ABSTRACT
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.
Subject(s)
Computer Simulation , Models, Cardiovascular , Algorithms , Anisotropy , Electric Conductivity , Membrane Potentials/physiology , Neural Conduction , RotationABSTRACT
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.
Subject(s)
Computer Simulation , Electric Countershock , Models, Cardiovascular , Algorithms , Animals , Anisotropy , Dogs , Electric Conductivity , Radiography, Thoracic , Tomography, X-Ray ComputedABSTRACT
In this paper, a data-parallel computer is used to provide the memory and reduction in computer time for solving large finite-difference bidomain problems. The finite-difference grid is mapped effectively to the processors of the parallel computer, simply by mapping one node to one (virtual) processor. Implemented on the connection machines (CM's) CM-200 and CM-5, the data-parallel finite-difference algorithm has allowed the solution of finite-difference bidomain problems with over 2 million nodes. Details on the algorithm are presented together with computational performance results.
Subject(s)
Computer Simulation , Heart/physiology , Models, Cardiovascular , Algorithms , Computing Methodologies , HumansABSTRACT
We present calculations of fluorescence from single molecules (modeled as damped oscillating dipoles) inside a dielectric sphere. For an excited molecule at an arbitrary position within the sphere we calculate the fluorescence intensity collected by an objective in some well-defined detection geometry. We find that, for the cases we model, integration over the emission linewidth of the molecule is essential for obtaining representative results. Effects such as dipole position and orientation, numerical aperture of the collection objective, sphere size, emission wavelength, and linewidth are examined. These results are applicable to single-molecule detection techniques employing microdroplets.
