A three-dimensional torso model for electrocardiology

Abstract

This thesis develops a new model of the human torso based on high-order elements, a coupled finite/boundary element method and least squares fitting to give anatomical accuracy with a minimum number of computational parameters. This approach differs substantially from previous models which use a large number of low-order (constant or linear) finite elements or boundary elements. The high-order interpolation used here is based on cubic Hermite basis functions. These basis functions use derivative information to obtain a derivative, or C¹, continuous field which is incorporated into a new anisotropic finite element formulation. Derivative boundary integral equations are used to incorporate the derivative information of the Hermitian basis functions into a boundary element method. These hypersingular derivative equations are regularised into a weakly singular form, suitable for numerical integration. The derivative boundary integral approach is extended to three-dimensions and the high-order finite element and boundary element methods are coupled together. To obtain an anatomically accurate torso geometry a new non-linear fitting procedure is developed. Non-linear constraints are incorporated into the procedure to ensure that the derivatives in the fitted mesh are with respect to a physical parameter and to ensure a C¹ continuous mesh. Smoothing is also incorporated using a procedure based on a Sobelov norm. The new procedure is used to fit the epicardial, lung, skeletal muscle, subcutaneous fat and body (skin) surfaces each to within an error of 2 mm RMS. These surfaces are assembled into a combined finite element/boundary element model of the torso in which the exterior surfaces of the heart and lungs are modelled with two-dimensional boundary elements and the layers of the skeletal muscle and subcutaneous fat are modelled with finite elements. Skeletal muscle anisotropy is incorporated into the model by fitting the skeletal muscle fibre direction angles to data obtained from measurements of an anatomical dummy. The resultant fibre field is thus allowed to vary continuously. The behaviour of the new high.:.order coupled approach is investigated using an accuracy and convergence analysis. When compared with traditional low-order approaches the new approach shows superior accuracy and convergence rates with respect to either the characteristic element size or number of solution degrees-of-freedom. The method also shows superior accuracy when compared to other numerical methods previously published in the literature. The new numerical approach and torso model are demonstrated by performing a number of forward simulations. These simulations investigate the effect on torso potentials of the individual torso inhomogeneities, the sensitivity of the potentials to changes in material properties and the sensitivity of the potentials to changes in the orientation and position of the heart. The number of nodes, elements and solution degrees-of-freedom used in the computational torso model are considerably smaller than previous torso models. of similar complexity. The new torso model does, however, produce a linear system that is harder to solve than traditional torso models. The results of the torso simulations show that the torso inhomogeneities do affect the torso potentials but do not affect the distribution, or pattern, of the torso potentials. The inhomogeneities considered are found to have a varying, but important, effect on the torso potentials. The effect of the subcutaneous fat is found to be more important and the effect of the skeletal muscle is found to be less important than previous reports in the literature. The results also show that the relative geometry of the heart and torso is very important in determining the torso potential magnitudes and distributions.