We investigate heterogeneous computing, which involves both multicore CPUs and manycore Xeon Phi coprocessors, as a new strategy for computational cardiology. In particular, 3D tissues of the human cardiac ventricle are studied with a physiologically realistic model that has 10,000 calcium release units per cell and 100 ryanodine receptors per release unit, together with tissue-scale simulations of the electrical activity and calcium handling. In order to attain resource-efficient use of heterogeneous computing systems that consist of both CPUs and Xeon Phis, we first direct the coding effort at ensuring good performance on the two types of compute devices individually. Although SIMD code vectorization is the main theme of performance programming, the actual implementation details differ considerably between CPU and Xeon Phi. Moreover, in addition to combined OpenMP+MPI programming, a suitable division of the cells between the CPUs and Xeon Phis is important for resource-efficient usage of an entire heterogeneous system. Numerical experiments show that good resource utilization is indeed achieved and that such a heterogeneous simulator paves the way for ultimately understanding the mechanisms of arrhythmia. The uncovered good programming practices can be used by computational scientists who want to adopt similar heterogeneous hardware platforms for a wide variety of applications.