Physics

Internal medicine

Finite element method

Electrophysiology

Fluid–structure interaction

Mathematics

Fluid mechanics

Mechanics

Partial differential equation

Politics

Statistics

Mathematical analysis

Political science

Representation (politics)

Computer science

Flexibility (engineering)

Cardiac electrophysiology

Discretization

Multiphysics

Computer simulation

Medicine

Thermodynamics

International Journal for Numerical Methods in Biomedical Engineering

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro‐mechanical and mechano‐electrical feedback as well as force‐strain and force‐velocity relationships. Moreover, it provides a three‐dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid–structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology‐force generation‐FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart