Rapid solution of the Bloch-Torrey equation in anisotropic tissue: Application to dynamic susceptibility contrast MRI of cerebral white matter

Blood vessel related magnetic resonance imaging (MRI) contrast provides a window into the brain's metabolism and function. Here, we show that the spin echo dynamic susceptibility contrast (DSC) MRI signal of the brain's white matter (WM) strongly depends on the angle between WM tracts and the main magnetic field. The apparent cerebral blood flow and volume are 20% larger in fibres perpendicular to the main magnetic field compared to parallel fibres. We present a rapid numerical framework for the solution of the Bloch-Torrey equation that allows us to explore the isotropic and anisotropic components of the vascular tree. By fitting the simulated spin echo DSC signal to the measured data, we show that half of the WM vascular volume is comprised of vessels running in parallel with WM fibre tracts. The WM blood volume corresponding to the best fit to the experimental data was 2.82%, which is close to the PET gold standard of 2.6%. •The spin echo dynamic susceptibility contrast MRI signal depends on the orientation of the brain's white matter with respect to the main magnetic field.•We show that about half of the white matter blood resides in vessels that run in parallel with white matter tracts.•We present a solution of the Bloch-Torrey equation that is two orders of magnitude faster to compute than direct matrix exponential based methods.