When modelling tissue-level cardiac electrophysiology, a continuum approximation to the discrete cell-level equations, known as the bidomain equations, is often used to maintain computational tractability. The bidomain equations are derived from the discrete equations using a mathematical technique known as homogenisation. As part of this derivation conductivity tensors are specified for use in the continuum model. Analysing the derivation of the bidomain equations allows us to investigate how microstructure, in particular gap junctions that electrically connect cells, affect tissue-level conductivity properties and model solutions. We perform two distinct but related strands of investigation in this thesis. In the first, we consider the effect of including gap junctions on the results of both discrete and continuum simulations, and identify when the continuum model fails to be a good approximation to the discrete model. Secondly, we perform a comprehensive study into how cell-level microstructure properties, such as cell shape, impact the homogenised conductivities to be used in a tissue-level continuum model. This will allow us to predict how the onset of a disease or a change in cellular microstructure will affect the propagation of action potentials. To do this, we first derive a modified version of the bidomain equations that explicitly takes gap junctions into account. We then derive analytic solutions for the homogenised conductivity tensors on a simplified two-dimensional geometry and find that diseased gap junctions have a large impact on the results of homogenisation. On this same geometry we compare the results of discrete and continuum simulations and find a significant discrepancy between model conduction velocities when we introduce gap junctions with lower coupling strength, or when we consider elongated cells. From this, we conclude that the bidomain equations are less likely to give an accurate representation of the underlying discrete system when modelling diseased states whose symptoms include reduced gap junction coupling or an increase in myocyte length. We then use a more realistic two-dimensional geometry and numerically approximate the homogenised conductivity tensors on this geometry. We discover that the packing of cells has a substantial effect on conduction, with a brick-wall geometry particularly beneficial for fast propagation, and that gap junctions also have a large effect on conduction. Finally, we consider a three-dimensional cellular geometry and show that the effect of changing gap junction properties is different when compared to two dimensions, and discover that the anisotropy ratios of the tissue are highly sensitive to changes in gap junction parameters. Overall, we conclude that gap junctions and cell structure have a large effect on discrete and continuum model results, and on homogenised conductivity calculations in tissue-level cardiac electrophysiology.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:711812 |
| Date | January 2014 |
| Creators | Bruce, Douglas A. W. |
| Contributors | Whiteley, Jon ; Pathmanathan, Pras |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ora.ox.ac.uk/objects/uuid:07709e63-4485-45d1-98be-8dd76cd41fe7 |
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