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This paper combines high-performance computing and grid computing technologies to accelerate multiple executions of a biomedical application that simulates the action potential propagation on cardiac tissues. First, a parallelization strategy was employed to accelerate the execution of simulations on a cluster of personal computers (PCs). Then, grid computing was employed to concurrently perform the multiple simulations that compose the cardiac case studies on the resources of a grid deployment, by means of a service-oriented approach. This way, biomedical experts are provided with a gateway to easily access a grid infrastructure for the execution of these research studies. Emphasis is stressed on the methodology employed. In order to assess the benefits of the grid, a cardiac case study, which analyzes the effects of premature stimulation on reentry generation during myocardial ischemia, has been carried out. The collaborative usage of a distributed computing infrastructure has reduced the time required for the execution of cardiac case studies, which allows, for example, to take more accurate decisions when evaluating the effects of new antiarrhythmic drugs on the electrical activity of the heart.