Utilising generalised polynomial chaos to refine the design of an electrode array to measure cardiac conductivities

Cardiac diseases continue to be one of the most prevalent illnesses worldwide due to fundamental gaps in knowledge about the functioning of the heart. Simulation studies, based on mathematical modelling, are increasingly becoming a valuable tool that can be used to explore and hence find treatments for such cardiac diseases. However, such models are reliant on fundamental parameters of the heart - one such being the cardiac conductivities which describe the electrical conduction in the three orthogonal directions in cardiac tissue. To date, a consensus does not exist on these values, with considerable variation in the sets of measured conductivities.

Recent simulation studies have demonstrated that it is possible to retrieve accurate cardiac conductivity values through the use of an electrode array on which cardiac potentials are measured. An inversion technique is further utilised to obtain the cardiac conductivities with the aid of the bidomain model of cardiac tissues. However, the difficulties lie both in making the potential measurements on the electrode array and in interpreting these measurements. This talk looks at implementing a General Polynomial Chaos-based technique to produce a map of sensitivities of output potentials to the input conductivities in a slab model of cardiac tissue. This data can then be utilised to re-design the electrode array to retrieve more accurate cardiac conductivities.