A Diffusion MRI model for axonal damage quantification based on axial diffusivity reduction in axons: a Monte Carlo simulation study

Axonal damage is the primary pathological correlate of long-term impairment in multiple sclerosis (MS). Previous work has demonstrated a strong, quantitative relationship between decrease in axial diffusivity and axonal damage. In the present work, we develop an extension of diffusion basis spectrum imaging (DBSI) which can be used to quantify the fraction of diseased and healthy axons based on reduction in axial diffusivity in axons. In this novel method, we model the MRI signal with the axial diffusion (AD) spectrum for each fiber orientation and use two component restricted anisotropic diffusion spectrum (RADS) to model the anisotropic component of the diffusion-weighted MRI signal. Diffusion coefficients and signal fractions are computed for the optimal model with the lowest Bayesian information criterion (BIC) score. This gives us the fractions of diseased and healthy axons. We test our method using Monte-Carlo (MC) simulations with the MC simulation package developed as part of this work. The simulation geometry for the voxel includes uniformly spaced cylinders to model axons, and uniformly spaced spheres to model extra-axonal cells. First we test and validate our MC simulations for the basic RADS model. It accurately recovers the fiber and cell fractions simulated, as well as the simulated diffusivities. For testing and validating RADS to quantify axonal damage, we simulate different fractions of diseased and healthy axons. Our method produces highly accurate quantification of diseased and healthy axons with Pearson's correlation (predicted vs true proportion) of r = 0.98 (p-value = 0.001); the one Sample t-test for proportion error gives the mean error of 2% (p-value = 0.034). Furthermore, the method recovers the axial diffusivities of the diseased and healthy axons very accurately with mean error of 4% (p-value = 0.001).