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

Area of Science:

• Computational physics
• Biomedical imaging
• Numerical methods

Background:

• Diffusion magnetic resonance imaging (dMRI) requires accurate modeling of transverse magnetization.
• The Bloch-Torrey equation governs dMRI signal evolution but faces computational challenges.
• Classical lattice Boltzmann methods (LBM) have limitations, particularly small time-step constraints.

Purpose of the Study:

• To implement a hybrid LBM scheme for solving the Bloch-Torrey equation.
• To develop and validate a membrane boundary condition for modeling biological tissues.
• To enhance the accuracy and applicability of LBM in dMRI simulations.

Main Methods:

• Implementation of a hybrid lattice Boltzmann method (LBM) scheme.
• Integration of the Bloch-Torrey equation with a novel membrane boundary condition.
• Comparison with analytical solutions and classical LBM for validation.

Main Results:

• The hybrid LBM scheme demonstrates superior accuracy compared to the classical LBM.
• The method accurately represents thin curvilinear membranes and finite membrane permeabilities.
• The scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy.
• Efficient parallel implementation on multi-CPU and GPU systems is achieved.

Conclusions:

• The proposed hybrid LBM is a flexible and accurate method for dMRI simulations.
• It offers advantages over finite element and Monte Carlo methods for biological tissue modeling.
• The scheme can be adapted for complex interfacial conditions and advanced dMRI sequences.