The deployment of third generation (3G) cellular systems is resulting in a transition from cellular systems that predominantly carry constant-bit-rate (CBR) voice traffic to multi-service packet based systems that predominantly carry variable-bit-rate (VBR) traffic. With 3G DS-CDMA cellular systems there is a direct relationship between user traffic and propagation dependent performance as additional traffic causes increased system interference. This thesis investigates the impact of VBR traffic on the propagation dependent performance of DS-CDMA cellular systems that utilise frame-by-frame dynamic resource allocation on the radio channel. A DS-CDMA cellular system model is developed and the downlink performance of both outdoor macro-cellular and indoor pico-cellular systems is evaluated with a variety of traffic types. Both traffic scheduling performance and propagation dependent performance are evaluated as the two are inter-linked. Scenarios are identified where propagation dependent performance is sensitive to the statistical properties of the user traffic streams and it is shown that a significant performance difference potentially exists between different traffic types when the number of users per cell is low. When a significant performance difference does exist, burstier more variable traffic generally results in superior propagation dependent performance. The base transceiver station (BTS) transmitter power mean and variance provides a good indication of the level of propagation dependent performance regardless of the specific traffic type. Traffic scheduling policies that deliberately reduce the variability of user traffic streams are considered and in terms of propagation dependent performance these are shown to have a minimal impact on the performance difference between different traffic types. The implications of VBR traffic on DS-CDMA cellular system design are outlined and it is shown that VBR traffic can be approximated as CBR traffic in many scenarios and this is a convenient approximation as it simplifies system design and detailed traffic models do not need to be developed.

This study is concerned with a theoretical, laboratory and in situ investigation of the propagation of seismic stress waves through soil media. Analyses are carried out to predict the surface response that results from earthquake motions being transmitted through the upper layers of the earth. The nature of the near surface geological layers affect to a marked degree the intensity of surface motion. The mathematical models presented are used in the evaluation of site response to earthquakes. The theoretical methods used depart from the traditional viscoelastic approach and use a nonlinear hysteretic soil model to describe the complex dynamic stress-strain relationships evident in soil response. The dynamic soil model is based on previous laboratory work carried out at this university. The theoretical solutions formulated are limited to one-dimensional situations. Three methods of analysis are presented for the propagation of seismic shear waves through nonlinear soil media and conclusions are drawn as to the best approach. The results of these analyses are generally significantly different from those obtained using a viscoelastic soil model. Seismic dilatational waves are also considered important and a method is presented to calculate the response of hysteretic soil media to these disturbances. The outcome from these dilatational and shear wave analyses is more accurate surface response spectra for use in aseismic structural design.

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.

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.

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.

The motivation for this research is a proposed UHF surface wave communication system in which the waveguides are the stranded, overhead earth wires of Power System transmission lines. Attention is confined largely to an investigation of certain aspects which affect the overall surfaces wave transmission loss, a full-scale system having been set up in the laboratory for experimental purposes. For the prediction of transmission loss the stranded conductor is assumed to be equivalent to a solid conductor of the same diameter but with surface anisotropy in the form of two mutually orthogonal surface impedances the major reactive component of which is attributed to the effects of the helical stranding. This reactance is determined from a consideration of the fields which are assumed to exist within the cavities between the strands, and externally. From a comparison between experimental and theoretical loss characteristics there is sufficient inducement to accept the anisotropic model of the stranded conductor for practical design purposes. Approximate equations are developed to simplify the calculation of transmission loss and the notion of ‘capture cross-section’ is employed for the estimation of the efficiency of conical horn launchers. It is deduced from ‘sensitivity’ relationships that the horn loss is relatively insensitive to small changes in the fictitious surface reactance representing the effects of helical stranding, which tends to justify the assumptions upon which the anisotropic model is based. On the other hand, variations in the helix angle are shown to have a marked effect upon the calculated horn loss. This influences the choice of the stranded conductor used as the waveguide for the experimental verification of the model. The Author’s experimental research is described at length, the principal objective being to establish the anisotropic model as an acceptable theoretical substitute for the stranded conductor. To reduce the horn loss, dielectric sheaths are ted to the waveguide in the vicinity of the horn apertures. The discrepancies which then appear between theory and experiment are attributed both to the scattering of the surface wave by the boundary discontinuities at the ends of the sheaths and to the anomalous behaviour of commercial-grade PVC dielectric. Considering the increase in the transmission efficiency which may be realised by fitting dielectric sheaths to the conductor near the horn apertures it is concluded that a theoretical investigation of the scattering properties of the discontinuities s in order. Thus, the remainder of the Thesis is devoted, to this scattering effect as it may be encountered in the proposed scheme, the theoretical analysis following the lines of earlier documented research. A short-cut method is applied for the determination of certain ‘half-plane’ functions which appear in the expressions for the scattered power. Theoretical results are presented together with a discussion of some experimental measurements and a brief theoretical examination of the effects on the horn loss of varying the thickness of the dielectric sheaths. It is argued that the horn loss may be reduced if the dielectric thickness is graded in steps to a value at the horn apertures consistent with the desired ‘power capture’. The Thesis is concluded with an Addendum which outlines a number of topics suggested by the Author for future research.

The motivation for this research is a proposed UHF surface wave communication system in which the waveguides are the stranded, overhead earth wires of Power System transmission lines. Attention is confined largely to an investigation of certain aspects which affect the overall surfaces wave transmission loss, a full-scale system having been set up in the laboratory for experimental purposes. For the prediction of transmission loss the stranded conductor is assumed to be equivalent to a solid conductor of the same diameter but with surface anisotropy in the form of two mutually orthogonal surface impedances the major reactive component of which is attributed to the effects of the helical stranding. This reactance is determined from a consideration of the fields which are assumed to exist within the cavities between the strands, and externally. From a comparison between experimental and theoretical loss characteristics there is sufficient inducement to accept the anisotropic model of the stranded conductor for practical design purposes. Approximate equations are developed to simplify the calculation of transmission loss and the notion of ‘capture cross-section’ is employed for the estimation of the efficiency of conical horn launchers. It is deduced from ‘sensitivity’ relationships that the horn loss is relatively insensitive to small changes in the fictitious surface reactance representing the effects of helical stranding, which tends to justify the assumptions upon which the anisotropic model is based. On the other hand, variations in the helix angle are shown to have a marked effect upon the calculated horn loss. This influences the choice of the stranded conductor used as the waveguide for the experimental verification of the model. The Author’s experimental research is described at length, the principal objective being to establish the anisotropic model as an acceptable theoretical substitute for the stranded conductor. To reduce the horn loss, dielectric sheaths are ted to the waveguide in the vicinity of the horn apertures. The discrepancies which then appear between theory and experiment are attributed both to the scattering of the surface wave by the boundary discontinuities at the ends of the sheaths and to the anomalous behaviour of commercial-grade PVC dielectric. Considering the increase in the transmission efficiency which may be realised by fitting dielectric sheaths to the conductor near the horn apertures it is concluded that a theoretical investigation of the scattering properties of the discontinuities s in order. Thus, the remainder of the Thesis is devoted, to this scattering effect as it may be encountered in the proposed scheme, the theoretical analysis following the lines of earlier documented research. A short-cut method is applied for the determination of certain ‘half-plane’ functions which appear in the expressions for the scattered power. Theoretical results are presented together with a discussion of some experimental measurements and a brief theoretical examination of the effects on the horn loss of varying the thickness of the dielectric sheaths. It is argued that the horn loss may be reduced if the dielectric thickness is graded in steps to a value at the horn apertures consistent with the desired ‘power capture’. The Thesis is concluded with an Addendum which outlines a number of topics suggested by the Author for future research.

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.

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.

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.