Section: New Results

Numerical methods for cardiac electrophysiology

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

In [51] the variability of phenomena described by parametric partial differential equations is studied. In particular, given population statistics on a system observables, 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 and compare it to other existing techniques.

In [50] a reduced order modeling method is proposed in order to speed-up the solution of reaction diffusion equations. It is based on the Approximated Lax Pair method, the discretisation is carried out by adopting an empirical interpolation framework in order to deal with non-polynomial nonlinearities. Some numerical examples on the FKPP equations as well as the equations in electrophysiology are proposed.

We published in [25] a discussion about the Comprehensive in vitro Proarrhythmia Assay (CiPA), which is a nonclinical Safety Pharmacology paradigm for discovering electrophysiological mechanisms that are likely to confer proarrhythmic liability to drug candidates intended for human use. In particular, we presented the use of mathematical modeling in Safety Pharmacology to better understand the electric signals acquired by multielectrode arrays.