Mechanisms and localised treatment for complex heart rhythm disturbances

A problem presented at the UK MMSG Imperial College 2009.

Presented by:
Prof Darryl Holm (Applied Mathematics and Mathematical Physics, Imperial College London)
Prof Nicholas Peters (National Heart and Lung Institute, Imperial College London)
Participants:
CG Bell, K Bentahar, EC Chang, AJE Foss, LD Hazelwood, HD Holm, Z Jones, S Naire, FZ Nouri, JC O'Flaherty, NS Peters, CP Please, SF Pravdin, G Richardson, A Setchi, RJ Shipley, JH Siggers, MJ Tindall, JP Ward

Problem Description

There are currently intractable problems in the study and treatment of heart rhythm disturbances. The most complex of the heart rhythm disturbances lead to apparently random electrical activation of the heart muscle, known as fibrillation and can be responsible for sudden arrhythmic death. The need for better treatment strategies for fibrillation currently challenges the limits of our understanding.

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Study Group Report

During the Study Group, we considered a variety of simple problems within the area of cardiac electrophysiology. These problems were based on understanding electrical action potential propagation in one or two mono-layers of myocardium, with additional complexities such as anisotropy or presence of slow-conducting or non-conducting obstacles. We discussed and used several known mathematical models when considering these problems — notably the Fitzhugh Nagumo and Eikonal equations, while we also used a lattice model to model propagation through sheets of cells. With each model we attempted to compute both analytical and numerical solutions to our problems. These generated several interesting results, such as the importance of obstacle curvature and spacing on the successful propagation of an action potential.

Many of the results generated here were encouraging and generated lengthy discussions with both problem proposers. However the short duration of the study group restricted the depth in which we could review the relevant literature and investigate the complexities of the problems to be solved. For example, in the analytical solution to the Eikonal equation for waves propagating around two circles, it was concluded that we would require further analysis to understand the structure of the resultant shock and how it affects the evolution of the waves.

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Follow-Up Activities

The following follow-up meetings have occured to continue work on aspects of this problem:

2010 Cardiac Arrhythmias Followup Meeting
Thursday 11th March 2010, Imperial College London