Manuel Schneider^{1}, Felix Lugauer^{1}, Dominik Nickel^{2}, Brian M Dale^{3}, Berthold Kiefer^{2}, Andreas Maier^{1}, and Mustafa R Bashir^{4,5}

MRI is not only capable of quantifying the fat content, but also the fatty acid composition of human adipose tissue. Especially for low fat fractions, fatty acid quantification is sensitive to image noise. Including prior information or additional parameter approximations into the quantification method helped to improve the noise propagation behavior, but also introduced a systematic bias. Performing spectral denoising in between image reconstruction and fatty acid quantification kept the systematic bias as well as the noise in the parameter maps low, and hence allows for more flexible protocol selection and shorter acquisition times.

Three FA quantification
approaches were considered, which differ in the derivation of the number of
double bonds (ndb), number of methylene-interrupted double bonds (nmidb), and
the chain length (CL). All of them incorporate a heuristic approximation for
the CL^{5}. In the first method (termed “Pinv”), water, fat and two
additional fat contribution parameter maps are calculated using a linear model
as has been previously described^{4}. The second technique (termed
“IneqConst”) additionally adds inequality constraints based on prior FA
composition information ($$$ndb\leq6$$$; $$$nmidb\leq3$$$), and solves the resulting
inequality-constrained linear least-squares problem using quadratic
programming. The third method (termed “Iter”) makes use of an additional
approximation for the nmidb and solves two subsequent non-linear
least-square fits iteratively^{6}. The calculated parameters were used
to determine the fractions of unsaturated FAs (UFAs), saturated FAs (SFAs),
mono-unsaturated FAs (MUFAs), and poly-unsaturated FAs (PUFAs). Every
experiment was conducted twice: once without denoising, and once including a
Dixon water-fat spectral denoising method^{7} prior to the FA
quantification.

FA compositions that span
symmetrically over typical adipose human tissue values^{8} (UFA = 72.9±15%, PUFA = 23.4±15%) were taken into account when generating the
synthetic dataset. Fat
fractions (FFs) from 15% to 50% were simulated. For every FA composition and FF
combination, a complex-valued signal was synthesized for 8 different echo times
(TE1 = 1.35ms, ΔTE = 1.25ms). The mean absolute errors and mean standard
deviations of the calculated parameter maps were derived numerically by
employing additive Gaussian noise and repeating the simulation 1000 times.

For
in-vivo validation, eight echoes of MR data (2D GRE with 16 slices, TE1 = 1.28ms,
ΔTE = 1.19ms, TR = 175ms, flip angle = 10°, spatial resolution: 3.75x3.75x10mm^{3},
bandwidth = 1953Hz/px, bipolar readout) from a clinical trial subject suffering
from non-alcoholic fatty liver disease (NAFLD) were acquired on a 3T MR scanner
(MAGNETOM Trio, Siemens Healthcare, Erlangen, Germany) under IRB approval.
Prior to the FA quantification, complex-valued images were calculated using a
prototype, and compensated for field inhomogeneities and eddy current effects.
The field map and eddy current-correcting phase were calculated using a
variable projection least-squares fit, which employed region growing to enforce
spatial smoothness. The phase-corrected complex images were used to estimate
T2* relaxation by means of variable projection.

The numerical simulation results are summarized in Table 1. “Pinv” achieved the lowest mean errors. In comparison, adding inequality constraints (method “IneqConst”) led to slightly lower mean standard deviations, while barely increasing the mean errors. The method “Iter” resulted in the lowest standard deviations (especially for the PUFAs and MUFAs), but also introduced a systematic bias. “Pinv” led to uniform standard deviations for all FA combinations (Fig. 1a), whereas “IneqConst” and “Iter” reduced the noise level for some FA values (Fig. 1b-c). The applied spectral denoising method consistently improved the noise propagation behavior of all analyzed methods four- to five-fold. Particularly for small fat fractions, the methods including spectral denoising performed superiorly compared to the unfiltered cases (Fig. 2).

Representative
in-vivo UFA maps are depicted in Fig. 3. For the methods “Pinv” and
“IneqConst”, the mean UFA values in the ROI were in compliance with previously
published results^{3,8}. For these methods the UFA maps from denoised
images were more uniform in appearance, and edges were preserved. The method
“Iter” (with and without denoising) calculated homogenous UFA values in the
subcutaneous tissue (very high FF), but failed to reliably estimate hepatic UFA
values.

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