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Multicomponent Analysis of High b-value Diffusion-Weighted MRI for Tracking Progression of Amyotrophic Lateral Sclerosis in A Mouse Model
Jin Gao1,2, Mingchen Jiang3, Richard Magin4, Andrew Larson5, and Weiguo Li2,4,5

1Department of Electrical & Computer Engineering, University of Illinois at Chicago, Chicago, IL, United States, 2Research Resources Center, University of Illinois at Chicago, Chicago, IL, United States, 3Department of Physiology, Northwestern University, Chicago, IL, United States, 4Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, United States, 5Department of Radiology, Northwestern University, Chicago, IL, United States

### Synopsis

Amyotrophic lateral sclerosis (ALS) is a progressive disease of motor neuron degeneration in brain and spinal cord with an unknown etiology. Diffusion MRI has potential to track the disease progression in ALS due to the technique’s intrinsic advantages in detecting structure changes and non-invasive nature. In this study, we investigated the feasibility of analyzing multiple high b-value diffusion-weighted images using a non-negative least squares method (requiring no prior assumptions about components) and a bi-compartment model with restricted and hindered diffusion components. Both methods were able to detect alterations of spinal cord in the G93A-SOD1 mouse model of ALS.

### Introduction

Amyotrophic lateral sclerosis (ALS) is a fatal disease characterized by degeneration of motor neurons in spinal cord [1, 2]. The microstructure changes of the damaged nerves in ALS may potentially be reflected in altered diffusion properties, thus detectable with diffusion-weighted (DW) MRI. The classical mono-exponential model fails to precisely depict DW signal decay at high b values [3-7]. Here, we aim to investigate signal decay behaviors at ultra-high b values for the non-invasive assessment of spinal cord alterations in the transgenic G93A-SOD1 mouse model of ALS.

### Methods

Two groups of G93A-SOD1 mice (n=5) and wild-type mice (n=4) were euthanized (approved by IACUC) on postnatal days 100 and MRI scans performed. All MRI data were acquired with 31cm bore 9.4 T Agilent MRI scanner at $16^{\circ}C$. A DW stimulated echo sequence was applied with following acquisition parameters: TR/TE 2000/30.5 ms, mixing time 382 ms, $\delta$/$\triangle$ 11/400 ms, slice thickness 1.5 mm, field of view (FOV) 36 × 50 mm2, matrix 64 × 96 and 30 b values ranging from 0 to 858,022 s/mm2 with a maximal diffusion gradient strength of 50 Gauss/cm and direction perpendicular to long axis of mouse spinal cord. T2 weighted images were acquired using a fast spin echo sequence with parameters: TR/TE 1000/12 ms, echo train length 8, matrix 192 × 192, FOV 36 × 50 mm2, slice thickness 1.5 mm. Image post-processing was performed in MATLAB (MathWorks). Normalized signal intensities were calculated from regions of interest (ROIs) at lumbar level that were manually drawn in DW images for each mouse in both groups. Non-negative least squares (NNLS) was employed to analyze normalized signal intensities on 200 possible diffusion coefficients (Dps) that were logarithmically spaced over the interval of [$1\times10^{-8}$, $3\times10^{-3}$] mm2/s. To minimize noise influence in analysis, a regularization term based on ‘energy’ in spectrum was introduced

$$argmin_{s}\frac{1}{2}||A\vec{S}-\vec{y}||_{2}+\mu\vec{S}^{H}\vec{S}$$

, subject to $\vec{S}\geq0$, where A is a 200 x 30 matrix containing kernels exp(−b, Dps), $\vec{S}$ is weights of Dps, $\vec{y}$ is normalized signal intensities, $\mu$ is a regularizer computed from $\chi^{2}$ distribution condition when regularized fit is 101% of the non-regularized $\chi^{2}$[8]. Additionally, we proposed a bi-compartment model to evaluate the DW data $$\vec{y}=(1-f)E_{\alpha}(-(\vec{b}D_{1})^\alpha)+fe^{-\vec{b}D_{2}}$$, where $D_{1}$, $D_{2}$ are diffusion coefficients, $f$ is the fraction of the mono-exponential compartment, $\vec{b}D_{1}$is raised to $\alpha$ power. In this model, a Mittag-Leffler function ($E_{\alpha}$) was employed to represent restricted diffusion and a mono-exponential function to depict the hindered diffusion components [9,10]. A Student’s t test was applied to compare parameters ( $D_{1}$, $D_{2}$, $\alpha$ and $f$) extracted from the bi-compartment model.

### Results

In DW images of a wild type representative mouse, signal intensities in spinal cord persisted while intensities in other tissues decayed away with increased b values (Fig. 1B-D). At high b values (b > $1\times10^{4}$ s/mm2), the normalized signal intensities were found to be much lower for the diseased mouse at all the b values, when compared to those of the wild type mice (Fig. 2). Furthermore, a non-linear behavior between b values and log-scaled normalized signal intensities was found, indicating multiple diffusion components in spinal cord (Fig. 2A). On the averaged Dps distribution curves of both groups from NNLS analysis, obvious differences were observed on the weights of Dps in the neighborhoods of $1\times10^{-5}$ and $2\times10^{-4}$ mm2/s (Fig. 3). No significant differences were observed in $D_{1}$, $D_{2}$ and $\alpha$ from the bi-compartment model (Fig. 4A, B), whereas $f$, the fraction of mono-exponential compartment, was found to be significantly larger (P < 0.05) in mutant mice than that in wild type mice (Fig. 4C).

### Discussion

Novel diffusion-weighted MRI techniques can be beneficial to non-invasively monitor disease progression and to evaluate treatment outcomes. In this study, the signal differences with the Dps weights in the neighborhoods of $1\times10^{-5}$ and $2\times10^{-4}$ mm2/s between diseased and wild type groups likely reflect damage of microstructures caused by degeneration in white matter. Additionally, in the bi-compartment model, the significantly larger $f$ detected in G93A-SOD1 mice may alternatively indicate fine structure damages in the spinal cord. Therefore, both Dps weightings from NNLS and the fraction in the bi-compartment model showed potential to detect structural and pharmacodynamic changes of ALS in the G93A-SOD1 mice.

### Conclusion

We demonstrated that spinal cord alternations in a symptomatic mouse model of ALS can be detected by both NNLS and a bi-compartment model analysis of a series of DW images with b-value extended to extremely high values. Further studies are necessary to validate these methods for tracking progression in ALS or other neurodegenerative diseases.

### Acknowledgements

This study is sponsored in part by NIH R01 CA181658 and CA159178; this work made use of instruments in the Preclinical Imaging Core Facility (Research Resources Center, University of Illinois at Chicago)

### References

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### Figures

Fig. 1 MR images of the representative ex vivo mice, (A) anatomic sagittal T2 weighted image (Red region shows the lumbar spinal cord), (B) diffusion weighted image with b = 2.15 × 103 s/mm2, (C) diffusion weighted image with b = 4.20 × 105 s/mm2, (D) diffusion weighted image with b = 8.58 × 105 s/mm2. The diffusion gradient direction is perpendicular to the long axis of the spinal cord in (B) - (D).

Fig. 2 Normalized signal intensity vs b-value in log-scale, (A) log-scaled normalized signal intensity vs b-value, (B) log-scaled normalized signal intensity vs log-scaled b-value.

Fig. 3 Dps Fraction vs log-scaled Dps values in NNLS analysis.

Fig. 4 Parameter statistics in the bi-compartment model, (A) parameter α and diffusion coefficient D1, (B) diffusion coefficient D2, (C) fraction f, for wild type group (averaged f = 0.32) and mutant group (averaged f = 0.45)

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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