We present implementations of tissue-scale 3D simulations of the human cardiac ventricle using a physiologically realistic cell model. Computational challenges in such simulations arise from two factors, the  first of which is the sheer amount of computation when simulating a large number of cardiac cells in a detailed model containing 10^4 calcium release units, 10^6 stochastically changing ryanodine receptors and 1.5 × 10^5 L-type calcium channels per cell.

Additional challenges arise from the fact that the computational tasks have various levels of arithmetic intensity and control complexity, which require careful adaptation of the simulation code to the target device. By exploiting the strengths of GPUs and manycore accelerators, we obtain a performance that is far superior to that of the basic CPU implementation, thus paving the way for detailed whole-heart simulations in future generations of leadership class supercomputers.