4 results for Austin, Travis

  • Solving the cardiac bidomain equations for discontinuous conductivities

    Austin, Travis; Trew, Mark; Pullan, Andrew (2006)

    Journal article
    The University of Auckland Library

    An open access copy of this article is available and complies with the copyright holder/publisher conditions. Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.

    View record details
  • Modeling Cardiac Electrical Activity at the Cell and Tissue Levels

    Austin, Travis; Hooks, Darren; Hunter, Peter; Nickerson, David; Pullan, Andrew; Sands, Gregory; Smaill, Bruce; Trew, Mark (2006-10)

    Journal article
    The University of Auckland Library

    Significant tissue structures exist in cardiac ventricular tissue, which are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhythmogenesis, and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements,we use tissue-specific structure and mathematical modeling. Our models,which can incorporate ion channel models at the cell level into the reaction–diffusion equations at the tissue level, have enabled us to consider key hypotheses regarding discontinuous activation.

    View record details
  • A Comparison of Multilevel Solvers for the Cardiac Bidomain Equations

    Austin, Travis; Trew, Mark; Pullan, Andrew (2005)

    Conference paper
    The University of Auckland Library

    An open access copy of this article is available and complies with the copyright holder/publisher conditions. Computing the extracellular potentials in a bidomain cardiac activation model is a computationally significant step in the solution process. Thus, using a fast solver can drastically reduce the overall time of simulation. Solving for the extracellular potentials involves inverting the matrix coming from the elliptic equation describing the extracellular-intracellular potential coupling. Elliptic equations are known to yield matrices that become progressively more ill-conditioned as the spatial resolution is increased. However, optimal multilevel solution methods are known to exist for these equations given enough effort is placed into developing the correct solution components. Two multilevel solvers that automatically perform much of this work are Black Box Multigrid (BOXMG) and Algebraic Multigrid (AMG). In this paper, we compare the performance of BOXMG and AMG as solvers for the elliptic component of the bidomain equations. Our investigation is with respect to simulations of reentry in two-dimensional cardiac tissue.

    View record details
  • Effects of gastrointestinal tissue structure on computed dipole vectors

    Austin, Travis; Li, Liren; Pullan, Andrew; Cheng, Leo K (2007)

    Journal article
    The University of Auckland Library

    BACKGROUND:Digestive diseases are difficult to assess without using invasive measurements. Non-invasive measurements of body surface electrical and magnetic activity resulting from underlying gastro-intestinal activity are not widely used, in large due to their difficulty in interpretation. Mathematical modelling of the underlying processes may help provide additional information. When modelling myoelectrical activity, it is common for the electrical field to be represented by equivalent dipole sources. The gastrointestinal system is comprised of alternating layers of smooth muscle (SM) cells and Interstitial Cells of Cajal (ICC). In addition the small intestine has regions of high curvature as the intestine bends back upon itself. To eventually use modelling diagnostically, we must improve our understanding of the effect that intestinal structure has on dipole vector behaviour.METHODS:Normal intestine electrical behaviour was simulated on simple geometries using a monodomain formulation. The myoelectrical fields were then represented by their dipole vectors and an examination on the effect of structure was undertaken. The 3D intestine model was compared to a more computationally efficient 1D representation to determine the differences on the resultant dipole vectors. In addition, the conductivity values and the thickness of the different muscle layers were varied in the 3D model and the effects on the dipole vectors were investigated.RESULTS:The dipole vector orientations were largely affected by the curvature and by a transmural gradient in the electrical wavefront caused by the different properties of the SM and ICC layers. This gradient caused the dipoles to be oriented at an angle to the principal direction of electrical propagation. This angle increased when the ratio of the longitudinal and circular muscle was increased or when the the conductivity along and across the layers was increased. The 1D model was able to represent the geometry of the small intestine and successfully captured the propagation of the slow wave down the length of the mesh, however, it was unable to represent transmural diffusion within each layer, meaning the equivalent dipole sources were missing a lateral component and a reduced magnitude when compared to the full 3D models.CONCLUSION:The structure of the intestinal wall affected the potential gradient through the wall and the orientation and magnitude of the dipole vector. We have seen that the models with a symmetrical wall structure and extreme anisotropic conductivities had similar characteristics in their dipole magnitudes and orientations to the 1D model. If efficient 1D models are used instead of 3D models, then both the differences in magnitude and orientation need to be accounted for.

    View record details