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The objective of this paper is to develop a computationally efficient simulation model of Calcium signalling in cardiomyocytes. The model considered here consists of more than two million stiff, nonlinear, and stochastic systems, each of which is composed of 62 state equations. The size of the model, combined with the broad numerical scale, non-continuous stochastic state-transitions, and underlying physiological constraints, presents a significant implementation challenge. The method involves development of specialised algorithms for paral