Diffusion effects in myelin sheath free induction decay

[Display omitted] •Changes in myelin sheath integrity are implicated in many neurological diseases.•Recent model of MR signal decay in neuronal fibers considered regimes of no and of very fast diffusion.•Model is extended for all diffusion effects by solving the Bloch-Torrey equation with a perturbation expansion method.•Model variations of diffusion strengths lead to substantially different MR signal decays.•Model may be used to adjust or control simulations for water diffusion in neuronal structures. Myelin sheath microstructure and composition produce MR signal decay characteristics that can be used to evaluate status and outcome of demyelinating disease. We extend a recently proposed model of neuronal magnetic susceptibility, that accounts for both the structural and inherent anisotropy of the myelin sheath, by including the whole dynamic range of diffusion effects. The respective Bloch-Torrey equation for local spin dephasing is solved with a uniformly convergent perturbation expansion method, and the resulting magnetization decay is validated with a numerical solution based on a finite difference method. We show that a variation of diffusion strengths can lead to substantially different MR signal decay curves. Our results may be used to adjust or control simulations for water diffusion in neuronal structures.