Multicompartment Darcy Flow Model With Patient‐Specific Parameterization: Effect of Heterogeneity and Anisotropy in Porous Parameters

Blood perfusion in cardiac tissues involves intricate interactions among vascular networks and tissue mechanics. Perfusion deficit is one of the leading causes of cardiac diseases, and modeling certain cardiac conditions that are clinically infeasible, invasive, or costly can provide valuable supplementary insights to aid clinicians. However, existing homogeneous perfusion models lack the complexity required for patient-specific simulations. In this study, we develop a computational framework for modeling perfusion using a multicompartment Darcy flow model with heterogeneous anisotropic perfusion that incorporates the nonlinear deformation and compliance of blood vessels with poroelastic parameters derived from realistic vascular data. Through numerical simulations and a comparison of pore pressure results obtained from the proposed model and the Poiseuille flow approach in a benchmark problem, we demonstrate that the heterogeneous anisotropic model outperforms homogeneous models in predicting perfusion, particularly by accurately capturing the spatial heterogeneity of the poroelastic parameters and the permeability transitions from large vessels to microvessels. Additionally, the proposed model successfully simulates patient-specific conditions, such as vessel blockages, highlighting its potential for personalized medical applications.