Computationally Efficient Simulation of Calcium Signaling in Cardiomyocytes.

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 parallelisation, which include fully-implicit Runge-Kutta integration with both L-stability and step-size control, Newton's root finding method with exception handling, and Conjugate Residual Squared for solving linear systems not of full-rank within available computational precision. Parallelisation of the problem across the systems is employed to allow for practical scaling with computing resources. The results produce sparks and waves akin to those observed in actual laboratory experiments within an acceptable timeframe. Performance measures of the simulation model with respect to accuracy and computation time are also given. The conclusion is that the methodologies utilised in this work are can simulate cardiomyocyte's calcium signalling in a computationally efficient manner with the results produced replicating those in the laboratory. The significance of this paper is that computational models such as the one developed here provide a way to simulate and understand the complex biological interactions operating in organisms. Accurate simulations are extremely computationally intensive and this pursuit is considered as the grand challenge for computational science into the 21st century.