Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart

Abstract

For more than a century, electrophysiologists, cardiologists and engineers have studied the electrical activity of the human heart to better understand rhythm disorders and possible treatment options. Although the depolarisation sequence of the heart is relatively well characterised, the repolarisation sequence remains a subject of great controversy. Here, we study regional and temporal variations in both depolarisation and repolarisation using a finite element approach. We discretise the governing equations in time using an unconditionally stable implicit Euler backward scheme and in space using a consistently linearised Newton–Raphson-based finite element solver. Through systematic parameter-sensitivity studies, we establish a direct relation between a normal positive T-wave and the non-uniform distribution of the controlling parameter, which we have termed refractoriness. To establish a healthy baseline model, we calibrate the refractoriness using clinically measured action potential durations at different locations in the human heart. We demonstrate the potential of our model by comparing the computationally predicted and clinically measured depolarisation and repolarisation profiles across the left ventricle. The proposed framework allows us to explore how local action potential durations on the microscopic scale translate into global repolarisation sequences on the macroscopic scale. We anticipate that our calibrated human heart model can be widely used to explore cardiac excitation in health and disease. For example, our model can serve to identify optimal pacing sites in patients with heart failure and to localise optimal ablation sites in patients with cardiac fibrillation.

Keywords::

• electrophysiology
• depolarisation
• repolarisation
• electrocardiogram
• T-wave
• refractoriness
• finite element method

Acknowledgements

This work has been motivated by stimulating discussions with Jonathan Wong, Stanford University, Serdar Göktepe, METU Ankara and Michael Ortiz, Caltech. Their help is gratefully thanked. This research was supported by the Chilean Fondo Nacional de Ciencia y Tecnología (FONDECYT) through Grant ⧣11121224, the National Science Foundation CAREER award CMMI-0952021 and the INSPIRE award CMMI-1233054 and the National Institutes of Health Grant U54 GM072970. DH also acknowledges the support of the Engineering School and the Vicerrectoría Académica of the Pontificia Universidad Católica de Chile through the Fondo de Internacionalización.