Atrial fibrillation is one of the most prolific heart conditions in the UK, now affecting over 800,000 people and costing the NHS over £500m in direct treatment and follow-up care. With an ageing population this is only going to increase. While not usually fatal by itself, atrial arrhythmias typically lead to other more serious complications such as strokes. In a healthy heart, an electrical impulse is produced periodically at the sinoatrial node and propagates in a prescribed manner through the atrial tissue resulting in a regular coordinated muscle contraction. Damage to the atrial myocardium alters its conduction and restitution properties which may lead to the creation of complex patterns known as arrhythmias. These prevent the atrial muscles contracting in a coordinated manner.
Treatment is frequently through catheterization in which RF energy is delivered to the endocardium to create electrically isolating lesions to destroy or isolate problematic regions of the chamber. They may also be used to break re-entrant circuits that can form due to slow conduction in diseased tissue. Surprisingly little advancement of clinical techniques has been made in the last two decades. Front-line approaches are still empirically based on interpreting electrograms and targeting regions with complex fractionated signals, with a less than 40% success rate for persistent atrial fibrillation. Understanding the mechanisms promoting atrial fibrillation, identifying the driver in a specific patient and designing the most appropriate placement of lesions to address their condition is therefore an important area of research with the potential for a high impact.
Personalised computer modelling of cardiac electrophysiology using data acquired through intracardiac electrograms and non-invasive imaging has the potential to significantly enhance treatment. The mono-domain and bi-domain models are reaction-diffusion equations which homogenise the electrochemical activity of cardiac cells. The bi-domain model captures electrical activity in both intracellular and extracellular domains which are spatially co-localised. The mono-domain model is a reduced form of the bidomain model where the conductivities in the intracellular and extracellular spaces are assumed to be proportional. This reduction allows for the simulation of electrical conduction on a complete atrial geometry using more modest computing resources. The mono-domain model is of the form
where is the transmembrane potential and is a current due to the transport of ions in and out of the cell. The latter is described by a cell model, some of which are highly complex consisting of many tens of ODEs.
Cell models are either phenomenological (reproducing the shape of properties of the action potential) or ionic (representing the underlying ionic movement causing the action potential). An example of phenomenological models is the FitzHugh-Nagumo model
which was originally developed to study squid nerve axons:
In modelling the human atrium, a common cell model of choice is the Courtemanche et al model.
I have developed a high-order spectral/hp element solver for the monodomain and bidomain equations of cardiac electrophysiology. My research now focuses on developing novel approaches to treating arrhythmias using personalised models.
- C.D. Cantwell, S. Yakovlev, R.M. Kirby, N.S. Peters, S.J. Sherwin, High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology, Journal of Computational Physics, vol 257, 2014, p813-829.
- R. L. Ali, C. D. Cantwell, C. H. Roney, N. A. Qureshi, P. B. Lim, J. H. Siggers, S. J. Sherwin, N. S. Peters, A novel method for quantifying localised correlation of late-gadolinium intensity with conduction velocity, Computing in Cardiology (Boston, US), 2014
- C. H. Roney, C. D. Cantwell, J. H. Siggers, F. S. Ng, N. S. Peters, A Novel Method for Rotor Tracking Using Bipolar Electrogram Phase, Computing in Cardiology (Boston, US), 2014