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


UBC MRI Research Centre, University of British Columbia, 2221, Wesbrook Mall, Vancouver, BC, Canada; Department of Physics and Astronomy, University of British Columbia, 6224, Agricultural Road, Hennings Building, Room 325, Vancouver, BC, Canada. Electronic address: [Email]


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%.


Bloch-torrey equation,Brain perfusion,Cerebral blood flow,Cerebral blood volume,Diffusion,Functional MRI,Tissue anisotropy,