Soft Tissue Modelling of Cardiac Fibres for Use in Coupled Mechano-Electric Simulations |
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Authors: | Jonathan P Whiteley Martin J Bishop David J Gavaghan |
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Institution: | (1) Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK |
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Abstract: | The numerical solution of the coupled system of partial differential and ordinary differential equations that model the whole
heart in three dimensions is a considerable computational challenge. As a consequence, it is not computationally practical—either
in terms of memory or time—to repeat simulations on a finer computational mesh to ensure that convergence of the solution
has been attained. In an attempt to avoid this problem while retaining mathematical rigour, we derive a one dimensional model
of a cardiac fibre that takes account of elasticity properties in three structurally defined axes within the myocardial tissue.
This model of a cardiac fibre is then coupled with an electrophysiological cell model and a model of cellular electromechanics
to allow us to simulate the coupling of the electrical and mechanical activity of the heart. We demonstrate that currently
used numerical methods for coupling electrical and mechanical activity do not work in this case, and identify appropriate
numerical techniques that may be used when solving the governing equations. This allows us to perform a series of simulations
that: (i) investigate the effect of some of the assumptions inherent in other models; and (ii) reproduce qualitatively some
experimental observations. |
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Keywords: | Cardiac modelling Electrophysiology Soft tissue modelling |
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