A Multiscale Poromechanics Model Integrating Myocardial Perfusion and the Epicardial Coronary Vessels

The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes.Universidade Federal de Juiz de Fora (UFJF)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Australian Research CouncilMinistry of Science and Higher Education of the Russian FederationUCR::Sedes Regionales::Sede de Occidente::Recinto San RamónUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic