Predicting Mesoscopic Larmor Frequency Shifts in White Matter With Diffusion MRI-A Monte Carlo Study in Axonal Phantoms

Magnetic susceptibility MRI offers potential insights into the chemical composition and microstructural organization of tissue. However, estimating magnetic susceptibility in white matter is challenging due to anisotropic subvoxel Larmor frequency shifts caused by axonal microstructure relative to the B0 field orientation. Recent biophysical models have analytically described how axonal microstructure influences the Larmor frequency shifts, relating these shifts to a mesoscopically averaged magnetic field that depends on the axons' fiber orientation distribution function (fODF), typically estimated using diffusion MRI. This study is aimed at validating the use of MRI to estimate mesoscopic magnetic fields and determining whether diffusion MRI can faithfully estimate the orientation dependence of the Larmor frequency shift in realistic axonal microstructure. To achieve this, we developed a framework for performing Monte Carlo simulations of MRI signals in mesoscopically sized white matter axon substrates segmented with electron microscopy. Our simulations demonstrated that with careful experimental design, it is feasible to estimate mesoscopic magnetic fields. Additionally, the fODF estimated by the standard model of diffusion in white matter could predict the orientation dependence of the mesoscopic Larmor frequency shift. We also found that incorporating the intra-axonal axial kurtosis into the standard model could explain a significant amount of signal variance, thereby improving the estimation of the Larmor frequency shift. This factor should not be neglected when fitting the standard model.