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How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle

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Abstract

The bidomain model, which describes the behavior of many electrically active tissues, is equivalent to a multi-dimensional cable model and can be represented by a network of resistors and capacitors. For a two-dimensional sheet of tissue, the intracellular and extracellular conductivity tensors can be visualized as two ellipses. For any pair of conductivity tensors, a coordinate transformation can be found that reduces the extracellular ellipse to a circle and aligns the intracellular ellipse with the coordinate axes. The eccentricity of the intracellular ellipse in this new coordinate system is an important parameter. It can have two special values: zero (in which case the tissue has equal anisotropy ratios) or one (in which case the tissue is comprised of one-dimensional fibers coupled through the two-dimensional extracellular space). Thus the bidomain model provides a unifying framework within which the electrical behavior of a wide variety of nerve and muscle tissues can be studied.

When the anisotropy ratios in the intracellular and extracellular domains are not equal, stimulation with an anode always causes depolarization of some region of tissue. An analogous effect occurs in models that describe one-dimensional fibers, in which an “activating function” determines the site of stimulation. Experiments indicate that cardiac muscle does not have equal anisotropy ratios. Therefore, models developed to describe stimulation of axons may also help in understanding stimulation of two- or three-dimensional cardiac tissue, and may explain the concept of anodal stimulation of cardiac tissue through a “virtual cathode”.

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  1. Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bldg. 13, Rm. 3W13, 20892, Bethesda, MD, USA

    Bradley J. Roth

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Roth, B.J. How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle. J. Math. Biol. 30, 633–646 (1992). https://doi.org/10.1007/BF00175610

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  • DOI: https://doi.org/10.1007/BF00175610

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