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 different assumptions appear in the literature dealing with differences in interspecies cardiac properties. Generally, these new models update the physiological knowledge using new equations which reflect better the molecular basis of process. New equations require the fitting 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 find 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 different 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 find that it reduces the Genetic Algorithm execution in an order of \(10^3\) 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.