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Forced vibrations of a circular muscle ring

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Abstract

We consider the small radial displacement of a circular ring of cardiac muscle subjected to periodic forcing. The ring in question is that in the middle layer, at the transverse midsection, of the left ventricle. We show that the ring reacts in a periodic manner when forced in a periodic manner. This is accomplished by writing the differential equation for the ring and solving it for two cases-one for constant and one for variable ring thickness.

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Literature

  • Timoshenko, S. and D. H. Young. 1955.Vibration Problems in Engineering (3rd Edn.). New York: Van Nostrand.

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  • Vayo, H. W. 1966. “The Motion of the Left Ventricle—I.”Bull. Math. Biophys.,28, 355–362.

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  • — 1970. “The Motion of the Left Ventricle—III.”—Ibid.,,32, 279–291.

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Author notes

  1. Pierre Delsemme (undergraduate major)

    Present address: Department of Mathematics, University of Toledo, 43606, Toledo, Ohio

Authors and Affiliations

  1. Department of Mathematics, University of Toledo, 43606, Toledo, Ohio

    H. Westcott Vayo

Authors
  1. Pierre Delsemme
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  2. H. Westcott Vayo
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Delsemme, P., Vayo, H.W. Forced vibrations of a circular muscle ring. Bltn Mathcal Biology 35, 467–474 (1973). https://doi.org/10.1007/BF02575190

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  • DOI: https://doi.org/10.1007/BF02575190

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