Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (AP) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Mathematical models of the action potential have grown increasingly complex and include many subcellular phenomena such as calcium handling and complex Markov formulations of the gating dynamics of the ion channels. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level AP wave behaviour without subcellular details. We use some techniques for parameter estimation to fit the morphology of the AP in the four variable Bueno-Orovio phenomenological model. We establish an approximation of a nonlinear ordinary differential equation model that corresponds to the given phenomenological model of the cardiac action potential. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder-Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. We demonstrate the successful fitting of data generated from a well known biophysically detailed model. We also show that we can produce a successful fit to an experimental AP recording that contains both noise and experimental artefacts. The Discipline of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia. mailto:[email protected] Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.