Parameter estimation for a phenomenological model of the cardiac action potential

The action potential 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. Biophysically detailed mathematical models of the action potential have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. 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 excitable cardiac tissue is a phenomenological model, which reconstructs tissue level action potential wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the action potential in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established 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 optimisation then solves the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental action potential recording that contains both noise and experimental artefacts is also produced. The parameter estimation method's ability to fit a complex morphology to a model with substantially more parameters than previously used is established. References E. Carmeliet and J. Vereecke, Cardiac Cellular Electrophysiology , Springer, 2002. V. Iyer, R. Mazhari and R. Winslow, A computational model of the human left--ventricular epicardial myocyte, Biophys. J. , 87, 2004, 1507--1525, doi:10.1529/biophysj.104.043299 S. Niederer, M. Fink, D. Noble and N. P. Smith, A meta-analysis of cardiac electrophysiology computational models, Exp. Physiol. , 94, 2009, 486--495, doi:10.1113/expphysiol.2008.044610 F. Fenton, and A. Karma, Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation, Chaos , 8, 1998, 20--47, doi:10.1063/1.166311 A. Bueno-Orovio, E. M. Cherry and F. H. Fenton, Minimal model for human ventricular action potentials in tissue, J. Theor. Biol. , 253, 2008, 544--560, doi:10.1016/j.jtbi.2008.03.029 J. Walmsley, G. Mirams, M. Bahoshy, C. Bollensdorff, B. Rodriguez and K. Burrage, Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated Guinea Pig ventricular myocytes, Conf. Proc. IEEE Eng. Med. Biol. Soc. 2010 , 2010, 1457--60, doi:10.1109/IEMBS.2010.5626858 C. Luo and Y. Rudy, A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction, Circ. Res. , 68, 1991, 1501--1526, doi:10.1161/01.RES.68.6.1501 J. Keener and J. Sneyd, Mathematical Physiology , Springer, 1998. M. M. Macconi, B. Morini and M. Porcelli, A Gauss-Newton method for solving bound-constrained underdetermined nonlinear systems, Optimization Method and Software, 24(2), 2010, 219--235, doi:10.1080/10556780902753031 J. A. Nelder and R. A. Mead, A simplex method for function minimization, Computer Journal, 7, 1965, 308--313, doi:10.1093/comjnl/7.4.308 R. C. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, Proc. of the Sixth International Symposium on Micro Machine and Human Science , Nagoya, Japan, 1995, 39--43, doi:10.1109/MHS.1995.494215 F. Liu and K. Burrage, Novel techniques in parameter estimation for fractional dynamical models arising from biological systems, Computers and Mathematics with Applications , 2011, doi:10.1016/j.camwa.2011.03002