A new approach to modelling the dynamics of cardiac action potentials
Duckett, Graham, Ph.D. (1998) A new approach to modelling the dynamics of cardiac action potentials. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1364749~S15
This thesis is concerned with the development of a new approach to the modelling
of cardiac action potentials. Electrophysiological models of the heart have become
very accurate in recent years giving rise to extremely complicated systems of differential
equations. Although describing the behaviour of cardiac cells well, the models
are computationally demanding for numerical simulations and are very difficult to
analyse from a mathematical (dynamical-systems) viewpoint. Simplified mathematical
models that capture the underlying dynamics to a certain extent are therefore
frequently used. However, from a physiological viewpoint these equations are unrealistic
and often fail to reproduce important quantitative properties of the tissue.
In this thesis we introduce a different approach to the mathematical modelling of
cardiac action potentials with the aim of gaining a clearer insight into the origin of
the dynamics of electrophysiological models.
Chapter 1 contains an introduction to the research and outlines the main aims of the
work. In Chapter 2 various background material is introduced. This includes some
basic electrophysiology, ideas currently used in mathematical modelling of excitable
media, and details of models previously developed for the study of cardiac tissue. In
Chapter 3, following a detailed analysis of an early physiological model, we develop a
mathematical model based on the currents involved. This model reproduces, to good
accuracy, action potentials of heart tissue and we discuss the essential ideas behind
the dynamics. In Chapter 4 the mathematical model developed in the previous
chapter is analysed in more detail and simpler equations using similar ideas are
introduced. Various types of action potentials of varying behaviours are studied. In
Chapter 5 we investigate some spatial simulations of the new mathematical models.
We principally concentrate on one-dimensional studies but towards the end of the
chapter we look at some two-dimensional simulations. Finally, in Chapter 6, we
discuss our conclusions and some possible ideas for further related work. Details of
our methods of numerical simulation are included in Appendix A.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics
Q Science > QP Physiology
|Library of Congress Subject Headings (LCSH):||Action potentials (Electrophysiology) -- Mathematical models, Heart -- Electric properties -- Mathematical models|
|Official Date:||July 1998|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC)|
|Extent:||vi, 129 leaves|
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