The determination of the bidomain conductivity tensors of heart tissue

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 conductivities. 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 (SVD). 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