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

Jonathan Doucette; Luxi Wei; Enedino Hernández-Torres; Christian Kames; Nils D Forkert; Rasmus Aamand; Torben E Lund; Brian Hansen; Alexander Rauscher

doi:10.1016/j.neuroimage.2018.10.035

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

Neuroimage. 2019 Jan 15:185:198-207. doi: 10.1016/j.neuroimage.2018.10.035. Epub 2018 Oct 15.

Authors

Jonathan Doucette¹, Luxi Wei², Enedino Hernández-Torres³, Christian Kames⁴, Nils D Forkert⁵, Rasmus Aamand⁶, Torben E Lund⁶, Brian Hansen⁶, Alexander Rauscher⁷

Affiliations

¹ 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: jdoucette@phas.ubc.ca.
² UBC MRI Research Centre, University of British Columbia, 2221, Wesbrook Mall, Vancouver, BC, Canada; Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada.
³ UBC MRI Research Centre, University of British Columbia, 2221, Wesbrook Mall, Vancouver, BC, Canada; Department of Pediatrics, University of British Columbia Faculty of Medicine, Rm 2D19, 4480, Oak Street, BC Children's Hospital, Vancouver, BC, Canada.
⁴ 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.
⁵ Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada.
⁶ Center of Functionally Integrative Neuroscience (CFIN) and MINDLab, Department of Clinical Medicine, Aarhus University Hospital, Nørrebrogade 44, Building 10G, 5th floor, 8000, Aarhus C, Denmark.
⁷ 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; Department of Pediatrics, University of British Columbia Faculty of Medicine, Rm 2D19, 4480, Oak Street, BC Children's Hospital, Vancouver, BC, Canada.

PMID: 30332614
DOI: 10.1016/j.neuroimage.2018.10.035

Abstract

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%.

Keywords: Bloch-torrey equation; Brain perfusion; Cerebral blood flow; Cerebral blood volume; Diffusion; Functional MRI; Tissue anisotropy.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Anisotropy
Brain / blood supply*
Brain / metabolism
Brain Mapping / methods*
Cerebrovascular Circulation / physiology
Humans
Magnetic Resonance Imaging
Models, Neurological*
White Matter / blood supply*
White Matter / metabolism