Hasan I. Saleheen

A new three-dimensional finite-difference bidomain formulation for inhomogeneous anisotropic cardiac tissues

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 tissues 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. Here, the authors 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.

New finite difference formulations for general inhomogeneous anisotropic bioelectric problems

Due to its low computational complexity, finite difference modeling offers a viable tool for studying bioelectric problems, allowing the field behaviour 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. Here, the authors 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.

Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency

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.

Three-dimensional finite-difference bidomain modeling of homogeneous cardiac tissue on a data-parallel computer

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 (CMs) 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.

Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment

Light scattering by radially inhomogeneous fuel droplets has been calculated using both geometrical optics (GO) and the exact separation of variables (SV) solutions. The refractive index profiles of the fuel droplets were those calculated by Kneer et al. The GO and SV solutions agree very well in the forward direction (for scattering angles between 30 and 60 degrees), and less well in the backward direction (for scattering angles between 140 and 170 degrees). Both amplitudes and phases of the scattered light are compared. The agreement in the backward direction is much better for 40 micrometers diameter droplets than for 20 micrometers diameter droplets.

Three-dimensional bidomain simulation of electrical propagation in cardiac tissue

Though cardiac tissues are inherently three-dimensional in nature, three-dimensional bidomain models have been used only in a limited number of studies due to the constraints on computer processing power. Here, the authors describe the study of three-dimensional propagation effects in cardiac tissues using a data parallel finite difference bidomain model. The data parallel approach allows the use of a massively parallel computer to provide the solutions for large problems. Electrical propagation results are presented for different stimulation schemes, various ionic current models and different conductivities.

Parallel finite difference solution of general inhomogeneous anisotropic bio-electrostatic problems

Finite difference solution of bio-electrostatic problems have been limited mainly to systems where the conductivity is orthotropic, i.e., a strictly diagonal conductivity tensor. This in turn has limited the use of the finite difference technique in modeling the detailed structure of various muscles, where the fibers can be in arbitrary directions and an accurate representation demands a non-diagonal conductivity tensor. Here, the authors describe a new three-dimensional finite difference formulation that is valid for solving the governing Laplace equation in structures with an inhomogeneous and non-diagonal conductivity tensor. In addition, a data parallel computer is used in the finite difference implementation to provide the memory and reduction in solution time for solving large problems. The finite difference algorithm will be described together with its parallel implementation, and numerical results is presented.

Three-dimensional parallel finite-difference bidomain modelling of cardiac tissue

Three-dimensional finite-difference bidomain models of cardiac tissues can lead to a large number of equations for which an effective solution with the computational power of conventional computers may be difficult. Here, the authors describe the application of a massively parallel computer to provide the memory and reduction in solution time for solving large finite-difference bidomain problems. The finite-difference grid can be mapped effectively to the processors of the parallel computer, simply by mapping one node to one processor. The parallel finite-difference algorithm for a general three-dimensional bidomain model is presented together with test results.<<ETX>>

Inhomogeneous anisotropic bidomain modeling of cardiac tissue

In this paper we describe a new finite difference bidomain formulation for a cardiac tissue with intramural fiber rotation. The cardiac tissue consists of discrete layers of fibers arranged at different angular orientations within the tissue. The angular rotation of the fiber creates anisotropy in the tissues intracellular and interstitial conductivities which vary from one layer to another, i.e., inhomogeneous. The new inhomogeneous anisotropic bidomain formulation will allow a more realistic modeling of the cardiac tissue. Mathematical formulation of the new method and its validation are presented.