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Mathematical Models of Pacemaker Tissue in the Heart

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Theory of Heart

Part of the book series: Institute for Nonlinear Science ((INLS))

Abstract

This chapter is concerned with basic issues in modeling electrophysiological responses in pacemaker tissue in the heart. In a structural sense, this type of tissue is complex, consisting of a network of different kinds of interconnected cells. The least complex cell in this network is the primary pacemaker cell; one of the more complex in terms of its ion channel configuration is the working atrial cell from the zone bordering the pacemaker region. Transitional cells of intermediate complexity (e.g., subsidiary pacemaker cells) are interposed between these two types of cardiac cells. This study focuses primarily on the membrane dynamics of pacemaker and atrial cells, the two extreme cases regarding ion channel complexity; in addition we study both amphibian and mammalian cardiac tissue. Importantly, the study also brings in the topic of modification of the electrical behavior of these cells, by the parasympathetic neurotransmitter acetylcholine (ACh). In general, conduction in a network of interconnected cells of different types depends on: (1) the distribution of resistive coupling properties between cells, (2) the distribution of cellular membrane properties in the network, and (3) the distribution of autonomic neural influences that may dramatically change the properties of the component cells of the network.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Rice University, Houston, Texas, 77251-1892, USA

    J. W. Clark, J. M. Shumaker & C. R. Murphey

  2. Departments of Medical Physiology and Medicine, University of Calgary Medical School, Calgary, Alberta, T2N 4N1, Canada

    W. R. Giles

Authors
  1. J. W. Clark
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  2. J. M. Shumaker
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  3. C. R. Murphey
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  4. W. R. Giles
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Editor information

Editors and Affiliations

  1. Department of Physiology, McGill University, Montreal, Quebec, H3G 1Y6, Canada

    Leon Glass

  2. Department of Engineering Science, University of Auckland, Auckland, New Zealand

    Peter Hunter

  3. Department of Applied Mechanics and Engineering Science—Bioengineering, University of California, San Diego, La Jolla, CA, 92093, USA

    Andrew McCulloch

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© 1991 Springer-Verlag New York, Inc.

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Clark, J.W., Shumaker, J.M., Murphey, C.R., Giles, W.R. (1991). Mathematical Models of Pacemaker Tissue in the Heart. In: Glass, L., Hunter, P., McCulloch, A. (eds) Theory of Heart. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3118-9_11

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  • DOI: https://doi.org/10.1007/978-1-4612-3118-9_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7803-0

  • Online ISBN: 978-1-4612-3118-9

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