Mathematical methods for modelling of the human heart from sub-dyadic to organ scales

The function of the heart involves processes on many different time and length scales. The electrical action potential wave from the sinoatrial node travels across the whole organ, and coordinates the contractile behavior of billions of cells into the pump function. The actual coupling between this action potential and contraction uses tiny sub-cellular volumes, the dyadic clefts, the behavior of which is very noisy. It is known that the microscopic and structural parameters and the micoroscopic noise affect the propensity of the heart for pathological behavior, but a detailed mechanistic understanding is lacking due to the difficulties of mathematical modelling and simulation of such models across the scales. Vice versa, the processes on organ level impose behavioral regimes on individual myocytes which they cannot generate as isolated cells, and which are therefore difficult to investigate experimentally. The proposed research in multi-scale mathematical modelling of the heart will address both angles of views. It will follow up on the effect of microscopic parameters on organ behavior by informing organ models by very detailed cell simulations. It will investigate cell behavior in tissue by imposing the behavioral regimes generated by organ simulations on detailed cell models.