MATHEMATICAL AND NUMERICAL MODELING OF CARDIAC ELECTROMECHANICS AND CARDIOVASCULAR FUNCTIONS

The investigation and simulation of the main cardiac functions are increasingly using biophysically detailed mathematical and numerical models that couple multiscale submodels ranging from the sub-cellular membrane models of ionic channels and concentrations dynamics to the macroscopic bio-electrical and mechanical models of the whole heart, as well as of the blood flow dynamics in the ventricles and its interactions with the global circulation. These models consists of coupled systems of partial and ordinary differential equations that in the bioelectrical models are of reaction-diffusion type, in the mechanical deformation models are of nonlinear quasi-static finite elasticity type and in the haemodynamical models are of Navier-Stokes type. The efficient simulation of these cou-pled models is very challenging because of the wide range of spatio-temporal scales and nonlinear dynamics involved. Advanced numerical techniques are currently being developed by combining multiscale methods, decoupling and operator splitting techniques, adaptivity in space and time, par-allel computing and domain decomposition solvers. The target of these research efforts is to reduce the computational time and increase the simulation accuracy in order to be able to predict the effects of cardiovascular pathologies and medical interventions. Such interdsciplinary research projects are currently carried out at several research groups around the world, making intensive collaboration an