On the role of neuronal magnetic susceptibility and structure symmetry on gradient echo MR signal formation.

Purpose: Phase images obtained by gradient-recalled echo (GRE) MRI provide new contrast in the brain that is distinct from that obtained with conventional T1-weighted and T2-weighted images. The results are especially intriguing in white matter where both signal amplitude and phase display anisotropic properties. However, the biophysical origins of these phenomena are not well understood. The goal of this article is to provide a comprehensive theory of GRE signal formation based on a realistic model of neuronal structure.

Methods: We use Maxwell equations to find the distribution of magnetic field induced by myelin sheath and axon. We account for both anisotropy of neuronal tissue "magnetic micro-architecture" and anisotropy of myelin sheath magnetic susceptibility.

Results: Model describes GRE signal comprising of three compartments-axonal, myelin, and extracellular. Both axonal and myelin water signals have frequency shifts that are affected by the magnetic susceptibility anisotropy of long molecules forming lipid bilayer membranes. These parts of frequency shifts reach extrema for axon oriented perpendicular to the magnetic field and are zeros in a parallel case. Myelin water signal is substantially non-monoexponential.

Conclusions: Both, anisotropy of neuronal tissue "magnetic micro-architecture" and anisotropy of myelin sheath magnetic susceptibility, are important for describing GRE signal phase and magnitude.