Mathematical Models of Pacemaker Tissue in the Heart

  • J. W. Clark
  • J. M. Shumaker
  • C. R. Murphey
  • W. R. Giles
Part of the Institute for Nonlinear Science book series (INLS)


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.


Pacemaker Cell Atrial Cell Phase Response Curve Sinus Venosus Pacemaker Potential 
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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • J. W. Clark
    • 1
  • J. M. Shumaker
    • 1
  • C. R. Murphey
    • 1
  • W. R. Giles
    • 2
  1. 1.Department of Electrical and Computer EngineeringRice UniversityHoustonUSA
  2. 2.Departments of Medical Physiology and MedicineUniversity of Calgary Medical SchoolCalgaryCanada

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