The bulletin of mathematical biophysics

, Volume 31, Issue 3, pp 433–439 | Cite as

The left ventricle as confocal prolate spheroids

  • Jean-Marie Dieudonné


A model of left ventricle is described which takes into account the physiologic variations of thickness, a function of time and distance prior to and during ejection, by assuming that the prolate spheroids are confocal at a given instant. The hyperbolic segment of arc between innermost and outermost spheroids, confocal with the latter, defines a so-called functional thickness, for which a derivation is given. Results show that this model operates in a range of eccentricity wherein thickness change per unit internal volume change are greatest.


Left Ventricle Minor Axis Thickness Change Prolate Spheroid Concentric Sphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brady, A. J. 1968. “Active State in Cardiac Muscle”.Physiol. Rev.,48, 570–600.Google Scholar
  2. Dieudonné, J. M. 1969. “La détermination expérimentale des contraintes myocardiques.”J. Physiol. (Paris), (In press).Google Scholar
  3. Feigl, E. D. and D. L. Fry. 1964. “Myocardial Mural Thickness During the Cardiac Cycle.”Circulation Res.,14, 541–545.Google Scholar
  4. Fisher, V. J., R. J. Lee, A. Gourin, H. Bolooki, J. H. Stuckey and F. Kavaler. 1966. “Muscle Fiber Length, a Determinant of Left Ventricular Contraction Pattern”.Am. J. Physiol.,211, 301–306.Google Scholar
  5. Hawthorne, E. W. 1961. “Instantaneous Dimensional Changes of the Left Ventricle in Dogs”.Circulation Res.,9, 110–119.Google Scholar
  6. — 1966. “Dynamic Geometry of the Left Ventricle”.Am. J. Cardiol.,18, 566–573.CrossRefGoogle Scholar
  7. Sandler, H., and H. T. Dodge. 1963. “Left Ventricular Tension and Stress in Man”.Circulation Res.,13, 91–104.Google Scholar
  8. Scher, A. M. and A. C. Young. 1956. “The Pathway of Ventricular Depolarization in the Dog”.Circulation Res.,4, 461.Google Scholar
  9. Vayo, H. W. 1967. “Fourier Series Analysis of Ventricular Dimensions”. InFactors Influencing Myocardial Contractility. New York: Academic Press. pp. 141–148.Google Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • Jean-Marie Dieudonné
    • 1
  1. 1.Department of Physiology, Faculty of MedicineUniversity of MontréalMontréalCanada

Personalised recommendations