Local magnetic field perturbations caused by magnetic susceptibility heterogeneity in myelin-water layers within an axon
Magnetic resonance imaging has been used to map the myelin water fraction in neural tissue. One hypothesis is that a reduction in T*2 arises from microscopic perturbations in the magnetic field caused by heterogeneities in the magnetic susceptibility of myelin. In this paper, the perturbed magnetic field distribution is calculated analytically using a perturbation expansion written in terms of a small dimensionless parameter corresponding to the magnetic susceptibility. When the magnetic field is applied perpendicular to the axon, the magnetic field in the intracellular space is not influenced by the myelin, the magnetic field in the myelin sheath oscillates between the fat and water layers, and the magnetic field in the extracellular space just outside the myelin sheath is heterogeneous. This heterogeneity causes the spins to dephase, shortening T*2. When the magnetic field is applied along the axon, it is homogeneous within water-filled regions between myelin layers, and therefore the spins will not dephase and the magnetic susceptibility will have no effect on T*2. These two solutions predict the perturbed magnetic field distribution in and around an axon arbitrarily oriented in the main magnetic field.
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