Electromechanical Simulations of the Left Ventricle - Approaches and Implications in Heart Failure Research

Heart failure remains a significant health and economic burden in the developed world, resulting in millions of deaths and billions of dollars of expenditure annually. In order to better understand the electromechanical function and dysfunction of the failing heart as well as to theoretically test possible treatments, a mathematical model describing myocardial electromechanics has been developed. The mathematical framework of this model consists of a number of interconnected sub systems: 1) a physiological model describing cellular electrical dynamics and the resulting changes in myofiber active stress, 2) a bidomain electrical diffusion solver governing the propagation of the electrical signal, and 3) a non-linear mechanics system describing the hyperelastic behavior of myocardium tissue. These subsystems are coupled and solved using a multi-grid finite element model and operator splitting. Using this framework, MRI measured ventricular geometries can be meshed onto finite element grids with defined myofiber orientations, and cycled through the complete cardiac loop of passive inflation, isovolumic contraction, ejection against the circulation, and isovolumic relaxation. These simulations can be used to understand how geometric and tissue irregularities, such as those brought about by myocardial infarctions, can give rise to mechanical and electrical abnormalities in the myocardium, as well as to theoretically test emerging treatments for heart failure such as cardiac resynchronization therapy or tissue engineering methods.