From microscopic calcium sparks to the ECG: Model reduction approaches for multi-scale cardiac simulation

Malfunctions in the intracellular calcium handling system are being increasingly linked to multiple cardiac arrhythmias. Feedback mechanisms in spatio-temporal sub-cellular calcium dynamics are critical for the development of spontaneous calcium waves which may underlie ectopic focal activity. However, computational models which account for such processes are unsuitable for incorporation into organ-scale simulations, thus limiting the ability of multi-scale modeling approaches to explain and dissect the role of spatio-temporal calcium handling in organ-level arrhythmogenesis. In this study we demonstrate two methods to increase the computational efficiency of models which account for spatio-temporal calcium dynamics, thus facilitating true multi-scale modeling approaches. One method is guided by empirical analysis of the microscopic model; the second method takes advantage of mesoscopic physics approaches to naturally capture critical stochastic behaviour. Both methods successfully reproduced the macroscopic consequences of spatio-temporal calcium dynamics in efficient single cell models. This allowed integration into a whole-organ model of the ventricle and simulation of the ECG.