Citation: Pedan, V.; Koehling, R.;
Drexel, L.; Breitruck, K.; Rueck, A.;
Rohn, S.; Rienitz, O.; Pramann, A.;
Seidel, T.; Allenspach, E.; et al.
Combination of Standard Addition
and Isotope Dilution Mass
Spectrometry for the Accurate
Determination of Melamine and
Cyanuric Acid in Infant Formula.
Foods 2024,13, 2377. https://
doi.org/10.3390/foods13152377
Academic Editor: Roberto
Romero-González
Received: 18 June 2024
Revised: 19 July 2024
Accepted: 23 July 2024
Published: 27 July 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
foods
Article
Combination of Standard Addition and Isotope Dilution Mass
Spectrometry for the Accurate Determination of Melamine and
Cyanuric Acid in Infant Formula
Vasilisa Pedan 1, Rudolf Koehling 1,*, Lukas Drexel 1, Kathrin Breitruck 1, Alexander Rueck 1, Sascha Rohn 2,
Olaf Rienitz 3, Axel Pramann 3, Tim Seidel 1, Eric Allenspach 1and Markus Obkircher 1
1Sigma-Aldrich Production GmbH (Subsidiary of Merck KGaA), Industriestrasse 25,
kathrin.breitruck@merckgroup.com (K.B.); alexander.rueck@merckgroup.com (A.R.);
tim.seidel@merckgroup.com (T.S.); eric.allenspach@merckgroup.com (E.A.);
markus.obkircher@merckgroup.com (M.O.)
2Institute of Food Technology and Food Chemistry, Department of Food Chemistry and Analysis,
3Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany;
*Correspondence: rudolf.koehling@merckgroup.com; Tel.: +41-81-755-23-01
Abstract:
In the melamine scandals of the early 2000s, different companies of the dairy industry
cheated their products by applying chemical substances to feign a higher content of nitrogen. How-
ever, this had a severe toxic impact on the kidney health of consumers. As a result, tremendous
effort was put into the prevention of further harm to the public. In the present study, a fast–screening
method for the determination of melamine and cyanuric acid in infant formula was developed.
While a 1D–LC approach is faster and easier to set up, a 2D–LC approach allows for a more accurate
result with better selectivity and sensitivity. For both instrumental approaches, the signal ratio
of the isotopologues was crucial and had a dominant effect on the results and the measurement
uncertainty. For this reason, the different contributions to the measurement uncertainty were deter-
mined experimentally using Matched Standard Addition–IDMS and compared to the Exact Matching
Double IDMS.
Keywords:
isotope dilution mass spectrometry; proficiency testing; infant formula; two–dimensional
liquid chromatography; residues
1. Introduction
Chemical contaminants in food and feed are of great public concern due to their
potential health threats. The animal feed scandal in 2007 and the milk scandal in the
following year were significantly severe food safety incidents. Especially in the latter
scandal, the intentional adulteration with melamine (MEL) and cyanuric acid (CYA) did
not only lead to a non–negligible number of deaths of animals and humans, but also to food
recalls and widespread public outrage. As long–term consequence, intensified analytics
regarding food contaminants in dairy products were intended. Before those scandals,
only chemists dealing with plastics analysis knew about these industrial chemicals and
their use, but today, all kinds of food scientists must deal with adulteration of sources
of non–protein nitrogen. Both compounds are still in use in significant amounts as bulk
chemicals, whereby MEL formaldehyde is used as raisin for the fabrication of laminates,
plastics, glues, tableware, etc. [
1
]. CYA is a byproduct of the industrial use of melamine. It
is used as bleaches, disinfectant, and is most known as a stabilizer for chlorine in outdoor
pools [
2
]. Both compounds are chemicals with a high nitrogen content, which can induce
Foods 2024,13, 2377. https://doi.org/10.3390/foods13152377 https://www.mdpi.com/journal/foods
Foods 2024,13, 2377 2 of 17
misinterpretation of data from non–specific total protein measurement methods such as
Kjeldahl analysis.
MEL and CYA are water–soluble compounds, whereby MEL shows a water solubility
of 3.24 mg/mL H
2
O [
3
] and CYA shows a water solubility of 2.59 mg/mL H
2
O at 25
◦
C [
4
].
However, in concentrations exceeding 2
µ
g/mL, MEL and CYA crystallize in a one–to–
one ratio to form melamine cyanurate, a very poorly water–soluble complex [
5
]. Several
toxicology studies found evidence that the poorly soluble complex of MEL–CYA can cause
kidney failure in humans and animals [6,7].
Due to the increasing intensity and severity of food fraud in the past years, diverse
analytical methods have been developed and reported for MEL and its analogous CYA,
whereas lots of them use sample clean-up preparation to remove matrix compounds,
potentially disturbing analysis. Several sample preparation methods use and recommend
SPE (solid phase extraction) [
5
,
8
–
10
]. Because of complex matrices and to protect the
sensitive mass spectrometric (MS) systems, some working groups are using alternatively
LC–MS/MS [8] and GC–MS [8,11], also immunoassays [12] or HPTLC methods [13].
Trace analysis in food matrices is very challenging. Here, multidimensional separation
techniques are currently the state of the art. The 2D–LC method is claimed to be a more
powerful tool regarding peak capacity and sample complexity, further enabling the mass
spectrometer to analyze more compounds with high sensitivity [
14
]. Furthermore, a
2D–LC system can be used to overcome matrix effects that might interfere separation or
the following MS ionization.
To minimize matrix effects, the National Institute of Standards and Technology (NIST)
uses techniques based on isotope dilution mass spectrometry (IDMS), which can offer fur-
ther advantages to overcome matrix effects due to the similar behavior of the stable isotopes
and analyte in sample preparation, extraction, chromatography, and MS ionization [
15
].
In general, IDMS is applied preferably when the accuracy of the results is of predominant
analytical importance [
16
]. Especially the Exact Matching Double IDMS (EMD–IDMS)
technique eliminates instrumental biases and allows for a precise measurement of the
amount of substance in a sample against a similar reference material [17–19].
Despite instrumental effects on the measurement of the isotopologue amount, ratio
differences in the sample matrix itself can also lead to biases. To reduce the matrix effect,
MSA–IDMS can be introduced as a combination of standard addition and IDMS (Figure 1),
which was first presented by Pagliano and Meija [
20
] and improved a couple of years later
by Brauckmann and co–workers [21].
Foods 2024, 13, 2377 2 of 17
which can induce misinterpretation of data from non−specific total protein measurement
methods such as Kjeldahl analysis.
MEL and CYA are water−soluble compounds, whereby MEL shows a water solubility
of 3.24 mg/mL H2O [3] and CYA shows a water solubility of 2.59 mg/mL H2O at 25 °C [4].
However, in concentrations exceeding 2 µg/mL, MEL and CYA crystallize in a one−to−one
ratio to form melamine cyanurate, a very poorly water−soluble complex [5]. Several
toxicology studies found evidence that the poorly soluble complex of MEL–CYA can cause
kidney failure in humans and animals [6,7].
Due to the increasing intensity and severity of food fraud in the past years, diverse
analytical methods have been developed and reported for MEL and its analogous CYA,
whereas lots of them use sample clean−up preparation to remove matrix compounds,
potentially disturbing analysis. Several sample preparation methods use and recommend
SPE (solid phase extraction) [5,8–10]. Because of complex matrices and to protect the
sensitive mass spectrometric (MS) systems, some working groups are using alternatively
LC−MS/MS [8] and GC−MS [8,11], also immunoassays [12] or HPTLC methods [13].
Trace analysis in food matrices is very challenging. Here, multidimensional
separation techniques are currently the state of the art. The 2D−LC method is claimed to
be a more powerful tool regarding peak capacity and sample complexity, further enabling
the mass spectrometer to analyze more compounds with high sensitivity [14].
Furthermore, a 2D−LC system can be used to overcome matrix effects that might interfere
separation or the following MS ionization.
To minimize matrix effects, the National Institute of Standards and Technology
(NIST) uses techniques based on isotope dilution mass spectrometry (IDMS), which can
offer further advantages to overcome matrix effects due to the similar behavior of the
stable isotopes and analyte in sample preparation, extraction, chromatography, and MS
ionization [15]. In general, IDMS is applied preferably when the accuracy of the results is
of predominant analytical importance [16]. Especially the Exact Matching Double IDMS
(EMD−IDMS) technique eliminates instrumental biases and allows for a precise
measurement of the amount of substance in a sample against a similar reference material
[17–19].
Despite instrumental effects on the measurement of the isotopologue amount, ratio
differences in the sample matrix itself can also lead to biases. To reduce the matrix effect,
MSA−IDMS can be introduced as a combination of standard addition and IDMS (Figure
1), which was first presented by Pagliano and Meija [20] and improved a couple of years
later by Brauckmann and co−workers [21].
Figure 1. The principle of MSA−IDMS measurement is shown.
Although several MS methods are proposed for the analysis of MEL and CYA in
different matrices, there is still a need for high accuracy methods especially for developing
Figure 1. The principle of MSA–IDMS measurement is shown.
Foods 2024,13, 2377 3 of 17
Although several MS methods are proposed for the analysis of MEL and CYA in
different matrices, there is still a need for high accuracy methods especially for developing
certified reference materials (CRM) [
8
,
22
]. The aim of the present study was to develop a
fast–screening method for MEL and CYA. Beneath the one–point calibration as single IDMS,
additional sophisticated methods are used, like the combination of standard addition and a
double IDMS as described by Brauckmann and co–workers [
21
]. The adoption of MSA–
IDMS has been attempted for the analysis of organic analytes. For comparison, results
and uncertainty estimations were evaluated with the classic approach of EMD–IDMS as
well as MSA–IDMS. All samples and calibration blends were prepared gravimetrically
in a controlled environment with traceable temperature, relative air humidity, and air
pressure [
23
]. Further, this method should be verified through participation in The Food
Analysis Performance Assessment Scheme (FAPAS
®
) program of the UK, operating under
the Food and Environment Research Agency (FERA) of the UK, to gain ISO/IEC 17025:2017
accreditation for both chemical compounds and especially infant formula as a matrix
of interest.
2. Materials and Methods
2.1. Reference Materials
The non–isotopically labeled CRM of melamine (2,4,6–triamino–1,3,5–triazine), MEL,
was purchased from Merck KGaA (Buchs, Switzerland), while cyanuric acid (2,4,6–triol–
1,3,5–triazine), CYA, was purchased from Dr. Ehrenstorfer
™
(LGC Standards GmbH,
Wesel, Germany). The isotopic labeled materials were both purchased from Merck KGaA
(Buchs, Switzerland). The non–isotopically labeled homologous MEL has a chemical purity
of 0.9995 g/g. The CYA CRM was certified with a content 0.983 g/g. The isotopically
labeled homologous
13
C
3
–MEL has a chemical purity of 0.988 g/g. The chemical purity of
13
C
3
–CYA was stated with 0.996 g/g. Details about the distribution of the isotopologues
were not given.
For HPLC analysis, individual stock solutions of MEL, CYA, and their isotopically
homologous
13
C
3
–MEL and
13
C
3
–CYA were prepared at 1 mg/mL in water by adding
6% (60 mL/L) formic acid. The individual working solution was obtained at 0.01 mg/mL
by further dilution with acidified water. All solutions were stored in the dark at
−
20
◦
C.
In contrary to MEL, CYA is less water–soluble; for this reason, CYA and MEL were dis-
solved by sonication for 30 min in the volumetric flask. HPLC–grade ammonium formate,
acetonitrile, formic acid (0.99 g/g), and water were purchased from Merck KGaA.
2.2. Preparation of MEL and CYA in Infant Formula as an In–House Matrix Reference Material
CRM producers and laboratories need to participate in interlaboratory comparisons
for their accreditation according to ISO/IEC 17025. In this context, proficiency testing
(PT) vendors provide laboratories with specific samples contaminated with an appropriate
amount of the requested chemical substances added to the matrix [
19
]. The item code for
the PT sample in this study was 30,110 with a size of 50 g. In general, this PT round for 2021
was announced for food manufacturers and testing laboratories, whereby 22 participants
were subscribed for CYA and 39 participants were subscribed for MEL.
In the present study, a pure solution containing a known amount of CYA,
13
C
3
–CYA,
and MEL,
13
C
3
–MEL, respectively, was prepared as reference sample in the context of
double IDMS. The preparation of a reference sample for double IDMS resulted in smaller
uncertainties than single IDMS [
24
–
26
]. However, to better understand the influence of
the matrix on the measured result, a self–made in–house matrix reference material with a
known amount of CYA and MEL was prepared.
Hereby, the in–house matrix reference material was obtained by spiking the analytes
at the beginning of the sample preparation to compare chromatographic peculiarities
regarding matrix effect and peak shape with those of solvent–based curves. Therefore,
1 kg of infant formula was purchased from a local market and analyzed by an accredited
LC–MS/MS method to confirm that it was free of MEL and CYA. An initial powder to be
Foods 2024,13, 2377 4 of 17
used as working standard with a concentration of 4.3 mg/kg for MEL, and 3.8 mg/kg for
CYA, respectively, was gravimetrically prepared by dissolving an appropriate quantity of
the neat material in water by 38
◦
C. An accurately weighed aliquot of standard solution
was added into the infant formula by stirring for 30 min at 4
◦
C to ensure a homogenous
distribution of MEL and CYA in the infant formula. The sample was lyophilized and
ground to a fine powder with a blender. The mixed powder samples were dispensed into
clean amber bottles and immediately capped with lids. The final product was stored at
room temperature before analysis.
2.3. Sample Preparation for LC–MS Analysis
A homogenized test portion of 0.5 g infant formula was weighed into a 15 mL
polypropylene centrifugal vessel. An extraction solvent (8 mL) of 50% (V/V) aqueous
acetonitrile containing 6% (V/V) formic acid was added to extract the maximum amount of
MEL and CYA. Protein precipitation was performed by adding acetonitrile as part of the ex-
traction and precipitation solution. An aliquot of ca. 100
µ
L of each sample
13
C
3
–MEL and
13C3–CYA with a concentration of 0.01 mg/g was added to the extraction solvent. Herein,
the appropriate quantities of
12
C–MEL and
13
C
3
–MEL, as well as
12
C–CYA and
13
C
3
–CYA,
respectively, should have a mass ratio as similar as possible. The vessel was placed in
an ultrasonic bath for 30 min, mixed for another 30 min using an overhead shaker, and
centrifuged at RCF = 12,000
×
gfor 20 min (Labofuge
™
400, Fisher Scientific AG, Reinach,
Switzerland). The supernatant formed after centrifugation was filtered through a 0.45
µ
m
Filter (PP w/GMF, Whatman
™
, Huberlab AG, Industriestrasse 123, Aesch, Switzerland)
and transferred to vials for LC–MS analysis.
2.4. 2D–HILIC–ESI–MS/MS Analysis
In the 2D chromatography, only a part of the peak in 1D is cut out and running over
a second column, whereby less matrix contaminants enter the MS system. Furthermore,
just minor sample pretreatment can be applied as well, which is crucial for a precise
determination of the signal ratios with a large set of samples and multiple injections. Crude
infant formula solutions were analyzed directly by 2D–HILIC–ESI–MS/MS. Calibration
curves were obtained by injecting different concentrations of the standards, and the areas
obtained were used to plot a linear curve. For quantitative analysis, linear regression was
used (r2> 0.999 and N= 4).
Chromatographic separation was achieved using an Agilent 1260 Series LC system
(Agilent Technologies Inc., Waldbronn, Germany) coupled with ESI–MS/MS. Due to their
hydrophilic character, a hydrophilic interaction liquid chromatography (HILIC) column
was used. For 1D, the analysis was performed on a TSKgel
®
amide 80 (150 mm, 3 mm
ID, particle size 3
µ
m, Tosoh Bioscience GmbH, Griesheim, Germany) and for 2D on a
TSKgel
®
amide 80 (20 mm, 2 mm ID, particle size 3
µ
m, Tosoh Bioscience GmbH, Griesheim,
Germany), whereby both were maintained at 40 ◦C.
The 1D separation was achieved with a mobile phase consisting of (A) 5 mmol/L
ammonium formate in water (pH 3.0) and (B) acetonitrile and at a flow rate of 0.4 mL/min
with a gradient elution employed with the ratio of (A) and (B) varied as follows: 25% A
(0–4 min)
, 20–95% A (4–4.2 min), 95% A (4.2–7 min), 95–25% A (7–7.1 min), and a re-
equilibration with 25% A (7.1.1–11.5 min) (
≈
4 column void volumes). Sample injection
volume was 1
µ
L. CYA was eluted under these conditions at 2.47 min and MEL at 4.14 min.
Both compounds were cut out for the 2D separation with a sampling time of 0.1 min and a
loop filling of 40 µL.
In the present study, the same mobile phase was used for 1D as well as for 2D, but
with the following gradient for the solvents (A) and (B): 40% A (0–0.4 min), 40–90% A
(0.4–0.6 min), 90% A (0.6–1.4 min), and 40% A (1.4–2.8 min).
The MS detection was performed in multiple reaction monitoring (MRM) mode.
MRM transitions, optimized collision energy (CE), and fragmentor (V) parameters are
listed in Table 1. Shortly, mass detection was set at m/z 127
→
85 for
12
C–MEL and m/z
Foods 2024,13, 2377 5 of 17
130.1
→
86.9 for
13
C
3
–MEL with positive electrospray ionization mode, respectively, at
m/z 128
→
42 for
12
C–CYA and m/z 131
→
43.1 for
13
C
3
–CYA with negative electrospray
ionization mode. Nitrogen was used as curtain, nebulizer, and collision gas. The source
parameters including gas temperature, gas flow, nebulizer, sheath gas temperature, sheath
gas flow, and nozzle voltage were set to 220
◦
C, 6 L/min, 40 psi, 330
◦
C, 10 L/min,
and 1800 V, respectively. MassHunter Workstation (Quantitative Analysis for QQQ 10.1,
Agilent Technologies Inc., Waldbronn, Germany) software was used for system control,
data collection, and processing.
Table 1. The optimized fragmentor and collision energy for each transition of the 2D–LC–MS.
Name Precursor Ion
[m/z]
Product Ion
[m/z]
RT
min
Ion
Polarity
Collision
Energy V
Fragmentor
V
CYA 128.0 42.0 2.7 negative 12 50
13C3–CYA 131.0 43.1 2.7 negative 12 50
MEL 127.0 85.0 6.7 positive 16 113
13C3–MEL 130.1 86.9 6.7 positive 16 113
In general, the chromatographic sequence was set up as followed including the sample
with spiked IS, the reference sample with labeled and unlabeled MEL and CYA sample
including the IS spike and procedural blanks. For every 10 samples, HPLC grade water
was injected into LC–MS/MS to check for carry–over of target chemicals between samples.
2.5. Method Validation
The Eurachem Method Validation Guideline (Eurachem/CITAC) by Ellison, Roesslein,
and Williams [
27
] is the basis for the evaluation process of the LC–MS/MS methods with
respect to selectivity, repeatability, linearity, sensitivity, and robustness. The concept behind
the method validation is based on a single stock solution of the analyte for both parts,
sample and reference. The spike solution for all blends is also from one stock solution. As a
result, the content or concentration is kept constant and all biases and contributions to the
measurement uncertainty can be detected and measured.
Concerning the selectivity, both isotopologues showed no overlap in the monoisotopic
signals of the analytes, which is also crucial for the derivation of the IDMS equation. The
corresponding equations are described in the following sections.
This concept is applied for EMD–IDMS and MSA–IDMS, allowing for the determina-
tion of their performance characteristics including the trueness and precision of the result
including the sample preparation procedure and weighing, the precision of the signal ratio,
and intermediate precision. The concept also allows for the differentiation between single
contributions to the measurement uncertainty, e.g., instrumental bias, repeatability, sample
preparation, as well as the influence of matrix. All binary and ternary blends were prepared
from the same CRM and spike stock solutions, so that the content in sample and reference
is the same (w
X
=w
Z
). In that case, the target value of Equations (1) and (8) becomes
dimensionless. Deviations from the average value of a measurement to this target value can
be referred to as biases. The standard deviation of the repeated measurement of one blend
is used to determine the uncertainty contribution of the instrument u(inst), and the repeated
measurement of the whole set of blends yields the uncertainty contribution of instrument
and preparation u(inst) + u(prep), which also covers biases, e.g., undetected sample loss or
insufficient removal of static charges. The validation of the robustness focuses on a possible
bias caused by non–matched samples. Thus, two repetitions of non–matched standard
addition experiments were conducted with the PT 30110 sample (FERA/FAPAS
®
). The same
sample was analyzed also with the EMD–IDMS method as part of the corresponding PT by
FAPAS
®
, allowing for the cross–validation and comparison of the two different and partly
new methods.
Foods 2024,13, 2377 6 of 17
3. Results
3.1. Exact Matching Double IDMS (EMD–IDMS)
The aim of the present study was to develop a high–precision method for the deter-
mination of MEL and CYA in matrix samples. This method should be verified through
participation in the UK–based FAPAS
®
program, operating under the FERA of the UK, to
gain accreditation according to ISO/IEC 17025 for both chemical compounds and especially
infant formula as a matrix of interest. The results and uncertainty measurement were
evaluated with the classic approach of an EMD–IDMS as well as the MSA–IDMS.
IDMS is considered as a metrologically traceable method concerning the International
Systems of Units (SI) [
28
]. The EMD–IDMS quantification in the present study bases
on the equation derived by Henrion [
29
] and by Sargent, Harrington, and Harte [
18
].
Therefore, to achieve an accurate and precise measurement, all preparations were conducted
gravimetrically according to metrological weighing procedures [30].
However, one should bear in mind the differing definitions of the isotope amount
ratio, as they define the calculation of the signal ratios of analyte with natural isotopic
composition (A1) and its labeled isotopologue (A2).
wX=wZ·mY
mX
·mZc
mYc
·RB
RBc
(1)
wX= mass fraction of analyte in sample X (µg/g);
wZ= mass fraction of analyte in spike Y (mol L−1);
mY= mass of spike Y added to the sample X to prepare the blend B (mg);
mX= mass of sample X added to the spike Y to prepare the blend B (mg);
m
Zc
= mass of primary standard solution Z added to the spike Y to make calibration
blend BC(mg);
m
Yc
= mass of spike Y added to the primary standard solution Z to make calibration
blend BC(mg);
RB= isotope amount ratio of sample blend B;
RBc = isotope amount ratio of calibrant blend BC.
As described by Sargent, Harrington, and Harte [
18
], the isotope amount ratio is
defined by Equation (2):
RB=nX1E+nY1E
nX(2E)+nY(2E)∼A1
A2
(2)
n
X,Y
= amount of analyte
1
E (MEL, CYA) and isotopologue
2
E (
13
C
3
–MEL,
13
C
3
–CYA)
in sample X and spike Y;
A
1
,A
2
= signal areas of analyte or reference (A
1
) and the isotopologue or monitor (A
2
).
As discussed in other publications, the contributions to the measurement uncertainty can
be referred to the weighing of the sample, contributions of reference and spike solutions, and
the measurement of the signal ratios of sample–spike and reference–spike mixtures [
29
,
31
].
Usually, the major contribution arises from the signal ratios, which is influenced by the
ionization process, chromatographic system, and effects by the sample matrix itself. The
analysis of the measurement uncertainty for the EMD–IDMS measurements according to
the Eurachem/CITAC guide and the NIST calculation tool according to Ellison, Roesslein,
and Williams [
27
] is presented in Table 2. As the two mixtures are measured in a bracketed
sequence, the standard deviation of the signal ratio and the ratio of the signal ratios R
B
/R
Bc
are calculated from each subsequent pair. Each pair is injected repeatedly.
Foods 2024,13, 2377 7 of 17
Table 2.
Calculation parameters for the MCS (NIST Uncertainty Machine) of a typical EMD–IDMS
measurement of MEL in the PT 30110 sample (FERA/FAPAS
®
). Mean value and standard deviation of
the gaussian distribution and their results are w
X
(MCS) = 12.44 mg/kg (u(w
X
(MCS)) = 0.52 mg/kg)
and wX(GUM) = 12.43 mg/kg (u(wX(GUM)) = 0.52 mg/kg).
Measurand Mean uMonte Carlo Simulation
ANOVA (Relative Contributions in %)
GUM
ciGUM Index (ur2in %)
mX/mg 500 0.144 0.01 −0.025 0.0047
mY/mg 594 0.229 0.01 0.021 0.0085
mZc/mg 595 0.172 0.01 0.021 0.0048
mYc/mg 598 0.173 0.01 −0.021 0.0048
RB1.02 0.025 34.31 12.000 34.0000
RBc 0.97 0.030 54.37 −13.000 55.0000
wZc/mg/kg 10.0 0.14 11.13 1.2 11.0000
Residual – – 0.16 – –
IDMS requires a linear response of analyte and isotopologue. The signal area ratios
A(
13
C
3
–MEL)/A(MEL) or A*/Aversus the corresponding mass fractions m(
13
C
3
–MEL)/
m(MEL) or m*/mresults in a straight line through the origin with a defined slope, indicating
no interferences or instrumental biases between labeled and unlabeled compounds [
32
]. The
evaluation of the signal areas as a function of weighing ratios shows a straight line with
r
2
> 0.999 (Figure 2). The area ratio of CYA/
13
C
3
–CYA and MEL/
13
C
3
–MEL in the calibration
blend R
BC
and the sample blend R
B
should be within 0.95–1.15 and their corresponding
ratio R
B
/R
Bc
should be close to unity for minimum measurement uncertainty and instrumen-
tal bias.
Foods 2024, 13, 2377 7 of 17
Table 2. Calculation parameters for the MCS (NIST Uncertainty Machine) of a typical EMD−IDMS
measurement of MEL in the PT 30110 sample (FERA/FAPAS®). Mean value and standard deviation
of the gaussian distribution and their results are wX(MCS) = 12.44 mg/kg (u(wX(MCS)) = 0.52 mg/kg)
and wX(GUM) = 12.43 mg/kg (u(wX(GUM)) = 0.52 mg/kg).
Measurand Mean u Monte Carlo Simulation
ANOVA (Relative Contributions in %)
GUM
ci GUM Index (ur2 in %)
mX/mg 500 0.144 0.01 −0.025 0.0047
mY/mg 594 0.229 0.01 0.021 0.0085
mZc/mg 595 0.172 0.01 0.021 0.0048
mYc/mg 598 0.173 0.01 −0.021 0.0048
RB 1.02 0.025 34.31 12.000 34.0000
RBc 0.97 0.030 54.37 −13.000 55.0000
wZc/mg/kg 10.0 0.14 11.13 1.2 11.0000
Residual − − 0.16 − −
IDMS requires a linear response of analyte and isotopologue. The signal area ratios
A(13C3−MEL)/A(MEL) or A*/A versus the corresponding mass fractions
m(13C3−MEL)/m(MEL) or m*/m results in a straight line through the origin with a defined
slope, indicating no interferences or instrumental biases between labeled and unlabeled
compounds [32]. The evaluation of the signal areas as a function of weighing ratios shows
a straight line with r2 > 0.999 (Figure 2). The area ratio of CYA/13C3−CYA and
MEL/13C3−MEL in the calibration blend RBC and the sample blend RB should be within
0.95–1.15 and their corresponding ratio RB/RBc should be close to unity for minimum meas-
urement uncertainty and instrumental bias.
Figure 2. The linear calibration curve of analyte and isotopologue. Calibration curves are calculated
with individual (a) 12C3−CYA and 13C3−CYA mixtures; (b) 12C3−MEL and 13C3−MEL with five m*/m
ratios. MEL and CYA are in a high linear working range.
The standard deviations of the signal ratios s(RB/RBc) and of Equation (1) s(wx/wz) with
wx = wz are used to determine the repeatability and robustness (intralab, interday). Biases
can be calculated from the difference between the mean value and the target value of wx/wz
= 1. As the signals of the analytes MEL and CYA were separated by chromatography and
the measurement of the pure solutions did not indicate any interferences, additional bi-
ases must stem from the matrix itself or fractionation caused by overload of the HPLC
columns.
In the present study, CYA/13C3−CYA and MEL/13C3−MEL were used. However, with
regard to matrix removal and matrix effect, a heart−cut 2D−LC method was developed
and compared to the 1D−LC. For the 2D−LC, the retention time (RT) of the MS signals
must not vary more than 0.05 min. Otherwise, the system must be equilibrated longer.
Furthermore, the signal area of CYA and MEL in 2D should be constant. Figure 3 shows
the chromatogram(s) of the PT 30110 sample (FERA/FAPAS®) 30110 extract spiked with
Figure 2.
The linear calibration curve of analyte and isotopologue. Calibration curves are calculated
with individual (
a
)
12
C
3
–CYA and
13
C
3
–CYA mixtures; (
b
)
12
C
3
–MEL and
13
C
3
–MEL with five m*/m
ratios. MEL and CYA are in a high linear working range.
The standard deviations of the signal ratios s(R
B
/R
Bc
) and of Equation (1) s(w
X
/w
Z
)
with w
X
=w
Z
are used to determine the repeatability and robustness (intralab, interday).
Biases can be calculated from the difference between the mean value and the target value
of w
X
/w
Z
= 1. As the signals of the analytes MEL and CYA were separated by chro-
matography and the measurement of the pure solutions did not indicate any interferences,
additional biases must stem from the matrix itself or fractionation caused by overload of
the HPLC columns.
In the present study, CYA/
13
C
3
–CYA and MEL/
13
C
3
–MEL were used. However, with
regard to matrix removal and matrix effect, a heart–cut 2D–LC method was developed
and compared to the 1D–LC. For the 2D–LC, the retention time (RT) of the MS signals
must not vary more than 0.05 min. Otherwise, the system must be equilibrated longer.
Furthermore, the signal area of CYA and MEL in 2D should be constant. Figure 3shows
the chromatogram(s) of the PT 30110 sample (FERA/FAPAS
®
) 30110 extract spiked with
13
C
3
–CYA and
13
C
3
–MEL with an RT of 2.8 min for CYA and RT 4.4 min for MEL in 1D,
Foods 2024,13, 2377 8 of 17
and an RT of 4.0 min for CYA and RT 5.7 min for MEL in 2D. The analysis time nearly
doubled for the LC
×
LC. However, a negligible slope deviation was observed with low
impact on the resulting signal ratios.
Foods 2024, 13, 2377 8 of 17
13C3−CYA and 13C3−MEL with an RT of 2.8 min for CYA and RT 4.4 min for MEL in 1D,
and an RT of 4.0 min for CYA and RT 5.7 min for MEL in 2D. The analysis time nearly
doubled for the LC × LC. However, a negligible slope deviation was observed with low
impact on the resulting signal ratios.
Figure 3. Visual comparison of 1D−LC and 2D−LC implementation, whereby heart−cut LC × LC was
used where one single fraction of the 1D column is injected onto the 2D column.
As shown with the boxplot analysis for the isotope ratio (Figure 4), separations in 1D
and 2D for both compounds are not in accordance with each other, whereby a lower scat-
tering was observed for the 2D. This can be explained by the increasing resolution for 2D
as a result of the online sample clean−up in 1D. This result is in accordance with the study
described by Breidbach and Ulberth [31], who observed identical medians for their 1D
and 2D approaches, but with a smaller dispersion for the LC × LC. According to them [31],
the signal of the 2D was much higher and therefore had less scattering. However, although
the 2D displays a certain asymmetry especially for the MEL peak, it is very stable through-
out the sequence.
Figure 4. The repeatability was analyzed by repeated injection of the same sample (N = 12). A box-
plot representation for CYA (a) using 1D−LC and MEL (b) using 2D−LC shows the difference be-
tween the two methods. The black line in the middle of the boxplot depicts the mean of the two ion
ratios. Since A/A* is proportional to RB and RBc, the repeatability is a crucial factor in the combined
measurement uncertainty.
The distribution of all single results of the present study are shown as Monte Carlo
Simulation (MCS) in Figure 5. EMD−IDMS yielded the following content for infant for-
mula with 12.6 mg kg−1 ± 1.4 mg kg−1 for CYA and 12.2 mg kg−1 ± 1.0 mg kg−1 for MEL (k =
2). The certified value of the PT 30110 sample (FERA/FAPAS®) was set to 11.8 mg kg−1 for
CYA and 12.4 mg kg−1 for MEL, respectively.
Figure 3.
Visual comparison of 1D–LC and 2D–LC implementation, whereby heart–cut LC
×
LC was
used where one single fraction of the 1D column is injected onto the 2D column.
As shown with the boxplot analysis for the isotope ratio (Figure 4), separations in
1D and 2D for both compounds are not in accordance with each other, whereby a lower
scattering was observed for the 2D. This can be explained by the increasing resolution
for 2D as a result of the online sample clean-up in 1D. This result is in accordance with
the study described by Breidbach and Ulberth [
31
], who observed identical medians for
their 1D and 2D approaches, but with a smaller dispersion for the LC ×LC. According to
them [
31
], the signal of the 2D was much higher and therefore had less scattering. However,
although the 2D displays a certain asymmetry especially for the MEL peak, it is very stable
throughout the sequence.
Foods 2024, 13, 2377 8 of 17
13C3−CYA and 13C3−MEL with an RT of 2.8 min for CYA and RT 4.4 min for MEL in 1D,
and an RT of 4.0 min for CYA and RT 5.7 min for MEL in 2D. The analysis time nearly
doubled for the LC × LC. However, a negligible slope deviation was observed with low
impact on the resulting signal ratios.
Figure 3. Visual comparison of 1D−LC and 2D−LC implementation, whereby heart−cut LC × LC was
used where one single fraction of the 1D column is injected onto the 2D column.
As shown with the boxplot analysis for the isotope ratio (Figure 4), separations in 1D
and 2D for both compounds are not in accordance with each other, whereby a lower scat-
tering was observed for the 2D. This can be explained by the increasing resolution for 2D
as a result of the online sample clean−up in 1D. This result is in accordance with the study
described by Breidbach and Ulberth [31], who observed identical medians for their 1D
and 2D approaches, but with a smaller dispersion for the LC × LC. According to them [31],
the signal of the 2D was much higher and therefore had less scattering. However, although
the 2D displays a certain asymmetry especially for the MEL peak, it is very stable through-
out the sequence.
Figure 4. The repeatability was analyzed by repeated injection of the same sample (N = 12). A box-
plot representation for CYA (a) using 1D−LC and MEL (b) using 2D−LC shows the difference be-
tween the two methods. The black line in the middle of the boxplot depicts the mean of the two ion
ratios. Since A/A* is proportional to RB and RBc, the repeatability is a crucial factor in the combined
measurement uncertainty.
The distribution of all single results of the present study are shown as Monte Carlo
Simulation (MCS) in Figure 5. EMD−IDMS yielded the following content for infant for-
mula with 12.6 mg kg−1 ± 1.4 mg kg−1 for CYA and 12.2 mg kg−1 ± 1.0 mg kg−1 for MEL (k =
2). The certified value of the PT 30110 sample (FERA/FAPAS®) was set to 11.8 mg kg−1 for
CYA and 12.4 mg kg−1 for MEL, respectively.
Figure 4.
The repeatability was analyzed by repeated injection of the same sample (N= 12). A
boxplot representation for CYA (
a
) using 1D–LC and MEL (
b
) using 2D–LC shows the difference
between the two methods. The black line in the middle of the boxplot depicts the mean of the two ion
ratios. Since A/A* is proportional to R
B
and R
Bc
, the repeatability is a crucial factor in the combined
measurement uncertainty.
The distribution of all single results of the present study are shown as Monte Carlo
Simulation (MCS) in Figure 5. EMD–IDMS yielded the following content for infant formula
with 12.6 mg kg
−1±
1.4 mg kg
−1
for CYA and 12.2 mg kg
−1±
1.0 mg kg
−1
for MEL
(k= 2). The certified value of the PT 30110 sample (FERA/FAPAS
®
) was set to 11.8 mg kg
−1
for CYA and 12.4 mg kg−1for MEL, respectively.
Foods 2024,13, 2377 9 of 17
Table 3.
Results of the MSA–IDMS experiment for MEL/CYA in solution including the standard
deviations of the experimental data and the Monte Carlo simulation (MCS). They are similar to the
results of the EMD–IDMS experiments with two blends from the same CRM and spike stock solutions.
Target value for a0/a1= 1 with wZ=wX.
MEL CYA
<Rb,i> 1.221 ±0.008 (0.6%) 1.056 ±0.008 (0.8%)
urel (Rb,i) 3.7% 1.7%
a0/a11.003 ±0.034 (MCS) 0.994 ±0.017
Foods 2024, 13, 2377 9 of 17
Figure 5. Distribution of output quantity calculated from the MCS results of the NIST Uncertainty
Machine for CYA (a) and MEL (b) of the EMD−IDMS measurements of the PT 30110 sample
(FERA/FAPAS®, 2021) using Equation (1) and the parameter set in Table 2 for the NIST Uncertainty
Machine. Due to the symmetric Gaussian distribution of the simulated results, the mean values and
standard deviations do not differ significantly from median and coverage interval with 95% proba-
bility. The other numerical results are presented in Table 3.
Table 3. Results of the MSA−IDMS experiment for MEL/CYA in solution including the standard
deviations of the experimental data and the Monte Carlo simulation (MCS). They are similar to the
results of the EMD−IDMS experiments with two blends from the same CRM and spike stock solu-
tions. Target value for a0/a1 = 1 with wz = wx.
MEL CYA
<Rb,i> 1.221 ± 0.008 (0.6%) 1.056 ± 0.008 (0.8%)
urel (Rb,i) 3.7% 1.7%
a0/a1 1.003 ± 0.034 (MCS) 0.994 ± 0.017
3.2. Matched Standard Addition−IDMS (MSA−IDMS)
Based on the standard addition−IDMS technique [21], the present study also used a
procedure for the analysis of organic molecules, where the corresponding isotopologue
(“spike”) has no detectable overlap with the signals of the analyte molecule. This is usu-
ally the case for mass differences of 3 Da or more and a high content of the “spike” isotop-
ologue (>97% (g/g)). If an overlap occurs, it is necessary to characterize the “spike”, “sam-
ple”, and “reference” solutions individually and use Equation (2) with the individual con-
tributions to the isotope/isotopologue amount ratios for blend Rb,i, sample Rx, and spike
Ry as described in Brauckmann [21]:
𝑚,
𝑚, ⋅𝑅−𝑅
,
𝑅, −𝑅
=1
𝑤⋅𝑀
𝑀⋅∑𝑅
∑𝑅⋅𝑤
⋅𝑚,
𝑚,
+1
𝑤⋅𝑀
𝑀⋅∑𝑅
∑𝑅⋅𝑤
(3)
my,i = mass of “spike” (y) in blend i (g);
mx,i = mass of sample (x) in blend i (g);
mz,i = mass of “reference” (z) in blend i (g);
Ry, Rb,i, Rx = isotope/isotopologue amount ratio in “spike” (y), blend i (b,i), sample (x)
(mol/mol);
wy, wy, wz = mass fraction of the analyte in “spike” (y), sample (x), “reference” (z) used
to prepare the blends b,i (g/g).
Since there are no overlapping contributions of the “spike” to the amount ratios of
“sample” or “reference”, the “eq. A12” in the manuscript by Brauckmann et al. [21],
Figure 5.
Distribution of output quantity calculated from the MCS results of the NIST Uncer-
tainty Machine for CYA (
a
) and MEL (
b
) of the EMD–IDMS measurements of the PT 30110 sample
(FERA/FAPAS
®
, 2021) using Equation (1) and the parameter set in Table 2for the NIST Uncertainty
Machine. Due to the symmetric Gaussian distribution of the simulated results, the mean values
and standard deviations do not differ significantly from median and coverage interval with 95%
probability. The other numerical results are presented in Table 3.
3.2. Matched Standard Addition–IDMS (MSA–IDMS)
Based on the standard addition–IDMS technique [
21
], the present study also used a
procedure for the analysis of organic molecules, where the corresponding isotopologue
(“spike”) has no detectable overlap with the signals of the analyte molecule. This is usually
the case for mass differences of 3 Da or more and a high content of the “spike” isotopologue
(>97% (g/g)). If an overlap occurs, it is necessary to characterize the “spike”, “sample”, and
“reference” solutions individually and use Equation (2) with the individual contributions to
the isotope/isotopologue amount ratios for blend R
b,i
, sample R
x
, and spike R
y
as described
in Brauckmann [21]:
my,i
mx,i
·Ry−Rb,i
Rb,i−Rx
| {z }
=yi
=1
wY
·My
Mx
·∑Ry
∑Rx
·wZ
| {z }
=a1
·mz,i
mx,i
|{z}
=xi
+1
wY
·My
Mx
·∑Ry
∑Rx
·wX
| {z }
=a0
(3)
my,i = mass of “spike” (y) in blend i(g);
mx,i = mass of sample (x) in blend i(g);
mz,i = mass of “reference” (z) in blend i(g);
R
y
,R
b,i
,R
x
= isotope/isotopologue amount ratio in “spike” (y), blend i(b,i), sample
(x) (mol/mol);
w
Y
,w
Y
,w
Z
= mass fraction of the analyte in “spike” (y), sample (x), “reference” (z)
used to prepare the blends b,i(g/g).
Foods 2024,13, 2377 10 of 17
Since there are no overlapping contributions of the “spike” to the amount ratios
of “sample” or “reference”, the “eq. A12” in the manuscript by Brauckmann et al. [
21
],
Equation (3), simplifies to Equation (4) under the constraints that the amount fraction of the
target analyte (denoted as 1) in the “spike” is x
y1
= 0 and the amount fraction of the “spike”
(denoted as 2) in the sample is also x
x2
= 0. Equation (5) represents the linearized form with
the dimensionless y-axis values of the ternary mixtures i, the corresponding x-axis values,
and the definition of slope a1and intercept a0.
my,i
mx,i
·xy2 −Rb,i·xy1
Rb,i·xx1 −xx2
=1
wY
·My
Mx
·wZ·mz,i
mx,i
+1
wY
·My
Mx
·wX(4)
⇔my,i
mx,i
·xy2
Rb,i·xx1
=1
wY
·My
Mx
·wZ·mz,i
mx,i
+1
wY
·My
Mx
·wX(5)
⇔my,i
mx,i
·1
Rb,i
| {z }
=yi
=1
wY
·My·xx1
Mx·xy2
·wZ
| {z }
=a1
·mz,i
mx,i
|{z}
=xi
+1
wY
·My·xx1
Mx·xy2
·wX
| {z }
=a0
(6)
One should keep in mind the difference in the definition of the blend’s isotopologue
amount ratios R
b,i
(see “eq. A1” written in the manuscript by Brauckmann et al. [
21
] et al.
to the EMD–IDMS equation above, which is still the sum of the amounts of monitor (spike)
denoted as 2 and the reference (target analyte) denoted as 1, but is now the inverted signal
ratio Rb,i =finst·A2/A1.
Rb,i=nx2,i+nz2,i+ny2,i
nx1,i+nz1,i+ny1,i
=finst ·A2
A1
(7)
As the instrumental biases f
inst
are part of slope and intercept, they are eliminated
when Equation (7) is derived from Equation (5), which is used to calculate the content
of the analyte in the sample w
X
. Additive biases from the instrument were excluded
during the validation of the method. They should be detectable by repeated injection of the
reference–spike mixture.
wX=a0
a1
·wZ(8)
For the standard addition experiment, one binary mixture of sample and spike and
three–to–four ternary mixtures of sample, spike solution, and reference solutions were
prepared. The first mixture of sample and spike solution represents the intercept with the
y-axis. When possible, this mixture should be matched in the signal ratio close to 1 for
minimizing measurement uncertainty. For the ternary mixtures, the spike and reference
solution were added to a constant amount of sample with the same ratio to keep the
signal ratios constant, which is crucial for minimum instrumental biases and the validity of
the calculations.
For the method validation of the MSA–IDMS technique, four blends were prepared
gravimetrically using dispenser pipettes to guarantee a matching of all signal ratios. Again,
one stock solution was prepared of the analytes MEL and CYA once and represents both
the sample and reference solution to eliminate the content of sample and reference in
Equation (8). In that case, slope a
0
and intercept a
1
should have the same values to yield
the target value of w
X
/w
Z
= 1. Deviations from this target value indicate a systematic bias
of instrument or sample preparation and can be used as contribution to the measurement
uncertainty. Repeatability and biases can be determined from the standard deviation of
the signal ratios (N= 3) of repeated injections and the deviation from the target value from
repeated experiments.
All blends need to be measured in sequence over a much longer period compared to
the bracketing technique used for the EMD–IDMS measurement, which makes all standard
addition approaches more prone to instrumental drift and higher influences of outliers
Foods 2024,13, 2377 11 of 17
on the resulting content of the sample and less robust compared to EMD–IMDS. Both
effects, instrumental drift and outlier, have a significant influence on the slope and intercept
of the regression analysis if the number of mixtures (<4) and measurements is too low
(<3). Calculating the measurement uncertainty from the regression may underestimate
the contributions from these effects. Outliers should be tested by applying the whole
calculation and MCS results in higher uncertainties and broader coverage intervals, as
shown in Figure 6.
Foods 2024, 13, 2377 11 of 17
(<3). Calculating the measurement uncertainty from the regression may underestimate the
contributions from these effects. Outliers should be tested by applying the whole calcula-
tion and MCS results in higher uncertainties and broader coverage intervals, as shown in
Figure 6.
Figure 6. (a) Standard addition results of the binary and ternary mixtures of one CYA and 13C3−CYA
stock solution using Equation (6) for the calculation of yi and xi. Linear regression shows a very good
fit. Slope and intercept result in a good agreement with the target value wx/wz = 0.994 with u(wx/wz)
= 0.009. Including the outliers leads to the result wx/wz = 0.979 with u(wx/wz) = 0.021. A t−test for the
comparison of the expected value 1 to the measured value results t(n = 8, α = 0.975) = 1.89 < 2.36. (b)
Standard addition results of the binary and ternary mixtures of one MEL and 13C3−MEL stock solu-
tion using Equation (6) for the calculation of yi and xi. Linear regression shows a very good fit. Slope
and intercept result in a good agreement with the target value wx/wz = 1.004 with u(wx/wz) = 0.012. A
t−test for the comparison of the expected value 1 to the measured value results t(n = 8, α = 0.975) =
0.94 < 2.36.
The results of the MSA−IDMS experiment for MEL and CYA of the CRM solutions
without matrix are shown in Table 3. The mean value of <Rb,i> for all four blends has a
small standard deviation for MEL and CYA from 0.6 to 0.8%, indicating a good matching
for all blend preparations. The experimental relative standard uncertainty of the average
signal ratios Rb,i is 3.7% (MEL) and 1.7% (CYA) and agrees with the standard deviation
from the MCS for a0/a1. This also fits to the usual repeatability of the signal ratio measure-
ment of these 2 analytes ranging from 2.0 to 3.0% (RSD).
Finally, additional contributions of the matrix to the measurement uncertainty or to
a possible bias were evaluated by individual MSA−IDMS measurements of the PT 30110
sample (FERA/FAPAS®) with unmatched blends, which should simulate deviations from
the above assumption in the equations, as it was also tested for EMD−IDMS [33]. Due to
low signal intensities for CYA, reasonable results could only be achieved for MEL. The
mean value of the two measurements for wx(MEL) = 12.5 mg/kg with a standard deviation
s(wx(MEL)) = 0.4 mg/kg. This is in good agreement with the assigned value for MEL in this
PT sample of 12.4 mg/kg (see PT 30110 report (FERA/FAPAS®)) and the value from
EMD−IDMS measurements of the same material of 12.2 mg/kg (U(MEL) = 1.0 mg/kg, k =
2).
3.3. Uncertainty Estimation of EMD−IDMS and MSA−IDMS
The combined measurement uncertainty of the EMD−IDMS and MSA−IDMS experi-
ments was estimated according to the GUM [34] and the Eurachem/CITAC guide [27]. The
uncertainties of both techniques were determined by repeated measurements of CRM so-
lutions, in−house produced reference material, and an external PT material to compare
both techniques under the influence of a sample matrix and the precision of the measure-
ment.
MCS is conducted using Microsoft Excel to calculate the mean and median values,
standard deviations, and coverage intervals (95% confidence) for the content wx with re-
spect to Equations (1), (6) and (8). Equation (1) serves as model for EMD−IDMS experiment
Figure 6.
(
a
) Standard addition results of the binary and ternary mixtures of one CYA and
13
C
3
–CYA
stock solution using Equation (6) for the calculation of y
i
and x
i
. Linear regression shows a very
good fit. Slope and intercept result in a good agreement with the target value w
X
/w
Z
= 0.994 with
u(w
X
/w
Z
) = 0.009. Including the outliers leads to the result w
X
/w
Z
= 0.979 with u(w
x
/w
Z
) = 0.021. A
t-test for the comparison of the expected value 1 to the measured value results t(n= 8,
α
= 0.975) = 1.89
< 2.36. (
b
) Standard addition results of the binary and ternary mixtures of one MEL and
13
C
3
–MEL
stock solution using Equation (6) for the calculation of y
i
and x
i
. Linear regression shows a very
good fit. Slope and intercept result in a good agreement with the target value w
X
/w
Z
= 1.004 with
u(wX/wZ) = 0.012. A t-test for the comparison of the expected value 1 to the measured value results
t(n= 8, α= 0.975) = 0.94 < 2.36.
The results of the MSA–IDMS experiment for MEL and CYA of the CRM solutions
without matrix are shown in Table 3. The mean value of <R
b,i
> for all four blends has a
small standard deviation for MEL and CYA from 0.6 to 0.8%, indicating a good matching for
all blend preparations. The experimental relative standard uncertainty of the average signal
ratios R
b,i
is 3.7% (MEL) and 1.7% (CYA) and agrees with the standard deviation from the
MCS for a
0
/a
1
. This also fits to the usual repeatability of the signal ratio measurement of
these 2 analytes ranging from 2.0 to 3.0% (RSD).
Finally, additional contributions of the matrix to the measurement uncertainty or to
a possible bias were evaluated by individual MSA–IDMS measurements of the PT 30110
sample (FERA/FAPAS
®
) with unmatched blends, which should simulate deviations from
the above assumption in the equations, as it was also tested for EMD–IDMS [
33
]. Due to
low signal intensities for CYA, reasonable results could only be achieved for MEL. The
mean value of the two measurements for w
X
(MEL) = 12.5 mg/kg with a standard deviation
s(w
X
(MEL)) = 0.4 mg/kg. This is in good agreement with the assigned value for MEL in
this PT sample of 12.4 mg/kg (see PT 30110 report (FERA/FAPAS
®
)) and the value from
EMD–IDMS measurements of the same material of 12.2 mg/kg (U(MEL) = 1.0 mg/kg,
k= 2).
3.3. Uncertainty Estimation of EMD–IDMS and MSA–IDMS
The combined measurement uncertainty of the EMD–IDMS and MSA–IDMS experi-
ments was estimated according to the GUM [
34
] and the Eurachem/CITAC guide [
27
]. The
uncertainties of both techniques were determined by repeated measurements of CRM solu-
Foods 2024,13, 2377 12 of 17
tions, in–house produced reference material, and an external PT material to compare both
techniques under the influence of a sample matrix and the precision of the measurement.
MCS is conducted using Microsoft Excel to calculate the mean and median values,
standard deviations, and coverage intervals (95% confidence) for the content w
X
with re-
spect to Equations (1), (6) and (8). Equation (1) serves as model for EMD–IDMS experiment
and Equations (6) and (8) for the MSA–IDMS experiment performed by Ellison, Roesslein,
and Williams [
27
]. The online tool “Uncertainty Machine” by NIST can also run MCS and
deliver more precise results with larger numbers of data points compared to Excel but only
for the EMD–IDMS experiments. It is based on R core [
35
] but allows only a single model
equation and one output quantity. Finally, the software GUM Workbench Pro (version
2.4.1.406, Metrodata GmbH, Germany) is used to estimate the combined measurement
uncertainty of Equations (6) and (8) including the nested linear regression analysis for slope
a1and intercept a0.
3.4. Uncertainty of EMD–IDMS of MEL/13C3–MEL of the PT Sample
The combined measurement uncertainty is calculated for a typical measurement of
MEL in the PT 30110 sample (FERA/FAPAS
®
). The results of the PT will be compared to the
MSA–IDMS results in a matrix to validate the methods performance. MCS and linear GUM
approach are calculated within the online NIST tool “Uncertainty Machine” (Table 3).
3.5. Uncertainty Determination of MSA–IDMS of Neat MEL/13C3–MEL Solution in
Reference Matrix
MCS was applied for the analysis of a single sample set of pure aqueous MEL solutions
to compare both approaches. Table 4shows the definition of all single measurands for the
four blends including their uncertainties u, sensitivity coefficients c, and indices of MEL.
Table 4.
Definition of the MCS for the MSA–IDMS with 4 blends including the binary blend 1. Masses
of the MEL stock solution m
x
,m
z
(N= 1) and the
13
C
3
–MEL spike solution m
y
(N= 1) are simulated
for each standard addition blend 1–4. Sensitivity coefficients c
i
and the indices are calculated for
experimental data 1/Rb,i (N= 3) according to (NIST/SEMATECH, 2012).
Measurand Mean u cici2·ur2/10−5Index
mx,1/mg 48.510 0.049 1.00 0.10 0.2%
my,1/mg 49.002 0.049 1.00 0.10 0.2%
mz,1/mg 0.000 – – – –
Rb,1 1.217 0.013 0.58 3.90 8.4%
mx,2/mg 49.523 0.050 1.00 0.10 0.2%
my,2/mg 99.193 0.099 1.00 0.10 0.2%
mz,2/mg 49.053 0.049 1.00 0.10 0.2%
Rb,2 1.231 0.038 0.58 32.20 69.4%
mx,3/mg 48.851 0.049 1.00 0.10 0.2%
my,3/mg 147.450 0.147 1.00 0.10 0.2%
mz,3/mg 98.266 0.098 1.00 0.10 0.2%
Rb,3 1.224 0.020 0.58 8.50 18.3%
mx,4/mg 47.388 0.047 1.00 0.10 0.2%
my,4/mg 198.577 0.199 1.00 0.10 0.2%
mz,4/mg 148.252 0.148 1.00 0.10 0.2%
Rb,4 1.213 0.005 0.58 0.67 1.5%
Like in the EMD–IDMS experiment, the standard deviation of the signal ratio 1/R
b,i
dominates contributions to the uncertainty budget. The simulation is calculated with
10,000 data points due to the slow calculation of the linear regression parameters within
Excel. Figure 7shows the resulting distribution of the results for w
X
/w
Z
for CYA and MEL.
Foods 2024,13, 2377 13 of 17
Foods 2024, 13, 2377 13 of 17
Figure 7. (a) Distribution of the simulated results for the case of a single CYA CRM stock solution
representing sample x and reference z. The target value is 1. The coverage interval ranges from 0.961
to 1.030 with 95% confidence (N = 10,000). (b) Distribution of the simulated results for the case of a
single MEL CRM stock solution representing sample x and reference z. The target value is 1. The
average value is 1.005 with a coverage interval of 0.937–1.071 (95% confidence). A reasonable distri-
bution with N = 10,000 results.
Table 5 shows the definition of all single measurands for the four blends including
their uncertainties u, sensitivity coefficients c and indices of CYA.
Table 5. Definition of the MCS for the MSA−IDMS with 4 blends including the binary blend 1.
Masses of the CYA stock solution mx, mz (N = 1) and the 13C3−CYA spike solution mz (N = 1) are
simulated for each standard addition blend 1–4. Sensitivity coefficients ci and the indices are calcu-
lated for experimental data 1/Rb,i (N = 3) according to NIST/SEMATECH (2012).
Measurand Mean u ci ci2·ur2
/
10−5 Index
mx,1/mg 48.695 0.049 1.00 0.10 1.0%
my,1/mg 48.943 0.049 1.00 0.10 1.0%
mz,1/mg 0.000 − − − −
Rb,1 1.051 0.007 0.58 1.28 12.3%
mx,2/mg 48.218 0.048 1.00 0.10 1.0%
my,2/mg 98.725 0.099 1.00 0.10 1.0%
mz,2/mg 48.900 0.049 1.00 0.10 1.0%
Rb,2 1.048 0.003 0.58 0.34 3.2%
mx,3/mg 49.055 0.049 1.00 0.10 1.0%
my,3/mg 147.418 0.147 1.00 0.10 1.0%
mz,3/mg 98.247 0.098 1.00 0.10 1.0%
Rb,3 1.067 0.014 0.58 5.67 54.5%
mx,4/mg 48.991 0.049 1.00 0.10 1.0%
my,4/mg 197.813 0.198 1.00 0.10 1.0%
mz,4/mg 147.505 0.148 1.00 0.10 1.0%
Rb,4 1.057 0.008 0.58 2.01 19.4%
After the measurement of the CRM solutions without matrix, the standard addition
technique was applied also to the PT 30110 sample (FERA/FAPAS®). The number of re-
peats is smaller for this experiment. Thus, a relative standard uncertainty urel(Rb) = 2.0% is
assumed (Table 6) to allow for a comparison to the results in Table 2 and the results of the
GUM Workbench program in the Table 7.
Figure 7.
(
a
) Distribution of the simulated results for the case of a single CYA CRM stock solution
representing sample x and reference z. The target value is 1. The coverage interval ranges from
0.961 to 1.030 with 95% confidence (N= 10,000). (
b
) Distribution of the simulated results for the case
of a single MEL CRM stock solution representing sample x and reference z. The target value is 1.
The average value is 1.005 with a coverage interval of 0.937–1.071 (95% confidence). A reasonable
distribution with N= 10,000 results.
Table 5shows the definition of all single measurands for the four blends including
their uncertainties u, sensitivity coefficients cand indices of CYA.
Table 5.
Definition of the MCS for the MSA–IDMS with 4 blends including the binary blend 1. Masses
of the CYA stock solution m
x
,m
z
(N= 1) and the
13
C
3
–CYA spike solution m
z
(N= 1) are simulated
for each standard addition blend 1–4. Sensitivity coefficients c
i
and the indices are calculated for
experimental data 1/Rb,i (N= 3) according to NIST/SEMATECH (2012).
Measurand Mean u cici2·ur2/10−5Index
mx,1/mg 48.695 0.049 1.00 0.10 1.0%
my,1/mg 48.943 0.049 1.00 0.10 1.0%
mz,1/mg 0.000 – – – –
Rb,1 1.051 0.007 0.58 1.28 12.3%
mx,2/mg 48.218 0.048 1.00 0.10 1.0%
my,2/mg 98.725 0.099 1.00 0.10 1.0%
mz,2/mg 48.900 0.049 1.00 0.10 1.0%
Rb,2 1.048 0.003 0.58 0.34 3.2%
mx,3/mg 49.055 0.049 1.00 0.10 1.0%
my,3/mg 147.418 0.147 1.00 0.10 1.0%
mz,3/mg 98.247 0.098 1.00 0.10 1.0%
Rb,3 1.067 0.014 0.58 5.67 54.5%
mx,4/mg 48.991 0.049 1.00 0.10 1.0%
my,4/mg 197.813 0.198 1.00 0.10 1.0%
mz,4/mg 147.505 0.148 1.00 0.10 1.0%
Rb,4 1.057 0.008 0.58 2.01 19.4%
After the measurement of the CRM solutions without matrix, the standard addition
technique was applied also to the PT 30110 sample (FERA/FAPAS
®
). The number of repeats
is smaller for this experiment. Thus, a relative standard uncertainty u
rel
(R
b
) = 2.0% is
assumed (Table 6) to allow for a comparison to the results in Table 2and the results of the
GUM Workbench program in the Table 7.
Foods 2024,13, 2377 14 of 17
Table 6.
Definition of the MCS for the MSA–IDMS with 4 blends including the binary blend 1. Masses
of the PT 30110 sample (FERA/FAPAS
®
)m
x
, reference solutions m
z
(N= 1) and the
13
C
3
–MEL spike
solution m
z
(N= 1) are simulated for each standard addition blend 1–4. Sensitivity factors c
i
and the
indices are calculated for experimental data 1/Rb,i (N= 2) according to NIST/SEMATECH (2012).
Measurand Value u cici2·ur2/10−5Index
mx1 500.770 0.501 1.00 0.10 0.12%
my1 99.340 0.099 1.00 0.10 0.12%
mz1 0.000 0.000 – 0.00 –
Rb,1 10.428 0.209 0.71 20.00 24.60%
mx2 502.790 0.503 1.00 0.10 0.12%
my2 101.460 0.101 1.00 0.10 0.12%
mz2 49.430 0.049 1.00 0.10 0.12%
Rb,2 10.877 0.218 0.71 20.00 24.60%
mx3 500.760 0.501 1.00 0.10 0.12%
my3 100.460 0.100 1.00 0.10 0.12%
mz3 99.320 0.099 1.00 0.10 0.12%
Rb,3 11.787 0.236 0.71 20.00 24.60%
mx4 507.570 0.508 1.00 0.10 0.12%
my4 100.670 0.101 1.00 0.10 0.12%
mz4 149.410 0.149 1.00 0.10 0.12%
Rb,4 12.822 0.256 0.71 20.00 24.60%
wz10.080 0.020 0.71 0.20 0.25%
Table 7.
Results of the MCS using the setting in Table 5compared to the results of the GUM approach
(GUM Workbench).
MCS GUM
a02.0534 ±0.0355 2.0541 ±0.0359
a11.6202 ±0.2101 1.617 ±0.211
Index (Rb,1) 24.7% 41.0%
Index (Rb,2) 24.7% 6.3%
Index (Rb,3) 24.7% 3.8%
Index (Rb,4) 24.7% 48.4%
wX/mg/kg
(95% confidence, k= 2) 12.8 [+4.8, −2.9] 12.8 ±3.7
Contrary to the previous MCS results of the pure solutions, an asymmetric distribution
is observed, which also leads to differences between the mean value of the simulated results,
calculated result of the measurement, and the percentiles of the MCS distribution (Figure 8).
Foods 2024, 13, 2377 15 of 17
Figure 8. (a) Standard addition results of MEL in infant formula (PT sample (FERA/FAPAS®) 30110,
2021) using a CRM solution with wz = 10.08 mg/kg for the ternary mixtures. A lower precision caused
by the effect of the matrix on the measurement of signal ratio and the smaller number of repeats (N
= 2, total number n = 8) leads to a lower r2 value compared to the solutions. Slope and intercept result
in a content of wx = 12.8 mg/kg with an uncertainty U(wx) = 0.85 mg/kg according to Brauckmann et
al. [21]. The assigned value of the CRM for MEL is w(MEL)CRM = 12.4 mg/kg +/−0.2 mg/kg (k = 2).
Using a t−test (two−way, one sample), the results for the comparison with the MSA−IDMS measure-
ment is a value of t(n = 8, α = 0.975) = 0.92 < 2.36. (b) Distribution of the mass fraction of MEL in the
PT sample resulting from MCS with the parameters set in Table 2. The mean value of wx(MCS) = 13.2
mg/kg has a standard deviation of s(wx) = 2.6 mg/kg. The deviation from the experimental value wx
= 12.8 mg/kg originates from the asymmetric distribution with a tailing towards higher values. The
calculation of the median and coverage interval with a probability of 95 % results the following
percentiles at 9.4 mg/kg (2.5 %), 12.8 mg/kg (50 %, median), and 19.4 mg/kg (97.5 %).
4. Conclusions
A new standard addition method for IDMS for the analysis of MEL and CYA in infant
formula based on the previously published method by Brauckmann et al. (2021) was pre-
sented [21]. Additionally, a validation scheme with stock solutions of pure neat and matrix
CRM allows for the detailed evaluation of single contributions to the combined measure-
ment uncertainty according to the Eurachem/CITAC guidelines (Ellison, Roesslein, and
Williams, 2012, [27]).
As previously mentioned, the melamine–cyanurate complex is somewhat more toxic
than each chemical alone, whereby the limits for melamine in powdered infant formula is
defined by 1 mg/kg (WHO, 2009) [36]. By using the 2D−LC method, a simple and fast
sample preparation can be considered, ensuring a smaller error bar than the more com-
monly used 1D−LC method.
The present study showed that EMD−IDMS and MSA−IDMS were both effective
quantitative methods with similar quantitative results indicating that the quantification
of MEL and CYA in infant formula is barely affected by matrix. Both methods could be
used to assign values for mass fractions of these analytes in matrix−based CRM or test
material for inter−laboratory PT schemes. A comprehensive approach in the evaluation of
the measurement uncertainty including Monte Carlo simulations was applied to allow a
detailed picture about the main contributions to uncertainty and sources of experimental
errors, e.g., precision and robustness of the signal ratios, instrumental drift during
MSA−IDMS measurements, and sufficient number of mixtures depending on the desired
precision of the sample mass fraction wx.
Moreover, in these days, the addition of chemical by−products like MEL or CYA can
be considered as a real threat not only in infant formula but also in alternative proteins,
for example, in the future−oriented meat sector. In summary, an LC−IDMS method for the
quantification of MEL and CYA in infant formula was developed that shows to be precise
and exact, which is not affected by analyte loss or sample carry−over effect, and can be
Figure 8.
(
a
) Standard addition results of MEL in infant formula (PT sample (FERA/FAPAS
®
) 30110,
2021) using a CRM solution with w
Z
= 10.08 mg/kg for the ternary mixtures. A lower precision caused
Foods 2024,13, 2377 15 of 17
by the effect of the matrix on the measurement of signal ratio and the smaller number of repeats
(N= 2, total number n= 8) leads to a lower r
2
value compared to the solutions. Slope and intercept
result in a content of w
X
= 12.8 mg/kg with an uncertainty U(w
X
) = 0.85 mg/kg according to
Brauckmann et al. [
21
]. The assigned value of the CRM for MEL is w(MEL)
CRM
= 12.4 mg/kg
+/–0.2 mg/kg (k= 2). Using a t-test (two-way, one sample), the results for the comparison with the
MSA–IDMS measurement is a value of t(n= 8,
α
= 0.975) = 0.92 < 2.36. (
b
) Distribution of the mass
fraction of MEL in the PT sample resulting from MCS with the parameters set in Table 2. The mean
value of w
X
(MCS) = 13.2 mg/kg has a standard deviation of s(w
X
) = 2.6 mg/kg. The deviation from
the experimental value w
X
= 12.8 mg/kg originates from the asymmetric distribution with a tailing
towards higher values. The calculation of the median and coverage interval with a probability of 95%
results the following percentiles at 9.4 mg/kg (2.5 %), 12.8 mg/kg (50 %, median), and 19.4 mg/kg
(97.5 %).
4. Conclusions
A new standard addition method for IDMS for the analysis of MEL and CYA in infant
formula based on the previously published method by Brauckmann et al. (2021) was
presented [
21
]. Additionally, a validation scheme with stock solutions of pure neat and
matrix CRM allows for the detailed evaluation of single contributions to the combined
measurement uncertainty according to the Eurachem/CITAC guidelines (Ellison, Roesslein,
and Williams, 2012, [27]).
As previously mentioned, the melamine–cyanurate complex is somewhat more toxic
than each chemical alone, whereby the limits for melamine in powdered infant formula
is defined by 1 mg/kg (WHO, 2009) [
36
]. By using the 2D–LC method, a simple and
fast sample preparation can be considered, ensuring a smaller error bar than the more
commonly used 1D–LC method.
The present study showed that EMD–IDMS and MSA–IDMS were both effective
quantitative methods with similar quantitative results indicating that the quantification
of MEL and CYA in infant formula is barely affected by matrix. Both methods could be
used to assign values for mass fractions of these analytes in matrix–based CRM or test
material for inter–laboratory PT schemes. A comprehensive approach in the evaluation of
the measurement uncertainty including Monte Carlo simulations was applied to allow a
detailed picture about the main contributions to uncertainty and sources of experimental
errors, e.g., precision and robustness of the signal ratios, instrumental drift during MSA–
IDMS measurements, and sufficient number of mixtures depending on the desired precision
of the sample mass fraction wX.
Moreover, in these days, the addition of chemical by–products like MEL or CYA can
be considered as a real threat not only in infant formula but also in alternative proteins,
for example, in the future–oriented meat sector. In summary, an LC–IDMS method for
the quantification of MEL and CYA in infant formula was developed that shows to be
precise and exact, which is not affected by analyte loss or sample carry–over effect, and
can be used as a high throughput method. The sample preparation is simple, so that in
general this method went from a reference method to a routine method and can be used as a
routine laboratory method. The method meets all the requirements of European regulations
regarding the analysis of MEL and CYA, and the quality of the results obtained is supported
by accreditation according to ISO/IEC 17025.
Author Contributions:
Conceptualization, V.P. and R.K.; methodology, R.K.; software, S.R.; valida-
tion, L.D. and K.B.; formal analysis, A.R.; investigation, T.S.; resources, A.P.; data curation, E.A.;
writing—original draft preparation, R.K.; writing—review and editing, O.R.; visualization, L.D.;
supervision, M.O.; project administration, K.B.; funding acquisition, A.R. All authors have read and
agreed to the published version of the manuscript.
Funding: This research received no external funding.
Foods 2024,13, 2377 16 of 17
Data Availability Statement:
The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding author.
Conflicts of Interest:
Author Vasilisa Pedan, Rudolf Koehling, Lukas Drexel, Kathrin Breitruck,
Alexander Rueck, Tim Seidel, Eric Allenspach and Markus Obkircher was employed by the company
Sigma–Aldrich Production GmbH (Subsidiary of Merck KGaA). The remaining authors declare that
the research was conducted in the absence of any commercial or financial relationships that could be
construed as a potential conflict of interest.
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