Section: New Results

Numerical methods for cardiac electrophysiology

Participants : Muriel Boulakia, Jean-Frédéric Gerbeau, Damiano Lombardi, Fabien Raphel, Eliott Tixier.

In [32], we propose a model to represent the electrical potential of cardiomyocytes derived from stem cells in Multi Electrodes Arrays (MEA). This model based on the bidomain equations and a model for the MEA electrodes is used to analyze experimental signals. Our numerical algorithm is able to provide for different drugs dose-response curves which are in very good agreement with known values.

In [14], we are interested in the electrical activity of cardiomyocytes under the action of drugs in MEA devices. We present numerical simulations based on the same model as in [32] enriched with a pore block model to assay the action of drugs. The simulation results show that the model properly reflects the main effects of several drugs on the electrical potential.

In [33] the variability of phenomena in cardiac electro-physiology is investigated by using a moment matching approach. The cells activity is described by parametric systems of Ordinary Differential Equations. Given the population statistics on a system observables (which is the action potential of the cells), the probability density distribution of the parameters is sought such that the statistics of the model outputs match the observed ones. An uncertainty quantification step is solved once for all by using a non-instrusive approach, and then the inverse problem is solved by introducing an entropy regularisation. Several numerical experiments are considered to validate the approach on realistic datasets.

In [34] a realistic application on the classification of the drugs effect on cardiac cells is investigated. In particular, the electrical activity of the cells is recorder by Micro Electrode Arrays in normal conditions and under drugs, at different concentrations. In order to perform a classification of a drug in terms of promoting or inhibit the activity of certain ion channels a machine learning approach is used (support vector machine). Since the data amount is not big and the variability and alea sources have a large impact on the signals recorded, the data set is augmented by in silico experiments. Several tests on realistic data are performed.