From action potentials to whole-heart dysfunction: a mathematical tour of cardiac electromechanics

The heart is a remarkable example of multiphysics complexity: electrical signals propagate through cardiac tissue, trigger active mechanical contraction, and interact with the surrounding fluid and mechanical environment in a tightly coupled feedback loop. Understanding and reproducing this behaviour mathematically requires bridging several topics, from partial differential equations to numerical analysis and scientific computing.This lecture offers a guided tour of cardiac electromechanics modelling, starting from the cellular scale and building up to organ-level simulations of whole-heart function. We will discuss the multiphysics coupling that lies at the heart of the problem and the main computational strategies used to tackle it. A significant portion of the lecture will be devoted to clinical applications: we will examine how computational models have been used to study hypertrophic cardiomyopathy (HCM), cardiac amyloidosis, and atrial fibrillation (AF), illustrating the potential of in silico approaches to inform diagnosis and support treatment planning. Time permitting, we will conclude with an introduction to surrogate modelling for cardiac safety assessment, showing how machine learning techniques can be coupled with high-fidelity simulations to achieve the throughput required by industrial workflows.