A lattice Boltzmann approach to mathematical modeling of myocardial perfusion

A mathematical model of myocardial perfusion based on the lattice Boltzmann method (LBM) is proposed and its applicability is investigated in both healthy and diseased cases. The myocardium is conceptualized as a porous material in which the transport and mass transfer of a contrast agent in blood flow is studied. The results of myocardial perfusion obtained using LBM in 1D and 2D are confronted with previously reported results in the literature and the results obtained using the mixed‐hybrid finite element method. Since LBM is not suitable for simulating flow in heterogeneous porous media, a simplified and computationally efficient 1D‐analog approach to 2D diseased case is proposed and its applicability discussed. A mathematical model of myocardial perfusion based on the lattice Boltzmann method and contrast agent transport based on advection–diffusion equation is proposed in 1D and 2D and its applicability is discussed in both healthy and diseased cases in relation to the perfusion magnetic resonance imaging exam. A simplified, computationally efficient 1D‐analog approach to 2D diseased case is proposed and its applicability discussed.