A lattice Boltzmann method for simulation of diffusion-weighted MRI in biological tissue

The lattice Boltzmann method (LBM) is used to integrate the Bloch-Torrey equation, which describes the evolution of the magnetization signal in diffusion-weighted magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, a hybrid LBM scheme is developed that accommodates piece-wise uniform transport, MRI sequence parameters, and periodic outer boundary conditions. A membrane boundary condition is implemented that accurately represents the effects of thin curvilinear membranes with finite membrane permeabilities as typically found in biological tissues. In comparison with analytical solutions of limiting cases, the hybrid LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous, multiphase tissue models and to accommodate sophisticated dMRI sequences.