The basic formulation and some preliminary results of the utilization of impedance based measurements for obtaining cardiac geometry information are presented. This geometrical information is required for forward and inverse bioelectric calculations and could be utilized to enhance the display of epicardial surface recordings. The measured potentials are affected by the strength of the source, the distances to the source and the sink electrodes, the conductivity of the volume and the shape of the epicardial surface. The formulation and preliminary results emphasize the estimation of epicardial recording Electrode coordinates from the impedance measurements. It is shown that the measurements can also yield information about the geometry of the boundary of the heart.< >
A method for determining the strain distribution through the thickness of thin metallic films is developed. The strain distributions of the films are related to the directions in which the films curl and, through a set of nonlinear simultaneous equations, to the shapes of their x-ray diffraction peaks. These equations are solved by assuming a piecewise linear approximation of the strain distributions. This resulting approximation is fit by a five-parameter nonlinear distribution, which is derived from elasticity theory for materials of ``grade 2.'' This x-ray method is applied to vacuum-deposited gold films deposited onto a Bi2O3 nucleation layer which has similarly been deposited onto a glass substrate. The deduced nonlinear strain distributions are nearly antisymmetric with the substrate side in tension and the free side in compression as measured normal to the substrate. Surface strains are as high as ±2.5% and decay approximately exponentially from the surfaces.
The distribution of the transmembrane potential along an infinite strand of cardiac cells generated by a point source under steady-state conditions has been calculated using the asymptotic analysis method. With the intracellular conductivity changing periodically in space, the problem can be treated as dependent upon two variables: the large scale variable x covering the whole strand, and the small scale variable y defined on the unit cell. The solution is given as a two-scale expansion in powers of the period length. Each term of the expansion can be determined by solving the differential equations derived by decomposing the original problem. These equations do not have to be solved simultaneously; moreover, the linearity of the problem allows the separation of the x and y dependence in the higher order terms. The series converges quickly, and for all practical purposes, the solution containing zero-, first-, and second-order terms has a negligible truncation error. The subsequent terms of the solution have the following physiological interpretation: The zero-order term is the solution to the classical core-conductor model obtained by the homogenization of the periodic model, the first-order term acts as the dipole sources located at junctions, and finally, the second-order term resembles the monopole sources arising at junctions.
ABmCT An impedance catheter volume measurement system was modeled in spherical and spheroidal configurptions to see if geometric and conductivitypamnekm could be estimated from measured potentials. Good dts were obtained in both noise free and noise added signal cases for the sphere estimating radius and conductivity. However, in the spheroidal case sufficient estimates could be obtained in the noiseless case for major and minor axes and conductivity, but in the added noise case the results were Poor.
This paper investigates the influence of uncertainties in geometrical coordinates on calculated torso and epicardial potentials. Two types of sources, spherical epicardial and multipolar, are both considered. A concentric sphere model with the epicardial surface represented by a unit sphere and the torso surface represented by a spherical surface of radius 1.4 is utilized. While the representation of biological surfaces with spheres is a highly idealized situation, the dimensions chosen and the approximations utilized are such that the results should be indicative of those using measured biological coordinates.
This paper is a comparison of the major methodologies utilized in computer simulations of electrocardiographic potential calculations. Two integral equation methods (Green's theorem and the equivalent single layer) and finite element methods are compared for forward and inverse solutions. The results suggest that the differences in accuracy between the two integral equation formulations are small. However, the use of a basic finite element formulation improves the accuracy over that obtainable with integral equations, and the improvement in accuracy is particularly notable for inverse estimation.
The concepts of dynamic programming and multistage process theory are used to determine an analytic, least-squares solution to overdetermined linear algebraic equations. The method requires the calculation of a secondary system matrix which, together with the primary matrix, makes evident the relative dependence of the system equations. It is shown that the minimum-sum-square residual, a measure of the fit of the solution, can be determined without explicit calculation of the solution.
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