Simultaneous modeling of spectra and apparent diffusion coefficients.
Victor Adalid Lopez1, André Doering1, Sreenath Pruthviraj Kyathanahally 1, Christine S. Bolliger1, and Roland Kreis1

1Depts. Radiology and Clinical Research, University Bern, Bern, Switzerland


Diffusion weighted spectroscopy can provide information on the diffusion of metabolites and the microstructure of brain tissue. A method for simultaneous fitting of spectra related by mono-exponential diffusion weighting is introduced, which is similar to simultaneous fitting of a 2DJ or inversion recovery data set. As shown for simulated white matter data, the method improves both, accuracy and precision of ADC estimation for all metabolites. It is also illustrated with diffusion data obtained from human gray matter at 3T.


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


Diffusion weighted spectroscopy (DWS) can provide information on the diffusion of metabolites, but also the microstructure of tissue 1-3. This information relies crucially on the correct estimation of apparent diffusion coefficients (ADC) along different direction. The traditional way to obtain ADC’s is to measure spectra with different b-factors, to fit them separately, and subsequently to fit the estimated area values to a mono-exponential decay, $$$\exp(-ADC*b)$$$ - at least in the case of Gaussian diffusion. Here, a method to model the spectra with varying b-factors simultaneously with the metabolite ADCs is proposed. This is analogous to fitting 2DJ or inversion recovery spectra simultaneously.


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/mm2) 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 VeSPA4 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). T2’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/mm2).


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.

An application to human in vivo data is shown in Figure 2.

Discussion and Conclusions

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.


This research is supported by the Swiss National Science Foundation (#320030_156952)


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4 VeSPA - Versatile Simulation, Pulses, and Analysis

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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)