Non standard mathematical approaches for capturing variability

Kevin Reseacrh

Mathematical modelling in Computational Cardiac Electrophysiology has a long history of over 50 years and can be broadly characterized by the modeling of ion flux dynamics in single cells, coupled, where appropriate, with models for the propagation of an action potential in tissue. The traditional approaches to this have been via ordinary differential equations and partial differential equations, based on the reaction diffusion equation, respectively. In the case of whole heart modeling the implementations often make use of high performance computing. Furthermore, these cell models are often highly tuned. These features of models being highly tuned and deterministic mean that it is very difficult to capture the underlying variability manifested by experiments and additionally that it is impossible to capture the stochasticity that is evident in all biological processes and that occurs at many different spatial and temporal scales.

This strand of work attempts to underpin, using novel mathematical and computer software approaches, the other lines of research in the group.

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