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Heterogeneous anisotropic magnetic susceptibility of the myelin‐water layers causes local magnetic field perturbations in axons

One goal of MRI is to determine the myelin water fraction in neural tissue. One approach is to measure the reduction in T2* arising from microscopic perturbations in the magnetic field caused by heterogeneities in the magnetic susceptibility of myelin. In this paper, analytic expressions for the induced magnetic field distribution are derived within and around an axon, assuming that the myelin susceptibility is anisotropic. Previous models considered the susceptibility to be piecewise continuous, whereas this model considers a sinusoidally varying susceptibility. Many conclusions are common in both models. When the magnetic field is applied perpendicular to the axon, the magnetic field in the intraaxonal space is uniformly perturbed, the magnetic field in the myelin sheath oscillates between the lipid and water layers, and the magnetic field in the extracellular space just outside the myelin sheath is heterogeneous. These field heterogeneities cause the spins to dephase, shortening T2*. When the magnetic field is applied along the axon, the field is homogeneous within water‐filled regions, including between lipid layers. Therefore the spins do not dephase and the magnetic susceptibility has no effect on T2*. Generally, the response of an axon is given as the superposition of these two contributions. The sinusoidal model uses a different set of approximations compared with the piecewise model, so their common predictions indicate that the models are not too sensitive to the details of the myelin‐water distribution. Other predictions, such as the sensitivity to water diffusion between myelin and water layers, may highlight differences between the two approaches. Copyright © 2016 John Wiley & Sons, Ltd.