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We present a computational modeling and numerical simulation framework that enables the integration of multiple physics and spatiotemporal scales in models of physiological systems. This framework is the foundation of the IUPS (International Union of Physiological Sciences) Physiome Project. One novel aspect is the use of CellML, an annotated mathematical representation language, to specify model- and simulation-specific equations. Models of cardiac electromechanics at the cellular, tissue, and organ spatial scales are outlined to illustrate the development and implementation of the framework. We quantify the computational demands of performing simulations using such models and compare models of differing biophysical detail. Applications to other physiological systems are also discussed.
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