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The determination of the bidomain conductivity tensors of heart tissue


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Graham, Leon Simon 2008 , 'The determination of the bidomain conductivity tensors of heart tissue', PhD thesis, University of Tasmania.

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The bidomain model is often used to simulate the electrical activity in cardiac
tissue. It has applications in the inverse problem of electrocardiology, which
is inferring the electric potential in the heart from non-invasive body surface
potentials. Currently, the 12-lead electrocardiogram (ECG) is being used on
a daily basis, though the ECG is not being used to its full potential, as the
12-lead resolution is limited. The inverse problem of electrocardiology would
provide greater information; it would benefit in making predictions and clinical
diagnosis, such as interpreting the relationship between ST segment changes in
the electrocardiogram and ischaemia.
The electrical activity in cardiac tissue is strongly influenced by the myocardial
fibre arrangement. There is strong experimental evidence which shows that
current propagates much faster along the tissue fibres than across them; this
directional dependence in its conduction is termed as anisotropic. When modelling
this electrical activity, the bidomain conductivity tensors represent this
anisotropy. These conductivities are defined for intracellular and extracellular
domains, in each of the principal directions; for along, across, and perpendicular
to the tissue fibres. Hence, in three-dimensions there are six conductivity
parameters that describe how the electric current flows.
Several measurements of the bidomain conductivities have been obtained, but
they have been inconsistent with each other, leading to a degree of uncertainty
regarding the correct values. It has been shown that the different measured
conductivity values produce different bidomain simulation results, which can significantly
effect the outcome of the inverse problem, and so it is important to
determine the correct conductivity set. One of the major difficulties in measuring
the bidomain conductivity values is separating the intracellular and extracellular
In this thesis, a method for determining the bidomain conductivity tensors is described. It takes a different approach to the conventional four-electrode technique,
as it does not require the small electrode separation needed to separate
the extracellular current from the intracellular.
The method involved recording the propagation of electrical activation, initiated
by point simulation, via extracellular electrodes, and time-dependent bidomain
modelling to simulate the electrical phenomena. The optimum set of conductivity
values were achieved by minimising the difference between the bidomain model
output and measured extracellular potential, by means of inverse techniques in
parameter estimation, such as Least-Squares (LS) or Singular Value Decomposition
Overall, the LS method with the use of the Marquardt parameter, which
determines how large a step the parameters are updated between optimisation
iterations, seemed to work best, where as the SVD method tended to overshoot
the optimum parameter set, when involving experimental data. Other parameters
in the bidomain model could also be determined such as membrane capacitance
and local myocardial fibre direction.

Item Type: Thesis - PhD
Authors/Creators:Graham, Leon Simon
Keywords: Electrocardiography, Electrocardiography, Coronary heart disease, Inverse problems (Differential equations)
Copyright Holders: The Author
Copyright Information:

Copyright 2008 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
would be pleased to hear from the copyright owner(s).

Additional Information:

Available for library use only and copying in accordance with the Copyright Act 1968, as amended. Thesis (PhD)--University of Tasmania, 2008. Includes bibliographical references

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