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Multicomponent Analysis of High b-value Diffusion-Weighted MRI for Tracking Progression of Amyotrophic Lateral Sclerosis in A Mouse Model1Department 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
1. B. R. Foerster, et al., "25 years of neuroimaging in amyotrophic lateral sclerosis," Nat Rev Neurol, vol. 9, pp. 513-524, 2013.
2. F. Agosta, et al., "The Present and the Future of Neuroimaging in Amyotrophic Lateral Sclerosis," AJNR Am J Neuroradiol, vol. 31, pp. 1769-1777, 2010.
3. D. L. Bihan, et al., "Separation of Diffusion and Perfusion in Intravoxel Incoherent Motion MR Imaging," Radiology, vol. 168, pp. 497-505, 1988.
4. K. M. Bennett, et al., "Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model," Magn Reson Med, vol. 50, pp. 727-734, 2003.
5. J.-P. Cercueil, et al., "Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T," Eur Radiol, vol. 25, pp.1541-1550, 2015.
6. R. L. Magin, et al., "Anomalous diffusion expressed through fractional order differential operators in the Bloch–Torrey equation," Journal of Magnetic Resonance, vol. 190, pp. 255-270, 2008.
7. X. Z. Zhou, et al., "Studies of Anomalous Diffusion in the Human Brain Using Fractional Order Calculus," Magn Reson Med, vol. 63, pp. 562-569, 2010.
8. K. P. Whittall, et al., " Quantitative Interpretation of NMR Relaxation Data," Journal of Magnetic Resonance, vol. 84, pp. 134-152, 1989.
9. Y. Assaf, et al., "New Modeling and Experimental Framework to Characterize Hindered and Restricted Water Diffusion in Brain White Matter," Magn Reson Med, vol. 52, pp. 965–978, 2004.
10. R. Metzler, et al., "The random walk's guide to anomalous diffusion: a fractional dynamics approach," Physics Reports, vol. 339, pp. 1-77, 2000.
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