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A mathematical model for first degree block and the Wenckebach phenomenon

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Abstract

A simple mathematical model of first and second degree heart block is developed on the assumption that eachR wave, with its associated ventricular contraction, results in the release of a substance which raises the excitation threshold of the conducting tissue lying between theS-A andA-V nodes. The conduction pathway is represented by a chain of excitatory elements, the first member of which is acted upon by a regularly occurringP wave. The rate constant of the removal of this inhibitory substance, i.e., recovery rate, is the only constant necessary to be varied in order to pass from normal to first degree block to second degree.

In this latter case one can predict the progressive increase inP-R interval until anR wave is missed, as occurs in the Wenckebach phenomenon. The model indicates that an increasedP wave frequency which would have little effect on theP-R inerval for a normal individual with rapid recovery, could produce a Wenckebach pattern in an individual with even a mild first degree block.

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Authors and Affiliations

  1. Department of Biochemistry and Biophysics, University of California at San Francisco, San Francisco, USA

    H. D. Landahl & D. Griffeath

Authors
  1. H. D. Landahl
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  2. D. Griffeath
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Landahl, H.D., Griffeath, D. A mathematical model for first degree block and the Wenckebach phenomenon. Bulletin of Mathematical Biophysics 33, 27–38 (1971). https://doi.org/10.1007/BF02476662

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  • DOI: https://doi.org/10.1007/BF02476662

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