Origins of R2* orientation dependence in gray and white matter

Estimates of the apparent transverse relaxation rate (R2*) can be used to quantify important properties of biological tissue. Surprisingly, the mechanism of R2* dependence on tissue orientation is not well understood. The primary goal of this paper was to characterize orientation dependence of R2* in gray and white matter and relate it to independent measurements of two other susceptibility based parameters: the local Larmor frequency shift (fL) and quantitative volume magnetic susceptibility (Δχ). Through this comparative analysis we calculated scaling relations quantifying R2' (reversible contribution to the transverse relaxation rate from local field inhomogeneities) in a voxel given measurements of the local Larmor frequency shift. R2' is a measure of both perturber geometry and density and is related to tissue microstructure. Additionally, two methods (the Generalized Lorentzian model and iterative dipole inversion) for calculating Δχ were compared in gray and white matter. The value of Δχ derived from fitting the Generalized Lorentzian model was then connected to the observed R2* orientation dependence using image-registered optical density measurements from histochemical staining. Our results demonstrate that the R2* and fL of white and cortical gray matter are well described by a sinusoidal dependence on the orientation of the tissue and a linear dependence on the volume fraction of myelin in the tissue. In deep brain gray matter structures, where there is no obvious symmetry axis, R2* and fL have no orientation dependence but retain a linear dependence on tissue iron concentration and hence Δχ.