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Cardiovascular diseases are the major cause of death in the developed countries. Identifying key cellular processes involved in generation of the electrical signal and in regulation of signal transduction pathways is essential for unraveling the underlying mechanisms of heart rhythm behavior. Computational cardiac models provide important insights into cardiovascular function and disease. Sensitivity analysis presents a key tool for exploring the large parameter space of such models, in order to determine the key factors determining and controlling the underlying physiological processes. We developed a new global sensitivity analysis tool which implements the Morris method, a global sensitivity screening algorithm, onto a Nimrod platform, which is a distributed resources software toolkit. The newly developed tool has been validated using the model of IP3-calcineurin signal transduction pathway model which has 30 parameters. The key driving factors of the IP3 transient behaviour have been calculated and confirmed to agree with previously published data. We next demonstrated the use of this method as an assessment tool for characterizing the structure of cardiac ionic models. In three latest human ventricular myocyte models, we examined the contribution of transmembrane currents to the shape of the electrical signal (i.e. on the action potential duration). The resulting profiles of the ionic current balance demonstrated the highly nonlinear nature of cardiac ionic models and identified key players in different models. Such profiling suggests new avenues for development of methodologies to predict drug action effects in cardiac cells.