Simultaneous modeling of spectra and apparent diffusion coefficients.

Victor Adalid Lopez^{1}, AndrĂ© Doering^{1}, Sreenath Pruthviraj Kyathanahally ^{1}, Christine S. Bolliger^{1}, and Roland Kreis^{1}

To improve fitting of apparent metabolite diffusion coefficients in diffusion-weighted MR spectroscopy.

To test the concept and the fitting tool, simulated
diffusion-weighted brain spectra were created (3T, PRESS, TE 30ms, 8 b-values:** **b = [250; 500; 1000; 2000; 4000; 6000;
8000; 10000] s/mm^{2}) including nine metabolites: Glycerophosphorylcholine (GPC), Creatine (Cr), Glutamate (Glu),
Glutamine (Gln), N-acetylaspartate
(NAA), N-acetylaspartylglutamate (NAAG), Taurine (Tau), myo-Inositol (mIns)
and Gamma-Aminobutyric acid (GABA). They
were generated in VeSPA^{4}
using literature values for typical white matter concentrations ^{5},
and ADCs ^{6}.
Experimental macromolecular baseline spectra were also included (averaged from
10 subjects, 3T, metabolite-nulled with inversion time of 900 ms). T_{2}’s
were assumed to be identical, while the effect of different shimming and SNR
was included with three different Gaussian dampings (GD) (3, 5 and 9Hz) at three
different noise levels each (escalating by a factor of 2; 100 noise realizations
for each setting, where SNR (NAA at b=250) ranged from 58 (3Hz, lowest noise) to
3 (9Hz, largest noise).

Simultaneous fitting was implemented in the 2D fitting
tool FitAID ^{7},
which allows to fit multiple spectra using prior knowledge in both dimensions;
here modified to fit the ADC for each metabolite including the factor $$$\exp({-ADC*b})$$$
together with the rest of the parameters (area, phase, offset, widths). For *in silico* testing, prior knowledge was
implemented within spectra for a common phase, GD, and most offsets (individual
shifts for macromolecules, Cr and GPC). Lorentzian damping constants were
linked between spectra and partially within. Frequency shifts and changes in
shim between scans were allowed for in order to simulate potential patient
motion.

To compare, identical spectral fits (but without prior knowledge along the second dimension) were performed where ADC values were fitted subsequently in Matlab.

The method is also illustrated with human *in vivo* data (single case, gray matter, STEAM, TE 37 ms, TM 150ms, 3T, b = [427; 722; 962; 1235; 1710; 2261; 2671] s/mm^{2}).

As documented in *Table 1*, the estimated metabolite ADC
values are better for
simultaneous spectral fitting and ADC modeling both with respect to accuracy (bias) as well as precision
(variance) for almost
all cases considered. The results are summarized for the usually
evaluated singlet metabolites (Cr, NAA, GPC) in part A) and the main broader
components (Glu, mIns) in part B). Gln, GABA and Tau were not fitted reliably for
all cases, though with larger success rate in the case
of simultaneous fitting. On
average for the major metabolites, bias was reduced between 30% and 86% and
variance dropped between 13% and 58% when introducing simultaneous fitting. *Figure
1* illustrates resulting fits for both methods compared to ground truth in a
case with 9Hz GD and largest noise level (x4). The sequential fit shows some nonexistent peaks in the noisy large-b spectra that are not present in the simultaneous fit.

Simultaneous fitting of spectra and metabolite ADC
values has been shown to improve accuracy and precision of the estimated ADC
values for simulated data and the preliminary application *in vivo* shows promise
for improved performance *in vivo*, likely reducing the minimum acquisition times
for diffusion-weighted MRS.

Metabolite ADCs can be obtained either by sequential spectral fitting followed by diffusion modeling, where: a) each spectrum is fitted independently, b) spectra are fitted independently, but restrictions obtained from summed spectra are enforced, c) spectra are fitted simultaneously with restraints regarding spectral parameters only. Or, d) ADCs are fitted simultaneously with 2D-relations as in c) but also enforcing exponential signal decay with a defined diffusion equation. Here we showed that d) is better than a). Method c) would be preferred in cases where the diffusion model is under investigation.

The current implementation has some limitations. Only the simple case of mono-exponential diffusion has been considered. Also, simultaneous evaluation of the whole diffusion tensor has not been targeted yet.

^{1} Nicolay K, Braun KP, Graaf RA, Dijkhuizen RM, Kruiskamp MJ.* Diffusion NMR spectroscopy.* NMR
Biomed. 2001;14(2):94-111

^{2} Ronen
I, Ercan E, Webb A. *Axonal and glial microstructural information obtained with
diffusion-weighted magnetic resonance spectroscopy at 7T*. Front Integr
Neurosci. 2013;13;7-13. doi: 10.3389/fnint.2013.00013.

^{3} Marchadour
C, Brouillet E, Hantraye P, Lebon V, Valette J. *Anomalous diffusion of brain
metabolites evidenced by diffusion-weighted magnetic resonance. spectroscopy in
vivo.* J Cereb Blood Flow Metab. 2012;32(12):2153-60

^{4}* VeSPA - Versatile Simulation, Pulses, and Analysis* https://scion.duhs.duke.edu/vespa/

^{5} Pouwels PJW, Brockmann K, Kruse B, Wilken B, Wick M, Hanefeld F, Frahm J. *Regional age dependence of human brain metabolites from infancy to adulthood as detected by quantitative localized proton MRS.* Pediatric Research 1999;46:474–474

^{6} Kan HE, Techawiboonwong A, van Osch MJP, Versluis MJ, Deelchand DK, Henry P-G, Marjanska M, van Buchem MA, Webb AG, Ronen I, *Differences in apparent diffusion coefficients of brain metabolites between grey and white matter in the human brain measured at 7 T*. Magn Reson Med, 2012;67:1203–1209. doi: 10.1002/mrm.23129

^{7} Chong DG, Kreis R, Bolliger CS, Boesch C, Slotboom J. *Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a Fitting Tool for Arrays of Interrelated Datasets.* MAGMA 2011;24:147

Table 1. Compilation of averaged results for deviations and fluctuations of ADCs obtained with simultaneous or sequential determination of spectral fits and ADC values in simulated datasets. (average bias and standard deviations expressed as percentage of true values given as average for A) singlet metabolites and B) Glu and mIns).

Figure 1. Typical fitting results for a set of simulated diffusion weighted spectra. (i) Simultaneous and (iii) Sequential fits of spectra and ADCs, (ii) Ground truth spectra. (top) Simulated spectra in red, fit in black. (bottom) Fit residues (noise subtracted), which are smaller for simultaneous fitting. (GD 9Hz, SNR 3).

Figure 2. Fitting results for a set of diffusion weighted spectra acquired from human gray matter as described in methods. a) simultaneous and b) sequential fit strategies (measured spectra in red, fits in black). Deviations between measured spectra and model are similar and due to incomplete fit models.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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