In this thesis, the forward problem of electrocardiography is investigated from a cellular level through to potentials on the surface of the torso. This integrated modelling framework is based on three spatial scales. At the smallest spatial resolution, several cardiac cellular models are implemented that are used to represent the underlying cellular electrophysiology. A bidomain framework is used to couple multiple individual cells together and this provides a mathematical model of the myocardial tissue. The cardiac geometry is described using finite elements with high order cubic Hermite basis function interpolation. An anatomically based description of the fibrous laminar cardiac microstructure is then defined relative to the geometric mesh. Within the local element space of the cardiac finite elements, a fine collocation mesh is created on which the bidomain equations are solved. Each collocation point represents a continuum cell and contains a cellular model to describe the local active processes. This bidomain implementation works in multiple coordinate systems and over deforming domains, in addition to having the ability to spatially vary any parameter throughout the myocardium. On the largest spatial scale the passive torso regions surrounding the myocardium are modelled using a generalised Laplace equation to describe the potential field and current flows. The torso regions are discretised using either finite elements or boundary elements depending on the electrical properties of each region. The cardiac region is coupled to the surrounding torso through several methods. A traditional dipole source approach is implemented that creates equivalent cardiac sources through the summation of cellular dipoles. These dipoles are then placed within a homogeneous cardiac region and the resulting potential field is calculated throughout the torso. Two new coupling techniques are developed that provide a more direct path from cellular activation to body surface potentials. One approach assembles all of the equations from the passive torso regions and the equations from the extracellular bidomain region into a single matrix system. Coupling conditions based on the continuity of potential and current flow across the myocardial surfaces are used to couple the regions and therefore solving the matrix system yields a solution that is continuous across all of the solution points within the torso. The second approach breaks the large system into smaller subproblems and the continuity conditions are iii iv imposed through an iterative approach. Across each of the myocardial surfaces, a fixed point iteration is set up with the goal of converging towards zero potential and current flow differences between adjacent regions. All of the numerical methods used within the integrated modelling framework are rigorously tested individually before extensive tests are performed on the coupling techniques. Large scale simulations are run to test the dipole source approach against the new coupling techniques. Several sets of simulations are run to investigate the effects of using different ionic current models, using different bidomain model simplifications, and the role that the torso inhomogeneities play in generating body surface potentials. The main question to be answered by this study is whether or not the traditional approach of combining a monodomain heart with an equivalent cardiac source in a two step approach is adequate when generating body surface potentials. Comparisons between the fully coupled framework developed here and several dipole based approaches demonstrate that the resulting sets of signals have different magnitudes and different waveform shapes on both the torso and epicardial surface, clearly illustrating the inadequacy of the equivalent cardiac source models. It has been found that altering the modelling assumptions on each spatial scale produces noticeable effects. At the smallest scale, the use of different cell models leads to significantly different body surface potential traces. At the next scale the monodomain approach is unable to accurately reproduce the results from a full bidomain framework, and at the largest level the inclusion of different torso inhomogeneities has a large effect on the magnitude of the torso and epicardial potentials. Adding a pair of lungs to the torso model changes the epicardial potentials by an average of 16% which is consistent with the experimental range of between 8 and 20%. This provides evidence that only a complex, coupled, biophysically based model will be able to properly reproduce clinical ECGs.
| Identifer | oai:union.ndltd.org:ADTP/290264 |
| Date | January 2001 |
| Creators | Buist, Martin L. |
| Publisher | ResearchSpace@Auckland |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated., http://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm, Copyright: The author |
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