oxford Instruments low loss transfer tube (LLT): The helium coolant is taken up over
the Dewar leg, which fits into our helium transport vessels. The GRP Cryostat is attached at the tip
of the flexible section. At the tip, the helium cryostat inlet cools the GRP Cryostat and retrieves the
warm helium gas. The returning helium is released over an outlet at the knee of the transfer tube.
The stepper motor off the automated needle valve and its corresponding serial interface also located
at the knee.
Figure 9.5: Close-up picture of the sample holder with an installed sample during the cooling
process.
Figure 9.6: The virtual interface (VI) for the Mercury ITC gives the user an easy method for sending
commands and receiving data. The VI constantly measures the temperature of the permanent sensor
with the option to save the data to an ASCII text file. The commands that can be sent to the ITC
include manual opening of the helium needle valve to a defined percentage. In addition, an ASCII
text file can be loaded in order to perform temperature sweeps. The VI allows to initiation of both
cool–down and warm–up sweep procedures.
9.3 Technical Drawings of the GRP Cryostat 129
9.3 Technical Drawings of the GRP Cryostat
Figure 9.7: General assembly drawing of the cryostat
Figure 9.8: Rear end cover
130 Chapter 9. Construction
Figure 9.9: Front end flange
Figure 9.10: Vacuum valve housing
9.3 Technical Drawings of the GRP Cryostat 131
Figure 9.11: Vacuum valve plug
Figure 9.12: Outer vaccum tube
132 Chapter 9. Construction
Figure 9.13: Inner vaccum tube
Figure 9.14: Sample rod
9.3 Technical Drawings of the GRP Cryostat 133
Figure 9.15: Sample holding
134 Chapter 9. Construction
9.3.1 MPMS measurements from Chapter 6.4
Figure 9.16: TMRX analyses of MNP samples presented in Chapter 6.4. The analyses were
performed in the long time regime of the MPMS at
Bmag =1 mT
. The resulting TMRX spectra
were not usable for quantification.
Figure 9.17: Relaxation data for the MNP samples (m82,
T=290 K
) presented in Chapter 6.4. The
analyses were performed in the long time regime of the MPMS at
Bmag =1 mT
. Except for the
reference sample, the signal to noise ratios in the relaxation curves were too low for interpretation.
9.3 Technical Drawings of the GRP Cryostat 135
9.3.2 Measurement and Fit Data from Chapter 5.3
Name Mass [mg]Iron per gram dry sample [mgFe
gsample ]Total Iron [mgFe]Relative Iron Amount
C6 46.7 0.16 0.0074 1
C5 44.1 0.79 0.0348 4.66
C4 42.6 3.98 0.169 22.69
C3 31.7 20.6 0.653 87.41
C2 50.8 45.5 2.3 307.0
C1 49.8 58.9 2.9 392.2
S 14.2 106 1.5 200.0
Table 9.1: Given parameters of the Endorem dilution series.
Name d[nm]σ[−]Amplitude Factor Estimated relative iron Match [%]
C6 8.25 0.25 2.72E-6 1 100
C5 8.25 0.27 1.19E-5 4.37 93
C4 8.50 0.27 5.80E-5 21.3 93
C3 8.75 0.27 2.28E-4 83.82 95
C2 9.75 0.27 5.46E-4 200.9 65
C1 9.75 0.30 5.92E-4 217.6 55
S 9.75 0.30 2.12E-4 77.94 39
Table 9.2: Fit parameters obtained by simulation without interaction energy. Iron amount estimated
via peak comparison.
Name d[nm]σ[−]D[nm]Amplitude Factor Estimated relative iron Match [%]
C6 8.00 0.283 60 0.01 1 100
C5 8.00 0.283 48 0.03 4.5 96
C4 8.00 0.283 38.9 0.14 23.5 103
C3 8.00 0.3 38.9 0.54 89.17 102
C2 8.00 0.31 25.3 1.49 248.33 80
C1 8.00 0.33 25.3 1.52 253.33 64
S 8.00 0.35 31.4 0.51 85.00 42
Table 9.3: Fit parameters obtained by simulation with approach A. Iron amount estimated compari-
son of the amplitude factor.
136 Chapter 9. Construction
Name d[nm]σ[−]D[nm]Amplitude Factor Estimated relative iron Match [%]
C6 8.00 0.266 45 0.0078 1 100
C5 8.00 0.266 43.28 0.035 4.49 96
C4 8.00 0.266 37.64 0.198 25.49 112
C3 8.00 0.266 32.7 0.929 119.1 136
C2 8.00 0.266 25.9 4.19 537.18 174
C1 8.00 0.266 22.57 6.03 773.08 197
S 8.00 0.266 22.5 2.24 287.18 143
Table 9.4: Fit parameters obtained by simulation with approach C. Iron amount estimated compari-
son of the amplitude factor.
Name d[nm]σ[−]D[nm]Amplitude Factor Estimated relative iron Match [%]
C6 8.25 0.266 23.4 0.0078 1 100
C5 8.25 0.266 20.5 0.035 4.49 96
C4 8.25 0.266 15.78 0.198 25.49 112
C3 8.25 0.266 12.96 0.929 119.1 136
C2 8.25 0.266 9.33 4.19 537.18 174
C1 8.25 0.266 8.18 6.03 773.08 197
S 8.25 0.266 8.18 2.24 287.18 143
Table 9.5: Fit parameters obtained by simulation with approach D. Iron amount estimated compari-
son of the amplitude factor.
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