Comparison of two-compartment exchange and continuum models of dMRI in skeletal muscle

Clinical diffusion MRI (dMRI) is sensitive to micrometer spin displacements, but the image resolution is $\sim$mm, so the biophysical interpretation of the signal relies on establishing appropriate subvoxel tissue models. A class of two-compartment exchange models originally proposed by K\"arger have been used successfully in neural tissue dMRI. Their use to interpret the signal in skeletal muscle dMRI is challenging because myocyte diameters are comparable to the root-mean-square of spin displacement and their membrane permeability is high. A continuum tissue model consisting of the Bloch-Torrey equation integrated by a hybrid lattice Boltzmann scheme is used for comparison. The validity domain of a classical two-compartment tissue model is probed by comparing with the prediction of the continuum model for a 2-D unidirectional composite continuum model of myocytes embedded in a uniform matrix, the validity domain of a classical two-component tissue model is probed. This domain is described in terms of two dimensionless parameters inspired by mass transfer phenomena, the Fourier (F) and Biot (B) numbers. The two-compartment model is valid when B << 1 and F >> 1, or when F << 1 and F ∙ B << 1. The model becomes less appropriate for muscle dMRI as the cell diameter and volume fraction increase, with the primary source of error associated with modeling diffusion in the extracellular matrix.