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      Cardiac anisotropy in boundary-element models for the electrocardiogram

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          Abstract

          The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.

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          Most cited references38

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          Simulating the electrical behavior of cardiac tissue using the bidomain model.

          The complex microstructure of cardiac muscle comprised of coupled cells, enveloped by an interstitium made up of blood vessels, connective tissue, and fluid, presents some obvious problems to those interested in understanding the tissue as an electrical medium. One approach that has gained considerable favor in recent years views the tissue not as a discrete structure, but rather as two coupled, continuous domains: one for the intracellular space and the other for the interstitial space. For convenience, the averaged potentials and currents in both domains are defined at every point in space. The structure is partially preserved by assigning a conductivity tensor at each point. One advantage of using this space-averaged model is that the governing equations for the electric fields can be described by partial differential equations that on occasion lead to analytical solutions. This formal treatment of cardiac tissue as two coupled continua is referred to as the bidomain model. This article presents a mathematical description of the bidomain model and reviews the use of the model for simulating the electrical behavior of cardiac tissue.
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            The application of electromagnetic theory to electrocardiology. II. Numerical solution of the integral equations.

            In an earlier paper exact integral equations were derived for the surface potentials resulting from sources within an irregularly shaped inhomogeneous body. These exact equations cannot usually be solved. In this paper a discrete analogue is constructed which is not straightforward to solve, but which can be treated by careful mathematical methods. In particular a deflation procedure greatly facilitates the iterative solution of the problem and overcomes the divergence encountered by other authors. Numerical solutions obtained for simple geometries are compared to the exact analytic solutions available in such cases. The necessary convergence of the solutions of the discrete analog towards the solution of the continuous problem is shown to occur only if the coefficients of the discrete analogue are carefully evaluated. Calculations are then presented for realistic thoracic geometries, typical results being presented as surface potential maps. Finally the important effect of the internal regional inhomogeneities, particularly a realistic cardiac blood mass, is demonstrated by obtaining vector loops with and without these effects.
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              Application of the fastest route algorithm in the interactive simulation of the effect of local ischemia on the ECG.

              A method is described to determine the effect on the ECG of a reduced propagation velocity within an ischemic zone. The method was designed to change the activation sequence throughout the ventricles interactively, i.e. with a response time in the order of a second. The timing of ventricular ischemic activation was computed by using the fastest route algorithm, based on locally reduced values of the propagation velocities derived from a standard, normal activation sequence. The effect of these local reductions of the velocities on the total activation sequence, as well as the changes in the electrocardiogram that these produce, are presented.
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                Author and article information

                Contributors
                +1-514-3382222 , +1-514-3382694 , mark@potse.nl
                bruno.dube@umontreal.ca
                alain.vinet@umontreal.ca
                Journal
                Med Biol Eng Comput
                Medical & Biological Engineering & Computing
                Springer-Verlag (Berlin/Heidelberg )
                0140-0118
                1741-0444
                21 March 2009
                July 2009
                : 47
                : 7
                : 719-729
                Affiliations
                [1 ]Research Center, Sacré-Coeur Hospital, 5400 Boulevard Gouin Ouest, Montreal, QC H4J 1C5 Canada
                [2 ]Interuniversity Cardiology Institute of The Netherlands, Utrecht, The Netherlands
                [3 ]Laboratory for Experimental Cardiology, Heart Failure Research Center, Academic Medical Center, Amsterdam, The Netherlands
                Article
                472
                10.1007/s11517-009-0472-x
                2688616
                19306030
                eea533ac-934d-4e32-88ae-fc68ff437562
                © The Author(s) 2009
                History
                : 17 November 2008
                : 22 January 2009
                Categories
                Original Article
                Custom metadata
                © International Federation for Medical and Biological Engineering 2009

                Biomedical engineering
                finite-difference model,myocardial anisotropy,boundary-element methods,computer model,electrocardiogram

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