Angéline Nemeth^{1}, Benjamin Leporq^{1}, Amandine Coum^{2,3}, Giulio Gambarota^{2,3}, Kévin Seyssel^{4}, Bérénice Segrestin^{5}, Pierre-Jean Valette^{6}, Martine Laville^{5}, Olivier Beuf^{1}, and Hélène Ratiney^{1}

Monte Carlo simulations and in vivo measurements on human abdominal adipose tissue were used to analyze the effect of the phase variation induced by eddy currents on localized spectroscopy fatty acid composition quantification (proportion of polyunsaturated, monounsaturated and saturated fatty acid). Monte Carlo simulations showed that base line distortions were able to strongly impact estimation of fatty acid composition. So we proposed a simple method to correct the base line using a second signal acquired with a longer TE. Test-retest variability of quantitative results was reduced using this correction.

The lipid resonances are fitted by two different methods as
a combination of Gaussian and Lorentzian line shapes: LCModel and M_{peak} as
described below:

*LCModel*

LCModel with the Control parameter SPTYPE set to ‘Lipid-8’
was used only on in vivo data. In the
case of lipid signals, this quantification method fits a flexible combination
of Gaussian and Lorentzian line shapes to the lipid resonances^{1,2}.

*M _{peak}
*

To perform Monte Carlo simulations, we used a model function
which permitted to fit Voigt lines shapes^{3}
described by:

[1]

$$f(t)=e^{i\phi_0}\sum_{k=1}^9c_k*e^{\alpha_kt+(\beta_kt)^2+i2{\pi}f_kt}$$

where
$$$\phi_0$$$ is
the zero order phase, $$$c_k$$$
the amplitudes,
$$$\alpha_k$$$ the Lorentzian damping factors, $$$\beta_k$$$
Gaussian damping factors,
$$$f_k$$$ the frequency of the kth proton
group. The algorithm implementing of M_{peak}^{3} used multiple random starting values for the
$$$f_k$$$, $$$\alpha_k$$$ and
$$$\beta_k$$$ to compute the starting
values of $$$c_k$$$ and $$$\phi_0$$$ using a linear least
squares as in AMARES^{4}. Then a
nonlinear least squares algorithm was employed to fit the global model function
given in [1].
In the Table 1, amplitudes ($$$c_k$$$) were expressed
in terms of ndb, nmidb, CL^{5}, Aw and
Af. Ratio of amplitudes permitted to estimate ndb and nmidb (Table 1). The
proportion of the different fatty acid was then calculated by:

$$PUFA=\frac{nmidb}{3}*100$$

$$MUFA=\frac{(ndb-2*nmidb)}{3}*100$$

$$SFA=100-PUFA-MUFA$$

*Monte Carlo Simulation
*

The fatty acid composition of human subcutaneous abdominal
adipose tissue^{6 }(18% PUFA, 54.6% MUFA
and 27.4% SFA) was used as reference in the simulated data which corresponded
to ndb^{target} = 2.7,
nmidb^{target} = 0.54
and CL = 17.47. Monte Carlo simulation was performed using 10-peak lipid
signal. A gold standard signal was designed with the equation [1] and one
hundred Gaussian noise realizations with zero mean and a variance determined
according to the desired SNR were randomly generated and added. $$$c_k$$$
were defined
as described in the Table 1 with ndb^{target },nmidb^{target} ,
Aw = 1 and Af = 37 and then multiplied by exp(-TE/T2k)
with TE = 14ms, $$$\alpha_k$$$ were equal to 1 /T2k (T2k
in Table 1), $$$\beta_k$$$ = 27.29Hz (T2' = 22ms
$$$\beta_k=\sqrt{\frac{1}{4*log(2)*(T2^{'})^2}}$$$) and $$$\phi_0=0$$$. Additionally, phase distortions were introduced
to simulate the effect of eddy currents, as illustrated in Figure 1.

*In vivo acquisitions
*

Nine volunteers underwent a STEAM sequence, using respiratory triggering, on a Philips Ingenia 3T system on abdominal subcutaneous adipose tissue using two TE (parameters in Figure 2). MR spectra were acquired twice in a row to measure the test-retest variability of the quantification methods as:

$$Var=\frac{1}{9}\sum_{i=1}^9\frac{{\mid}test_i-retest_i{\mid}}{(test_i-retest_i)/2}*100$$

LCModel and M_{peak}
methods were applied only on the spectrum of the first echo with and without
the phase correction, described in details in Figure 2, which exploit the phase
term of the second echo acquisition free from phase variation due to eddy
current.

- Provencher SW. Estimation of metabolite concentrations from localized in vivo proton NMR spectra. Magn Reson Med. 1993 Dec 1;30(6):672–9.
- Provencher SW. Automatic quantitation of localized in vivo1H spectra with LCModel. NMR Biomed. 2001 Jun 1;14(4):260–4.
- Ratiney H, Bucur A, Sdika M, Beuf O, Pilleul F, Cavassila S. Effective voigt model estimation using multiple random starting values and parameter bounds settings for in vivo hepatic 1H magnetic resonance spectroscopic data. In: 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. 2008. p. 1529–32
- Vanhamme L, van den Boogaart A, Van Huffel S. Improved Method for Accurate and Efficient Quantification of MRS Data with Use of Prior Knowledge. J Magn Reson. 1997 Nov 1;129(1):35–43.
- Hamilton G, Schlein AN, Middleton MS, Hooker CA, Wolfson T, Gamst AC, et al. In vivo triglyceride composition of abdominal adipose tissue measured by 1H MRS at 3T. J Magn Reson Imaging. 2017 mai;45(5):1455–63.
- Garaulet M, Hernandez-Morante JJ, Lujan J, Tebar FJ, Zamora S. Relationship between fat cell size and number and fatty acid composition in adipose tissue from different fat depots in overweight/obese humans. Int J Obes. 2006 Jan 31;30(6):899–905

Table
1: Knowledge
of the theoretical relative amplitude of the resonance associated to the
chemical structure of a typical triglyceride have been described by Hamilton et
al.
frequency shift, ck amplitude of
each resonance k; ndb number of double bonds; nmidb
number of methylene-interrupted double bonds; CL chain length; Aw number of
water molecules
and Af number of triglyceride molecules. T2k
were used in Monte Carlo simulations.

Figure 1: Simulated adipose
tissue lipid MR spectra used in the Monte Carlo studies, with different degree
of baseline distortion, simulating the eddy current effect, SNR = 210. The
phase variation was simulated using the following exponential model: $$$\phi_i(t)=exp({-\frac{t}{\tau_i}}),{\tau_i}=\frac{50+50i}{3}ms$$$ for $$$0\leq{t}\leq{100ms}$$$, with i=0…5, for the 6 above spectra.

Figure 2: The
phase of the signal of the first echo (TE1 = 14 ms) was corrected
with the phase of the second echo (TE2 = 28 ms) which was less
impacted by eddy current effects This correction is considered as possible
because 1) the methylene –CH2n- amplitude peak is the unique
preponderant component , and 2) ΔTE=TE2-TE1
is small compared to the lipid T2 and 1/J; where the J scalar coupling
constants are between 4 to 8 Hz for in vivo fatty acid spectra.

Figure 3: Error = (value^{target} – estimated
value)/ value^{target} *100 (in %) where value could be ndb or nmidb. Monte
Carlo simulation showed an increase of the error and of the variability in the
estimation of ndb and nmidb when the base line was more and more distorted. The
error of the nmidb estimation could be higher than 100% with a small distortion
of the base line.

Table 2:
For in vivo measurements, test-retest
variability was calculated. According to Garaulet M et al^{6}. the fatty acid
composition of human subcutaneous abdominal adipose tissue was expected to be
around 18% PUFA 54.6% MUFA and 27.4% SFA using gas chromatography. The phase
correction improved the test-retest variability and the ndb estimation for the
two methods. The very low nmidb values of M_{peak} show the difficulty
of M_{peak} to estimate the amplitude of CH=CH-CH2-CH=CH
peak and then explain why the test-retest variability was so high for nmidb.