Isochrones of cardiac activation computed from source-field relationships

The relationship between the electrical activity of cardiac muscle and the time-varying electrical potentials measured on the body surface as electrocardiograms (ECGs) has been studied for over a century. Although models for this relationship and analytical solutions are known, accurate numerical solutions incorporating fine functional and anatomical details of the heart have only been possible recently with advances in computing power. A map of the isochronas of electrical activation on the heart surface is the most concise way of displaying cardiac electrical events. Determining these isochronal maps from source-field relationships has been the focus of this thesis. We found that by formulating the problem using transmembrane potential it was possible to directly compute the activation times. In order to validate this transmembrane potential formulation, our numerical solutions were first compared with exact analytical solutions for eccentric spheres geometries. The solution methods developed in this work were then used to compute isochronal maps from multiple ECGs of a patient undergoing radiofrequency catheter ablation. Images of the isochronal maps were then compared to images generated by very accurate (but time-consuming) electromechanical mapping currently in use to guide this therapy and the agreement was found to be very good.