A system and mathematical framework to model shear flow effects in biomedical DW-imaging and spectroscopy

The pulsed-field gradient (PFG) MR experiment enables one to measure particle displacements, velocities, and even higher moments of complex fluid motions. In diffusion-weighted MRI (DWI) in living tissue, where the PFG MRI experiment is used to measure diffusion, Brownian motion is assumed to dominate the displacements causing the observed signal loss. However, motions of water molecules caused by various active biological processes occurring at different length and time scales may also cause additional dephasing of magnetization and signal loss. To help understand their relative effects on the DWI signal attenuation, we used an integrated experimental and theoretical framework: a Rheo-NMR, which served as an experimental model system to precisely prescribe a microscopic velocity distribution; and a mathematical model that relates the DW signal intensity in the Rheo-NMR to experimental parameters that characterize the impressed velocity field. A technical innovation reported here is our use of 'natural' (in this case, polar) coordinates both to simplify the description the fluid motion within the Couette cell of the Rheo-NMR, as well as to acquire and reconstruct magnitude and phase MR images obtained within it. We use this integrated model system to demonstrate how shear flows appears as pseudo-diffusion in magnitude DW MR signals obtained using PFG spin-echo (PGSE) NMR and MRI sequences. Our results lead us to reinterpret the possible causes of signal loss in DWI in vivo, in particular to revise and generalize the previous notion of intra-voxel incoherent motion (IVIM) in order to describe activity driven flows that appear as pseudo-diffusion over multiple length and time scales in living tissues.