Investigating time- and orientation-dependent transverse relaxation from magnetic susceptibility of white matter microstructure

Transverse relaxation in MRI is modulated by magnetic field variations arising from tissue microstructure, offering a potential window into the underlying chemical composition and structural organization at the cellular scale. However, the transverse relaxation rate in white matter depends on both echo time and the orientation of axons relative to the external field. Such anisotropy complicates the interpretation of transverse relaxation in general and as a biomarker for neurodegenerative disease. Understanding this anisotropy is therefore crucial for accurately analyzing MRI signals. While previous modeling studies have investigated these effects, they often relied on simplified or idealized tissue geometries. In this study, we investigate magnetic field variance and intra-axonal transverse relaxation using realistic axonal microstructure extracted from 3D electron microscopy, incorporating myelinated axons with embedded spherical susceptibility sources. We derive how transverse relaxation depends on the angle between axons and the external magnetic field. Simulations show that the time-dependent power-law signature arising from white matter structural disorder is weak and may be difficult to detect at currently achievable noise levels, echo times, and field strengths. This is because the power-law curvature over a typical range of echo times deviates only slightly from a linear trend. Our findings highlight the influence of axonal geometry on intra-axonal transverse relaxation and suggest that accounting for both time and orientation dependence may facilitate the development of more precise neuroimaging biomarkers.