Although it is now feasible to compute multi-cellular models of the heart on a personal desktop or laptop computer, it is not feasible to undertake the detailed sweeps of high-dimensional parameter spaces required if we are to undertake in silico experimentation of the complex processes that constitute heart disease. For this research, modelling requirements move rapidly beyond the limit of commodity computers' resource both in terms of their memory footprint and the speed of calculation, so that multi-processor architectures must be considered. In addition, as such models have become more mature and have been validated against experimental data, there is increasing pressure for experimentalists to be able to make use of these models themselves as a key tool for hypothesis formulation and in planning future experimental studies to test those hypotheses. This paper discusses our initial experiences in a large-scale project (the Integrative Biology (IB) e-Science project) aimed at meeting these dual aims. We begin by putting the research in context by describing in outline the overall aims of the IB project, in particular focusing on the challenge of enabling novice users to make full use of high-performance resources without the need to gain detailed technical expertise in computing. We then discuss our experience of adapting one particular heart modelling package, Cellular Open Resource, and show how the solving engine of this code was dissected from the rest of the package, ported to C++ and parallelized using the Message-Passing Interface. We show that good parallel efficiency and realistic memory reduction can be achieved on simple geometries. We conclude by discussing lessons learnt in this process.