Finite element modelling of discontinuous action potential propagation in larval zebrafish and human cardiac tissue

Recently the larval zebrafish has emerged as a model organism which is used to assist in the studies of human cardiac electrophysiology. Although they share many similar electrophysiological characteristics, it has been found that the conduction velocity (CV) of action potential (AP) propagation in larval zebrafish heart is up to two orders of magnitude smaller than in the adult mammalian heart. To address this difference, we have developed three dimensional discrete models of larval zebrafish ventricular fibres (LZVF) in order to simulate AP propagation, taking into account the cellular nature of the tissues and intercellular conduction via gap junctions. Since our ultimate goal is to simulate a whole larval zebrafish heart, we have used the phenomenological Fitzhugh Nagumo (FHN) equations to describe transmembrane currents, and manually adjusted the FHN parameters, to fit published AP shapes for larval zebrafish ventricular cells. This has the benefit of reduced computational load compared to approaches based on biophysical ion current models. We have created models for 48 and 72 h post fertilisation LZVF tissue using published AP and cell size data for zebrafish embryos and used mammalian values for passive electrical parameters. Using the gap junction resistivity per myocyte as an adjustable parameter, we were able to obtain CVs in both of our LZVF models which agree with experimental observations. In order to validate our approach, we have applied it to a human ventricular fibre (HVF) model similar in structure and parameters to other models of the mammalian heart, but adjusting the FHN parameters to fit published AP shapes for human ventricular cells. We find good agreement with the human models. The gap junction resistivities used in the LZVF models are significantly higher than in the HVF case and are consistent with a lower density of gap junctions connecting cells.