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Abstract:  Cardiovascular disease, and the cardiovascular side effects of drugs, are essentially multifactorial problems involving interactions between many proteins, dependent on highly organized cell, tissue and organ structures. This is one reason why the side effects of drugs are often unanticipated. It is impossible to unravel such problems without using a systems approach, i.e. focussing on processes, not just molecular components. This inevitably involves modelling as the interactions require quantitative analysis. Modelling is a tool of analysis aimed at understanding, first, and predicting, eventually. We illustrate these principles using modelling of the heart. Models of the cardiac myocyte have benefited from several decades of interaction between experimentation and simulation. They are now sufficiently detailed to have been of use in the development of new drug compounds like ranolazine and ivabradine. With the help of cardiac modelling, we have also been able to unravel the mechanisms underlying the beneficial effect of sodium calcium exchange block for long QT syndrome (LQTS) 2 and LQTS3 patients. Detailed models of the interaction between ion channels and blocking agents provide the basis for modelling drug action from basic principles and predict changes in the inhomogeneous tissue of the heart. We demonstrate that mathematical models are beneficial for unravelling the complex interactions of pharmacodynamics in the heart. Embedding these detailed biophysical cellular scale models into anatomically correct models of the ventricle geometry will enable reconstructions of Torsades de Pointes arrhythmias and of fibrillation, providing a mechanism for linking detailed cellular scale experimental data to clinical applications.