Sudden cardiac death due to the development of lethal arrhythmias is the dominant cause of mortality in the UK, yet the mechanisms underlying their onset, maintenance and termination are still poorly understood. Therefore biomarkers are used to determine arrhythmic risk within patients and of new drug compounds. In recent years, the magnitude of variations in the length of successive beats, measured over a short period of time, has been shown to be a powerful predictor of arrhythmic risk. This beat-to-beat variability is thought to be the manifestation of the random opening and closing dynamics of individual ion channels that lie within the membrane of cardiac cells. Computational models have become an important tool in understanding the electrophysiology of the heart. However, current state-of-the-art electrophysiology models do not incorporate this intrinsic stochastic behaviour of ion channels. Those that do use computationally costly methods, restricting their use in complex tissue scale simulations, or employ stochastic simulation methods that result in negative numbers of channels and so are inaccurate. Therefore, using current stochastic modelling techniques to investigate the role of stochastic ion channel behaviour in beat-to-beat variability presents difficulties. In this thesis we take a mathematically rigorous and novel approach to develop accurate and computationally efficient models of stochastic ion channel dynamics that can be incorporated into existing electrophysiology models. Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. The first model is based on an existing SDE model from population dynamics called the Wright-Fisher model. The second approach incorporates boundary conditions into the SDE model of ion channel dynamics that is obtained in the limit from the discrete-state Markov chain model, and is called a reflected SDE. Of these two methods, the reflected SDE is found to more accurately capture the stochastic dynamics of the discrete-stateMarkov chain, seen as the ‘gold-standard’ model and also provides substantial computational speed up. Thus the reflected SDE is an accurate and efficient model of stochastic ion channel dynamics and so allows for detailed investigation into beat-to-beat variability using complex computational electrophysiology models. We illustrate the potential power of this method by incorporating it into a state-of-the-art canine cardiac cell electrophsyiology model so as to explore the effects of stochastic ion channel behaviour on beat-to-beat variability. The stochastic models presented in this thesis fulfil an important role in elucidating the effects of stochastic ion channel behaviour on beat-to-beat variability, a potentially important biomarker of arrhythmic risk.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:581064 |
| Date | January 2012 |
| Creators | Dangerfield, C. E. |
| Contributors | Burrage, Kevin; Kay, David; Rodriguez, Blanca |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:cd0be850-1ff0-4792-8171-438ff8fc0161 |
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