Due to its low computational complexity, finite difference modeling offers a viable tool for studying bioelectric problems, allowing the field behavior to be observed easily as different system parameters are varied. Previous finite difference formulations, however, have been limited mainly to systems in which the conductivity is orthotropic, i.e., a strictly diagonal conductivity tensor. This in turn has limited the effectiveness of the finite difference, technique in modeling complex anatomies with arbitrarily anisotropic conductivities, e.g., detailed fiber structures of muscles where the fiber can lie in any arbitrary direction. In this paper, we present both two-dimensional and three-dimensional finite difference formulations that are valid for structures with an inhomogeneous and nondiagonal conductivity tensor. A data parallel computer, the connection machine CM-5, is used in the finite difference implementation to provide the computational power and memory for solving large problems. The finite difference grid is mapped effectively to the CM-5 by associating a group of nodes with one processor. Details on the new approach and its data parallel implementation are presented together with validation and computational performance results. In addition, an application of the new formulation in providing the potential distribution inside a canine torso during electrical defibrillation is demonstrated.
Bidomain modeling of cardiac tissues provides important information about various complex cardiac activities. The cardiac tissue consists of interconnected cells which form fiber-like structures. The fibers are arranged in different orientations within discrete layers or sheets in the tissue, i.e., the fibers within the tissue are rotated. From a mathematical point of view, this rotation corresponds to a general anisotropy in the tissue's conductivity tensors. Since the rotation angle is different at each point, the anisotropic conductivities also vary spatially. Thus, the cardiac tissue should be viewed as an inhomogeneous anisotropic structure. In most of the previous bidomain studies, the fiber rotation has not been considered, i.e., the tissue has been modeled as a homogeneous orthotropic medium. In this paper, we describe a new finite-difference bidomain formulation which accounts for the fiber rotation in the cardiac tissue and hence allows a more realistic modeling of the cardiac tissue. The formulation has been implemented on the data-parallel CM-5 which provides the computational power and the memory required for solving large bidomain problems. Details of the numerical formulation are presented together with its validation by comparing numerical and analytical results. Some computational performance results are also shown. In addition, an application of this new formulation to provide activation patterns within a tissue slab with a realistic fiber rotation is demonstrated.
As shown previously for two-dimensional geometries, anisotropy effects should not be ignored in electrical impedance tomography (EIT) and structural information is important for the reconstruction of anisotropic conductivities. Here, we will describe the static reconstruction of an anisotropic conductivity distribution for the more realistic three-dimensional (3-D) case. Boundaries between different conductivity regions are anatomically constrained using magnetic resonance imaging (MRI) data. The values of the conductivities are then determined using gradient-type algorithms in a nonlinear-indirect approach. At each iteration, the forward problem is solved by the finite element method. The approach is used to reconstruct the 3-D conductivity profile of a canine torso. Both computational performance and simulated reconstruction results are presented together with a detailed study on the sensitivity of the prediction error with respect to different parameters. In particular, the use of an intracavity catheter to better extract interior conductivities is demonstrated.
Discusses the inclusion of anatomical constraints and anisotropy in static Electrical Impedance Tomography (EIT) using a two-step approach to EIT. In the first step, the boundaries between regions of different conductivities are anatomically constrained using Magnetic Resonance Imaging (MRI) data. In the second step, the conductivity values in different regions are determined. Anisotropic conductivity regions are included to allow better modeling of the muscle regions (e.g., skeletal muscle) which exhibit a greater conductivity in the direction parallel to the muscle fiber. This two-step approach is used to reconstruct the conductivity profile of a canine torso, illustrating its potential application in extracting conductivity values for bioelectric modeling.
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