Bulletin of Mathematical Biology

, Volume 50, Issue 1, pp 35–41 | Cite as

A mathematical derivation of the P-V relation at end-systole

  • R. M. Shoucri
Article

Abstract

A dynamical model of the left ventricle as a thick-walled cylinder contracting radially is used to derive the P-V (pressure-volume) relation in the left ventricular cavity during contraction. It is shown how the mathematical results derived could apply to experimental results.

Keywords

Left Ventricle Halothane Stroke Volume Oxygen Consumption Rate Left Ventricular Cavity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Belcher, P., L. E. Boerboom and G. N. Olinger. 1985. “Standardization of End-Systolic Pressure-Volume Relation in the Dog.”Am. J. Physiol. 249, H547-H553.Google Scholar
  2. Borow, K. M., A. Neumann and J. Wynne. 1982. “Sensitivity of End-Systolic Pressure-Dimension and Pressure-Volume Relations to the Inotropic State in Humans.Circulation 65, 988–997.Google Scholar
  3. Ince, E. L. 1956.Ordinary Differential Equations. Dover Publications, Inc.Google Scholar
  4. Maughan, W. L., A. A. Shoukas, K. Sagawa and M. L. Weisfeldt. 1979. “Instantaneous Pressure-Volume Relationship of the Canine Right Ventricle.”Circulation Res. 44, 309–315.Google Scholar
  5. Shoucri, R. M., J. G. Dumesnil, J. Rouleau and G. R. Dagenais. 1982. “Some Applications of the Concept of Body Forces for the Myocardium.”Bull. math. Biol. 44, 819–840.MATHCrossRefGoogle Scholar
  6. Suga, H., R. Hisano, S. Hirata, T. Hayashi and I. Ninomiya. 1982. “Mechanism of Higher Oxygen Consumption Rate: Pressure-Loaded vs Volume-Loaded Heart.”Am. J. Physiol. 242, H942-H948.Google Scholar
  7. —, K. Sagawa and D. P. Kostiuk 1976. “Controls of Ventricular Contractibility Assessed by Pressure-Volume RatioEmax.”Cardiovascular Res. 10, 582–592.CrossRefGoogle Scholar
  8. — and K. Yamakoski. 1977. “Effects of Stroke Volume and Velocity of Ejection on End-Systolic Pressure of Canine Left Ventricle.”Circulation Res. 40, 445–450.Google Scholar

Copyright information

© Society for Mathematical Biology 1988

Authors and Affiliations

  • R. M. Shoucri
    • 1
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada

Personalised recommendations