Non-Lorentzian Sphere Behavior of Magnetic Susceptibility Induced MR Signal Frequency Shift in White Matter: Validation Study

Introduction: Recently reported contrast in MR gradient echo phase images between brain gray matter (GM) and white matter (WM) holds a great promise for in vivo study of biological tissue structure with substantially improved resolution, which is profoundly enhanced at high field [1]. Possible origins of this contrast have been debated but mostly attributed to magnetic susceptibility effects. It is usually assumed that a relationship between local tissue magnetic susceptibility χ and corresponding MR frequency shift can be calculated using Lorentzian sphere approximation: 0 (4 / 3) f f π χ Δ = ⋅ ⋅ . While this approximation is adequate for isotropic structures [2, 3], it fails taking into account anisotropic microstructure of WM where magnetic susceptibility has contribution from longitudinal structures like protein-rich cytoskeleton fibers, myelin sheath, etc. Recently a theory of phase contrast has been proposed based on a newly introduced concept of generalized Lorentzian approach that takes into account anisotropic microstructure of axons and dendrites [4]. The theory quantitatively explained the frequency contrast between GM, WM, and CSF previously reported in brain motor cortex area [1]. In this study, the concept of generalized Lorentzian approximation is validated using ex vivo fresh rat optic nerve model. The ex vivo isolation of optic nerve ensures a well-defined environment to eliminate any field contamination from neighboring tissues during phase measurement.