Document [original]

Pilot tone–based prospective respiratory

motion correction for cardiac MRI

vorgelegt von

M. Sc.

Juliane Ludwig

ORCID: 0000-0003-4042-8071

an der Fakult¨at V – Verkehrs- und Maschinensysteme

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktorin der Naturwissenschaften

– Dr. rer. nat. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Marc Kraft

Gutachter: Prof. Dr. Ingolf Sack

Gutachter: Prof. Dr. Tobias Sch¨affter

Tag der wissenschaftlichen Aussprache: 30. Juni 2022

Berlin 2022

Zusammenfassung

Kardiovaskul¨

are Erkrankungen (CVD), einschließlich Koronarer Herzkrankheit,

Herzinsuffizienz, Kardiomyopathie und Myokarditis sind f¨

ur 32% aller Todesf¨

alle

verantwortlich und bleiben weltweit die h¨

aufigste Todesursache (17,9 Millionen pro

Jahr; WHO, 2019). In der Kardiologie ist die Magnetresonanztomographie (MRT)

wegen des hervorragenden Weichteilkontrasts ein wichtiges klinisches Bildgebungs-

instrument zur Differentialdiagnose.

Mit einer MR-Untersuchung k¨

onnen nicht-invasiv verschiedene Parameter des

Herzens untersucht werden, die z.B. Aufschluss ¨

uber die Funktionsf¨

ahigkeit, den

Blutfluss oder die Gewebezusammensetzung geben. Dabei werden je nach Anwen-

dungsgebiet spezielle kardiale MRT-Techniken eingesetzt. Zur Darstellung von Herz-

bewegungen und regionalen Herzwandbewegungsst¨

orungen eignet sich beispielsweise

die Cine-MRT, w¨

ahrend die Beurteilung des Verlaufs einer Myokarditis mit Hilfe des

T1-Mappings m¨

oglich ist.

Von Nachteil f¨

ur viele Techniken ist jedoch die f¨

ur MR-Untersuchungen typisch

lange Aufnahmedauer pro Bild, die haupts¨

achlich auf physiologische Bewegungen

zur¨

uckzuf¨

uhren ist. Um sicherzustellen, dass die Bildqualit¨

at nicht durch Bewegungs-

artefakte beeintr¨

achtigt wird, kommt in der klinischen Praxis h¨

aufig die Ateman-

haltestrategie zum Einsatz, bei der die Atembewegung unterdr¨

uckt wird. F¨

ur ei-

ne vollst¨

andige Untersuchung m¨

ussen die PatientInnen jedoch mehrere instruierte

Atemanhaltephasen bew¨

altigen, was f¨

ur Kranke, ¨

altere Menschen oder Kinder oft

schwierig sein kann.

Daher wurden Methoden entwickelt, die eine kardiale MR-Untersuchung unter

freier Atmung erm¨

oglichen. H¨

aufig basieren diese Ans¨

atze auf einer zus¨

atzlichen Mes-

sung eines MR-Navigators, welcher Informationen ¨

uber den Atembewegungszustand

liefert. F¨

ur eine kontinuierliche Messung ist der MR-Navigator jedoch ungeeignet,

da seine Erfassung die Bildaufnahme unterbricht.

Eine neue Alternative f¨

ur ein Bewegungssurrogat ist der Pilotton (PT). Der PT ist

ein zus¨

atzliches in den Scanner eingebrachtes RF-signal, welches w¨

ahrend der Mes-

sung aus den aufgenommenen MR-Daten extrahiert werden kann. Die Intensit¨

at des

nicht skalierten Signals ¨

andert sich in Abh¨

angigkeit von der Atembewegung. Daher

kann der PT als Bewegungssurrogat verwendet werden. Quantitative Bewegungsin-

formationen, die f¨

ur eine Bewegungskorrektur genutzt werden k¨

onnten, wurden mit

dem PT bisher noch nicht gewonnen.

In dieser Dissertation wurde erstmals eine PT-basierte Atembewegungskorrektur

f¨

ur die kardiale MRT entwickelt. Auf Basis von Phantom- und in vivo-Daten konnte

nachgewiesen werden, dass die Bewegungskorrektur mit dem PT zu einer Verbesse-

rung der Bildqualit¨

at im Vergleich zu unkorrigierten Bildern f¨

uhrt.

Die zeitliche Stabilit¨

at des PT wurde f¨

ur ca. 50 Minuten gezeigt. Aus einem

Kalibrierungsscan wurden personenspezifische Bewegungsmodelle abgeleitet, die es

erm¨

oglichen, den qualitativen PT in ein quantitatives Signal umzuwandeln, das In-

iii

formationen ¨

uber die Atembewegung liefert. Dar¨

uber hinaus wurde ein Vergleich

des PT mit anderen Bewegungssurrogaten durchgef¨

uhrt. Bei einem 3D-MR-Scan

verbesserte die retrospektive Bewegungskorrektur mit dem PT die Sichtbarkeit der

Koronararterien ¨

ahnlich wie mit dem MR-Navigator.

Ferner wurde ein prospektiver PT-basierter Ansatz zur Bewegungskorrektur ent-

wickelt, der schon w¨

ahrend der Messung, eine atemangepasste Schichtmitf¨

uhrung

(Slice Tracking) erm¨

oglicht. Bewegungsartefakte in funktionellen Cine-Aufnahmen

mit kartesischem Aufnahmeschema konnten mit dieser prospektiven Bewegungskor-

rektur stark reduziert werden. Das Kontrast-Rausch-Verh¨

altnis in Bezug auf Be-

wegungsartefakte und auch die Kantensch¨

arfe des Endokards verbesserten sich im

Vergleich zu den unkorrigierten Bildern signifikant. Dar¨

uber hinaus wurden die links-

ventrikul¨

aren Blutpoolfl¨

achen bestimmt, wobei es keinen signifikanten Unterschied

zwischen der Referenzmethode und dem vorgestellten bewegungskorrigierten Ansatz

gab.

Ahnliche Verbesserungen wurden bei der quantitativen Messmethode T1-Mapping

erzielt. Hier wurde ein radiales Akquisitionsschema f¨

ur die Datenerfassung verwen-

det. Ohne Bewegungskorrektur f¨

uhrte die Atembewegung zu einer ¨

Ubersch¨

atzung

der T1-Werte im Vergleich zu den Referenzdaten, was mit der Anwendung der PT-

basierten Methode korrigiert werden konnte.

Die vorgestellten Ergebnisse zeigen, dass die PT-basierte Atembewegungskorrek-

tur robust, akkurat und vielseitig einsetzbar ist und damit zuk¨

unftigen Entwicklun-

gen, wie beispielsweise hochaufl¨

osenden Bildgebungsstrategien unter freier Atmung

den Weg ebnet.

Abstract

Cardiovascular disease (CVD), including coronary artery disease, heart failure,

cardiomyopathy, and myocarditis, accounts for 32% of deaths and remains the lead-

ing cause of death worldwide (17.9 million per year; WHO, 2019). In cardiology

Magnetic resonance imaging (MRI) is an essential clinical imaging tool because it

provides excellent soft-tissue contrast.

MR examination can be used to examine non-invasively various parameters of

the heart, providing information on, for example, functionality, blood flow, or tissue

composition. Depending on the intended application, different cardiac MRI tech-

niques are utilized. For example, cine MRI is suitable for visualizing cardiac motion

and regional wall motion abnormalities, while the assessment of the progression of

myocarditis can be achieved with the use of T1mapping.

Of disadvantage to many techniques are the long examination times mainly due

to physiological motion such as breathing. To ensure that image quality is not

compromised by motion artifacts, the breathhold strategy is commonly used in

clinical practice. But for a complete examination, the patients must manage several

instructed breath-holding phases, which can often be difficult for the sick, elderly,

or children.

Therefore, methods have been developed that allow cardiac MR examination un-

der free breathing. Often these approaches are based on an additional measurement

of an MR-navigator, which provides information about the respiratory motion state.

However, the MR-navigator is not suitable for continuous measurements because its

acquisition interrupts the steady-state during the measurement.

A novel alternative for a motion surrogate is the pilot tone (PT). The PT is

an additional RF signal introduced into the scanner, which can be extracted from

the acquired MR data during the measurement. The intensity of the scale-free

signal changes depending on the respiratory motion and can, therefore, be used as

a motion surrogate. Nevertheless, quantitative motion information is required for

motion correction.

In this thesis, a new PT-based method for respiratory motion correction for car-

diac MRI was developed. Using phantom- and in vivo data, it was demonstrated

that motion correction using the PT leads to an improvement in image quality and

accuracy of quantitative parameters compared with uncorrected images.

The temporal stability of the PT was shown for at least 50 min. Subject-specific

motion models were derived from a calibration scan, that allow to convert the quali-

tative PT into a quantitative signal providing information about respiratory motion.

Furthermore, a comparison of the PT with other motion surrogates was performed.

For a 3D MR scan, retrospective motion correction using the PT improved the

visibility of the coronary arteries similar to the MR-navigator.

Thereafter, a novel prospective PT-based motion correction approach was devel-

oped, which enables slice tracking during the running sequence. The quantitative

PT was used to adapt the slice position during the measurement to ensure the cur-

rent imaging slice follows the respiratory motion of the heart. Motion artifacts in

functional cine images with Cartesian acquisition scheme could be strongly reduced

with this prospective motion correction approach. The contrast-to-noise ratio with

respect to motion artifacts and also the sharpness of the endocardium improved

significantly compared with the uncorrected images. Furthermore, left ventricular

blood pool areas were determined, and there was no significant difference between

the reference breathhold method and the presented motion-corrected free-breathing

approach.

Similar improvements were achieved for quantitative T1-mapping of the my-

ocardium. Here a radial acquisition scheme was used for data acquisition. Without

motion correction respiratory motion led to an overestimation of T1values compared

to breathhold data, which was successfully corrected with the PT-based approach.

The presented results demonstrate that PT-based respiratory motion correction

is robust, accurate, and versatile, and thus may enable future developments such as

high-resolution imaging strategies under free-breathing.

Contents

Zusammenfassung ii

Abstract iv

Abbreviations ix

1 Introduction 1

1.1 Scopeofthisthesis ............................ 3

1.2 Outline................................... 3

2 Cardiac MRI and motion 5

2.1 Anatomy and physiology of the heart . . . . . . . . . . . . . . . . . . 5

2.2 Rapid cardiac imaging techniques . . . . . . . . . . . . . . . . . . . . 8

2.3 Cardiacmotion .............................. 8

2.4 Respiratory motion correction approaches . . . . . . . . . . . . . . . 9

2.5 Common applications of MR in radiology . . . . . . . . . . . . . . . . 13

3 Pilot tone 19

3.1 Introduction................................ 19

3.2 Methods.................................. 20

3.2.1 Phantomsetup .......................... 20

3.2.2 Pilot tone generation . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.3 Pilot tone acquisition . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.4 Pilot tone calculation . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Adjustable PT parameters . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Experiments................................ 27

3.4.1 Dataacquisition.......................... 27

3.4.2 Optimization of PT parameters . . . . . . . . . . . . . . . . . 27

3.5 Results................................... 28

3.5.1 PTamplitude........................... 28

3.5.2 PTfrequency ........................... 28

3.5.3 Artifact analysis . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6 Discussion................................. 33

3.7 Conclusion................................. 34

4 Calibration and temporal stability 35

4.1 Introduction................................ 35

4.2 Methods.................................. 36

4.2.1 Calibration ............................ 36

4.2.2 Motion model formation . . . . . . . . . . . . . . . . . . . . . 36

Contents vii

4.3 Experiments................................ 37

4.3.1 Calibrationscan.......................... 38

4.3.2 Registration of motion . . . . . . . . . . . . . . . . . . . . . . 38

4.3.3 Other motion surrogates . . . . . . . . . . . . . . . . . . . . . 38

4.3.4 Temporal stability of PT . . . . . . . . . . . . . . . . . . . . . 40

4.3.5 Temporal stability of three surrogates . . . . . . . . . . . . . . 41

4.4 Results................................... 42

4.4.1 Evaluation of temporal stability of PT . . . . . . . . . . . . . 42

4.4.2 Comparison of three motion surrogates . . . . . . . . . . . . . 46

4.5 Discussion................................. 48

4.6 Conclusion................................. 49

5 Respiratory motion correction 50

5.1 Introduction................................ 50

5.2 Methods.................................. 50

5.2.1 Retrospective motion correction with three surrogates . . . . . 50

5.2.2 Prospective motion correction with PT . . . . . . . . . . . . . 51

5.2.3 Online Signal Processing . . . . . . . . . . . . . . . . . . . . . 52

5.3 Experiments................................ 55

5.3.1 Motion correction . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3.2 Estimation of respiratory motion amplitudes . . . . . . . . . . 56

5.4 Results................................... 57

5.4.1 Retrospective motion correction . . . . . . . . . . . . . . . . . 57

5.4.2 Prospective motion correction . . . . . . . . . . . . . . . . . . 58

5.4.3 Range of respiratory motion magnitude . . . . . . . . . . . . . 58

5.5 Discussion................................. 60

5.6 Conclusion................................. 61

6 Pilot tone–based motion correction (PT-MOCO) for prospective res-

piratory compensated cardiac cine MRI 62

6.1 Introduction................................ 62

6.2 Methods.................................. 63

6.2.1 Prospective through-plane correction . . . . . . . . . . . . . . 64

6.2.2 Retrospective in-plane correction . . . . . . . . . . . . . . . . 64

6.3 Experiments................................ 65

6.3.1 Calibrationscan.......................... 65

6.3.2 Dynamicscan........................... 65

6.3.3 Cinescan ............................. 66

6.3.4 Analysis.............................. 66

6.4 Results................................... 67

6.4.1 Phantom.............................. 67

6.4.2 In vivo ............................... 67

viii Contents

6.5 Discussion................................. 73

6.6 Conclusion................................. 76

7 Pilot tone–based prospective correction of respiratory motion for free-

breathing myocardial T1 mapping and cine imaging 77

7.1 Introduction................................ 77

7.2 Methods.................................. 78

7.2.1 Calibrationscan.......................... 78

7.2.2 Continuous radial acquisition . . . . . . . . . . . . . . . . . . 79

7.2.3 Motion correction . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.4 Cine reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.5 T1 mapping analysis . . . . . . . . . . . . . . . . . . . . . . . 81

7.3 Experiments................................ 82

7.3.1 Scanparameters ......................... 83

7.3.2 Analysis.............................. 84

7.4 Results................................... 84

7.4.1 Phantom.............................. 84

7.4.2 In vivo ............................... 85

7.5 Discussion................................. 92

7.6 Conclusion................................. 94

8 Summary 95

References 99

List of Author’s Publications 115

List of Figures 116

List of Tables 117

Abbreviations

B0. . . . . . . . . . . . . Main magnetic field

T1. . . . . . . . . . . . . . Longitudinal relaxation time

T2. . . . . . . . . . . . . . Transverse relaxation time

4CHV . . . . . . . . . . 4-chamber view

AP . . . . . . . . . . . . . Anterior-posterior

BLAST . . . . . . . . Broad-use linear acquisition speed-up technique

bSSFP . . . . . . . . . Balanced steady-state free precession

CAD . . . . . . . . . . . Coronary artery disease

CMR . . . . . . . . . . . Cardiovascular magnetic resonance imaging

CNR . . . . . . . . . . . Contrast-to-noise ratio

CT . . . . . . . . . . . . . Computed tomography

CVD . . . . . . . . . . . Cardiovascular disease

ECG . . . . . . . . . . . Electrocardiogram

ECV . . . . . . . . . . . Extracellular volume

EF . . . . . . . . . . . . . Ejection fraction

FOV . . . . . . . . . . . Field of view

GRAPPA . . . . . . Generalized autocalibrating partial parallel acquisition

GRE . . . . . . . . . . . Gradient echo

HF . . . . . . . . . . . . . Head-feet

LA . . . . . . . . . . . . . Long axis orientation

LGE . . . . . . . . . . . Late-gadolinium enhancement

MR . . . . . . . . . . . . Magnetic resonance

MRF . . . . . . . . . . . Magnetic resonance fingerprinting

MRI . . . . . . . . . . . . Magnetic resonance imaging

PCA . . . . . . . . . . . Principal component analysis

PT . . . . . . . . . . . . . Pilot tone

PT-MOCO . . . . . Pilot tone-based motion correction

RF . . . . . . . . . . . . . Radio frequency

RL . . . . . . . . . . . . . Right-left

ROI . . . . . . . . . . . . Region of interest

SAX . . . . . . . . . . . Short axis orientation

SD . . . . . . . . . . . . . Standard deviation

SENSE . . . . . . . . . Sensitivity encoding

SNR . . . . . . . . . . . Signal-to-noise ratio

TI . . . . . . . . . . . . . . Inversion time

TR . . . . . . . . . . . . . Repetition time

1Introduction

In the last 60 years, the prevention, management, and treatment of cardiovascular

diseases (CVD) have advanced significantly. As a result, the worldwide CVD mor-

tality rate has already decreased by over 60%. An important factor driving this

development is the use of cardiovascular magnetic resonance imaging (CMR) [1].

CMR helps physicians to diagnose cardiac diseases, such as myocardial ischemia,

cardiomyopathies, myocarditis, iron overload, vascular diseases, and congenital heart

disease [2]. With the use of CMR, the beating heart and heart valves, as well as

coronary arteries and heart defects can be visualized and the viability of the heart

muscle can be assessed. Usually various imaging techniques are utilized to depict

the different cases of interest. Cine imaging, for example, is often used in clinical

routine because the heart motion is captured, which enables the assessment of the

heart function [3]. For the depiction of coronary arteries, 3D whole-heart imaging

is often utilized, and measurements of the spatial distribution of the T1relaxation

time allow assessment of diffuse fibrosis [4].

A major challenge of CMR is respiratory motion, as it causes artifacts in MR

images that can degrade the image quality strongly, impeding medical diagnosis.

Therefore, it is an important requirement for many 2D cardiac examinations that

patients hold their breath to suppress respiratory motion during the acquisition.

However, this can become a problem for some patient groups who cannot control

their breathing behavior, e.g., children or elderly [5]. Especially patients suffering

from cardiac diseases can find it very challenging to repeatedly hold their breath.

For 3D imaging, respiratory gating techniques based on the so called MR-

navigator is commonly used. The MR-navigator monitors the motion of the right

hemidiaphragm by an additional MR measurement, which is interleaved within the

MR scan. Only data from a specific respiratory phase and not all available data

are used for the final image reconstruction [6–8]. This reduces respiratory motion

artifacts but leads to longer scan times.

To address this issue, respiratory motion correction methods have been developed

that allow free-breathing CMR. These methods can be subdivided into retrospective

and prospective approaches. Retrospective approaches apply a motion correction

after data acquisition. This type of correction is suitable for 3D whole-heart imaging

because motion is captured in all three spatial directions and can retrospectively be

corrected. However, for 2D imaging, like cine imaging or T1mapping, retrospective

motion correction refers only to the motion captured in the image plane, whereas a

correction of through-plane motion is not possible.

To minimize through-plane motion, slice tracking, often based on the MR-

navigator, can be used. Slice tracking is an efficient through-plane motion cor-

rection method, where the slice position is updated according to the respiratory

motion in real-time during data acquisition. However, for the acquisition of the

MR-navigator, additional radio frequency (RF) pulses are used in the acquisition

sequence and, consequently, it is not applicable to continuous scans, i.e., scans that

cannot be interrupted because the magnetization of the continuous scan would be

disturbed.

For continuous scans, other motion surrogates describing the respiratory motion

must be used. The surrogate information can be evaluated during the measurement,

and thus enable a prospective respiratory motion correction. Respiratory belts, for

example, are suitable for this purpose. Respiratory belts are strapped around the

body and measure the change in circumference at a certain position based on an

air pressure method, but they can suffer from signal drifts and are mainly used for

gating rather than motion correction [9].

Recently a new approach, the pilot tone (PT) technology, was introduced to de-

termine respiratory motion [10]. The PT is an RF signal sent into the bore of the

scanner. Its signal intensity is modulated by the underlying tissue motion and it

can be extracted in real-time from the acquired MR data. The PT signal is a useful

tool to monitor patient motion but it does not provide any quantitative information

about organ motion.

A particular advantage of the PT over the MR-navigator is, that the PT is appli-

cable for continuous imaging sequences because image data recording does not have

to be interrupted. Although the PT is an external surrogate created by a setup

separated from the MR scanner, no effort must be made regarding the temporal

synchronization with the MR data. Because the PT is extracted from the MR raw

data, it is intrinsically synchronous with the MR acquisition.

In order to exploit the PT regarding promising new capabilities for motion nav-

igation, it is currently being investigated for many applications. The PT has been

used so far for monitoring respiratory motion [10, 11].

In this thesis the question to be addressed is: Can the PT be used for a reliable

prospective respiratory motion correction for cardiac MRI?

This question divides into the following aspects:

1. The pilot tone as a qualitative signal must be converted into a quantitative

signal describing the heart motion with high temporal resolution, in order to

allow reliable rigid motion correction.

2. For prospective motion correction the slice position is updated in real-time

during a scan. A framework must be developed which can access the PT and

apply a position shift for the current slice.

3. There may still be remaining non-rigid motion, not captured with the PT,

that affects the image quality. The prospective correction must, therefore, be

combined with a retrospective approach to correct for residual motion.

1.1 Scope of this thesis 3

1.1 Scope of this thesis

In this work, a novel PT-based motion correction method is developed and its ap-

plication is demonstrated with 3D whole-heart imaging, 2D cine imaging and 2D T1

mapping.

1. A PT signal is generated and analyzed regarding its robustness. The PT signal

is then quantified by calibrating it to the registered motion via motion models.

2. The PT is compared to other commonly used motion surrogates, i.e., MR-

navigator and respiratory belt. 3D data is motion corrected retrospectively

using three surrogates.

3. Further an online-framework is developed that enables translational PT-based

prospective motion correction (slice tracking). The prospective correction is

presented on free-breathing 2D cine data acquired with Cartesian trajectory.

4. A non-rigid retrospective correction is performed additionally to the prospec-

tive rigid correction using a T1mapping sequence with radial trajectory.

1.2 Outline

This thesis contains eight chapters:

Chapter 2 The structure and physiology of the heart will be presented, as well as

fast techniques to acquire cardiac MRI data. Thereafter, strategies will be

discussed, that correct for cardiac- and respiratory motion during the MR

acquisition. The chapter finishes with three important applications of MR in

radiology and their respective use cases for the heart, 3D anatomical imaging,

cine imaging and T1relaxation time mapping.

Chapter 3 The PT is introduced as a novel motion surrogate and the experimental

setup, acquisition and signal extraction are demonstrated. In addition, the op-

timal parameter settings are identified to obtain a stable signal. Furthermore,

a method to minimize image impairment is described and frequently occurring

artifacts are presented.

Chapter 4 A calibration scan is developed to correlate the PT with the cardiac

motion. Subject-specific linear motion models are derived from the data and

the initially qualitative PT signal is converted into a quantitative signal which

provides heart position values. Furthermore, the PT is compared with other

common motion surrogates, i.e., the MR-navigator and respiratory belts. Also,

the long-term stability of the PT and its robustness are evaluated on a motion

phantom and healthy subjects.

41.2 Outline

Chapter 5 The three motion surrogates introduced in chapter 4 are now used for a

retrospective motion correction of 3D anatomical images of the heart. In a fur-

ther step, a first proof-of-concept of a PT-based prospective motion correction

is performed on dynamic 2D cardiac images with transverse orientation. Also,

an existing dataset of 23 subjects is analyzed with respect to the predominant

respiratory cardiac motion directions.

Chapter 6 This chapter demonstrates the PT-based prospective motion correction

for free-breathing cine imaging. For this clinically relevant application, var-

ious angulated (oblique) slices of the heart are recorded during continuous

measurements. Phantom and in vivo measurements are performed, motion

models are derived, and the new correction approach is applied to Cartesian

cine imaging.

Chapter 7 The prospective motion correction approach is extended by an image-

based non-rigid retrospective correction. The additional correction relies on

motion fields and the PT. The combined approach is applied to T1mapping

and cine imaging on a phantom and healthy subjects. The T1maps and

cine images are reconstructed from data acquired using a continuous radial

trajectory.

Chapter 8 The main results of this work are shortly presented and the challenges

that still need to be overcome for future application areas are discussed.

2Cardiac MRI and motion

Significant advances in cardiovascular MRI have been accomplished over the past

few decades. Today, various cardiac magnetic resonance imaging techniques exist,

that allow non-invasive assessment of cardiac anatomy, function, tissue composition,

and disease progression. Other diagnostic imaging modalities such as echocardiog-

raphy or X-ray computed tomography are also available for the examination of the

heart [12–14], but CMR stands out for its superior soft-tissue characterization and

versatility with regards to the diagnosis and treatment assessment of patients [15].

This chapter begins with an overview of the anatomy and function of the heart

as well as the challenges for cardiac MRI arising due to physiological motion associ-

ated with breathing and the heartbeat. Current methods for motion correction are

discussed. Further, three common applications of MR in radiology are presented.

2.1 Anatomy and physiology of the heart

This section is based on the references [16–19].

The heart, as the central organ of the blood circuit, serves mainly as a pump to

transport 5-6 liter per minute of blood through the body. The heart weighs ≈300 g,

has a size of ≈(12×8×6) cm and is located in the mediastinum between the lungs

and the diaphragm. The longitudinal axis of the heart runs from the base to the

apex. Figure 2.1A illustrates the anatomy of the heart and Figure 2.1B its position

in the thorax. On the inner surface of the muscle is the endocardium, on the outer

surface the epicardium, which covers the myocardium and the coronary vessels and

secretes a fluid that allows the heart to move freely within the sac, the pericardium.

Anatomically, the heart consists of two ventricles, two atria, and four valves at-

tached to connective tissue rings of the cardiac skeleton shown in Figure 2.1C. The

two ventricles are separated by the septum, labeled in Figure 2.1A. The mitral

and tricuspid valves (atrioventricular valves), separate the atria from the ventri-

cles. These valves act like inlet valves. The aortic and pulmonary valves (semilunar

valves) are located at the outlet of the arterial outflow tracts from the ventricles.

Coronary vessels surround the heart muscle in the shape of a crown and originate

from the aorta directly after its exit from the left ventricle. They supply the heart

muscle tissue with oxygen and nutrients. About 5% of the cardiac output flows

through the coronary arteries. Under physical stress, blood flow can increase up

to fourfold. An occlusion in the coronary arteries often results in undersupply of

the heart resulting in infarction of myocardium. More information on the disease of

coronary heart vessels can be found in section 2.5.

The myocardium or heart muscle contributes the majority of the cardiac mass. Its

62.1 Anatomy and physiology of the heart

(A)

Superior vena cava

Right atrium

Right ventricle

Right coronary artery

Septum

Pulmonary valve

Tricuspid valve

Aorta

Pulmonary artery

Pulmonary vein

Left ventricle

Mitral valve

Left atrium

Aortic valve

Left coronary artery

Inferior

vena cava

(B)

Posterior

Left side

of heart

Right side

of heart

Pulmonary

valve

Mitral valve

Tricuspid

valve

Aortic valve

His bundle

Cardiac

skeleton

(C)

Right coronary

artery

Left coronary

artery

Right

ventricle

Left ventricle

Diaphragm

Aorta

Right

atrium

Diaphragm

Aorta abdominalis

Figure 2.1: (A) Anatomy of the heart (B) Heart position in the thorax (C) Cardiac

valves. Illustration based on [16], p. 25

glycogen-rich muscle fibers transport excitation signals, that trigger the rhythmic

contractions and relaxation phases. In consequence of the contraction of the heart

chambers, blood is transported through the body. Two blood flow circuits are

supported by the heart, the small circuit, which is the pulmonary circuit, and the

large circuit, which supplies organs and the body’s periphery. Figure 2.2 illustrates

the blood circulation in the body. Because the left ventricle myocardium pumps

blood throughout the body circuit at higher pressure it is stronger and bigger than

the right ventricle, which supplies only the pulmonary circulation at much lower

pressure. The same applies to the associated valves. The pulmonary valve and the

aortic valve have a similar structure, however, the aortic valve is thicker and bigger

than the pulmonary valve due to higher pressure conditions and mechanical stresses.

The cardiac cycle can be separated into the two phases systole and diastole. Inlet

valves control the bloodflow and pressure in the ventricles and atria. When the

pressure in the ventricles exceeds the pressure in the atria, systole, i.e., the contrac-

tion phase, begins. The ventricles pump about 70 ml of blood through the aortic

and pulmonary valves into the aorta and the arteria pulmonalis. After the ven-

2.1 Anatomy and physiology of the heart 7

Capillary system of the head

Capillary system of the lungs

Right atrium

Aorta

Pulmonary artery

Pulmonary vein

Left atrium

Left ventricle

Right ventricle

Lung

Capillary system of the body

Vena cava

Septum

Circulation with oxygen rich blood

Circulation with oxygen poor blood

Figure 2.2: Illustration of blood circulation in the body based on [20]

tricular ejection the relaxation phase begins. Because the pressure in the ventricles

decreased, the atrioventricular valves open to allow blood to enter from the atria

into the ventricles. This ventricular filling phase is called diastole. Through the

right atrium flows oxygen-poor blood, through the left atrium enters oxygen-rich

blood from the pulmonary cycle. When the ventricle pressure level is above the

atria pressure, the atrioventricular valves close and systole begins.

60-100 electronic impulses per minute passing through the His bundle from the

atria through the septum down to the apex stimulate the heartbeat. Figure 2.3

shows an illustration of an ECG signal with indicated QRS-complex, T-wave and

P-wave. The atrias systole occurs slightly earlier than the ventricles systole, and

right before the R-peak of the ECG signal. The ventricles systole begins with the

R-peak of the ECG signal and lasts about 400 ms [21].

RR cycle

Systole Diastole

Figure 2.3: ECG illustration with indicated systole and diastole of the ventricles

82.2 Rapid cardiac imaging techniques

2.2 Rapid cardiac imaging techniques

A main challenge of cardiac MRI is physiological motion. Imaging strategies have

been developed that allow high-speed data acquisition, thus minimizing the effects

of motion. For example, Low flip-angle gradient-echo (GRE) techniques enable very

short repetition times (TR). Balanced steady-state-free-precession techniques with

fully-balanced magnetic field gradients yield excellent contrast between myocardium

and blood with very short scan times [22].

Multi-coil parallel imaging techniques have achieved further advancement in data

acquisition speed. For cardiac imaging, the broad-use linear acquisition speed-up

technique (BLAST), or k-t sensitivity encoding (SENSE), or generalized autocali-

brating partially parallel acquisition (GRAPPA) are common time-saving strategies

[23, 24]. Using these techniques, k-space is effectively undersampled, i.e., many k-

space lines are omitted from the recording, while regions of k-space are sampled more

densely. The missing k-space lines are then estimated from previously gained cali-

bration data and/or knowledge of coil sensitivities [25, 26]. Undersampling factors

correspond directly to the time saved during acquisition.

Despite these advances in imaging speed, physiological motion is still a challenge.

In the following, different approaches to compensate for motion are discussed.

2.3 Cardiac motion

The heart motion can vary between heartbeats also due to the changing respiratory

position in the thorax. Breathholding phases, in particular, have an influence on

cardiac motion induced by heartbeat. The major components of left ventricular

motion are longitudinal shortening, radial contraction, and opposite-hand rotation

of the apex of the chamber relative to the base [27, 28].

Cardiac gating Heart motion can cause image artifacts in CMR. Therefore, motion

compensation strategies need to be applied. A straight forward way to minimize car-

diac motion is gating. Here only k-space data of a predefined cardiac motion window

and not of the entire cardiac cycle is used for image acquisition or reconstruction.

Using prospective ECG gating, the acquisition window is placed in a part of the

cardiac phase where motion is minimal, i.e., in diastole. A trigger delay is predefined

and valid for all heartbeats during the acquisition. The data acquisition is initiated

depending on the R-peak of the ECG signal. K-space is then filled over several RR

cycles.

For retrospective gating, the acquired data are resorted based on the ECG signal

and assigned to cardiac phases. To record the ECG signal, electrodes are a common

choice, but also other techniques, e.g., self-gating, exist, where the heart motion is

retrieved from the MR data.

2.4 Respiratory motion correction approaches 9

Free-breathing Breathhold

400

800

1200

1600

2000

Figure 2.4: Left: Free-breathing sagittal cine images (top) and short axis T1maps

(bottom) with motion artifacts. Right: Breathhold data

2.4 Respiratory motion correction approaches

Besides cardiac motion, respiratory-induced motion plays an important role in CMR.

During respiration, the inflation of the lungs displaces surrounding tissue and induces

cardiac motion. The most pronounced motion component is the head-feet direction

[29]. Between inhalation and exhalation, the heart can be displaced about 30 mm

[30].

These displacements can introduce strong motion artifacts in the reconstructed

images, like ghosting, blurring, signal cancellation, or misregistration [31]. For illus-

tration purposes, Figure 2.4 (top) shows a free-breathing cine image with impaired

image quality next to a breathhold image. Exemplary T1maps are shown at the

bottom of the figure.

In clinical routine, to reduce respiratory motion artifacts, often instructed breath-

holding (10-30 s) is performed when acquiring heart images [32, 33]. To cover the

whole heart or achieve a higher signal-to-noise ratio (SNR) or resolution, multiple

breathholds are required [34]. This implies the need for dedicated operator in-

volvement and high patient collaboration [35]. Despite optimal patient engagement,

respiratory drift can occur even during the breathhold phase, which also promotes

artifacts [5, 36]. Further strategies have been developed to correct for drift during

breathhold [28]. However, other solutions are necessary for patients who cannot

hold their breath, e.g., elderly, lung diseased, or children.

10 2.4 Respiratory motion correction approaches

Respiratory gating Respiratory gating techniques are utilized that minimize res-

piratory motion artifacts during free-breathing acquisitions [37]. Commonly, an MR

data-based navigator is used to determine the respiratory motion state of the heart.

Suitable monitoring regions are the chest wall, the heart, or the liver-lung interface.

In the clinical setting, the MR-navigator, also referred to as pencil beam or liver

navigator, is the tool of choice. The MR-navigator is a 2D column of magnetiza-

tion covering the right hemidiaphragm, which is frequently excited before image

acquisition. The dome of the right hemidiaphragm offers good conditions for clear

edge detection in the profile and the resulting motion information can be used as

motion surrogate [28, 38]. One shortcoming of the MR-navigator is that the acqui-

sition of diagnostic image information has to be interrupted for the acquisition of

the navigator data [6].

In a retrospective application of the gating method, a high amount of data is

recorded and the subsequent image reconstruction is based only on data acquired in

the predefined breathing state [6, 37, 39].

Mostly, however, the gating method is used in real time, i.e., data is only recorded

if the navigator indicates the predefined breathing state. The acquisition window is

commonly set at end-exhale, because this is a quiescent and reproducible phase in

the respiratory cycle [40]. This means that only a fraction of the actual scan time is

used for data acquisition, resulting in low scan efficiency and an unnecessary burden

on patients.

The MR-navigator technique can also be combined with prospective motion cor-

rection (slice tracking), where the acquisition scheme is adapted to the breathing

motion and compensates for it. For this, the navigator information is used to up-

date the slice position before every spin excitation [7, 41–43]. More about the slice

tracking method will follow in the next paragraph and the chapters 5 and 6.

Prospective motion correction A prospective correction enables the possibility

for through-plane correction and requires rapid processing [44]. Information about

the respiratory cycle must be available during the measurement so that respiratory

gating or a slice adaption can be performed during the running sequence.

The approach of prospective slice tracking for free-breathing MRI is very intuitive.

The image slice or volume position should follow the motion of the heart in real-

time [42]. This is achieved by adjusting the radio frequency (RF) pulses or the

magnetic gradients accordingly [45]. For rotations, the encoding gradients must

be rotated. Translational motion can be corrected by adjusting the transmit and

receive frequencies and -phases [46, 47]. A correction of linear expanding objects is

achieved by scaling the readout gradient [48].

Different regions in the body, e.g., liver or heart, move differently due to respi-

ration. Slice tracking can improve image quality only for areas that move like the

tracked slice. If the slice tracking is, for example, applied for the moving heart,

static anatomies (e.g, spine and back) will be wrongly corrected and artifacts will

2.4 Respiratory motion correction approaches 11

be introduced. The steady-state magnetization is preserved in the moving region of

interest (ROI) by slice tracking, whereas other regions may not achieve steady-state

magnetization.

For more information on prospective motion correction, please refer to chapters

5 and 6, where the slice tracking method is explained in detail. The section 5.2.3,

deals with the specifics of the implementation.

Retrospective motion correction While prospective correction methods avoid the

corruption of data by motion during the measurement, retrospective corrections

allow to compensate for motion after the measurement.

The commonly utilized strategy for free-breathing acquisitions is retrospective

gating [49, 50], which may lead to low scan efficiencies.

However, with the possibility of high computational power, retrospective motion

corrections incorporate sophisticated motion models, that enable, for example, high-

resolution motion registration and iterative motion correction for non-rigid motion

[45]. These approaches can provide scan efficiency to almost 100% by applying

motion fields to the recorded data [51, 52]. In principle, motion trajectories may

be estimated intrinsically from the measured data or from a navigator. Based on

the motion information the acquired data can be subdivided into small subsets

each containing data of an individual motion state [49, 53]. Data is then sorted

into different motion bins and images are reconstructed of each individual phase

separately. To correct for respiratory motion, motion fields between the binned

images are estimated and the different data is transformed to the same reference

motion state.

The calculated motion fields can then either be integrated into the image recon-

struction [40, 54, 55] or applied afterwards [52, 56] to minimize respiratory motion

artefacts in the images. Transformation models, which consider only affine trans-

formations can even be applied before reconstruction on the k-space data [40, 57].

From the Fourier theorem, a translational motion of the heart is corrected, by mul-

tiplying a phase factor to the k-space data. A rotation of the heart results in a

rotation of the k-space. Iterative approaches can improve the reconstruction scheme

[58].

A major drawback of retrospective correction is that through-plane motion for 2D

images cannot be corrected after the measurement. For 2D data the retrospective

correction is only effective in-plane.

Motion surrogates Information about cardiac motion is obtained by motion sur-

rogates. As discussed in section 2.4 on respiratory gating, the MR-navigator is well

suited as a motion surrogate, but cannot be applied to all sequences.

MR-independent external surrogates provide the advantage of being available re-

gardless of the sequence.

12 2.4 Respiratory motion correction approaches

An established modality offering high temporal resolution signals is the respi-

ratory belt [9]. Respiratory belts are based on air pressure systems and measure

the change in circumference of the patient’s thorax. Prior knowledge about the

breathing behavior can improve positioning. A signal phase shift is expected when

using this modality, because the strongest motion component during respiration is

in HF direction [51], while the respiratory belts monitor only the displacements in

anterior-posterior (AP) and right-left (RL) direction. Disadvantages of respiratory

belts are that signals are prone to drifts [9], patient preparation time is high and

patient comfort is affected especially for those with surgical wounds.

Furthermore, there exist respiratory cushions that are positioned below the pa-

tient. These are also based on air pressure variations but monitor less of the respi-

ratory movement because they only cover a small area of the bodies circumference

[9].

There are several other external surrogates which have been proposed such as

nasal airflow sensors, optical systems and ultrasound-based approaches [35, 37, 59–

62].

A promising non-contact motion tracking system, which has been little explored

to date is the radar. The radar’s electromagnetic waves can penetrate MRI RF coils,

clothing, and a few cm of tissue to register the movement of the thorax and even

the heartbeat at low amplitudes (≈0.1 mm). The signal is acquired simultaneously

but independent of the MR data and its frequency ranges roughly between 1.5 GHz

and 9 GHz [63–65].

The aforementioned external navigator strategies bear drawbacks of requiring

additional patient preparation time, not being well accepted by patients or simplistic

assumptions regarding the relationship between navigator signal and cardiac motion

[28].

There are other MR-based methods used for motion correction that do not affect

steady-state magnetization during image acquisition. The following methods rely

on the principle that moving tissue impacts the RF coil impedance, and thus causes

variations in receive signal [66]. In 1988 Buikman et al. exploited the RF receive

coils as respiratory and cardiac motion detectors [67] and in 2010, Graesslin et al.

monitored respiratory motion by using dedicated RF pick-up coils [68]. Nevertheless,

the imaging sequences must be strongly modified such that the SNR of the coils is

improved and motion information can be derived from the signals, which makes

it difficult to easily convert it to a large number of specific MR sequences. In

2014, Andreychenko et al. observed the respiratory motion-dependent thermal noise

variance of the receiver coils, which is directly linked to the impedance of the coil

[69, 70]. However, a disadvantage of this method is that the RF and gradient parts

of the sequence need to be switched off for the noise sampling [71].

Other MR-intrinsic methods for motion compensation include k-space-based and

image-based self-navigation [72–74]. These either extract the respiratory motion

information from the MR data itself or they employ separate real-time data acquisi-

2.5 Common applications of MR in radiology 13

tions interleaved with the MR sequence to provide instantaneous snapshots of one or

more motion dimensions. Real-time navigators have been implemented in different

ways [51, 75].

A 0-dimensional navigator extracted from the MR data can serve for k-space-based

motion monitoring. Here, the k-space center is frequently recorded and monitored

[44, 76]. This method is especially suited for non-Cartesian sampling schemes, where

the k-space center is sampled multiple times and no additional RF pulse needs to

be applied to acquire navigator data [73].

A 1-dimensional signal acquired on the dome of the right hemidiaphragm also

proved to be useful [77]. The navigator signal can be displayed as lines of data after

reconstruction. This pencil beam navigator tracks the FH motion of the diaphragm

which is directly linked to the motion of the heart with a correlation factor of 0.6

[38, 50, 78, 79].

Two-dimensional or 3-dimensional image-based navigators can be obtained from

low-resolution and/or highly undersampled data acquisition [80–82]. These naviga-

tors have the advantage that motion parameters can be derived directly from the

cardiac region but they require dedicated navigator scan planning [29, 83].

A solution that can be used for either Cartesian or non-Cartesian sampling

schemes and does not rely on sequence inherent MR pulses is the recently intro-

duced pilot tone [10]. The PT is an additional RF signal send into the scanner by

an external emitter coil. The signal is recorded in the MR data but outside the field

of view, in the oversampling region of each readout. It can, therefore, be classified

as a 0-dimensional navigator. Like the noise variance- and extra pick-up coil strate-

gies, this technology is based on the variability of the coil load depending on the

composition of the surrounding tissue. The PT will be discussed in detail in the

next chapter.

2.5 Common applications of MR in radiology

3D anatomical imaging The single largest cause of death in the world is coronary

artery disease (CAD) [84, 85]. One characteristic of this disease, also referred to

as coronary heart disease or ischemic heart disease, is the build-up of plaque in

the coronary arteries, as illustrated in Figure 2.5. This results in reduced blood

flow, which can lead amongst others to myocardial infarction or sudden death [84].

Preferred diagnostic modalities for the detection of CAD are echocardiograms, CT

and angiograms [78, 86, 87].

With MR angiography areas of narrowing or obstruction in a coronary artery can

be observed. Because MR angiography requires high spatial resolution to capture

the small coronary arteries and blocked areas, it is very time consuming and hence

challenging to apply in clinical routine [88]. In addition to the time it takes to acquire

all the required k-space information, scan times are prolonged due to cardiac and

respiratory motion, which was discussed in sections 2.3 and 2.4.

14 2.5 Common applications of MR in radiology

Coronary artery

Perfusion defect

Healthy heart muscle

Blood clot blocks artery

Plaque build up in artery

Blocked blood flow

Figure 2.5: Illustration of build-up plague in the coronary artery and blocked blood

flow based on [89]

Functional assessment In clinical routine, cine imaging is used to visualize cardiac

function, determine volume and mass and to investigate abnormal myocardial con-

tractility [90]. With this imaging technique local defects, enlargement of the atria

or abnormal tricuspid valves can be diagnosed [91, 92]. Typically, 10-30 cardiac

phases are depicted for several slice positions. Cines of short axis orientation (SAX)

and long axis orientation (LA) are acquired during several breathholds. For 2D cine

imaging, balanced steady-state free precession (bSSFP) techniques are well suited

[93]. Their contrast is proportional to the ratio T2/T1leading to a high contrast

between blood (high signal) and myocardium (low signal) [94], with T1being the

longitudinal- and T2the transverse relaxation time. Also gradient-echo techniques

are commonly used for cardiac cine imaging. These sequences avoid banding arti-

facts, which are often seen as a result of signal modulation due to B0(main magnetic

field) inhomogeneity [95].

A cardiac sequence is usually ECG-triggered and continues to play out RF pulses

for the complete scan period in order to maintain a steady-state magnetization.

To acquire the maximum amount of data during a scan, segmented k-space ap-

proaches are used [96], as illustrated in Figure 2.6. During several RR cycles, data

of different cardiac phases are recorded until k-space for all cardiac phases has been

completely scanned, which can be possible within one breathhold. Then, data is

binned retrospectively to the cardiac phase using the ECG signal, and images are

reconstructed for each cardiac phase specifically.

In addition to the visual evaluation of the cine images, diagnostic measures such

as the ejection fraction can be calculated from the images.

For this purpose, a stack of end-diastolic and end-systolic images covering the

entire left ventricle is acquired. The blood pool volumes, i.e., end-diastolic volume

(EDV) and end-systolic volume (ESV), are then determined by multiplying the

2.5 Common applications of MR in radiology 15

...

RR cycle

Phase 1 Phase 2

RF Echo

...

Phase N Phase 1 Phase N

Phase 2

Figure 2.6: Map of k-space demonstrates the segmented acquisition for N cardiac

phases. Illustration based on [97]

respective blood pool areas with the slice thickness and summing across all slices.

The difference between EDV and ESV is the volume of blood ejected every cardiac

cycle, also called stroke volume (SV) [97]:

SV =EDV −ESV. (1)

The ejection fraction (EF) is then the percentage of blood ejected in each heartbeat

with reference to the end-diastolic volume [98] and is calculated with

EF =SV

EDV ×100%.(2)

For information about motion correction on cine imaging and calculations regard-

ing the EF, please refer to chapter 6.

Myocardial characterization There are several methods that are particularly use-

ful for myocardial tissue characterization. For example, T2mapping is suitable for

myocardial edema identification [99] and T∗

2mapping can be used for detecting my-

ocardial iron accumulation in iron storage diseases [100]. The quantification method

that will be discussed in more detail in this section is T1mapping. This technique

is particularly suitable for the detection of fibrosis.

Fibrosis is the pathological process in which increased myocardial collagen depo-

sition occurs as a consequence of various diseases such as hypertensive heart disease,

diabetic hypertrophic cardiomyopathy and idiopathic dilated cardiomyopathy [101,

102]. Fibrosis leads to abnormalities in matrix composition and quality, and is as-

sociated with deteriorated left ventricular function, arrhythmia, and increased mor-

tality, which are linked to heart failure and sudden cardiac death [103–105]. There

are two classes of fibrosis: replacement fibrosis and diffuse interstitial fibrosis.

The reference standards for non-invasive imaging of myocardial scar and fibrosis

in cardiomyopathy are Late-Gadolinium Enhancement (LGE) techniques and T1

16 2.5 Common applications of MR in radiology

mapping [106–108]. Gadolinium-based contrast agents shorten the T1times of tissues

in which they accumulate, resulting in high signal intensity in T1weighted images.

To detect diseased tissue, the signal of healthy and diseased regions must generate

a contrast between the two tissue types. But for diffuse interstitial fibrosis, where

diseased tissue can no longer be distinguished from normal healthy myocardium

and no contrast can be detected, LGE imaging reaches its limits [107]. Here, the

quantitative imaging method T1mapping can be used, also allowing comparison of

tissue between different subjects or between follow-up examinations [15].

T1maps and T1weighted images rely on the T1relaxation time, meaning the

time it takes for the longitudinal magnetization to return to the equilibrium state

after excitation by an RF pulse. The longitudinal relaxation time contributes to the

high degree of soft-tissue contrast in CMR and can be used for myocardial tissue

quantification [109].

For a long time, only T1weighted images showing different voxel intensities were

available to detect pathologies, such as acute myocardial infarction, chronic scar

tissue or fatty infiltration in myocardial tissue. But diffuse, reactive fibrosis is char-

acterized by an increased accumulation of collagen in the heart, which causes only

very diffuse structural changes that cannot be detected with T1weighted images

[110].

In comparison to T1weighted images, where a contrast is created in arbitrary

units, T1mapping has the advantage that each voxel can be assigned a quantitative

voxel value, and thus color-encoded T1maps can be generated. Vendors supply

corresponding color maps to facilitate diagnosis.

Because T1depends on different tissue compositions, it is used as a biomarker for

many myocardial pathological conditions such as iron overload, myocardial edema,

and the presence of myocardial infarcts and scarring [110]. With T1mapping even

diffuse fibrosis can be detected without the presence of healthy tissue [111]. T1values

are higher for voxels containing fibrotic cells [15]. When T1mapping is performed

before and after injection of a contrast agent, the diagnostic parameter, extracellular

volume (ECV) can be determined. The ECV provides information about the relative

expansion of the extracellular matrix as a result of diffuse reactive fibrosis in various

cardiac diseases [110].

Also normal and fibrotic myocardium can be differentiated because T1times are

sensitive to fibrotic changes [111].

To measure the T1relaxation times very accurately, several inversion recovery

pulses with varying inversion times (TI) are necessary. The signal intensity SI at

each TI is given by

SI(TI) = M0[︃1−2 exp (︃−TI

T1)︃+ exp (︃−TR −TI

T1)︃]︃.(3)

But this gold-standard accurate measurement technique is very time-consuming

because very long repetitions times (TR) are required to restore full longitudinal

2.5 Common applications of MR in radiology 17

magnetization M0[97]. It is, therefore, not practical in clinical routine.

A faster alternative for acquiring T1maps is the Look-Locker method [112]. Here,

an inversion pulse is played out at the beginning of the sequence followed by a series

of low flip angle αpulses. With each αpulse, the magnetization Mzis slightly

flipped into the transverse direction so that a signal of Mzsin αcan be measured.

Each application of the αpulse leads to a small loss in the total longitudinal mag-

netization. Therefore, instead of the longitudinal relaxation time T1, an effective

relaxation time T∗

1is obtained [113]:

T∗

1=[︃1

−1

ln(cos α)]︃−1

.(4)

With TR≪T∗

1, the equilibrium magnetization M0is not reached anymore, instead

the effective magnetization M∗

0is determined with

M∗

0≈M0

T∗

.(5)

As Mzrelaxes from −M0to M∗

0, the low flip angle pulses generate an image series

that show this relaxation process [97]:

Mz(t) = M∗

0−(M0+M∗

0) exp (︃−t

T∗

1)︃.(6)

The adapted Look-Locker method is the MOdified Look-Locker Imaging (MOLLI)

sequence [114, 115] which is suitable for cardiac imaging within one breathhold.

Figure 2.7A illustrates the original 3(3)3(3)5 scheme of the MOLLI. This breathhold

scan is ECG-triggered, such that it captures data in a predefined cardiac phase, and

acquired during 17 heartbeats. It starts with an inversion pulse, followed by 3

αpulses and a recovery period. This part is then repeated and after the second

recovery period the third inversion pulse is played out, followed by 5 αpulses. In

Figure 2.7B data is sorted according to their inversion recovery times (TI), and a

T1model is fitted to the data. The model calculation is described by [114]. The

acquired images are sorted with respect to their accumulative time from inversion

(t) given by

t=TI + (n−1)RR, (7)

where RR and nare the heartbeat interval and image number, respectively. Knowing

the signal intensity SI, a voxelwise three-parameter fitting algorithm [116, 117] is

then applied to estimate A, B and T∗

1with

SI =A−Bexp (︃−t

T∗

1)︃.(8)

T1can then be calculated voxel-wise with the estimated parameters using

18 2.5 Common applications of MR in radiology

R-R cycle

(A)

(B) (C)

Recovery period 1

TI=100 ms TI=200 ms TI=350 ms

Recovery period 2

Time (ms)

Signal

1000 2000 3000

Figure 2.7: (A) 3(3)3(3)5 scheme with Modified Look-Locker Imaging (MOLLI) over-

layed on an ECG signal. The yellow bars indicate the inversion pulses, and the red,

green, and blue bars are bSSFP images with αexcitation pulses. (B) Images are used

for the fitting of a magnitude inversion recovery model to estimate T1. (C) a T1map.

Illustration based on [97], p. 329

T1=T∗

1[︃B

A−1]︃.(9)

Figure 2.7C shows a calculated T1map of a heart in SAX. Besides the 3(3)3(3)5

MOLLI, there are other MOLLI scanning schemes and methods that are suitable

for shorter breathhold durations, such as shortened MOLLI (ShMolli) [118]. Again

other T1mapping methods rely on variable flip angles [119] or saturation pulses

[120].

3Pilot tone

3.1 Introduction

The proof-of concept showing that the use of the PT could enable patient motion

monitoring in the future was first published and patented in 2015 [10, 121]. Speier

et al. proved on three different MR scanners that a coherent signal emitted by

an external source and received in parallel with the MR signal exhibits respiratory

motion patterns. The technology is based on the principle of inductive coupling

between the PT emitter coil and the MR scanner’s receive coils [122]. The underlying

moving tissue causes coil load variations which result in small variations in the

receive signals. Predominantly the respiratory motion is visible in the PT signal,

but the heartbeat can also be extracted from the signal.

There have been several developments in the field of respiratory and cardiac mo-

tion detection based on the PT signal [123–125]. In particular, it was shown that

the PT is independent of k-space sampling, that the PT is available with a high

temporal resolution, and that the PT can map respiratory motion information of

the heart [11]. It was further shown that respiratory motion could be characterized

for two dimensions with the PT [11].

Further research activities focused on using the PT as a substitute for an electro-

cardiogram to perform cardiac triggering [123, 125]. For this approach, the cardiac

signal component is separated from the respiratory signal by an independent com-

ponent analysis, and an extended Kalman filter is applied to the signal to obtain a

real-time noise reduced PT signal [126]. Based on in vivo cine images it has been

shown that the PT is capable of cardiac triggering [127]. Furthermore, the PT can

be used to quantify head motion [128]. In a model experiment on a volunteer, it was

shown that guided ”yes” and ”no” motions with the head, could be discriminated

with the PT.

The PT has also been used to detect respiratory motion during simultaneous

PET/MR examinations and to correct retrospectively coronal diffusion-weighted

images of a volunteer in 2019 [124].

Very recently, in 2020, it was demonstrated, that retrospective respiratory motion

correction using the PT is feasible for abdominal magnetic resonance fingerprinting

by [129].

The PT is currently an active field of research with constant advancements [122,

130]. So far it has been used for a wide range of different applications as a qualitative

motion surrogate.

However, the modulation of the scale-free PT signal depending on motion is not

yet sufficient if the PT ought to be used for motion correction. It must also be pos-

20 3.2 Methods

sible to determine a quantitative surrogate from the acquired PT signal describing

the motion of the heart with direction and on a scale.

In this chapter the feasibility of the PT to encode motion is demonstrated. The

individual goals are, to examine the PT as a motion surrogate and find its optimal

parameter settings. The parameters to be considered here are the amplitude with

which the PT is operated and the frequency. For this a test bed with a motion

phantom was build. The PT generation and acquisition is demonstrated and the

effect of the PT signal strength and frequency (i.e., location in the MR image) on the

accuracy of the PT signal is evaluated. Frequently occurring artifacts are analyzed.

Furthermore, steps are undertaken to minimize any negative impact of the PT on

the image data.

3.2 Methods

3.2.1 Phantom setup

The phantom setup is displayed in Figure 3.1. A stepper motor controlled by an

Arduino system is placed outside the scanner room (Fig. 3.1B). A rotating wheel is

attached to the stepper motor, which pulls a string. Inside the scanner room, this

string moves a wheel and via a connecting rod, a small cart is pushed back and forth.

A wooden table (Fig. 3.1C) supports the receiver coil so that the phantom can move

freely underneath. The cart performs a translational sinusoidal-like movement along

the bore direction of the scanner with an adjustable motion amplitude and velocity,

imitating translational breathing motion along the head-feet (HF) direction (Fig.

3.1A). Different agarose phantoms are used throughout this work. These are put

onto the cart and held in place with a belt.

3.2.2 Pilot tone generation

The PT is a coherent, continuous RF signal generated by an independent RF source

and transmitted into the bore of the MR scanner by an external antenna. It is

produced with a prototype set-up similar to previous applications for respiratory

gating and cardiac triggering [10]. A commercial RF synthesizer (Hewlett Packard,

ESG 1000A) is connected to a non-resonant surface coil. The power of the PT signal

is in the same order of magnitude as the received MR signal and it is about a factor

of 10−8smaller than the standard RF power used for MR data acquisition.

The single loop coil, depicted in Figure 3.2A, with a loop diameter of ≈3 cm

was used partly in chapter 5 and was attached to the bore of the scanner. In all

other chapters the PT signal was generated with the coil depicted in Figure 3.2B

with ≈11 cm diameter. This coil was attached to a wooden holder that was placed

20 cm away from the head end of the bore. The head end of the scanner refers to

the scan setting head-first supine.

3.2 Methods 21

(A)

(C)

(B)

(4) (3)

(1)

(2)

RETROSPECTIVE APPLICATION OF

INPLANE CORRECTION

ACQUISITION OF

PILOT TONE

Coil

Figure 3.1: Phantom setup. (A) One receiver coil is placed onto a fixed table above

the phantom and one is integrated into the patient table. (B) The rotating wheel is

attached to a string going outside of the scanner room, pulled by a controlled step

motor. (C) The phantom is attached to a cart that performs translational motion

along the bore direction of the scanner. (1) phantom bottles (2) moving phantom on

cart (3) connecting rod (4) wheel. Parts of this figure were published in J1.

Figure 3.2: Two different PT transmitting coils used during this thesis. One is at-

tached directly to the bore of the scanner while the other one was placed on a wooden

holder at head end of the scanner.

22 3.2 Methods

The receive coil elements are sensitive to loading changes. Physiological motion

[67], like breathing or the heartbeat, impacts the loading of the receive coils and

the coupling between transmitter and receiver. The underlying principle is based

on the different wave impedances due to different loading conditions of the receiver

coils [68, 131]. The changes in local coil loading lead to changes of the received PT

signal. The amplitude of the PT signal can be associated with the motion, hence,

be used as a motion surrogate.

3.2.3 Pilot tone acquisition

The frequency of the PT is set close to the Larmor frequency and is picked up by

the receive coil arrays that are usually placed anterior and posterior of the subject.

Figure 3.3 illustrates the placement of the receiver coils for an in vivo scan. Each

coil element records the PT signal with a different intensity, see Figure 3.4. In this

scan coil 17 shows best correlation with the respiratory motion.

During an MR scan, the PT is usually acquired together with the image data. A

hybrid k-space was created by 1-dim Fourier transform of the acquired k-space data

along the frequency encoding direction (i.e., readout) only. In hybrid k-space all

frequencies can be distinguished and signals of a single frequency can be extracted

[70]. The emitted PT frequency defines the spatial position of the received PT in

hybrid k-space. Figure 3.5 shows an example of hybrid k-space and the extracted

PT for a moving phantom.

The PT is obtained simultaneously with each readout. Therefore, the sampling

rate of the PT is one sample per TR interval which is in the region of a few millisec-

onds for fast gradient echo sequences.

Figure 3.3: Receiver coil setup. An anterior and posterior receiver coil array is used.

Each single coil within the receiver array is surrounded by different tissue compositions

and has a different distance to the PT emitter. This figure was published in J1.

3.2 Methods 23

Figure 3.4: PT obtained with four different receiver channels. Channel 17 shows

highest agreement with the registered motion.

FFT(Readout)

Intensity

Time

(A)

(B)

OBJECT

Figure 3.5: (A) Hybrid k-space (ky=0) (i.e., k-space after Fourier transform in readout

direction) of a moving phantom. In the two-fold oversampled region the PT appears as

a straight line. (B) Raw PT showing variation in intensity. This figure was published

in J1.

24 3.3 Adjustable PT parameters

3.2.4 Pilot tone calculation

Speier et al. have presented a method of modeling the PT first and then subtracting

the modeled signal from the data to reduce the potential influence of the PT on the

image [10]. This method is described and applied next.

The MRI system performs adjustment procedures to adjust for B0drifts prior

to each scan and, therefore, the location of the PT signal in the readout can vary

between different scans even for a constant PT frequency. The location of the PT

can be estimated from the acquired data [132]. The readout position corresponding

to the PT frequency is obtained from the hybrid k-space data by finding the highest

absolute value in the oversampling region. The detected position is used to create

a complex reference signal of the form:

A·exp(i2πft),(10)

which is then scaled to match the data by multiplying the complex conjugate with

the k-space data. The complex scaling factor A of the signal model is logged as the

PT [10].

In order to ensure a minimum impairment of the final image by the PT, the model

is subtracted from the acquired k-space data. In Figure 3.6 the measured signal,

the PT model and the residual signal after subtraction are shown as profiles for one

readout. Figures 3.7 and 3.8 illustrate the PT subtraction from the k-space and

image data for a Cartesian and radial trajectory, respectively.

3.3 Adjustable PT parameters

Controllable parameters of the PT are the power with which it is operated and

the frequency. If the power is set too high, i.e., the PT magnitude is too strong,

image data may be obscured. However, if the power of the PT is set too low, the

algorithm cannot extract the PT in the oversampling region because it is impaired

by noise. At the signal generator the power is set in the unit dBm. The conversion

between dBm and Watt is: P(W) = 10P(dBm)−30

10 . The frequency of the PT must be

set optimally, such that the data of the object and PT do not superimpose, which

would result in impaired image quality and a wrongly estimated PT signal model.

In order to be able to use the PT for motion correction, both parameters, amplitude

and frequency, must be optimized.

3.3 Adjustable PT parameters 25

50 100 150 200 250 300 350

8*10-5

PT model

Measured signal (MS)

MS - PT model

abs(FT(readout))

Figure 3.6: PT subtraction for one readout

Image space

Hybrid k-space

Before

subtraction

After

subtraction

PT model

Cartesian

Before

subtraction

After

subtraction

Readout # Readout # Readout #

(A)

(B)

Figure 3.7: (A) Hybrid k-space, i.e., k-space after Fourier transform in readout di-

rection with the PT appearing as a straight line in the two-fold oversampled region

obtained with a Cartesian GRE cine sequence. Only the readouts for ky=0 are shown

for better visualisation. (B) Resulting image reconstructed for one cardiac phase with

the oversampling region before and after PT subtraction

26 3.3 Adjustable PT parameters

Image space

Hybrid k-space

PT model

Radial

Before

subtraction

Before subtraction

After

subtraction

After subtraction

Readout #

(B)

(A)

Figure 3.8: (A) Hybrid k-space obtained with a golden-angle radial GRE sequence (B)

Reconstructed image before and after PT subtraction

3.4 Experiments 27

3.4 Experiments

Experiments were performed with a Siemens 3T scanner (MAGNETOM Verio;

Siemens Healthcare, Erlangen, Germany) on a moving 2-L agarose phantom, con-

taining a hollowed egg-shaped region inside. Data analysis and image visualization

were carried out using MATLAB 2017a (The MathWorks, Natick, MA).

3.4.1 Data acquisition

Dynamic data were acquired over 60 seconds using an in-house modified gradient-

echo sequence in sagittal orientation with field of view (FOV) = 320×320 mm2,

voxel size = 1.7×1.7×8 mm3, echo time (TE) = 3.2, TR = 5.7 ms,

pixel bandwidth = 449 Hz/pixel, flip angle = 12, Cartesian trajectory, and

two-fold parallel imaging acceleration with 24 reference lines.

Quality assessment To determine how well the PT describes the phantom motion,

it was compared to the motion estimated from a dynamic sequence. The reference

motion information was determined by image registration from the reconstructed

images. For this, a region of interest was set manually in the first image, and

motion amplitudes in HF direction of the moving phantom were registered for the

image series. A coefficient of determination, R2, of the reference motion and the PT

was calculated by fitting a linear model between PT and motion signal. R2denotes

the proportion of the variability in the data sets, where a value of 1 indicates that

the model perfectly accounts for the data. The PT was median filtered in steps

of 100 data points with a sliding window. The step size was chosen to be larger

than the number of phase encoding points used to capture a dynamic image (in this

work). This ensures greater temporal stability throughout the measurement.

3.4.2 Optimization of PT parameters

Amplitude To prevent receiver coil saturation, the amplitude of the PT should be

selected, such that the received signal intensity is of the same order of magnitude

as the signal of the object. In Figures 3.6, 3.7 and 3.8, which were displayed in

section 3.2.4, it could be seen, that after subtraction of the PT, there is still residual

signal in hybrid k-space, which could interfere with the signals of the object. To

minimize this effect, the PT amplitude should be as low as possible, but still high

enough to accurately determine the motion and not be affected by noise. In order to

determine the optimal signal strength, an evaluation of different PT signal strengths

was carried out. Twelve different PT amplitudes ranging from -55 dBm to 0 dBm

were set for 60 seconds during a phantom measurement.

Frequency In the next step, it was assessed whether the position of the PT in hy-

brid k-space has an influence on the accuracy of the motion model. It was assumed,

28 3.5 Results

that the further out in the oversampling range, the smaller the effect of the PT on the

object data. The PT was varied between a frequency range of 123.250 MHz ±82kHz

with 123.250 MHz being the center frequency of of the scanner. The edges of the

FOV were captured with 123.164 MHz and 123.336 MHz.

Assessment of external influences During the measurements, vibrations lead to

small changes of distance and orientation between the PT transmitter and the re-

ceive coil array. To assess the effect of these changes, experiments were conducted

with controlled disturbances of the PT transmit-receive system. A string was at-

tached to the receive coil array and pulled from outside the scanner room during

the measurement so that its position changed by <1 cm. The same procedure was

performed for the PT transmit coil, causing its position to change by <1 cm.

3.5 Results

3.5.1 PT amplitude

The obtained PT signals with different amplitudes are displayed in Figure 3.9. Fig-

ure 3.9A shows the reconstructed images of five measurements. Usually, the over-

sampling region is removed during reconstruction, but this operation was omitted

for illustration purposes. The signals in Figures 3.9B and 3.9C are realigned to be

in phase for better comparison.

For evaluation, the median filtered PT signals were correlated with the motion

found by image registration, as described in section 3.4.1. The last 20 data points

of the measurement conducted with an emitted PT amplitude of -15 dBm were

neglected due to an erroneous abrupt signal offset. Figure 3.10 shows the calculated

R2for the twelve tested amplitudes. For an amplitude higher than -30 dBm, the

signal quality indicated by R2does not improve further, but image quality decreases.

The gray shaded area marks the values that were subsequently used in the course

of this work.

3.5.2 PT frequency

Figure 3.11 shows the PT for eleven different frequencies. The FOV covered a

frequency range of 123.250 MHz ±86 kHz with a pixel bandwith of 449 Hz/pixel.

The frequency values in the Figures 3.11, 3.12 and 3.13 are given with respect to

the center frequency of 123.250 MHz. In 3.11A an overlay of eleven hybrid k-spaces,

i.e., after Fourier transform along readout direction, is shown. The position of the

PT in the image varies according to the frequency. A signal overlap of the PT and

the object data can be seen in Figure 3.11B for the frequencies close to the center

of the FOV.

3.5 Results 29

(A)

(B)

(C)

500 1000 1500 2000

Readout #

1.04

1.06

1.08

1.1

1.12

Median PT (a.u.)

-55 dBm

-50 dBm

-45 dBm

-40 dBm

-35 dBm

-30 dBm

-25 dBm

-20 dBm

-15 dBm

-10 dBm

-5 dBm

0 dBm

500 1000 1500 2000

Readout #

0.9

1.1

1.2

1.3

PT (a.u.)

-55 dBm

-45 dBm

-30 dBm

-15 dBm

0 dBm

Figure 3.9: (A) Reconstructed images showing the phantom and the the oversampling

region with the PT (B) Raw PT for five different amplitudes (C) Median filtered PT

of a moving phantom for twelve different signal amplitudes

30 3.5 Results

Figure 3.10: Coefficients of determination R2for PT with different amplitudes and

registered motion

1.2

1.1

0.8

1.2

4+10 kHz

0 kHz

0.8

1.2

1.1

0 500 1000 1500 2000 2500

1.1

Readout #

PT (a.u.)

Readout #

+82 kHz

+70 kHz

+50 kHz

+30 kHz

+10 kHz

0 kHz

-10 kHz

-30 kHz

-50 kHz

-70 kHz

-82 kHz

+30 kHz

+50 kHz

+70 kHz

+82 kHz

-82 kHz

-70 kHz

-50 kHz

-30 kHz

-10 kHz

(A) (B)

Object data

Figure 3.11: (A) Overlay of 11 images of 77 readout lines of hybrid k-space (ky=0)

(i.e., k-space after Fourier transform in readout direction) with different PT frequen-

cies. The given values indicate the difference to the center frequency. (B) Correspond-

ing PT signals of 2500 readouts indicating a signal overlap with the object data at the

center close frequencies

3.5 Results 31

0 500 1000 1500

Readout #

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

Median PT (a.u.)

+82 kHz

+70 kHz

+50 kHz

-50 kHz

-70 kHz

-82 kHz

Figure 3.12: Median filtered PT of a moving phantom for 6 different PT frequencies.

The values are given with respect to the center frequency.

-80 -60 -40 -20 0 +20 +40 +60 +80

Frequency (kHz)

0.75

0.8

0.85

0.9

0.95

Figure 3.13: Coefficients of determination R2for PT and registered motion for dif-

ferent frequency offsets with regard to the center frequency of 123.250 MHz

The median filtered PT for six different frequencies is shown in Figure 3.12. The

phases of the signals were aligned for better visualization. The PT variation due to

motion is independent of the frequency, but there is a background offset at different

frequencies.

Again the PT and the registered motion were correlated and the resulting R2

of the motion models are shown in Figure 3.13. The correlations were best for

frequency offsets away from the center frequency, that did not superimpose with

the object signals. The grey shaded area marks the frequency (center frequency+70

kHz) used for further experiments with similar scan parameters (FOV, pixel size,

32 3.5 Results

bandwidth). The PT was placed in the oversampling region in head end of the MR

scanner because less influence of body movement which is not involved in respiration

is suspected there.

3.5.3 Artifact analysis

Figure 3.14 shows the normalized unfiltered PT signals for three phantom- and one

in vivo measurements. The first experiment was performed on a moving phantom

without disturbances and the PT signal appears smooth throughout the measure-

ment. The next two scans were actively disturbed from outside the scanner room,

as described in section 3.4.2. First, the emitter coil was pulled twice via a con-

nected string during the measurement leading to irregular spikes in the receive sig-

nal starting at readout number ≈2900. Between the disturbances, the signal maps

the phantom motion and shows no spike-like artifacts. Next, the receive coil array

was manipulated at the beginning of the measurement, so that artifacts are visible

during the first ≈2000 readouts. The in vivo measurement (bottom signal in Figure

3.14) shows unintentionally caused irregular artifacts over the entire time period.

These could be caused either by unwanted movement of the receiver coil arrays or

the emitter coil. These cannot be distinguished from each other in terms of the

received signal.

Optimizing steps for the in vivo measurements were to fix the receiver coil very

carefully to the subject and place the PT emitter coil holder on vibration-absorbing

material. Nevertheless, these vibrational disturbances could not be eliminated com-

pletely with this setup.

One approach to minimize the influence of these artifacts is the use of signal

filters. As discussed by B¨uhrer et al. in [44], for real-time applications fast filters

should be used, which are causal and introduce only small delays. Bandpass filters

such as a Butterworth filter could be a suitable option. In order to extract the

respiratory motion signal reliably with such filters, very low frequencies must be

included. However, very low frequencies also lead to a delay of the filter. To minimize

the delay, high frequencies must additionally be included in the passband [44]. For

this particular application, this would mean that the coherent artifacts would be

considered in this filter and could distort the signal.

Due to the irregularly occurring artifacts, peak detection filters should also be

avoided. For the extraction of cardiorespiratory signals from non-contact sensor

data, often an adaptive Kalman filter is used [68, 125, 133]. This filter takes the

probability distributions of possible errors around each signal estimate into account

and previous estimates are combined with new measurement data for each time step

in an optimal way. Nevertheless, this filter assumes that noise, that contaminates the

respiratory signal, is Gaussian distributed [134, 135]. For an undisturbed signal, as

shown in Figure 3.14(top) this filter could be an optimal choice due to its prospective

behavior. For the signals that reveal vibrational disturbances, a filter must be chosen

3.6 Discussion 33

0 1000 2000 3000 4000 5000

Readout #

PT (a.u.)

Undisturbed phantom scan

PT emitter moved during scan

Receiver coil moved during scan

Disturbed in vivo scan

Figure 3.14: Normalized unfiltered PT (black) and sliding window median filtered PT

(green). Top to bottom: undisturbed phantom scan, phantom scan with intentionally

caused disturbance on the emitter, phantom scan with intentionally caused disturbance

on the receiver, in vivo scan with unwanted disturbances

that does not take any coherence as well as artefact signal strength into account.

A sliding window median filter, see Fig. 3.14(green), with a step size of 100,

minimized the effects of this specific error, because neither the intensity of the spikes

nor the amount of occurrence distort the filter strongly.

3.6 Discussion

Phantom measurements have shown that high PT amplitudes suffer less from noise

than low amplitudes (Fig. 3.9). However, if the PT amplitude was higher than

the object signal, it affected the image quality, as illustrated in Figure 3.9A. To

ensure best image quality, the PT amplitude was set to approximately the same

signal magnitude as the object to be imaged. Analysis of the correlation between

registered motion and PT amplitude showed high correlation values when setting

the amplitude around -30 dBm (=1 µW). For further measurements during this

thesis an amplitude of -30±5 dBm was chosen. The lower end of this range was

used for subjects who generate a low receive signal amplitude due to their physique.

The used power for the PT generation is 8 orders of magnitude smaller than the

average power of MR coils, which are limited according to the standard MR safety

guidelines of around 100 W (2 W/kg body weight) [136].

The position of the PT in the oversampling region did not affect its quality, as long

as it did not overlap with the imaged object. The higher the frequency difference

between PT and object data within the FOV, the smaller the possibility of a signal

34 3.7 Conclusion

superimposition. The PT signal quality appeared the same in both oversampling

regions. For future measurements the PT frequency was set to the head end (superior

side) of the FOV with a frequency offset of 70 kHz.

The PT was sensitive to small changes in the transmitter-receiver distance. In

principle, every receive channel was suitable for receiving the PT. Combining the

information from all receiver coils using a principal component analysis (PCA) could

be less sensitive to these influences and could lead to a more robust PT. However, due

to the strong and often coherent signal disturbances in the receive channels, a PCA

could yield results, that emphasize the artifacts. For all future in vivo measurements,

the PT signal was inspected at the beginning of the scan time. If strong irregular

artifacts appeared, as shown in the previous section 3.5.3, the emitter or receiver

coil position were optimized. This procedure was undertaken until the signal was

almost free of spike-like artifacts. The R2of the scan gave then further information

about the quality of the signal.

The applied median filter had a width of 100 readouts and reduced noise in the

signal. However, within the first 100 readouts the filtered PT may give inaccurate

results, because the filter is based on insufficient data. Another drawback of the

median filter is the introduced delay. The sliding window filter always used the last

100 data points to determine a value. This means that a change in the raw signal

was not immediately reflected in the filtered signal, but with a delay. Assuming a

TR of 5.7 ms and a step size of 100 readouts, a delay of ≈0.6 s could be introduced

between respiratory heart motion and PT signal. For adult subjects with a normal

breathing rate, this delay is negligible. For infants with a breathing period of ≈1.2 s,

this filter would need to be adapted.

The heartbeat also leads to a modulation of the PT [125]. Nevertheless, this

contribution is much smaller than the contribution due to respiratory motion and

is further attenuated by the applied median filter. Modulations induced by the

heartbeat are neglected during this thesis.

3.7 Conclusion

In this chapter, the behavior of the PT at different settings was tested, and the best

parameters for a stable PT that maps phantom motion were determined.

The next chapter presents the use of the PT as a quantitative motion surrogate.

For this purpose, the signal is calibrated to the respiratory motion. Furthermore, its

temporal stability is investigated and the results are compared with other motion

surrogates.

4Calibration and temporal

stability

4.1 Introduction

Parts of this chapter have been published in J1 and C1.

Commonly breathholding is the method of choice for 2D cardiac MRI to prevent

respiratory motion artifacts. Even though the breathholding technique has also been

proposed for high-resolution 3D acquisition of the whole heart [137], more often the

respiratory gating method is applied [28, 33, 37, 39, 76]. Depending on the breathing

pattern of the subject, the scan efficiency, i.e., the ratio between data used for the

final image reconstruction and the rejected data, can be very low. To improve

the scan efficiency, a variety of motion correction methods has been proposed that

correct either prospectively or retrospectively [40, 49, 52, 54]. Nevertheless, these

approaches often require dedicated data acquisition and cannot be combined with

arbitrary scans.

Additionally, the main challenge remains through-plane motion. The algorithms

cannot correct for tissue moving in or out of the image slice, which is especially a

problem for 2D imaging and 3D imaging of a thin slab.

Accurate motion surrogates are MR-based navigators, as discussed in section 2.4.

They are well suited for many applications, but not for continuous acquisitions,

where the magnetization should not be disturbed by the RF pulses played out to

acquire the navigator data.

Besides the MR-based navigators, external MR-independent surrogates can moni-

tor the respiratory motion. For example respiratory belts offer a very high temporal

resolution, are not coupled to the MR measurement and yield a qualitative signal

[138, 139]. But in order to use the signal for motion correction, a prescan must

be performed, that calibrates the signal to the respiratory heart motion via motion

models [9]. Disadvantages of the use of respiratory belts are the unreliability of the

signal due to sub optimal positioning, signal drifts and difficult synchronization with

the MR data [9, 45].

The PT can overcome these challenges [10]. Similar to the signal obtained with

the respiratory belt, the PT signal is a qualitative motion signal with high temporal

resolution, which may be used for continuous scans.

In this chapter the qualitative PT signal is converted for the first time into a

quantitative signal that can be used for motion correction. A calibration scan is

developed, that correlates the PT signal to the translational (rigid) heart motion,

and subject-specific motion models are estimated.

In a next step, the temporal stability of the PT with the motion model is examined

36 4.2 Methods

on a phantom and in vivo. Further, the performance of the PT is compared to a

standard MR-navigator and a respiratory belt. For this purpose the surrogates are

also tested for their stability.

4.2 Methods

This section describes how heart motion and surrogate signals can be calibrated and

how the temporal stability is evaluated.

4.2.1 Calibration

To gain quantitative motion information from the qualitative surrogates the signals

must be calibrated to the motion of the heart [33]. Figure 4.1 shows how image

data and surrogate data are combined to estimate motion models. In this thesis

the calibration scan consists of 2D images (sagittal and/or coronal), and is carried

out prior to the motion-corrected MR scans. Simultaneously with the 2D images,

the surrogate signals are acquired. The motion estimated from the images and the

surrogate data are used to form motion models.

Surrogate data

Imaging data

Motion estimates

Registration

...

Motion models

4.2 4.3 4.4 4.5 4.6

Surrogate (a.u.) x 10-5

Cardiac shift in HF (mm)

R2=0.94

1.95 2 2.05 2.1 2.15 2.2

Surrogate (a.u.) x 10-5

-6

-4

-2

Cardiac shift in HF (mm)

R2=0.98

Figure 4.1: Respiratory motion model formation. Surrogate data are acquired at the

same time as MR images depicting the heart in different respiratory positions. Motion

is determined from the image data by image registration, and the motion model ap-

proximates the relationship between the surrogate data and motion. Illustration based

on [33]

4.2.2 Motion model formation

Linear motion models are derived to calibrate the surrogate signals to the heart

motion. Only the translational component of the heart motion is taken into consid-

eration. Image registration with a 2D normalized cross-correlation function is used

to determine the motion of the heart in HF (∆HFreg), anterior-posterior (∆APreg)

4.3 Experiments 37

and right-left (∆RLreg) directions [49]. Three linear motion models are then derived

between ∆HFreg, ∆APreg, ∆RLreg and the surrogate signal (SU):

∆HFreg =a×SU +b(11)

∆APreg =m×SU +n(12)

∆RLreg =u×SU +v(13)

Time (s)

Surrogate signal (a.u.)

∆

Surrogate signal (a.u.)

Cardiac Shift (mm)

Linear model RL

Linear model HF

Linear model AP

Time (s)

Cardiac Shift (mm)

Figure 4.2: Respiratory motion estimation. 3D respiratory translational motion in-

formation is extracted from the respiratory-resolved images. Registered motion and the

surrogate signals are fitted by a linear regression curve. For following scans, the signals

give quantitative information about the motion state of the heart and can be used as

motion surrogates.

A PT signal is obtained with each coil element of the receiver array. For each coil

a motion model is formed. The coil which yields the motion model with the highest

coefficient of determination, R2, for ∆HFreg is selected for motion correction.

As discussed in section 3.6 a coil combination by means of PCA is not used,

because certain artifacts in the PT signal were coherent between different coils and

hence would be emphasized by a PCA. Leaving the coil signals uncombined ensured

that the coil without artifacts is selected as it most likely yields the highest R2.

4.3 Experiments

All experiments were performed at 3T (MAGNETOM Verio, Siemens Healthcare,

Germany). The assessment of the temporal stability of the PT was performed on

a phantom and 10 healthy subjects (6 male, 4 female, age 37±13 years, weight

72±15kg). The comparison with other motion surrogates was performed on 3 sub-

jects (2 female, 1 male, age 30±2 years). The local ethics board approved the in vivo

experiments and written informed consent was given by all subjects. Data analysis

38 4.3 Experiments

and image visualization were carried out using MATLAB 2017a (The MathWorks,

Natick, MA).

4.3.1 Calibration scan

Sixty cardiac, ECG-triggered, dynamic sagittal and coronal 2D images were ac-

quired for each cardiac cycle during the calibration scan as depicted in Figure 4.3.

An inhouse-modified FLASH sequence was used with TE=1.4 ms, TR=2.4 ms,

FOV=300x300 mm2, FA = 20◦and voxel size=1.56x1.56x8 mm3. Data of the PT,

the respiratory belts and MR-navigator were acquired together with the MR data.

For synchronization of the respiratory belt data, the subjects were asked to hold

their breath at the beginning and end of the scan. Only data where free-breathing

was performed was then used for the formation of the motion models.

Figure 4.3: For 60 cardiac cycles two images (sagittal, coronal) are acquired to deter-

mine the respiratory cardiac motion in three directions.

4.3.2 Registration of motion

The cardiac motion is estimated from dynamic images. For each cardiac cycle, a

coronal and sagittal 2D image with an acquisition window of 0.46 s per image were

acquired to capture the 3D motion of the heart. A region of interest around the heart

was chosen manually for coronal and sagittal orientation. A 2D normalized cross-

correlation function was applied to the coronal image series and yielded translational

motion information for the HF and RL direction. Sagittal images were used for

the AP direction. Thus, respiratory motion parameters were registered for three

dimensions with a temporal resolution of one value per cardiac cycle (≈1 s).

4.3.3 Other motion surrogates

The PT signal was compared to two other motion surrogates: respiratory belt and

MR-navigator.

4.3 Experiments 39

Respiratory belts Two respiratory belts, and an associated data acquisition and

analysis system (MP160WS) with AcqKnowledge software (BIOPAC Systems Inc.)

were used. The two belts were fixed to the subjects around the chest and abdomen

to capture abdominal and thoracic breathing, as shown in Figure 4.4 (left). The

change in circumference of the body during the breathing cycle was measured with

an internal air pressure system providing a temporal resolution of 0.5 ms. The

air pressure cables are connected to pressure to volt transducers which again were

connected to an amplifier. The apparatus is shown in Figure 4.4 (right). The signals

were recorded in mV and stored for further analysis. Respiratory data acquisition

with the belts was started before each scan session. Temporal synchronization of

the respiratory belt data with the MR data was done manually using breathhold

phases as a guide. Figure 4.5 shows exemplary data of a calibration scan. Only

the blue shaded area is used for calibration. At the beginning and end of a single

Figure 4.4: Respiratory belt system, consisting of two belts (left) and an air pressure

to volt transducer (right image, right side).

Figure 4.5: (A) Registered HF motion of the heart obtained from 2D coronal images.

(B) Continuously acquired data from two respiratory belts. The breathhold phases are

clearly visible and are used for the synchronization of the respiratory belt data with the

MR data.

40 4.3 Experiments

scan the subjects were asked to perform a breathhold and then proceed with normal

breathing. These breathhold phases were identified in the respiratory belt data

as well as in the MR data by analyzing the shift ∆HFreg gained from the image

registration. From the signal curve in Figure 4.5A, it can be seen that the heart

also moves slightly during the breathhold phase (drift), which is a known occurrence

shown by Xue et al. [5]. The respiratory belt that was fixed around the thorax also

shows this behavior. Only data of one belt, i.e., the one which showed higher motion

amplitudes during free breathing, was selected as navigator.

MR-navigator MR-navigator data were obtained retrospectively from the calibra-

tion scan by tracking the HF motion of the dome of the right hemidiaphragm with

a temporal resolution of one shift value per image. For this purpose, a rectangular

region was manually selected in the reconstructed MR images with coronal orienta-

tion. The transition from the diaphragm to the lung (Fig. 4.6 (red box)) was covered

and the first image served as a reference motion state. A 1D cross-correlation func-

tion was then applied to all data to show the motion of the diaphragm in the HF

direction. Every image yielded one data point of the MR-navigator, as depicted in

Figure 4.6 (right). The motion of the diaphragm related closely to the motion of

the heart.

0 10 20 30 40

Time (s)

0.2

0.4

0.6

0.8

Normalized Shift

Registered heart motion

MR-navigator

Figure 4.6: Left: Coronal image with indicated ROI around the heart (cyan) and ROI

for the MR-navigator (red). Right: Exemplary temporal evolution of the motion in HF

direction for the heart and the MR-navigator. Both normalized curves overlap.

4.3.4 Temporal stability of PT

The temporal stability was tested for the PT on a phantom and in vivo and also

compared to other surrogates. The scan parameters for the scans performed only

with the PT, and the scans performed with all three motion surrogates are summa-

rized in Table 1. The parameters of the two scans differ because they are derived

from calibration scans for different purposes. To evaluate the temporal stability of

4.3 Experiments 41

the PT, the dynamic scan was performed for 513 RR cycles. The first 60 acquisi-

tions of the measurement were used for calibration. Then by utilizing the motion

models and the PT, the motion was predicted for all 513 RR cycles retrospectively.

The motion models were not updated after initial calibration. For analysis and vi-

sualization, the values were averaged over ten RR cycles. The mean absolute error

(MAE) is calculated by subtracting the predicted shift from the registered shift:

MAE =|∆HFpred −∆HFreg|.(14)

For the in vivo data, the same approach was also used with |∆APpred −∆APreg|.

The MAE depends on the temporal stability of the surrogate, the motion amplitude

and the R2of the calibration.

Long-term measurement Because typical clinical MRI protocols last up to one

hour, the temporal stability of the PT was also examined by performing a long-term

phantom scan with 6×513 repetitions.

Phantom A 1.2-L agarose phantom containing cubic structures inside with side

lengths of 0.7 cm was used. The motion phantom performed a translational

sinusoidal-like movement along the HF direction of the scanner with an amplitude

of ≈3.2 cm and a frequency of 6 repetitions per minute (0.1 Hz). The phantom was

used to measure the temporal stability of the PT with the motion model.

In vivo The temporal stability was assessed in ten healthy subjects, who were

asked to perform normal continuous breathing. Additionally, one subject was asked

to breathe irregularly to show different breathing patterns that were not included

in the calibration. The sequence was ECG-triggered, and every sagittal dynamic

image was acquired in an acquisition window of 507 ms in end-diastole.

4.3.5 Temporal stability of three surrogates

The analysis of the temporal stability of the PT, respiratory belt and the MR-

navigator with their respective motion models was carried out according to Eqn. 14

based on data from the same recording, as specified in Table 1. The duration of

the used scan was 350 RR cycles and two breathhold phases were included in the

beginning and the end of the scan for synchronization of the data. The predicted

heart shifts along HF from the three motion surrogates were then compared to the

registered heart motion by examining the MAE.

42 4.4 Results

Temporal stability scan PT only

(for phantom and

in vivo study)

MR-nav, Resp. belt, PT

(for comparison of

surrogates)

Measurements 513 350

Triggering ECG-triggered* ECG-triggered*

Sequence GRE GRE

Orientation 2D sagittal 2D sagittal, coronal

TE/TR 3.2/5.7 ms 1.4/2.4 ms

Flip angle 12◦20◦

FOV 320×320 mm2300×300 mm2

Voxel size 1.7×1.7×8 mm31.6×1.6×8 mm3

Table 1: Sequence parameter for test series on the temporal stability. *For phantom

measurements an ECG signal was simulated with 1 Hz.

4.4 Results

4.4.1 Evaluation of temporal stability of PT

Phantom Due to the phantom setup, only motion along HF was present, and hence

the analysis was limited to that direction. Figure 4.7A shows the shift found by

image registration (∆HFreg) compared to the predicted shift (∆HFpred) estimated

from the model and the PT. The linear regression correlation coefficient for the

first 60 s was 0.95. The amplitude of the registered shift was 31.7 mm and for

the predicted shift 31.7±3.7 mm. Figure 4.7B shows the evolution of the MAE.

The average MAE over the complete measurement was 2.5±0.7 mm. Here it is

important to note that the motion amplitude of the phantom was much larger than

what would be expected in vivo and hence MAE is also much larger than for in-vivo

applications.

In a second experiment the PT was recorded for 51.3 min during 6 scans with

513 repetitions. The total time period of the experiment was 52.75 min including

small pauses to restart the sequence. The motion phantom did not move for the

last ≈6 min. Figure 4.8A shows the raw PT signal acquired with one channel. The

first 60 s were used to calibrate the registered shift and the raw PT, resulting in an

R2of 0.99. Figure 4.8B displays the MAE of the PT correlated with the registered

phantom shift in HF direction in steps of 10 acquisitions for the 6 scans. The mean

peak-to-peak amplitude was 27.5 mm and the mean of the MAE was 1.2±0.9 mm.

In vivo The respiratory heart motion for regular breathing was evaluated for 10

subjects in HF and AP direction from sagittal images, and the according MAE are

shown in Figure 4.9. The mean R2of the registered and predicted shift for the first

60 RR cycles was 0.94±0.04 in HF and 0.67±0.19 in AP direction. The measurement

duration of 513 RR cycles varied between 6.5 min and 11.1 min. The average peak-

to-peak difference along HF of all subjects was 5.7±3.0 mm with a maximum heart

4.4 Results 43

Figure 4.7: (A) Registered phantom shift and the predicted shift for a moving phantom

over 513 s. (B) Temporal stability of the motion model and difference between predicted

and registered shift. The first 60 s were used to calibrate the pilot tone to the phantom

motion (blue area). The motion was then predicted and compared to the registered

motion. The mean absolute errors were averaged over ten images (i.e., cardiac cycles),

and the corresponding standard deviations are displayed. This figure was published in

J1.

displacement of 28.3 mm. The average of the MAE along HF was 1.4±0.5 mm. For

AP, the average peak-to-peak difference was 1.8±0.5 mm for all measurements with

a maximum heart shift of 6.7 mm. The average MAE along AP was 0.5±0.1 mm.

Figure 4.10A shows the respiration curve in the HF direction of a subject who was

asked to breathe irregularly for 6.9 min. An approximately 10-second breathhold

after end-exhalation was also included in the calibration phase. The MAE of the

predicted shift (∆HFpred) compared to the registered shift (∆HFreg) was <1 voxel

for almost the entire measurement. Only very deep breathing led to an increase of

the MAE because the deep breathing was not part of the calibration, as shown in

Figure 4.10B (arrows). After the deep-breathing phase, the error decreases again.

44 4.4 Results

Time (min)

Raw PT (a.u.)

02468

1.05

1.1

10 12 14 16

1.05

1.1

18 20 22 24 26

1.05

1.1

28 30 32 34

1.05

1.1

36 38 40 42

1.05

1.1

44 46 48 50 52

1.05

1.1

Mean absolute error (mm)

(A)

(B)

Time (min)

Figure 4.8: (A) Unfiltered PT received at a single channel for a moving phantom over

a total time period of 52.75 min including short pauses between the scans. 6 scans

with each 513 repetitions were acquired, corresponding to a data acquisition time of

51.3 min. The phantom was not moving the last ≈6 min. (B) MAE for the PT and

the registered motion in steps of 10 acquisitions. The grey shaded area represents the

standard deviation.

4.4 Results 45

(B)

(A)

MAE (mm)

Figure 4.9: Comparison of the registered cardiac shift with the predicted shift. The

first 60 RR cycles were used to calibrate the pilot tone to the respiratory heart motion.

The heart motion was then predicted and compared to the registered heart motion.

The mean absolute errors averaged in steps of 10 RR cycles, and over 10 subjects are

displayed for respiratory induced heart motion in HF (A) and AP (B). This figure was

published in J1.

Figure 4.10: (A) Registered cardiac shift and predicted shift of a subject with irregular

breathing for 513 RR cycles. (B) Temporal stability of the motion model. The first 60

RR cycles were used to calibrate the pilot tone to the respiratory-induced heart motion.

The heart motion was then predicted and compared to the registered heart motion. The

mean absolute errors in steps of 10 RR cycles are displayed. This figure was published

in J1.

46 4.4 Results

0 10 20 30

0.2

0.4

0.6

0.8

Normalized motion signals (a.u.)

Time (s)

Registered heart motion

Pilot tone

Respiratory belt

MR-navigator

Figure 4.11: Overlay of the surrogate signals (pilot tone, respiratory belt and MR-

navigator) and the registered HF heart motion from the calibration scan. A modified

version of this figure was published in C1.

4.4.2 Comparison of three motion surrogates

Calibration scan Figure 4.11 shows an overlay of the different surrogate signals

obtained during a calibration scan compared to the estimated HF heart motion. The

surrogate signals are normalized and only the data which was used for calibration

is shown.

Very good agreement between all surrogate signals can be seen. The linear re-

lationship with a factor of 0.6 between the MR-navigator signal and the registered

heart motion, which was found by Wang et al. [50], could be verified. Signal curves

are not smooth because only one value per dynamic image is displayed, which corre-

sponds to the temporal resolution of the registered heart motion and MR-navigator,

i.e., one value per cardiac cycle. The beginning and end of the calibration scan in-

cluded breathhold phases, which were used for temporal synchronization of the respi-

ratory belt data. In total only 26 data points were used for deriving the motion mod-

els. The regression curves are displayed in Figure 4.12 for the MR-navigator, PT,

and respiratory belt with the respective correlation coefficients R2=0.95, R2=0.79,

R2=0.75.

Temporal stability The MAE of the surrogate signals of the motion correction

scan are displayed in Figure 4.13. The first 60 s after the breathhold phase of the

respective data were used for calibration. The MAE of the following 130 s is shown

in steps of 10 s for one subject for HF direction. The MR-navigator shows the best

temporal stability, followed by the PT and the respiratory belt.

4.4 Results 47

0 0.2 0.4 0.6 0.8 1

MR-navigator

-8

-4

Data

y=7.50*x-7.57

R2=0.95

0 0.2 0.4 0.6 0.8 1

Pilot tone

-8

-4

Cardiac shift

(mm)

Data

y=7.92*x-8.34

R2=0.79

0 0.2 0.4 0.6 0.8 1

Respiratory belt

-8

-4

Data

y=8.02*x-9.12

R2=0.75

Cardiac shift

(mm)

Cardiac shift

(mm)

Figure 4.12: Regression curves for the three surrogate signals and HF motion. The

best correlation was found for the MR-navigator but also the pilot tone and the respi-

ratory belt describe the estimated motion well. This figure was published in C1.

80 100 120 140 160 180

Time (s)

4MR-navigator

80 100 120 140 160 180

4Pilot tone

80 100 120 140 160 180

Mean errors w/ standard deviation (mm)

Respiratory belt

Figure 4.13: Temporal stability of the surrogate for HF motion after calibration phase.

The first 60 s after the breathhold phase (not shown) were used to calibrate the surrogate

signals to the respiratory heart motion. Using the motion model, the heart motion for

the next 130 s was then predicted in steps of 10 s and compared to the registered heart

motion. The mean average errors and standard deviations are displayed. This figure

was published in C1.

48 4.5 Discussion

4.5 Discussion

By analyzing the temporal stability of the PT and the motion models on 10 healthy

subjects, it was found that there is a slight increase of the MAE by approximately 1.6

mm in the HF direction over a period of 513 RR cycles, corresponding to 6% of the

maximum motion amplitude and in the order of image resolution. Despite this small

increase, the temporal stability of this approach was still very good. Also, errors

occurred for motion not captured during the calibration phase (see deep-breathing

in Fig. 4.10B).

A phantom long-term scan of ≈53 min showed that after calibration the PT with

the motion model was stable with an average MAE between the predicted and the

registered phantom motion of 1.2±0.9 mm.

A comparison between three different surrogate signals was presented. For this

purpose, PT-, respiratory belt- and MR-navigator data were recorded simultane-

ously. Linear motion models were derived from the calibration scan yielding the

highest R2for the MR-navigator (R2=0.95), followed by the PT (R2=0.79) and the

respiratory belt (R2=0.75). Using the motion models, the surrogates were examined

for their temporal stability. As expected, the MR-navigator showed the best tempo-

ral stability, but PT and respiratory belt also showed good temporal behavior. The

MR-navigator was obtained from the same images as the registered cardiac motion

and was, therefore, not susceptible to external sources of error.

In the presented temporal stability figures an increase in MAE between predicted

shift and true motion over time is visible (drift). Because the drift also occurs in

phantom measurements after ≈25 min and the motion does not change over time, a

heating of the system, leading to a change in coil loads and PT intensity, could be

the reason for this drift behavior. Also, each time a sequence is started, the center

frequency of the scanner is readjusted automatically, so that the position of the PT

might be slightly shifted and an intensity offset is introduced to the PT. This would

reduce the accuracy of the motion models and result in an increased MAE. In the

in vivo measurements, a change in the motion pattern of the subject could also be

the cause of this effect. The drift behavior appears stronger for motion in HF than

in AP. The underlying linear motion models assume that the relationship between

the PT and the motion does not change with time. However, with long scan times,

the breathing behavior of the subject can change significantly, e.g. because body

relaxation occurs [140–142].

A solution to correct the drift behavior would be adaptive motion models [135].

Here, a recalibration of the motion model is performed by analyzing the recorded MR

data and the surrogate throughout the MR exam. A recalibration during the data

acquisition is only feasible if the acquired data allows a real-time image registration

[143]. If a threshold is set beforehand, which specifies the accepted estimation errors,

the adaptive correction can be implemented in an auto-adaptive way [144]. However,

for continuous imaging techniques, such as cine imaging, the recalibration step must

4.6 Conclusion 49

be performed separately and a threshold cannot be preset. In this case, recalibration

is always at the expense of total scan time.

4.6 Conclusion

In this chapter, the qualitative PT signal was for the first time converted into a

quantitative signal by using motion models obtained from a calibration scan. Fur-

thermore, the temporal stability of the PT was tested and compared with two other

motion surrogates, the respiratory belt and the MR-navigator. In the next chapter,

the three surrogates are used for retrospective motion correction. A new prospective

correction approach based on the PT is also presented.

5Respiratory motion correction

5.1 Introduction

Parts of this chapter have been published in C1 and C2.

This chapter aims to demonstrate retrospective and prospective respiratory mo-

tion correction based on the PT.

A retrospective respiratory motion correction of free-breathing cardiac 3D data is

performed with the MR-navigator, the respiratory belt and the PT.

In a next step, a new framework for prospective motion correction is developed

and the implementation steps are presented. The PT is then used to demonstrate

the feasibility of a prospective motion correction for 2D cardiac imaging in transverse

orientation.

In an additional study on existing data of a cohort of healthy subjects, the dom-

inant motion components during respiration are assessed. The dominant motion

directions will be preferentially considered during calibration in the following chap-

ters.

5.2 Methods

This section describes how the retrospective motion correction is performed on 3D

data using a respiratory belt, an MR-navigator and the PT as motion surrogates.

Further, the prospective motion correction method and the signal processing pipeline

implemented for calibration and motion correction are explained.

5.2.1 Retrospective motion correction with three surrogates

Figure 5.1 gives an overview of the retrospective motion correction approach. With

the calibration scan, the respiratory motion of the heart is registered and linked to

the surrogate signals (PT, resp. belts, MR-navigator) via motion models. Simulta-

neously with the MR scan, the surrogate signals are acquired and subsequently used

together with the respective motion models to retrospectively estimate translational

motion.

Motion correction was performed offline with MATLAB before image reconstruc-

tion for every readout by applying a phase shift φto the k-space data Kuncorr, that

corresponds to the heart shift ∆(x, y, z)(t). The motion-corrected k-space Kcorr can

be calculated using equations 15 and 16. Nx,y,z is the total number of phase encod-

ing points along the k-space dimensions kx,kyand kz. For every readout, a phase

shift can then be calculated independently for the k-pace dimensions kx,kyand kz

using:

5.2 Methods 51

Figure 5.1: Overview of the PT-based retrospective motion correction approach. First,

2D respiratory motion-resolved MR images and the surrogate data are obtained for

about 60 s to calibrate the surrogate signals to the respiratory motion of the heart and

derive a motion model. The data of subsequent 3D scans can then be motion corrected

using the motion model and the respective surrogate data. This figure was published in

C1.

φ(kj(t)) = kj(t)·2π

·∆j(t) (15)

with j=x, y, z.

The corrected k-space is then calculated with:

Kcorr(kj, t) = Kuncorr(kj(t)) ·eiφ(kj(t).(16)

5.2.2 Prospective motion correction with PT

Figure 5.2 shows the prospective motion correction framework. During a calibration

scan, the PT is calibrated with the motion in the HF direction. In the next scan,

the PT signal is used to predict and apply the cardiac motion online by adjusting

the slice position.

For the transverse slice orientation, only through-plane motion along HF (HFpred)

is predicted in this chapter. The RF pulse frequency is adapted by redefining the slice

position vector in the running sequence to (︂0,0,∆HFpred)︂for every readout. This

52 5.2 Methods

Figure 5.2: Overview of the prospective motion correction method. First, simultaneous

acquisition of MR data and PT data is carried out for about 1 min to calibrate the PT

signal to the respiratory motion of the heart and derive a motion model. The data

of subsequent 2D scans can then be motion corrected prospectively during acquisition

using the motion model and the PT data and adapting the location of the excited slice.

A modified version of this figure was published in C2.

ensures that the excited layer follows the motion of the heart (i.e., slice tracking).

5.2.3 Online Signal Processing

The online signal processing is applied only for the prospective correction. Model

formation and signal extraction are implemented in the scanner software (syngo.MR

B17) written in C++ by adapting the data processing chain, as illustrated in Figure

5.3.

There are two main processing pipelines. The first pipeline performs the cali-

bration steps. Here, the PT signal is extracted from the acquired raw data, the

respiratory motion is estimated from motion-resolved images, and the motion mod-

els are build.

The second processing pipeline is the motion-correction pipeline, where correc-

tions are applied during the scan. For this purpose, real-time processing must be

implemented. This means that the PT is extracted for each readout and converted

to a shift value via the motion model. The shift is then applied during the running

sequence. The individual steps are now described in more detail.

5.2 Methods 53

READOUT PROCESSING IMAGE RECONSTRUCTION

READOUTS IMAGES

PROCESSING IMAGE DATA

EXTRACTION OF

PILOT TONE

REGISTRATION OF SHIFTS

FIT SHIFTS TO PILOT TONE

SAVE MOTION MODEL

FOR NEXT SCAN

PROCESSING READOUT

DATA

IMAGE

ASSEMBLER

CALIBRATION PIPELINE

MOTION CORRECTION PIPELINE

MOTION MODEL

PROCESSING READOUT DATA

EXTRACTION OF PILOT TONE

CALCULATION OF SLICE POSITION

SAVE CORRECTION VALUES

READOUT PROCESSING

SEQUENCE

APPLY SLICE SHIFT

Figure 5.3: Scheme of the reconstruction pipeline for the prospective motion correc-

tion. The PT is extracted readout-by-readout from the acquired data. Together with the

image data, a linear motion model is derived online. The model parameters are used

for the following scans. The calculated shift is then sent to the sequence, and the slice

position is adapted during the scan.

Calibration pipeline To derive motion models, all data of the calibration scan cov-

ering the respiratory cycles must be assembled. As a first step, the readout position

corresponding to the PT frequency is detected by finding the highest absolute signal

value in the oversampling region in all acquired data. The readout position is saved

for later scans, where the PT will be extracted only at that position. The reference

signal is subtracted from the data, which was earlier described in section 3.2.4.

The ROI for the correlation is defined manually by selecting a rectangular re-

gion around the heart utilizing the shimming box before the start of the sequence.

Taking all reconstructed images into account, the translational motion of the ROI

is registered using a normalized 2D cross-correlation function, with the first image

as a reference. The PT received with each coil is fitted with a linear model to the

estimated heart shifts, and the corresponding R2is calculated.

Figure 5.4A shows an exemplary cardiac shift in HF direction obtained from

54 5.2 Methods

(B)

Extracted pilot tone from 3 coils (out of 32)

(C)

Derived motion models from 3 coils (out of 32) for HF direction

1.448 1.454 1.46

PT (a.u.)

R2=0.896

1.118 1.12 1.122

R2=0.312

0800 1600

Readout #

0 800 1600

Readout #

0800 1600

Readout #

1.44

1.48

PT (a.u.)

1.11

1.13

0.36

0.38

median filtered PT

PT (a.u.)

Coil 1 Coil 2 Coil 3

Coil 1 Coil 2

0.36 0.37 0.38

R2=0.978

PT (a.u.)

Coil 3

Cardiac shift

(mm)

median filtered PT median filtered PT

(A)

Obtained respiratory induced heart motion in HF direction

Cardiac shift

(mm)

Cardiac cycle #

610 14 18 22

Figure 5.4: (A) Obtained respiratory induced cardiac shift in HF direction of a cal-

ibration scan. (B) PT signal acquired during a calibration scan for 3 out of 32 coils.

For illustration purposes, only a fraction of the complete signal is shown. (C) Derived

motion models for 3 out of 32 coils for HF motion. The coil leading to the highest

linear regression coefficient is used for the following slice tracking measurements. In

this example, coil 3. This figure was published in J1.

sagittal images of a calibration scan. The PT and the resulting motion models are

shown in Figure 5.4B and C for different coils.

The motion model parameters determined for the coil with the highest R2in HF

direction are stored in a text file. The model parameters, the coil number, as well

as the slice orientation are stored for the following scans on the host computer of

the scanner.

Motion-correction pipeline At the beginning of the motion-corrected scan, prior

to the data acquisition, the model parameters are loaded. During the running

sequence, the heart shift is predicted for every readout from the extracted PT and

the motion model. Through-plane motion correction is then applied prospectively

during the measurement by adapting the frequency of the RF pulse. This ensures

that the slice position follows the respiratory motion of the heart for each TR.

Slice tracking with the PT must be performed along the orthogonal of the imaging

plane. Otherwise the frequency position of the PT in k-space would change and the

PT could no longer be extracted. The PT signal is subtracted readout-by-readout

5.3 Experiments 55

from the k-space data, before passing the data on for further processing.

The rigid motion correction is designed for the selected ROI. Tissue that lies

outside the ROI and moves differently is not corrected or wrongly corrected with

this approach.

5.3 Experiments

The following experiments were performed at 3T (MAGNETOM Verio, Siemens

Healthcare, Germany). The retrospective motion correction was performed on 3

subjects (2 female, 1 male, age 30±2 years) and the prospective motion correction

was tested on four subjects (2 female, age 45±19 years). The local ethics board

approved the in vivo experiments and written informed consent was given by all

subjects. Data analysis and image visualization were carried out using MATLAB

2017a (The MathWorks, Natick, MA).

Calibration scan for retrospective motion correction The calibration scan pa-

rameter for the 3D motion correction were previously presented in section 4.3.1.

Respiratory belt data, MR-navigator data and the PT were acquired simultane-

ously with the MR data. For the calibration, two image orientations (sagittal and

coronal) were acquired per cardiac cycle.

Calibration scan for prospective correction In this chapter, the prospective mo-

tion correction scan with the PT is performed in transverse orientation. Therefore,

it is sufficient that only the translational HF motion of the heart is captured with

the calibration scan. The calibration scan for the prospective correction consisted of

60 cardiac, ECG-triggered, sagittal, dynamic images. An inhouse-modified bSSFP

sequence was used with TE=1.5 ms, TR=3.2 ms, FOV=300x300 mm2, FA = 30◦

and voxel size=1.6x1.6x5 mm3.

5.3.1 Motion correction

The sequence parameter of the retrospective and prospective motion correction

scans, which are performed after the calibration scans, are shown in Table 2.

Retrospective motion correction The 3D data was obtained during free-breathing

simultaneously with the motion surrogates. The shifts in HF, AP and RL were ret-

rospectively determined using the three surrogates. Image registration was carried

out and the shifts were applied to the data based on equations 15 and 16 for retro-

spective motion corrections in k-space. The results can be compared well, since the

surrogates were recorded simultaneously.

56 5.3 Experiments

Motion correction scan Retrospective Prospective

Measurements 1 20

Surrogates PT, Resp. belts, MR-nav PT

Triggering ECG-triggered ECG-triggered*

Sequence inhouse-modified FLASH inhouse-modified bSSFP

Orientation 3D 2D transverse

TE/TR 4.1/7.3 ms 1.5/3.2 ms

Flip angle 20◦30◦

FOV 300×244×32 mm3300×300 mm2

Voxel size 1.6×1.6×2 mm31.6×1.6×5 mm3

Table 2: Scan parameters for 3D (retrospective) and 2D (prospective) motion corrected

scans. *For phantom measurements an ECG signal was simulated with 1 Hz.

Prospective motion correction A dynamic MR acquisition consisting of 20 dy-

namic images with the same scan parameters as used for the calibration scan, but

in transverse orientation, was carried out during free-breathing, with and without

motion correction in HF direction.

5.3.2 Estimation of respiratory motion amplitudes

The amplitudes of respiratory motion in HF, AP, and RL direction during differ-

ent breathing patterns were analyzed using an existing data set to determine the

dominant motion directions which should be considered during calibration.

To gain knowledge about the magnitude of respiratory motion, a dataset provided

by King’s College, London, UK, was analyzed. These data are only used for this

specific analysis, since they were recorded without navigator signals. The dataset

contains cardiac data from 23 subjects. Dynamic respiratory resolved cardiac-

triggered images of the heart were present, acquired with a FOV=350×350×80 mm3

and voxel size= 2.43×2.43×4 mm3. The sagittal orientation shows images of

size 35×35 cm, while the coronal orientation shows only a smaller area of 8×35 cm,

see Figure 5.5. The blue line displayed in the figure serves as a guide to visu-

alize the different motion states. The MR scans were carried out for 120 s and

different breathing patterns, as in [135]. During the first 40 s, the subjects were

asked to breathe normally, then fast for 40 s, and then carry out deep breathing

for the remaining 40 s. Three subjects only performed normal and deep breathing

for a total of 80 s. The ROI for motion registration was chosen manually for each

subject, covering the heart in sagittal-, and the left ventricle in coronal direction.

Using the open-source registration algorithm package ”NiftyReg” [145], provided by

UCL, UK translation, rotation and scaling motion components (affine motion) were

determined.

In order to improve the accuracy of the motion estimation, the translational mo-

tion data for the three registered motion directions HF, AP and RL was spline inter-

polated along the time dimension giving 10 values/RR cycle instead of 1 value/RR

5.4 Results 57

Sagittal - end expiration Coronal - end inspiration

Sagittal - end inspiration

Figure 5.5: Images from data provided by King’s College London. The line serves as

orientation for the breathing states.

cycle. The maximum motion amplitude was found for each respiratory cycle using

MATLAB’s internal ”findpeak” function. The maximum motion amplitude was then

averaged for each breathing type over all subjects, yielding the mean translational

motion in HF, AP, and RL. The rotations and scaling of the ROI were determined

analogously.

5.4 Results

5.4.1 Retrospective motion correction

In Figure 5.6 reformatted images showing the coronary arteries for the different

motion surrogates are displayed. The visualization was carried out with the tool

Soap-Bubble [146]. Motion correction using the MR-navigator and PT improved

visibility of the coronary arteries. The motion correction using the respiratory belt

did not lead to an improvement in image quality.

Figure 5.6: Reformatted images for the different motion surrogates. The MR-

navigator leads to the best depiction of the coronary arteries but also the PT improves

the visibility of the coronary arteries. This figure was published in C1.

58 5.4 Results

5.4.2 Prospective motion correction

Figure 5.7 shows a comparison of dynamic 2D measurements without motion cor-

rection (A) and with the slice tracking method (B). Six respiratory motion states

are displayed. The respective heart shifts derived from the PT signal are also shown

as blue dashed lines. The PT indicates a heart position shift up to 16 mm in HF

direction. The shift curves are not continuous because the PT is acquired together

with the ECG-triggered MR data, and they are not smooth because a sliding win-

dow median filter was applied to the PT. Through-plane motion in the heart region

can be seen in the uncorrected images (yellow arrows) and is reduced after motion

correction. The red arrows point at anatomy around the vertebrae that is not in

motion during respiration. Therefore, this motionless anatomy appears unchanged

in the uncorrected images, while it changes with slice tracking.

5.4.3 Range of respiratory motion magnitude

Respiratory translation curves for HF, AP, and RL direction obtained with image

registration for a subject are displayed in Figure 5.8. The first 40 s show normal

breathing, followed by fast breathing and deep breathing phases.

The obtained results of the motion analysis for all subjects are summarized in

Table 3. The dominant breathing component for all breathing types was HF trans-

lation. For normal and fast breathing patterns, mean motion amplitudes along HF

and AP lay above the voxel resolution of this dataset. The translational motion

was least pronounced in RL direction and lay below the voxel resolution. For deep

breathing, all mean motion amplitudes exceeded the voxel resolution.

All values for normal breathing are in accordance with the literature values [28,

50, 147].

The maximum rotation of 3◦, as indicated in the table for deep breathing around

AP, would result in a displacement of ≈0.3 cm at the outermost point of the heart,

when assuming a heart radius of 6 cm. Scaling by 2% would result in an enlargement

of the ROI by ≈0.24 cm. Nevertheless, the obtained scaling and rotation values refer

to the entire heart. For a 2D slice of the heart these values would be much smaller.

5.4 Results 59

Figure 5.7: Two-dimensional dynamic scans with 20 repetitions (A) without slice

tracking and (B) with slice tracking. The heart motion (Shift) was derived from the

PT signal for both scans. MR images from six different respiratory motion states are

depicted. Position curves are not smooth because the PT signal was median filtered.

The through-plane motion of the heart was minimized with the slice tracking method.

(A) Respiratory heart motion through the image plane can be seen (yellow arrows).

The applied slice shift in (B) can be seen clearly as a change of the anatomy around

the vertebra (red arrows). Parts of this figure were published in C2.

60 5.5 Discussion

0 20 40 60 80 100 120

Time (s)

-15

-10

-5

Registered heart motion (mm)

Head-feet

Anterior-posterior

Right-left

Figure 5.8: Instructed breathing pattern of a volunteer. The first 40 s show normal

breathing, followed by a 40 s fast breathing phase and a deep breathing phase.

Normal Fast* Deep

Head-feet translation (mm) 8.53±2.55 4.18±2.75 15.75±5.49

Anterior-posterior translation (mm) 2.07±0.97 1.14±0.51 5.37±4.08

Right-left translation (mm) 1.52±0.92 1.16±0.60 2.24±1.16

Head-feet rotation (◦)†1.55±0.89 1.50±0.92 2.54±1.64

Anterior-posterior rotation (◦)†1.91±1.04 1.71±0.76 2.94±1.84

Right-left rotation (◦)†1.60±1.21 1.86±0.86 2.31±1.99

Head-feet scaling factor 0.98±0.02 0.99±0.03 1.00±0.03

Anterior-posterior scaling factor 1.01±0.02 1.01±0.03 1.00±0.02

Right-left scaling factor 1.02±0.05 1.02±0.06 1.02±0.05

Table 3: Translation, rotation and scaling factors of the heart motion due to respira-

tory motion averaged over 23 volunteers for normal, fast and deep breathing. *Values

for fast breathing refer to only 20 subjects of the cohort. †angle is around the given

axis (head-feet, anterior-posterior, right-left)

5.5 Discussion

This chapter demonstrated the feasibility of using the PT as a motion surrogate for

retrospective and prospective respiratory motion corrections.

The retrospective 3D motion correction using the MR-navigator and PT improved

visibility of the coronary arteries. Unsuccessful motion correction using the respi-

ratory belt may be due to inaccurate temporal synchronization. The identification

5.6 Conclusion 61

of breathholding phases in the respiratory belt (0.5 ms resolution) and MR data (1

image/RR cycle) could have led to inaccurate alignment between surrogate signal

and MR raw data.

Prospective through-plane motion correction using the PT reduced respiratory

motion artifacts in the dynamic 2D images with transverse orientation. So far, only

the dominant HF motion information was utilized to demonstrate the feasibility

of this new approach. Further improvement in image quality can be expected by

utilizing also the AP motion information, which will be discussed in the next chapter.

Analysis of affine respiratory motion in a cohort of 23 subjects showed that

the most prominent direction of translational motion during normal breath-

ing was HF with 8.53±2.55 mm, followed by AP with 2.07±0.97 mm and RL

with 1.52±0.92 mm. RL motion remains on average below one voxel size for normal

breathing, while HF and AP motions exceed the voxel size.

Affine motion models are advantageous to linear motion models, due to the higher

accuracy for motion mapping [56]. However, using the existing data set of 23 sub-

jects, it was shown that rotation and scaling values are very small, thus approxi-

mating the respiratory motion by only taking translational motion into account is

a suitable approach.

For retrospective corrections, the calibration scan consisted of sagittal and coronal

images, which allowed to estimate all three motion directions. The motion correction

was then applied to the data retrospectively without time constraints. But for

prospective motion correction, the time between calibration and subsequent scan

should be kept as short as possible to minimize errors that could be introduced by

an unsuited motion model and also in favour of the overall scanning time. The

time needed for model formation depends on the amount of data to be processed.

Contributing factors are the number of images, coils and voxels. Therefore, for

prospective motion correction, the number of images in the calibration scan can be

reduced by only acquiring images of one orientation. Based on the data presented in

Table 3, the sagittal orientation is most convenient because it captures the prominent

motion directions HF and AP. Consequently, in the following chapters only images

from sagittal orientation will be used for calibration. For the set parameters with

60 images acquired for calibration, the model formation step takes ≈5 min.

5.6 Conclusion

The feasibility of using the MR-navigator and the PT for motion correction with

high temporal resolution was demonstrated. The advantage of the PT over the

MR-navigator is its versatility. It can be used even for continuous sequences where

MR-navigator data cannot be acquired because it would disrupt the magnetization

needed for the imaging scan. In the next chapter, such a continuous scan is used. A

prospective motion correction with the PT for cardiac cine scans will be performed

and examined.

Pilot tone–based motion

correction (PT-MOCO) for

prospective respiratory

compensated cardiac cine MRI

6.1 Introduction

Parts of this chapter have been published in J1 and C2.

Cardiac cine MRI is a commonly used tool to assess cardiac function in clinical

practice. The excellent soft-tissue contrast allows for the evaluation of cardiac func-

tion, and calculation of diagnostic parameters such as ejection fraction [86]. One

major challenge for cine MRI is to minimize artefacts due to respiratory motion,

which can corrupt image quality and thus diagnostic accuracy [33]. The preferred

imaging strategy is to avoid respiratory motion by using a breathhold, in which

often only a single 2D cine slice can be acquired [28].

As already discussed in section 2.4, for a full cardiac examination, breathholding

has to be repeated multiple times to ensure the ventricle is well covered with multi-

ple 2D slices [148]. Real-time imaging has been proposed to allow for cine imaging

without breathholding but often requires dedicated sequences and advanced recon-

struction schemes and limits the achievable temporal and/or spatial resolution [149,

150]. In addition, respiratory motion artifacts might still be present.

Another method to minimize image artifacts is respiratory gating based on the

MR-navigator [37, 58, 76]. This technique can be used for retrospective and prospec-

tive motion correction (slice tracking) [7, 41–43]. Commonly, to avoid disturbing the

magnetization in the heart region, the navigator monitors the position of the liver

rather than the heart itself, but for this the acquisition of diagnostic image data has

to be interrupted, which is not a problem for cardiac triggered sequences but for

continuous sequences. For more details on the MR-navigator, please refer to section

2.4. Retrospective motion correction for 2D cine MRI has also been proposed [58].

Nevertheless, this approach can only correct for in-plane motion and cannot recover

artifacts caused by through-plane motion also requiring additional gating.

In this chapter, a respiratory motion correction approach that uses the PT [10,

121] to perform prospective slice tracking for cine MRI and various slice orienta-

tions is presented. Due to the angulation of the slice, additional in-plane shifts are

introduced, which are corrected retrospectively. This technique allows for contin-

uous data acquisition and effective use of scan time, yielding cine images without

the need for breathholding. A feasibility study of the method was conducted in a

6.2 Methods 63

Figure 6.1: Overview of the two-step method. First, simultaneous acquisition of MR

data and PT data is carried out to calibrate the PT to the respiratory motion of the

heart and derive a linear motion model. Then, the data of subsequent scans can be

motion corrected prospectively during acquisition using the motion model and the PT

by adapting the location of the excited slice. Additional phase shifts for in-plane motion

correction, derived from the PT and the motion model, are applied retrospectively to

k-space data. This figure was published in J1.

motion phantom and 10 healthy subjects.

6.2 Methods

An overview of the method is given in Figure 6.1. In a calibration phase, 2D images

of the moving heart are simultaneously acquired with the PT. A motion model

linking the intensity changes of PT to the motion of the heart is derived. In the

previous chapter 5, the shift in HF direction was applied to dynamic transverse

images and only through-plane motion was corrected. Since diagnostic cine images

show different orientations of the heart, the imaging plane must be angulated, which

introduces in-plane shifts. Therefore, in this chapter through-plane and in-plane

motion are corrected in the correction phase. Through-plane motion is compensated

for by performing nearly real-time prospective slice tracking during the running MR

cine sequence. The slice tracking also ensures that a steady-state magnetization can

be achieved in the ROI. In-plane motion is corrected retrospectively by applying

64 6.2 Methods

the corresponding phase shifts to k-space data before image reconstruction. The

approach was compared to the breathhold technique as a ground truth. For more

details about the application of retrospective correction values or about the model

formation, please refer to section 5.2.1 and Figure 5.4, respectively.

6.2.1 Prospective through-plane correction

First, a calibration of the PT and the heart motion is performed with the calibration

scan. The second step is the motion correction during the cine scan. Using the model

parameters and the PT, the respiratory motion of the heart (∆HFpred,∆APpred) is

predicted for every readout. This motion is separated into through-plane and in-

plane components, as illustrated in Figure 6.2. Through-plane motion correction is

then applied prospectively during measurements by adapting the frequency of the

RF pulse to ensure that the excited slice follows the motion of the heart. The change

in slice position ∆

# »

SL, which is applied during data acquisition, can be described

as the orthogonal projection of the predicted shifts ∆HFpred and ∆APpred onto the

slice normal (

# »

SN) of the scan orientation:

∆

# »

SL =P# »

SN (

# »

M),(17)

where

# »

Mis the motion vector (︂0,∆APpred,∆HFpred)︂.

∆

# »

SL is then used during the scan by adapting the RF pulse accordingly. This

ensures that the excitation follows the respiratory motion of the heart for each TR.

6.2.2 Retrospective in-plane correction

In-plane motion is corrected for by adapting the phase of the acquired k-space data

prior to image reconstruction, as previously described in section 5.2.1. The phase

correction is applied by multiplication of the correction values

∆PE =P# »

PE(

# »

M) (18)

and

∆RO =P# »

RO(

# »

M) (19)

with the k-space data, where

# »

PE and

# »

RO are the slice orientation vectors of the

readout and phase-encoding direction.

6.3 Experiments 65

0 1000 2000

0.36

0.37

0.38

0 1000 2000

-4

-2

Real-time slice tracking shifts

Shift along Sag

Shift along Cor

Shift along Tra

0 1000 2000

-2

Retrospective in-plane shifts

Best fitting motion model (max. R )

Sliding window median filtered PT

Cardiac shift

(mm)

0.36 0.37 0.38

R2=0.978

PT (a.u.)

Coil 3

PT (a.u.)

Readout #

Readout # Readout #

Cardiac shift (mm)

Figure 6.2: Using the motion model and the PT, the predicted slice tracking shift is

calculated, and the slice position is adapted during the sequence. In-plane shifts are

applied retrospectively to the k-space data before image reconstruction. This figure was

published in J1.

6.3 Experiments

All experiments were carried out on a Siemens 3T scanner (MAGNETOM Ve-

rio, Siemens Healthcare, Erlangen, Germany). The local ethics board approved

the in vivo experiments, which were performed on 10 subjects (6 male, 4 female,

age 39±16 years, weight 71±17 kg). The parts of image reconstruction and evalua-

tion required for the application of the prospective correction were implemented on

the scanner, customizing the reconstruction chain (software syngo.MR B17). Appli-

cation of correction values to k-space data and the image visualization were carried

out using MATLAB 2017a (The MathWorks, Natick, MA, USA). The PT was gen-

erated as described in chapter 3.2.2 and the PT transmitting coil as shown in Figure

3.2B was used. For the phantom experiments, calibration scans (sagittal) and the

dynamic scans (sagittal and transverse), i.e., scans with one image per RR cycle,

were performed with the same scanning parameters as for the in vivo scans. Cine

imaging was not tested on the phantom.

6.3.1 Calibration scan

For calibration, sagittal 2D ECG-triggered dynamic data was acquired over

60 cardiac cycles and 13.5±5.4 respiratory cycles with FOV=(320×320) mm2,

voxel size=1.7×1.7×8 mm3, TE/TR=3.22/5.7 ms, pixel bandwidth=449 Hz/pixel

and FA=12◦during free-breathing using an inhouse-modified GRE sequence and

two-fold parallel imaging acceleration with 24 reference lines. Each single dynamic

image was acquired in an acquisition window of 507 ms in end-diastole.

6.3.2 Dynamic scan

To assess the performance of the method, dynamic measurements with the same

parameters as for the calibration scan were acquired. 20 images were captured, with

motion correction and without motion correction.

66 6.3 Experiments

6.3.3 Cine scan

For the 2D cine scans, the slice orientation was changed to SAX. Depending on the

subject’s heart rate, 28-30 cardiac phases were captured within 15-25 s using the

same FOV, voxel size, FA, and TE as for the calibration scan and a TR of 5.9 ms.

During the free-breathing scans, 1-7.5 breathing cycles were completed. Data was

acquired with retrospective ECG gating and two-fold parallel imaging acceleration

with 24 reference lines. A full stack of 10 SAX images and additional LA, 4CHV, and

transverse cine scans were acquired in one subject. For evaluating the performance of

this approach, the cine scans were acquired during free-breathing, with and without

slice tracking, and for reference purposes during breathhold. Cine images were

reconstructed using SENSE [151] without temporal or spatial filtering of the data.

6.3.4 Analysis

To assess how well the geometry of the anatomy is preserved with the pilot tone-

based motion correction (PT-MOCO), information on cardiac function was obtained

from the cine images. For this analysis, the left ventricular blood pool area was

measured for systole and diastole in the cine images obtained with the motion cor-

rection approach, and compared against the reference breathhold method using a

Mann-Whitney-Wilcoxon test, where p<0.05 was considered significant. The areas

of the blood pools were segmented by manual selection.

Further analyses were carried out regarding the contrast-to-noise ratio (CNR)

between the myocardium and the blood pool. For comparison, images from diastole

without motion correction, with PT-MOCO, and a breathhold scan were used. To

determine the CNR regarding the motion artifacts, areas of the septum and the

blood pool were selected manually. In addition, the sharpness of the endocardium

along the septum was also determined similar to previous work for coronary arteries

and abdominal imaging [152–154]. The highest sharpness value is 1, describing the

edge of a Heaviside step function.

The images were reviewed and evaluated by two independent observers with more

than five years experience in cardiac MRI in a randomized, blinded reading session to

assess cine image quality. For this purpose, the overall image quality was evaluated

on a scale of 0 to 3 for each slice. The following scale was used for blinded reading:

0 - images with poor and non-diagnostic quality due to motion-induced blurring,

1 - image quality impaired by motion which may lead to misdiagnosis, 2 - good

image quality, motion artifacts hard to recognize, and 3 - excellent image quality,

no motion artifacts observed [155].

6.4 Results 67

6.4 Results

6.4.1 Phantom

Motion correction for dynamic images Dynamic images of the moving phantom,

with and without slice tracking, are shown in Figure 6.3 for the different scan orien-

tations, sagittal and transverse. To visualize the motion of the structures during the

entire measurement, all 20 images were summed up. Without motion correction, the

image content changes during data acquisition due to the motion of the phantom, see

Figure 6.3 (top row). With motion correction, the acquired slice follows the motion

of the phantom, leading to the same image content during measurement. Motion

correction improves the depiction of the same underlying structure compared to the

uncorrected scan, leading to reduced blurring in the summed images.

Uncorrected

PT-MOCO

Sum

Rep.Nr.:

1613 20 Sum

1620

TRANSVERSE

SAGITTAL

5 cm

Figure 6.3: Two-dimensional dynamic scans with 20 repetitions with and without the

motion correction PT-MOCO of a moving phantom. MR images from four different

motion states are depicted, as well as the sum of all 20 images for sagittal and for

transverse orientation. The phantom motion was minimized with this motion correction

technique. The motion direction was HF, and, therefore, in the sagittal images, the

phantom moves in-plane, and for the transverse images, there is only through-plane

motion. This figure was published in J1.

6.4.2 In vivo

Motion estimation succeeded for all subjects. Figure 6.4 shows the cardiac shift as a

function of the PT for all 10 volunteers distinguishing also between inspiration and

expiration and head-feet (Fig. 6.4A) and anterior-posterior motion (Fig. 6.4B). The

linear models fit well for the majority of volunteers with no visible hysteresis effect.

For volunteers 2 and 7 there is a small difference for inspiration and expiration but

the difference is between 1 and 2 mm.

68 6.4 Results

4.2 4.3 4.4 4.5 4.6

Pilot tone (a.u.) x 10-5

Cardiac shift in HF (mm)

Subject 1

R2=0.94

2.8 2.9 3 3.1 3.2

Pilot tone (a.u.) x 10-5

-2

Cardiac shift in HF (mm)

Subject 9

R2=0.98

9.3 9.4 9.5 9.6 9.7

Pilot tone (a.u.) x 10-5

-2

-1

Cardiac shift in HF (mm)

Subject 2

R2=0.83

2.85 2.9 2.95 3 3.05

Pilot tone (a.u.) x 10-5

-2

Cardiac shift in HF (mm)

Subject 8

R2=0.90

1.6 1.7 1.8

Pilot tone (a.u.) x 10-5

-2

Cardiac shift in HF (mm)

Subject 7

R2=0.81

9.2 9.4 9.6 9.8

Pilot tone (a.u.) x 10-5

Cardiac shift in HF (mm)

Subject 10

R2=0.97

3.6 3.65 3.7 3.75 3.8 3.85

Pilot tone (a.u.) x 10-5

-10

-5

Cardiac shift in HF (mm)

Subject 3

R2=0.91

4 5 6 7 8

Pilot tone (a.u.) x 10-6

Cardiac shift in HF (mm)

Subject 5

R2=0.98

1.95 2 2.05 2.1 2.15 2.2

Pilot tone (a.u.) x 10-5

-6

-4

-2

Cardiac shift in HF (mm)

Subject 4

R2=0.98

0.9 1 1.1 1.2 1.3

Pilot tone (a.u.) x 10-5

-8

-6

-4

-2

Cardiac shift in HF (mm)

Subject 6

R2=0.98

inhale

exhale

Figure 6.4: Calibration data for 10 subjects. The data from 60 dynamic acquisitions

were fitted with linear regression curves and used for the motion models. (A) motion

models for head-feet direction and (B) motion models for anterior-posterior direction.

Parts of this figure were published in J1.

6.4 Results 69

(A)

(B)

Uncorrected

PT-MOCO

2 5 9 11 15

4710 13 16

in in

in in in

ex ex ex

ex ex

Figure 6.5: Free-breathing, 2D dynamic scans with 20 repetitions (A) without and (B)

with PT-MOCO. MR images from five different respiratory motion states are depicted

with numbers indicating the repetition number. The images were chosen to alternatingly

show end-inspiration (in) and end-expiration (ex). (A) Changes in the anatomy due

to respiratory through-plane motion are indicated with arrows. The horizontal blue line

gives a reference for in-plane motion. The motion of the heart (through-plane and in-

plane) was minimized with the slice tracking method, as can be seen by comparing the

regions where the arrows point at and the heart position with reference to the blue line

in (A) and (B). This figure was published in J1.

Motion correction for dynamic images Dynamic MR images, acquired in ≈17 s

with the ECG triggering, without motion correction, and PT-MOCO, are depicted

in Figure 6.5. Images were selected from the image stream, such that the depicted

motion alternates between end-inhalation and end-expiration, identified based on the

PT. Anatomical features such as the papillary muscles (red arrows), the pericardium

(green arrows), and the liver (yellow arrows) change during the measurement as the

tissue moves through the slice. In-plane displacement of the left ventricle can also

be clearly seen (blue arrows) and was up to 11 mm. PT-MOCO accurately corrects

for these motion displacements.

Motion correction for cine imaging In Figure 6.6 the scale-free PT and the mo-

tion shifts calculated with the motion model along the slice direction (Fig. 6.6B)

and in-plane (Fig. 6.6C) are shown. PT-MOCO resulted in improved cine image

quality for all subjects relative to the uncorrected images.

The isolated effects of the in-plane and through-plane correction on the full FOV

are shown in Figure 6.7. Without motion correction, strong artifacts can be seen

in the heart region. After through-plane correction was applied, motion artifacts

appear stronger and more globally throughout the body and FOV. After through-

plane and in-plane correction, artifacts in the heart region are minimized.

70 6.4 Results

500 1500 2500

Readout #

0.57

0.59

0.61

Pilot tone (a.u.)

500 1500 2500

Slice tracking shift (mm)

500 1500 2500

-2

In-plane shift (mm)

(B) (C)

(A)

Readout # Readout #

Figure 6.6: (A) Median filtered PT acquired for each phase-encoding line (i.e., each

TR). Using the motion model from the calibration, correction values for the real-time

through-plane correction (B) and the retrospective in-plane correction (along readout

(RO) and phase encoding (PE)) (C) can be calculated from the PT. This figure was

published in J1.

Through- and in-plane correction

No correction

Figure 6.7: Full FOV without motion correction, after through-plane correction and

with through-plane and in-plane correction

6.4 Results 71

Uncorrected

PT-MOCO

Breathhold

Diastole

Systole

Diastole

Systole

Diastole

Systole

Diastole

Systole

Uncorrected

PT-MOCO

Breathhold

Subject 1

Subject 2

Subject 3

Subject 4

Figure 6.8: Comparison of cine MRI acquired during free-breathing without (uncor-

rected) and with PT-MOCO. A standard breathhold cine scan is also shown for refer-

ence. For each subject, end-systolic and mid-diastolic phases are shown. It is important

to note that each method is acquired in a separate scan, leading to small differences in

the visualized anatomy. This figure was published in J1.

4CHV SAX Long axis

Transverse

Uncorrected PT-MOCO Beathhold Uncorrected PT-MOCO Beathhold

Systole Diastole

Figure 6.9: Images of end-systole and mid-diastole for 4 different orientations in one

healthy subject. For comparison, the standard breathhold cine scan is also shown. This

figure was published in J1.

72 6.4 Results

200 400 600 800 1000

Average systole area (mm2)

-20

-10

Systole area difference (%)

Figure 6.10: Bland-Altman plots comparing the difference of the left ventricular blood

pool area between the motion-corrected data and the breathhold data for systole and

diastole. Black and dashed blue lines show mean and ±1.96 SD limits of agreement of

the difference.

Figure 6.8 shows end-systole and mid-diastole of four subjects acquired during

free-breathing without correction and with correction using PT-MOCO. For com-

parison, data were also obtained during a single breathhold. End-systole and mid-

diastole for 4 different orientations in one healthy subject are shown in Figure 6.9.

Again for comparison, the standard breathhold data is also shown.

Information on cardiac function obtained from cine images with PT-MOCO was

compared with the breathhold technique as a gold standard, as seen in Figure 6.10.

The left ventricular blood pool areas were determined by manual selection for all vol-

unteers for systole and diastole. The mean differences between the reference method

and the approach were <3%, with standard deviations (SD) of 12.7% and 14.7% for

systole and diastole, respectively. The differences between the two methods were

not significant (systole: p=0.91, diastole: p=0.97).

The CNR with regards to motion artifacts for the uncorrected diastolic images was

found to be 7.6±2.7, for PT-MOCO 12.8±4.0, and for the breathhold data 13.8±4.9.

Significant improvements of CNR by 75±47% (p≤0.01) were found between the un-

corrected data and PT-MOCO and by 88±60% (p≤0.01) between the uncorrected

data and the breathhold data. The difference of PT-MOCO compared to the breath-

hold was not significant (p=0.9).

The sharpness of the endocardium was 0.13±0.04 for the uncorrected images,

0.16±0.03 for PT-MOCO images, and 0.19±0.03 for breathhold images. The sharp-

ness improved significantly by 30±27% (p=0.04) between the uncorrected data and

PT-MOCO. For the uncorrected data compared to breathhold data, the sharpness

improved significantly by 58±45% (p≤0.01), whereas for the breathhold data com-

pared to PT-MOCO data, differences were not significant with -16±12% (p=0.054).

The image score for the uncorrected data was 0.3±0.6, which was increased to

1.4±0.7 using PT-MOCO (p≤0.01). The difference of PT-MOCO compared to the

6.5 Discussion 73

Slice 1

Slice 3

Slice 4

Slice 6

Slice 8

Slice 10

Uncorrected PT-MOCO Breathhold Uncorrected PT-MOCO Breathhold

Systole Diastole

Figure 6.11: SAX cine MRI in one healthy subject. 10 slices (6 displayed) covering

the complete left ventricle were recorded. PT-MOCO leads to a reduction of respiratory

motion artifacts. This figure was published in J1.

breathhold cines, with an image score of 2.6±0.6, was also significant (p≤0.01).

6 slices (out of 10) of a SAX stack covering the left ventricle of a healthy subject are

displayed in Figure 6.11. It is important to note that the three scans, uncorrected,

with PT-MOCO and breathhold, were acquired as separate scans and hence can be

at slightly different scan positions.

6.5 Discussion

This chapter demonstrates the feasibility of PT-based prospective motion correction

for free-breathing cardiac cine MRI. The prospective motion correction approach,

which was demonstrated in section 5.4.2 on 2D dynamic images, was for the first

74 6.5 Discussion

time used here for cine imaging. In the previous section, the prospective correction

approach was only shown for HF motion on images with transverse orientation. In

this chapter, cine images were acquired mainly in SAX, but also in LA, 4CV and

transverse orientation. The change of orientation resulted in in-plane shifts, which

were corrected in a retrospective step, as described in section 6.2.2.

It was shown on a phantom and 10 healthy subjects that this approach led to

accurate motion correction and respiratory motion artifacts could be reduced.

So far, during calibration, a single coil was selected based on the linear regression

correlation coefficient R2. Bulk patient motion during the scan (i.e., shifts of the

entire body) could lead to a displacement of the receiver coils and amplitude changes

of the PT, which result in errors in the motion prediction. The PT appeared very

sensitive to a change in distance of the receiver coils and transmitter coil. Analysis

of this behavior was carried out in section 3.5.3. Combining the PT signal from

multiple receiver coils could improve the slice tracking approach. Another option to

overcome this problem could be to integrate the PT coil into the MR receive coil

array.

In this chapter, only translational motion along HF and AP direction was cor-

rected. Although the respiratory motion of the heart is most prominent along these

directions, as shown in section 5.4.3, also calibrating RL motion could further im-

prove the image quality. This could be achieved by using a sagittal and a coronal

calibration slice, one acquired in diastole and one in systole of each cardiac cycle.

This two-orientation-calibration was done already in section 5.4.1 for the retrospec-

tive motion correction.

The patient-specific linear model proved to be useful for approximating the respi-

ratory motion of the left ventricle. Figure 6.4 shows that the calibration worked well

(lowest R2values is 0.8 for HF), and there are only small differences (i.e., hysteresis

effects) between inspiration and expiration. More advanced models, such as affine

motion models or taking hysteresis effects between inspiration and expiration into

account, could improve the prediction of respiratory motion and image quality [46,

135, 156].

Currently, the same motion model for each slice position was used. The registra-

tion is carried out for the entire left ventricle, so the motion model fits very well

for a mid-ventricular region but is less accurate for apical regions. The further the

scan position deviates from the original calibration plane, the greater the errors of

the correction since the motion model no longer fits there. For example, in Figure

6.9 for the LA, the motion correction in the apex works less accurately than for

the mid-ventricular region, where the PT was calibrated for. Also, slices 1 and 10

in Figure 6.11 displaying the apex and the base of the ventricle, respectively, show

more motion artifacts than the slices covering the mid-ventricular region. Affine

motion models would allow to adapt the motion model better to the current slice

position and overcome this problem.

A median filter with a width of 100 readouts was applied to the PT to reduce noise

6.5 Discussion 75

in the signal. Therefore, the PT of the first 100 readouts may not be as accurate

as of the following signal. However, this did not have any visible effect on the cine

images since at most 7 readouts per cardiac phase are affected. In addition, the

filter leads to a temporal smoothing of the motion signal and hence a short delay of

50 samples, corresponding to 285 ms for the cine scans, between the estimated and

true motion of the heart. However, this delay is short compared to the duration of a

respiratory cycle. Other filters could overcome this problem, such as Kalman filters

[134], which have already been used with the PT for prospective cardiac triggering

[125].

Applying the individual motion correction steps showed that after only applying

the through-plane correction, motion artifacts were more pronounced than without

correction, see Figure 6.7. That is because through-plane correction is performed

along the slice normal and not along the direction of motion, which inevitably leads

to additional in-plane shifts. Combining both through-plane (slice-tracking) and

in-plane correction successfully minimized motion artefacts.

The motion model was optimized for the left ventricle but is applied globally to the

entire slice. The retrospective correction reduces motion artifacts for the ROI, but

the surrounding static tissue (e.g., back and spine) or tissue moving differently to the

heart (e.g., liver), is wrongly corrected, leading to residual artifacts for segmented

k-space acquisitions.

A correction with the PT could work even better for trajectories that sample

the k-space center multiple times (i.e., radial sequences) because these sequences

are more robust against motion artifacts, and, therefore, wrongly corrected tissues

would produce fewer artifacts.

For the comparison between the breathhold method and PT-MOCO, the left ven-

tricular blood pool areas were determined, instead of the EF, because only one slice

in SAX was acquired. The breathhold scan was always performed in end-expiratory

state. In contrast, the respiratory state used for slice tracking was arbitrary, and

the motion-corrected image may show a different SAX position and lead to errors

in the quantitative comparison.

Based on the PT and the dynamic images used for calibration, end-expiration

could be identified and used as a reference for the motion model to ensure slice

tracking is carried out to a more well-defined motion state.

The PT is independent of k-space sampling and thus could also be combined with

other sampling trajectories. Motion information is available with a high temporal

resolution, taking also variations in the breathing cycles into account. In addition, in

this prospective implementation, motion corruption is prevented during data acqui-

sition and, therefore, no additional reconstruction time for a retrospective motion

correction [57, 157] is needed. This makes this approach easy to integrate into

clinical practice.

CNR and sharpness of the endocardium show a significant improvement using PT-

MOCO compared to the uncorrected cine scan but are still not as good as breathhold

76 6.6 Conclusion

acquisitions.

For healthy subjects, a breathhold acquisition will provide the best image qual-

ity. Still, for patients having difficulties holding their breath, the PT-MOCO ap-

proach can improve the image quality significantly compared to an uncorrected free-

breathing acquisition. Nevertheless, studies on patients are still required to assess

the applicability of this approach in clinical routine. So far, this method was used

for cine imaging, but other continuous acquisitions, like MRF [158] or T1mapping

[159] could also benefit from the method.

In the next chapter, the motion correction approach is tested for T1mapping.

6.6 Conclusion

The PT provides a suitable motion signal for prospective respiratory motion correc-

tion. PT-MOCO showed a significant improvement in image quality compared to an

uncorrected free-breathing acquisition for all subjects. Further studies are required

to assess this method for clinical application. The next chapter evaluates whether

the prospective motion correction method with the PT is feasible for cardiac T1

mapping.

Pilot tone–based prospective

correction of respiratory

motion for free-breathing

myocardial T1 mapping and

cine imaging

7.1 Introduction

Parts of this chapter have been published in J2 and C3.

T1mapping is a non-invasive tool to diagnose and investigate various pathological

changes in the myocardium, [114, 160, 161]. Ischemic and nonischemic cardiomy-

opathies [162, 163] like fibrosis [164, 165], amyloidosis [166] and iron overload [167]

can be detected with native T1mapping, i.e., without administration of a contrast

agent. Furthermore, with a contrast agent, the myocardial extracellular volume

(ECV) can be calculated by measuring native and postcontrast T1[168] allowing,

for instance, better diagnosis of myocarditis [164, 169].

Common techniques for myocardial T1mapping include modified Look-Locker

Inversion recovery (MOLLI) and SAturation-recovery single-SHot Acquisition

(SASHA) [114, 170, 171]. For these techniques, after an inversion or saturation

pulse multiple images are acquired in a predefined cardiac phase but at different

inversion or saturation times. A model is then fitted to these images to calculate

the T1for each voxel. Despite the fact that these images provide accurate T1maps,

data acquisition is not very efficient, because only a small part of the cardiac cycle

is utilized to obtain diagnostic information. In addition, the cardiac phase in which

the T1map should be acquired, has to be defined prior to the scan and cannot retro-

spectively be optimized. This is particularly challenging for patients suffering from

irregular heartbeats. Recently, a continuous radial acquisition has been proposed,

which allows for the reconstruction of T1maps in different cardiac phases from the

same scan [159]. Cine images can also be reconstructed from the same data, allowing

to retrospectively optimize the selection of the cardiac phase.

Nevertheless, respiratory motion is still a major cause of artifacts in the estima-

tion of T1. If the whole heart is to be covered, several breathholds are necessary

since only one slice is acquired per breathhold. Although patients are asked to hold

their breath, previous studies on T1mapping have shown that respiratory motion of

the heart was still present in more than 40% of patients due to limited breathhold-

ing capability [5, 172]. This leads to misalignment between the qualitative images

78 7.2 Methods

acquired at different inversion times and errors in the voxel-wise T1estimation.

Retrospective motion correction approaches have been proposed to compensate

for this by realigning the obtained qualitative images but they can only correct for

in-plane motion and not through-plane motion [5, 173, 174]. To ensure both in-plane

and through-plane motion correction of 2D imaging, slice tracking approaches are

required, which update the slice position in real-time during data acquisition. Slice

tracking using an MR-navigator has also been proposed for motion correction of

free-breathing T1mapping [8, 42, 175]. Nevertheless, this approach is not applicable

to a continuous MR scan because respiratory navigators would interrupt the data

acquisition.

This chapter presents the use of a PT-based motion correction for free-breathing

myocardial T1mapping and simultaneous cine imaging. During the measurements,

the slice position is adapted in nearly real-time, and the motion of the heart during

breathing is tracked. This ensures that data at different inversion times are acquired

at the same position in the heart during the entire respiratory cycle. In addition to

this prospective through-plane motion correction, in-plane motion correction is also

carried out during image reconstruction based on the quantitative PT signal. This

technique is used for high-resolution T1maps without the need for breathholding.

A feasibility study of the method is conducted in a motion phantom and 11 healthy

subjects.

7.2 Methods

An overview of the method is given in Figure 7.1. A continuous radial acquisition

with multiple inversion pulses at predefined time points is used to obtain T1maps

and cine data [176]. For the motion correction approach, the PT is first calibrated

to the motion of the heart via a calibration scan that consists of sagittal ECG-

triggered images, one image acquired per cardiac cycle over several breathing cycles.

Two motion models for HF and AP direction are derived from the calibration.

With the calibrated PT signal, the respiratory motion in HF and AP direction

is then estimated for every readout during the subsequent scans. Through-plane

motion correction is applied during measurements by changing the frequency of the

RF pulse, thus enabling prospective slice tracking. In-plane motion is corrected

retrospectively based on the PT and the motion models. Additionally, non-rigid

image registration is used retrospectively to estimate and correct any residual motion

not captured by the PT.

7.2.1 Calibration scan

For the calibration scan, the PT and 45 sagittal 2D images of the heart are acquired

simultaneously in ≈45 s, such that the whole breathing cycle is displayed a few times.

A ROI covering the heart is chosen prior to the scan. For this, the manually defined

7.2 Methods 79

1. CALIBRATION SCAN

LINEAR MOTION MODEL

2. DIAGNOSTIC SCAN

SLICE TRACKING

MOTION CORRECTED DATA

INPLANE CORRECTIONS

T1 MAPPING

CINE

...

(a.u.)

∆

Figure 7.1: The motion correction method with the PT consists of two steps, the

calibration scan, and the T1mapping scan. During the calibration, HF and AP motion

of the ROI covering the heart are registered and correlated with the PT by two motion

models. During the motion corrected T1mapping scans, the RF excitation pulse is

adjusted for every readout to follow the heart motion during the scan (slice tracking).

In-plane motion correction is applied to the acquired k-space data retrospectively. A

modified version of this figure was published in J2.

shimming volume was utilized. Translational motion of the heart in HF and AP

direction is then estimated using image registration. The registered displacement of

the heart and HF and AP direction, and the pilot tone can then be correlated by

linear motion models, as described previously in section 4.2.2. In the subsequent

T1mapping scan, these models are used to predict the shift of the heart based on

the obtained PT signal. The accuracy of the motion correction achieved by the PT

is limited by the linear motion model and the calibration scan, which only covers

motion in the sagittal plane.

7.2.2 Continuous radial acquisition

To obtain T1maps and functional cine images from the same raw data, a continuous

golden-angle radial data acquisition is used [176]. Seven inversion pulses, indicated

as yellow bars in Figure 7.2, are applied repeatedly with a fixed predefined delay of

2.1 s. This delay has been shown to allow for accurate T1mapping for a wide range

of different heart rates [159, 176]. The start of the scan is triggered to mid-diastole,

but the following inversion pulses and acquisitions are carried out independent of

the cardiac phase. From the same raw data cine images can be reconstructed that

allow to differentiate between cardiac phases and enable T1mapping for diastole and

80 7.2 Methods

systole.

7.2.3 Motion correction

The imaging slice orientation is oblique. Because the PT frequency position must

not change during acquisition, only shifts along the slice normal are applied prospec-

tively. For this, the excitation RF pulse is adjusted for each readout without delay.

The adapted slice position ∆

# »

SL is then the orthogonal projection of the predicted

shifts ∆HFpred and ∆APpred onto the slice normal (

# »

SN) of the scan orientation, as

previously described in section 6.2.1. A retrospective in-plane correction of trans-

lational motion, as described in section 6.2.2 with the correction values ∆PE and

∆RO is also performed.

The entire process of extracting the PT signal from the raw data and calculating

the corresponding slice shifts is implemented in the reconstruction pipeline of the

vendor allowing direct communication with the running sequence.

After motion correction, artifacts induced by RL heart motion, which is not ac-

counted for in the motion model, might be present. It is assumed that the amplitude

of this residual motion is small. Therefore, it is sufficient to subdivide the acquired

data into four different motion states based on the PT signal, to resolve the motion

accurately.

The non-rigid image registration using a b-spline-based algorithm with mutual

information as similarity metric is carried out using regularization with a bending

energy penalty [177]. The first 100 readouts were not used to estimate the motion

fields because after the first inversion pulse, the received MR signal is in a very

different transient state before reaching a steady-state compared to the rest of the

acquisition. Also, the PT of the first 100 readouts may not be as accurate as the

following signal because a median filter with a width of 100 readouts was applied to

the PT to reduce noise in the signal. This affects less than 5% of the total number of

radial lines and, hence, there is still sufficient data available for motion estimation.

The obtained motion fields are then applied in subsequent motion-corrected image

reconstruction to further minimize respiratory motion artifacts [57, 157, 178].

7.2.4 Cine reconstruction

Cine images are reconstructed from the same raw data used for T1mapping by

resorting the radial lines into different cardiac phases based on the recorded ECG

signal [159]. In addition to the first 100 readouts not used for motion correction,

image data acquired after an inversion pulse are excluded in the reconstruction to

ensure a consistent dark blood contrast over all cardiac phases [176]. Respiratory

motion fields are applied during TV-regularized respiratory motion-corrected im-

age reconstruction [179]. This image reconstruction problem is solved iteratively,

and the motion fields are included in the MR acquisition model [57]. The acquisi-

tion model, therefore, describes the weighting due to multiple receiver coils, motion

7.2 Methods 81

transformation, Fourier encoding and radial k-space sampling. Total variation (TV)

regularization is applied spatially (λ=10−3). Coil sensitivities were calculated com-

bining all radial data. From the reconstructed cine images the rest period in diastole

or systole are visually selected.

The cine images reconstructed from these data show a dark-blood contrast. This

contrast results from applying global inversion pulses in the sequence and the fact

that the T1of blood is longer than that of myocardium (1900 ms compared to 1100-

1350 ms at 3T [180, 181]). To enhance contrast, only data are used where the signal

from myocardium is already positive during relaxation. The signal of blood is not

yet completely positive but still partly negative because of the longer T1, resulting

in a cancellation of blood signal intensities. [159].

Also reference cine images are acquired as in the previous chapter 6. These images

show a bright-blood contrast, because no global pulses are applied and blood flows

constantly into the 2D imaging plane. For GRE sequences the short TR lead to a

reduction of the signal from static tissue in the slice because of saturation of the

magnetization. The new blood flowing into the slice can be completely magnetized

and thus emit a higher signal (”inflow effect”) [182].

7.2.5 T1 mapping analysis

T1mapping is carried out for a predefined cardiac phase (e.g., mid-diastole or mid-

systole). The acquisition windows for diastole are illustrated as part of an ECG

signal in Figure 7.2. The pink region corresponds to mid-diastole. One T1-weighted

image per cardiac cycle is reconstructed with 43 radial lines for diastole, correspond-

ing to an acquisition window of 202 ms. Because the cardiac cycle and the pattern of

the inversion pulses are asynchronous, the images correspond to different inversion

times (TI).

Figure 7.2: Magnetization curve for continuously acquired data with seven inversion

RF-pulses. In this scheme, only data from mid-diastole, indicated with pink dots, are

used for T1reconstruction. This figure was published in J2.

82 7.3 Experiments

T1maps are reconstructed using the same TV-regularized image reconstruction as

above. The respiratory motion fields are applied during image reconstruction to en-

sure all TI images are in the same respiratory phase. The longitudinal magnetization

Mafter an inversion pulse can be described with a Look-Locker model [112, 113].

An extended inversion recovery Look-Locker model is used in a three-parameter fit

to estimate M0,T1and the flip angle (FA) voxel-wise [176]:

M(t) = Meff

0−(M+

j+Meff

0)e−(t−(j−1)TI)/T eff

1,(20)

where j is the number of inversion, M(t) is the relaxation after j’s inversion, and M+

is the magnetization before an IR pulse. The steady-state magnetization is defined

as [113]:

Meff

0=M0Teff

1T−1

1(21)

and Teff

1is the effective relaxation time for low flip angles:

Teff

1= [1/T1−(1/TR ln(cos(α)))]−1.(22)

Besides the mid-diastolic T1maps, systolic T1maps are reconstructed. To find the

systolic cardiac phase, cine images are reconstructed, and the systole is visually

selected. The cine images are used as a cardiac motion scout. The radial sequence

provides optimal results for mid-diastole, i.e., it is started using cardiac triggering

in mid-diastole. To accurately determine the T1for systole as well, the M0, which

is included in the fitting process for the generation of the systolic T1maps, is taken

from the previously reconstructed diastolic T1maps.

7.3 Experiments

All measurements were performed with inhouse-programmed sequences on a 3T

scanner (MAGNETOM Verio, Siemens Healthcare, Erlangen, Germany) on 11

healthy subjects (7 male, 4 female, age 30±7 years, weight 72±11 kg) after approval

of the local ethics board. Written informed consent was obtained in all cases. In

addition, phantom scans were carried out with an inhouse-built T1phantom placed

on a moving cart, allowing for translational motion along the bore direction [183].

The diameter of the tubes inside the phantom is 2.75 cm and the motion amplitude

in HF direction is 26.7 mm. The parts of image reconstruction and evaluation, which

were required to apply the prospective correction, were implemented on the scanner,

customizing the reconstruction chain (software syngo.MR B17). Retrospective mo-

tion correction, image reconstruction, and estimation of T1were carried out using

Python 3.7.

7.3 Experiments 83

Figure 7.3: Phantom setup showing the T1phantom and slice orientation tilted to the

long axis in head-feet direction. This figure was published in J2.

7.3.1 Scan parameters

For calibration, 2D ECG-triggered data were acquired over 45 cardiac cycles

and 7.2±3.3 respiratory cycles in the diastolic phase in sagittal view with

FOV=320×320 mm2, voxel size=1.7×1.7×8 mm3, TE/TR=2.1/4.7 ms and FA=5◦

using an in-house-modified spoiled gradient-echo sequence.

The simultaneous cine and T1mapping scan was performed continuously

during ≈15 s using an inhouse-modified 2D spoiled gradient echo sequence

(FOV=320×320 mm2, voxel size=1.7×1.7×8 mm3, TE/TR=2.1/4.7 ms) with a

golden-angle radial trajectory [159] resulting in a total to 3080 radial lines. Seven

inversion pulses were applied every 2.1 s independent of the cardiac cycle. The

scan was carried out during free-breathing without (uncorrected) and with motion

correction (corrected) and during a breathhold.

For comparing the cine data, a breathhold reference scan was acquired

with the same scan parameters as used in section 6.3.3 for the cine scans

(FOV=320×320 mm2, voxel size=1.7×1.7×8 mm3, TE/TR=3.2/5.9 ms, FA=12◦,

retrospectively ECG-gated).

An inversion recovery spin echo sequence (TI=25/50/300/600/1200/2400/4800

ms, TE/TR=12/8000 ms) was used to obtain reference T1values for the phantom.

In vivo a standard 5(3)3 MOLLI sequence with FOV=360x360 mm2, slice

thickness=8 mm, and in-plane resolution=1.4×1.4 mm2was used. MOLLI data

were post-processed, and T1fitted inline at the scanner [184]. In addition,

cine images with a standard gradient-echo sequence, FOV=320×320 mm2, voxel

size=1.7×1.7×8 mm3, TE/TR=3.22/5.9 ms, and FA=12◦were acquired.

In all subjects, a mid-ventricular SAX image was obtained. Additionally, a full

stack of 10 SAX images, 4CHV images, and LA images were acquired in different

subjects of this cohort. To reconstruct phantom T1maps comparable to the in vivo

measurements, an ECG of a subject was used for cardiac gating of the phantom

data. The phantom setup is displayed in Figure 7.3.

84 7.4 Results

7.3.2 Analysis

For the analysis of the phantom data, nine ROIs were manually drawn in the cen-

ter of each tube, and mean T1values were calculated and compared between the

reference scans and the uncorrected and corrected scans, respectively. In vivo data

were analyzed by segmenting the left ventricle, according to the American Heart

Association consensus statement [185], and comparing T1values of the six segments

of all subjects of the breathhold data with the uncorrected and corrected data, re-

spectively. The effect of the motion fields is determined by calculating the R2of the

T1fit of these segments with and without applied motion fields. MATLAB R2017a

and Python 3.7 were used for the analysis. Statistical data result from the Wilcoxon

test, where p-values <0.05 are classified as significant.

7.4 Results

7.4.1 Phantom

Time (s)

Figure 7.4: Comparison of uncorrected (top) and corrected (bottom) data. Left: 66

images, each reconstructed from 43 radial lines were overlayed. Middle: Single line

from the left image (cyan) displayed over ≈15 s to show the change in phantom position

during measurement. Black dropouts are due to the inversion pulses. Right: Intensity

change of one pixel (red cross) over ≈15 s. This figure was published in J2.

Due to the angulation of the phantom through-plane and in-plane motion were

present. The shift along HF estimated with the calibration scan was 21.8 mm. The

correction applied during the diagnostic scan was 15.5 mm for through-plane motion

and 15.4 mm for in-plane motion in readout direction.

Figure 7.4 gives an overview of 66 images, each reconstructed from 43 radial lines

with and without motion correction. To reconstruct phantom T1maps comparable

7.4 Results 85

T1 Corrected

T1 Uncorrected

500

1000

1500

2000

2500

T1 Reference (ms)

T1 Corrected (ms)

T1 (ms)

T1 Reference (ms)

T1 Uncorrected (ms)

T1 Reference scan

0 500 1000 1500 2000 2500

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

500

1000

1500

2000

2500

(A)

(B)

Figure 7.5: (A) T1maps of a moving phantom without motion correction and with

motion correction. For comparison, a reference scan was performed using an inver-

sion recovery spin echo sequence. Circles indicate the ROI. (B) T1of the tubes for

the uncorrected with 14±4% difference and the corrected scans with 3±4% difference

compared to the reference. The gray line indicates the identity line. This figure was

published in J2.

to the in vivo measurements, an ECG of a subject was used for cardiac gating of

the phantom data yielding 16 images. The circular ROI was manually placed in

the center of each tube with a diameter of 1.7 cm each not covering the residual

motion artifacts at the border of the tubes. In Figure 7.5 the resulting T1maps

are displayed (A), and the T1values of the uncorrected and corrected scans were

compared to the reference T1(B). T1of the surrounding material is 713±23 ms.

T1of the uncorrected data were significantly higher by 14±4% (p=0.008) than the

reference T1values. This is because the model fitting based on the reconstructed

images does not work for some pixels, due to the motion of the phantom, and the

T1values are overestimated. The difference between the corrected T1values and

the reference T1values was 3±4% and was significant (p=0.02). The T1maps of

the reference scan have a higher resolution and its acquisition time was 7×23 min

during which the phantom was motionless, such that the estimation of T1is very

accurate.

7.4.2 In vivo

T1maps of one subject were excluded from analysis because the reference breathhold

scan was mistriggered, which affected the comparability. The mean amplitude of the

respiratory induced heart motion across all subjects in the two calibration directions

HF and AP were 13.9±6.5 and 4.8±3.4 mm, respectively. The mean through-plane

motion ∆

# »

SL corrected during the running sequence with the PT was 7.4±3.7 mm.

Retrospective in-plane motion correction based on the PT was applied for a mean

86 7.4 Results

motion amplitude of 6.5±5.2 mm. The average amplitude of the non-rigid MF in a

ROI around the heart was 1.1±0.4 mm.

Three in vivo T1maps of the systolic heart phase acquired during free-breathing

without correction and with correction are shown in Figure 7.6. For comparison,

data were also acquired during a single breathhold and using MOLLI as a visual

reference. Each method was acquired in a separate scan resulting in small differences

in the visualized anatomy. Motion artifacts were reduced by applying the motion

correction method. T1maps are visually comparable to T1maps obtained by the

MOLLI sequence. 15±3T1-weighted source images went into estimating the T1

maps on average. Motion artifacts were reduced by applying the motion correction

method. T1maps are visually comparable to T1maps obtained by the MOLLI.

Figure 7.7 shows Bull’s-eye plots representing the mean T1values and standard

deviations of ten subjects for 6 myocardial segments. Differences of the uncorrected

data to breathhold data and corrected data to breathhold data were calculated, and

segments marked with * are classified as significantly different. The mean values

across all segments and subjects for the uncorrected data are 1557±377 ms, for

the corrected data 1283±33 ms, and for the breathhold data 1240±57 ms. Motion

correction resulted in T1values being more uniform as for the uncorrected T1maps

Subject 1

Subject 2

Subject 3

T1 (ms)

Figure 7.6: Native T1maps of three subjects acquired with a continuous radial trajec-

tory during free-breathing without (uncorrected) and with motion correction (corrected).

For comparison, T1maps acquired during a breathhold and MOLLI (also acquired dur-

ing a breathhold) are displayed. Each method is acquired in a separate scan resulting

in small differences in the visualized anatomy. This figure was published in J2.

7.4 Results 87

Uncorrected Corrected Breathhold

Figure 7.7: Bull’s-eye plots representing six myocardial segments of mid-ventricular

slices displaying T1and standard deviations averaged across 10 subjects in millisec-

onds. Segments marked with * are classified as significantly different. This figure was

published in J2.

across the myocardium. Respiratory motion led to an average overestimation of

T1values by 26±31% compared to breathhold T1maps. Average difference of T1

between breathhold and the free-breathing approach was 3±2% (p<0.05). The

greatest improvements were achieved for the anterior and anterolateral segments,

i.e., the segments directly adjacent to the lung. Averaged over these two segments,

the T1values before correction were 69±7% higher than the reference breathhold

values. This difference was reduced to 4±1% with the motion correction.

The mean R2of the fitted T1model without applied motion fields and with motion

fields for 6 segments and 10 subjects are displayed in Figure 7.8A. Differences of

the R2without and with motion fields are not significant except in the inferior

segment. Figure 7.8B and 7.8C show the T1maps of a subject and the corresponding

R2of the model fit. The arrows point to areas where the motion fields result in

improvements of the fit. Although the differences in T1are very small between these

two reconstructions, the non-rigid motion correction leads to an improvement in R2

especially along the edges of the myocardium suggesting a better alignment between

the images used for the T1fit.

Cine images with 28±3 heart phases were reconstructed from the same k-space

data as the T1maps. Figure 7.9 shows systolic and mid-diastolic images acquired

during free-breathing with and without motion correction and additionally acquired

during a breathhold. As a reference, a standard GRE cine is also shown. With

motion correction, respiratory artifacts were strongly reduced and the visibility of the

myocardium was improved. This enabled accurate determination of static periods

in cardiac cycle.

88 7.4 Results

Figure 7.8: (A) Bull’s-eye plots representing the R2of T1model for T1maps without

applied motion fields and with motion fields. * indicates the segment where the differ-

ences are significant (B) T1maps of a subject without motion fields and with motion

fields (C) R2map of the same subject with arrows pointing at regions where the motion

fields result in improvements of the fit. Parts of this figure were published in J2.

7.4 Results 89

Uncorrected Corrected Breathhold Reference

Diastole Systole

Systole

Systole Diastole

Diastole

Subject 1

Subject 3 Subject 2

Figure 7.9: Systole and mid-diastole of three subjects acquired during free-breathing

with and without correction. For comparison, breathhold data is also shown together

with reference data. This figure was published in J2.

90 7.4 Results

Furthermore, the T1maps reconstructed in systole and diastole with motion cor-

rection and during a breathhold are shown in Figure 7.10 for two subjects. In order

to identify peak systole and optimize the reconstruction window to minimize car-

diac motion artifacts, cine images were used as a scout. 30 and 23 radial lines

corresponding to a reconstruction window of 141 and 108 ms were used for subject

4 and 5, respectively. The same window duration for systolic and diastolic static

periods were used for better comparability.

Corrected Breathhold T1 (ms)

Subject 4

Subject 5

Systole

Diastole Systole

Diastole

Figure 7.10: Native T1maps of systolic and diastolic heart phases of two subjects with

motion correction (corrected) and for comparison of breathhold data acquired during a

separate scan. This figure was published in J2.

7.4 Results 91

Figure 7.11: SAX T1maps in one healthy subject. 10 slices (5 displayed) were

recorded, covering the complete left ventricle. The same calibration data was used for

all corrected images. For comparison, resulting maps of a breathhold scan and MOLLI

are displayed. Motion correction leads to a reduction of respiratory artifacts. Each

method is acquired in a separate scan resulting in small differences in the visualized

anatomy. This figure was published in J2.

Figure 7.11 shows five out of 10 T1maps of Subject 2 covering the left ventricle

in SAX acquired during free-breathing without correction and with correction. The

motion correction was based on the same calibration scan for all slices. Again, for

comparison, data were also acquired during a single breathhold and using MOLLI

as a visual reference.

92 7.5 Discussion

(A) Uncorrected Corrected Breathhold MOLLI

Subject 6

(B) Uncorrected Corrected Breathhold MOLLI

Subject 7

Figure 7.12: (A) Mid-diastole in 4CHV and (B) LA for two subjects acquired during

free-breathing with and without correction. For comparison, breathhold data is also

shown together with MOLLI data. The black circles highlight the lateral wall of the left

ventricle. This figure was published in J2.

In Figure 7.12 T1maps of two different subjects in 4CHV and LA are shown with

and without motion correction under free-breathing conditions. For comparison, a

breathhold scan and a MOLLI T1map are also displayed. The T1values in the

lateral wall of the left ventricle, as highlighted with black circles in Figure 7.12, are

more uniform with motion correction than without motion correction.

7.5 Discussion

In this chapter, the feasibility of PT-based prospective motion correction for free-

breathing T1mapping and simultaneous cine imaging was shown using the PT as

a motion surrogate. Phantom and in vivo measurements demonstrated improved

image quality and T1quantification using the motion correction approach compared

to motion uncorrected imaging.

In a phantom study, T1values obtained with motion correction showed accurate

T1quantification over a wide range of T1. Changes of the phantom over time due

to motion lead to inaccurate T1estimation, especially in areas with large differences

between neighboring T1values. The material, surrounding the nine tubes, had a

low T1of 713±23 ms. Therefore, the error of T1quantification was highest for tubes

with a high T1value.

A similar effect could be seen in the in-vivo applications. The highest errors in T1

quantification were found in the anterior and anterolateral segments which border to

the lung and showed very large signal differences. Significant differences were found

between the uncorrected scan and the breathhold scan for all segments except the

inferoseptal segment. The motion-corrected T1maps showed very similar T1values

to the breathhold scan, except for the anteroseptal segment. Nevertheless, in this

7.5 Discussion 93

segment T1values were lower in the breathhold scan compared to the other segments.

The breathhold scan was always performed in the end-expiratory state. However, for

slice tracking, an arbitrary breathing state was used. The motion-corrected image

may, therefore, show a different position in the SAX and could lead to errors in the

quantitative comparison.

Variations in heart rate or arrhythmias may result in TI images acquired at dif-

ferent cardiac phases and produce inaccuracies in the T1maps [115, 186]. For such

patients, the short resting phase of systole must be found very precisely. For this

purpose, cine images were reconstructed, which were used as temporal scout to find

the systole. The cine images reconstructed from the continuous data acquisition

showed poorer image quality compared to a conventional cine scan. Nevertheless,

they provided cardiac motion information which allowed for the retrospective opti-

mization of the data used for T1mapping.

The calibration scan was performed in a mid-ventricular ROI. As a result, the

motion of the mid-ventricular area was assumed to be estimated best. Nevertheless,

high image quality could be seen for all SAX images in the full stack of slices of a

subject, covering 8 cm along the long axis of the heart. A radial acquisition scheme

was chosen because it allowed combining cine imaging and T1mapping in one scan.

In addition, radial acquisitions are more robust against motion artifacts.

One of the limitations of this study is, that the rigid motion correction was only

performed for HF and AP direction ( i.e., the two prominent directions of motion

[28]) was performed. Additional correction of RL motion could further improve

image quality. Also, the same motion model for inspiration and expiration was

used, neglecting any hysteresis effects. Nevertheless, previous results (section 6.4.2

Fig. 6.4) have shown that these effects are small.

The correction of each individual readout line leads to inconsistency for static

tissue, which is then seen as streaking. But the T1 fit is not affected by this,

because these streaking artifacts are incoherent along time.

Depending on the subject and the selected slice orientation, the motion amplitude

varied. The determined motion model and correction parameters were only valid for

the chosen heart region but were applied globally to all image data. The surrounding

static tissue (e.g., back and spine) or tissue that moves differently from the heart

(e.g., liver) are wrongly corrected, which can result in artifacts. However, for radial

trajectories, these artifacts mainly lead to streaking artifacts which did not impair

the T1estimation of the heart in this study.

After PT-based rigid motion correction in the cardiac region, the residual motion

fields were on average small (1.1±0.4 mm) for SAX orientation, which indicated

that the PT-based motion correction was already very accurate.

Although motion artifacts are not immediately visible in the T1maps, respiratory

motion still impacted T1quantification, as was shown in Figure 7.8C. The small

differences of R2are because the selected segments do not necessarily include tis-

sue transitions and because the T1values are averaged across the segment. The

94 7.6 Conclusion

additional motion correction with the motion fields could further minimize residual

motion and improve T1fitting. Correction of in-plane respiratory motion is applied

retrospectively, and motion fields were estimated from the same data used for T1

mapping. Hence this step did not require any additional scan time.

For the reconstruction of the T1maps for systole, the model parameter M0was

taken from the model fit of the previously reconstructed diastolic images. To improve

the T1quantification, the same sequence could be started in systole instead of mid-

diastole.

Studies in patients who may have more complicated cardiac motion due to disease

are still needed to assess the applicability of this approach to routine clinical practice.

7.6 Conclusion

In this chapter, free-breathing myocardial T1mapping and simultaneous cine imag-

ing using a radial acquisition trajectory combined with a PT-based prospective

respiratory motion correction was presented. The method was tested on a motion

phantom and improved the T1estimation accuracy compared to uncorrected data.

Also, for the motion corrected in vivo data more accurate T1values were obtained

for the myocardium than for the uncorrected data. Cine images showed fewer mo-

tion artifacts using the motion correction approach. A future application of the

method would be high-resolution T1mapping, where the scan time is longer than a

breathhold. Further studies are needed to confirm this method in clinical practice.

8Summary

In this thesis, a novel PT-based respiratory motion correction method for cardiac

MRI was developed. This real-time approach is particularly beneficial when breath-

holding techniques can not be applied. The PT technology provides a stable motion

surrogate which is independent of the MR data acquisition and its signal sampling

does not interrupt the steady-state during the measurement. Because of these fea-

tures, the technology is widely suited for many applications.

In this work, the robustness of the PT was shown to be comparable to other motion

surrogates. The scale-free PT signal was successfully converted into a quantitative

surrogate by performing calibration scans and deriving motion models. Further-

more, it was demonstrated that the motion correction technique is applicable to

retrospective correction of 3D data and prospective correction of 2D images, where

data was recorded using a Cartesian as well as a radial sampling scheme. The

presented respiratory motion correction method was tested on a phantom and on

healthy subjects and improved image quality compared to the uncorrected data in

three different applications.

In chapter 3 the experimental setup of the motion phantom and the PT as well as

the acquisition framework was presented. The adjustable parameters, i.e., amplitude

and frequency, were optimized by testing various settings, such that a robust motion

surrogate signal was available for further experiments. Image quality impairment

due to the PT was minimized by subtracting a PT model signal from the k-space

data.

Because the PT is a very sensitive detector its signal was degraded by high fre-

quency noise due to vibrations. By applying an adaptive median filter with a sliding

window step size of 100, the noise was removed from the signal. A signal delay of

≈0.6 s was introduced, which is short compared to the length of a respiratory cycle.

Chapter 4 addressed the calibration procedure of motion surrogates to respira-

tory heart motion. Utilizing calibration scans, subject-specific linear motion models

were derived. With the models the qualitative PT was converted to a quantitative

motion signal. Further, the temporal stability of the PT in conjunction with the

models was tested and was found to be very high, with only a small increase of

the mean absolute error (MAE) between the predicted and the registered shift by

approximately 1.6 mm in the HF direction after a period of ≈8 min. On a phantom

it was shown that the PT with the motion model is long-term stable with an MAE

of less than 2.5 mm after ≈53 min in HF direction.

Other commonly used motion surrogates, i.e., the respiratory belt and the MR-

navigator, were compared with the PT by acquiring cardiac MR data simultaneously

with the surrogates. Linear motion models from the calibration scan yielded the

highest R2and best temporal stability for the MR-navigator (R2=0.95), followed

by the PT (R2=0.79) and the respiratory belt (R2=0.75). The smallest R2resulted

from the respiratory belt because the temporal synchronization of the belt with the

MR data was possibly not accurate, due to the different temporal resolutions of the

surrogate signals.

In chapter 5 motion correction was performed retrospectively on 3D data using

the three motion surrogates. The PT and the MR-navigator led to an improvement

in visibility of the coronary artery. However, the advantage of the PT over the

MR-navigator is its applicability also for continuous scans.

Also, the PT was initially tested for prospective motion correction in chapter

5. For this purpose, dynamic transverse 2D images of the heart were corrected

prospectively along the dominant HF motion direction. This method was success-

ful in reducing respiratory motion artifacts and served as a proof-of-concept for a

prospective motion correction.

Further, the dominant respiratory motion amplitudes of the heart during an MR

examination were determined to gain more information for the specific design of the

calibration scan. Existing data of a study on 23 subjects was analyzed. The mean

motion magnitudes for normal breathing were 8.53±2.55 mm, 2.07±0.97 mm and

1.52±0.92 mm for HF, AP and RL direction, respectively, and are in accordance

with literature [147].

The objective in chapter 6 was to apply the PT-based motion correction to con-

tinuous cine imaging with oblique slice orientation. Because for the prospective

motion correction the time between calibration scan and motion correction scan

should be kept short, only sagittal 2D images were acquired for the calibration, as

this orientation captures the two dominant directions of motion, HF and AP.

Again dynamic images were acquired, but the slice orientation was changed from

transverse to short axis. It was shown on in vivo data, that the sharpness of anatom-

ical regions (e.g., the heart) enhanced. The surrounding static tissue (e.g., spine) or

tissue moving differently to the heart (e.g., liver), was wrongly corrected and lead

to residual artifacts in the images.

From the calibration scans it has been shown on 10 subjects, that only small

differences (i.e., hysteresis effects) between inspiration and expiration were found.

Therefore, subject-specific linear models were a suitable solution for approximating

the respiratory motion of the heart.

The quality of the PT-corrected cine images improved for all subjects relative to

the uncorrected images. Analysis of the left ventricular blood pool areas showed that

the mean differences between the breathhold method and the motion correction with

the PT were <3%, with SDs of 13% and 15% for systole and diastole, respectively,

and not significant. Compared to the uncorrected images, CNR was improved by

75±47% and the sharpness of endocardium was improved by 30±27% using the

PT approach. There was no significant difference between PT-corrected data and

breathhold data.

In addition to the qualitative cine images, the proposed PT motion correction

method also improved quantitative cardiac T1maps, presented in chapter 7. Motion

correction was extended by a retrospective non-rigid correction step, and resulted

in T1values across the myocardium being more uniform as for the uncorrected T1

maps. Without motion correction respiratory motion led to an overestimation of T1

values by 26±31% compared to breathhold T1maps, which was successfully corrected

using the PT-based approach (3±2% (p<0.05)). Specifically in the segments which

border the lung, i.e., anterior and anterolateral segments, the average T1values

before correction were 69±7% higher than the reference breathhold data. After

motion correction, average errors in these two segments were reduced to 4±1%.

The non-rigid motion fields that were estimated retrospectively did not lead to

a visible change of the T1maps. A significant difference of the R2without and

with motion field correction was found only in the inferior segment. The fact that

the application of motion fields to the image data causes only such small effects

underlines that the rigid correction with the PT is already very accurate.

Nevertheless, improvements of the novel method could still be achieved in the

future. Throughout this work, the PT was recorded with the same coils as were used

for imaging. Although the main PT signal can be removed from the oversampling

region, even a small residual signal can impair the final image quality. The setup

could be optimized, such that the PT is recorded by an independent integrated

receiver coil, which would allow for the PT to be shifted even further away from the

imaging signal and hence reduce the negative effect of any residual PT signals.

In order to get a signal, free of artifacts caused by vibrations, it would be possible

to integrate the PT emitter within the receiver coils. This would eliminate the

sources of error that degrade the PT signal, which were presented in chapter 3.

With signal quality improvements, other optimization steps would be enabled,

for example, multiple receive channel signals could be combined for a more robust

surrogate signal. A coil combination would have the advantage that it would sample

signals at different spatial points and in combination with a PCA possibly result in

a more reliable and noise reduced surrogate.

Furthermore, prediction filters like the Kalman filter could be applied to the sig-

nal. The filter determines an adaptive forecast based on the analysis of previous

estimations [134]. Applying this predict-ahead filter could compensate even the

delay of a single TR, and thus be suitable for real-time applications.

Another field for optimization is the use of more advanced models, such as affine

motion models [46, 47, 187]. With these motion models, different breathing types

can be classified, such as deep breathing and short breathing, and also hysteresis

effects could be included [135]. Affine correction could be applicable to the whole

heart and would be more accurate. But the computational complexity and process-

ing time would also increase.

Besides the potential improvements, there are also new future perspectives. In

this study, T1maps were reconstructed for two cardiac phases from the data acquired

with the applied radial sequence. Previously, Becker et al. [176] used this sequence

to obtain T1maps for multiple cardiac phases. In the future, it could be a goal

to use the respiratory motion correction method presented here for free-breathing

cardiac-resolved T1mapping.

Also, the PT could be used for other MR imaging strategies for the heart that

are limited by breathhold duration (e.g., perfusion or MRF). With the PT, free-

breathing acquisitions with accurate prospective motion correction can be performed

for up to ≈53 min, as the PT is temporally stable and available with high temporal

resolution.

Other fields of application of the PT are multimodal approaches, e.g., when MRI

is combined with PET [124] or motion correction is applied for other organs that

are also affected by respiratory motion such as the liver.

An advantage of the PT technology, not highlighted in this work, is its applica-

bility as an alternative to an ECG signal. Conventionally, the ECG electrodes are

attached to the chest in proximity to the heart. The electrodes may impair MR im-

age quality, and the correct placement costs patient preparation time. Both of these

issues could be avoided with the PT. For this technique, the PT signal transmitter

and emitter are placed close to the heart. The beating motion of the heart can be

extracted by applying a PCA to the PT signal and separate the cardiac and respi-

ratory components. Studies regarding cardiac triggering with the PT were recently

conducted [122, 125, 188]. Using the PT as an alternative to the ECG would be of

advantage in clinical environment.

In this work, it was shown for the first time that the use of the PT allows ac-

curate prospective correction for free-breathing CMR acquisitions. With further

optimization, e.g., calibration with advanced motion models and better integration

of the hardware into the scanner, the PT could enable high-resolution sequence-

independent respiratory motion corrected CMR.

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List of Author’s Publications

Journal Articles

J1 Ludwig J, Speier P, Seifert F, Schaeffter T, Kolbitsch C. Pilot

tone–based motion correction for prospective respiratory compensated

cardiac cine MRI. Magnetic Resonance in Medicine, 2020;00:1–14.

https://doi.org/10.1002/mrm.28580

J2 Ludwig J, Kerkering KM, Speier P, Schaeffter T, Kolbitsch C, Pilot tone-based

prospective correction of respiratory motion for free-breathing myocardial T1

mapping, Magnetic Resonance Materials in Physics, Biology and Medicine,

2022. https://doi.org/10.1007/s10334-022-01032-4

J3 Dietrich S, Aigner C, Kolbitsch C, Ludwig J, Mayer J, Schmidt S, Scha-

effter T, Schmitter S, 3D Free-breathing Multi-channel absolute B1+ Map-

ping in the Human Body at 7T , Magnetic Resonance in Medicine, 2020.

https://doi.org/10.1002/mrm.28602

Conference Proceedings

C1 Ludwig J, Speier P, Seifert F, Schaeffter T, Kolbitsch C, Comparison of three

surrogate-based respiratory motion correction methods for 3D high resolu-

tion cardiac MRI, Proceedings of the 26th Annual Meeting of ISMRM, Paris,

France, 2018.

C2 Ludwig J, Speier P, Seifert F, Schaeffter T, Kolbitsch C, Pilot tone-based

prospective respiratory motion correction for 2D cine cardiac MRI, Proceedings

of the 27th Annual Meeting of ISMRM, Montr´eal, Canada, 2019.

C3 Ludwig J, Kerkering KM, Speier P, Seifert F, Schaeffter T, Kolbitsch C, Pi-

lot tone–based respiratory motion correction for 2D myocardial T1 mapping,

Proceedings of the 28th Annual Meeting of ISMRM, virtual, 2020.

C4 Dietrich S, Aigner C, Ludwig J, Mayer J, Schmidt S, Kolbitsch C, Schaeffter

T, Schmitter S, Respiration-Resolved 3D Multi-Channel B1 mapping of the

body at 7T, Proceedings of the 28th Annual Meeting of ISMRM, virtual, 2020.

C5 Neumann T, Ludwig J, Kerkering KM, Seifert F, Kolbitsch C, Ultra-wide-band

radar for respiratory motion correction of T1 mapping in the liver, Proceedings

of the 29th Annual Meeting of ISMRM, virtual, 2021.

C6 Neumann T, Ludwig J, Kerkering KM, Speier P, Seifert F, Kolbitsch C,

Prospective respiratory motion correction for 2D T1-Mapping in the liver us-

ing ultra-wideband radar system, Proceedings of the 30th Annual Meeting of

ISMRM, London, 2022, (accepted).

List of Figures

2.1 Anatomyoftheheart........................... 6

2.2 Illustration of blood circuit . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Simple ECG illustration . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Sagittal cine and short axis T1maps .................. 9

2.5 Illustration of plaque in artery . . . . . . . . . . . . . . . . . . . . . . 14

2.6 Cine acquisition pattern . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.7 MOLLI acquisition scheme . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1 Phantomsetup .............................. 21

3.2 DifferentPTcoils............................. 21

3.3 Receivercoilsetup ............................ 22

3.4 PTatfourchannels............................ 23

3.5 Hybrid k-space and resulting PT . . . . . . . . . . . . . . . . . . . . 23

3.6 PTatonereadout ............................ 25

3.7 PT in Cartesian hybrid k-space . . . . . . . . . . . . . . . . . . . . . 25

3.8 PT in radial hybrid k-space . . . . . . . . . . . . . . . . . . . . . . . 26

3.9 PT with different amplitudes . . . . . . . . . . . . . . . . . . . . . . . 29

3.10 R2for different PT amplitudes . . . . . . . . . . . . . . . . . . . . . . 30

3.11 PT with different frequencies . . . . . . . . . . . . . . . . . . . . . . . 30

3.12 PT on moving phantom for different frequencies . . . . . . . . . . . . 31

3.13 R2for different PT frequencies . . . . . . . . . . . . . . . . . . . . . . 31

3.14 PT with disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1 Respiratory motion model formation . . . . . . . . . . . . . . . . . . 36

4.2 Respiratory motion estimation . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Illustration of image acquisition per cardiac cycle . . . . . . . . . . . 38

4.4 Respiratory belt system . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Synchronization of respiratory belt signal and MR data . . . . . . . . 39

4.6 MR-navigator data extraction . . . . . . . . . . . . . . . . . . . . . . 40

4.7 Temporal stability for phantom measurement . . . . . . . . . . . . . 43

4.8 Pilot tone long-term stability . . . . . . . . . . . . . . . . . . . . . . 44

4.9 Temporal stability of pilot tone in vivo ................. 45

4.10 Temporal stability of pilot tone for irregular breathing. . . . . . . . . 45

4.11 Overlay of the surrogate signals . . . . . . . . . . . . . . . . . . . . . 46

4.12 Regression curves for the three surrogate signals . . . . . . . . . . . . 47

4.13 Temporal stability of the surrogate for HF motion . . . . . . . . . . . 47

5.1 Overview of motion correction method for 3D cardiac MRI . . . . . . 51

5.2 Overview of prospective motion correction method . . . . . . . . . . . 52

5.3 Modification of data pipeline . . . . . . . . . . . . . . . . . . . . . . . 53

5.4 Steps for motion model formation . . . . . . . . . . . . . . . . . . . . 54

5.5 Depiction of the data from King’s College . . . . . . . . . . . . . . . 57

5.6 Reformatted images for the different motion surrogates . . . . . . . . 57

116 List of Figures

5.7 Dynamic transverse images with and without motion correction . . . 59

5.8 Instructed breathing pattern of a subject . . . . . . . . . . . . . . . . 60

6.1 Overview of the motion correction method for cardiac cine MRI . . . 63

6.2 Illustration of pipeline from PT to correction values . . . . . . . . . . 65

6.3 Motion correction on a phantom . . . . . . . . . . . . . . . . . . . . . 67

6.4 Motion models for 10 subjects . . . . . . . . . . . . . . . . . . . . . . 68

6.5 Dynamic images with and without motion correction . . . . . . . . . 69

6.6 Projections of shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.7 Step-wise correction on full FOV . . . . . . . . . . . . . . . . . . . . 70

6.8 Images of diastole and systole with and without correction . . . . . . 71

6.9 Cine MRI in 4 different orientations . . . . . . . . . . . . . . . . . . . 71

6.10 Bland-Altman plots for blood pool area . . . . . . . . . . . . . . . . . 72

6.11 Images from SAX stack . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.1 Overview of the motion correction method for T1mapping. . . . . . . 79

7.2 Magnetization curve for T1mapping................... 81

7.3 Phantom setup for T1mapping ..................... 83

7.4 Phantom motion over time . . . . . . . . . . . . . . . . . . . . . . . . 84

7.5 Phantom setup for T1mapping ..................... 85

7.6 SAX T1maps ............................... 86

7.7 Bull’s-eye Plots for T1maps ....................... 87

7.8 R2of T1.................................. 88

7.9 Cine data of radial acquisition . . . . . . . . . . . . . . . . . . . . . . 89

7.10 SAX T1maps of systolic and diastolic heart phases . . . . . . . . . . 90

7.11 Bull’s-eye Plots for T1maps ....................... 91

7.12 T1mapsin4CVandLA ......................... 92

List of Tables

1 Sequence parameter for temporal stability tests . . . . . . . . . . . . 42

2 Sequence parameter for 2D and 3D motion corrected scans . . . . . . 56

3 Translation, rotation and scaling factors of the heart motion . . . . . 60