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Future multiscale and multiphysics models that support research into human disease, translational medical science, and treatment can utilize the power of high-performance computing (HPC) systems. We anticipate that computationally efficient multiscale models will require the use of sophisticated hybrid programming models, mixing distributed message-passing processes [e.g., the message-passing interface (MPI)] with multithreading (e.g., OpenMP, Pthreads). The objective of this study is to compare the performance of such hybrid programming models when applied to the simulation of a realistic physiological multiscale model of the heart. Our results show that the hybrid models perform favorably when compared to an implementation using only the MPI and, furthermore, that OpenMP in combination with the MPI provides a satisfactory compromise between performance and code complexity. Having the ability to use threads within MPI processes enables the sophisticated use of all processor cores for both computation and communication phases. Considering that HPC systems in 2012 will have two orders of magnitude more cores than what was used in this study, we believe that faster than real-time multiscale cardiac simulations can be achieved on these systems.