# Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

## TL;DR

This paper introduces a hybrid lattice Boltzmann method for simulating diffusion MRI physics in complex biological tissues, improving accuracy and efficiency over classical methods and enabling modeling of realistic tissue interfaces.

## Contribution

The paper presents a novel hybrid LBM scheme with membrane boundary conditions for accurate, efficient simulation of diffusion MRI in multiphase tissue models, surpassing classical LBM limitations.

## Key findings

- Hybrid LBM scheme is more accurate than classical LBM.
- The explicit LBM scheme maintains second-order spatial and first-order temporal accuracy.
- Parallel implementation on CPUs and GPUs is efficient and straightforward.

## Abstract

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. 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.

---
Source: https://tomesphere.com/paper/1907.00908