Combining polynomial chaos expansions and genetic algorithm for the coupling of electrophysiological models

The number of computational models in cardiac research has grown over the last decades. Every year new models with di erent assumptions appear in the literature dealing with di erences in interspecies cardiac properties. Generally, these new models update the physiological knowledge using new equations which reect better the molecular basis of process. New equations require the fi tting of parameters to previously known experimental data or even, in some cases, simulated data. This work studies and proposes a new method of parameter adjustment based on Polynomial Chaos and Genetic Algorithm to nd the best values for the parameters upon changes in the formulation of ionic channels. It minimizes the search space and the computational cost combining it with a Sensitivity Analysis. We use the analysis of di ferent models of L-type calcium channels to see that by reducing the number of parameters, the quality of the Genetic Algorithm dramatically improves. In addition, we test whether the use of the Polynomial Chaos Expansions improves the process of the Genetic Algorithm search. We conclude that it reduces the Genetic Algorithm execution in an order of 103 times in the case studied here, maintaining the quality of the results. We conclude that polynomial chaos expansions can improve and reduce the cost of parameter adjustment in the development of new models.Peer ReviewedPostprint (author's final draft

Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes

The slowly inactivating or late Na+ current, INa-L, can contribute to the initiation of both atrial and ventricular rhythm disturbances in the human heart. However, the cellular and molecular mechanisms that underlie these pro-arrhythmic influences are not fully understood. At present, the major working hypothesis is that the Na+ influx corresponding to I(Na-L)significantly increases intracellular Na+, [Na]; and the resulting reduction in the electrochemical driving force for Na+ reduces and (may reverse) Na+/Ca2+ exchange. These changes increase intracellular Ca2+, [Ca2+]; which may further enhance I(Na-L)due to calmodulindependent phosphorylation of the Na+ channels. This paper is based on mathematical simulations using the O'Hara et al (2011) model of baseline or healthy human ventricular action potential waveforms(s) and its [Ca2(+)]; homeostasis mechanisms. Somewhat surprisingly, our results reveal only very small changes (<= 1.5 mM) in [Na] even when INa-L is increased 5-fold and steady-state stimulation rate is approximately 2 times the normal human heart rate (i.e. 2 Hz). Previous work done using well-established models of the rabbit and human ventricular action potential in heart failure settings also reported little or no change in [Na] when I(Na-L)was increased. Based on our simulations, the major short-term effect of markedly augmenting I(Na-L)is a significant prolongation of the action potential and an associated increase in the likelihood of reactivation of the L-type Ca2+ current, Ica-L. Furthermore, this action potential prolongation does not contribute to [Na]; increase.This work was supported by (i) the "VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica" from the Ministerio de Economia y Competitividad of Spain (grant number TIN2012-37546-C03-01) and the European Commission (European Regional Development Funds-ERDF-FEDER), (ii) by the Direccion General de Politica Cientifica de la Generalitat Valenciana (grant number GV/2013/119), and by (iii), Programa Prometeo (PROMETEO/2016/088) de la Conselleria d'Educacio Formacio I Ocupacio, Generalitat Valenciana. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.K Cardona; Trénor Gomis, BA.; W Giles (2016). Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes. PLoS ONE. 11(11). https://doi.org/10.1371/journal.pone.0167060S111