The bulletin of mathematical biophysics

, Volume 34, Issue 3, pp 379–392 | Cite as

Fiber stress profiles in the left ventricle of the heart during diastole: Effects of distension and hypertrophy

  • P. C. Voukydis


Pressure-volume and volume-dimensions relationships, obtained from excised dog left ventricles were used for calculating the stresses acting along the longitudinal axis of the individual myocardial fibers. The calculations were based on a set of empirical and theoretical equations. The pressure-volume relationship as well as the volume-dimensions relationships for the excised left ventricle were expressed in the form of empirical equations; the fiber orientation was written as a function of the fiber location within the left ventricular wall; finally, the fiber stress was determined by means of theoretically derived formulas. Simultaneous solutions for the fibers of a meridian cut through the left ventricular myocardial shell were obtained by means of a digital computer and presented in the form of diagrams. The results showed that at low degrees of distension of the left ventricle there are two zones of higher stresses at the equatorial area, one near the epicardium and one near the endocardium. As the distension proceeds under the effect of progressively increasing intraventricular pressure, these two zones become less well defined, whereas a new zone of higher stresses appears near the apex. At high degrees of distension, the ventricle assumes a more spherical shape and the equatorial zones of higher stresses are replaced by zones of lower stresses. Increase in the myocardial mass results in appearance of the equatorial lower stress zones at lower degrees of distension.


Left Ventricle Fiber Orientation Fiber Stress Myocardial Wall Transmural Pressure 
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  1. Armour, J. A. and W. C. Randall. 1970. “Structural Basis for Cardiac Function.”Am. J. Physiol.,218, 1517–1523.Google Scholar
  2. Ghista, D. N. and H. Sandler. 1969. “An Analytic Elastic-Viscoelastic Model for the Shape and Forces of the Left Ventricle.”J. Biomechanics,2, 35–47.CrossRefGoogle Scholar
  3. Grant, R. P. 1965. “Architecture of the Left Ventricle.”Circulation,32, 301–308.Google Scholar
  4. Johnson, J. R. and J.R. DiPalma. 1939. “Intramyocardial Pressure and its Relation to Aortic Blood Pressure.”Am. J. Physiol.,125, 234–243.Google Scholar
  5. Kreuzer, H. and W. Schoeppe. 1963. “Die Druckübertragung in der Wand des toten Herzens.”Pflüger's Arch. ges. Physiol.,278, 181–192.CrossRefGoogle Scholar
  6. Laszt, L. und Müller, A. 1959. “Der myocardiale Druck.”Helv. Physiol. Acta,16, 88–106.Google Scholar
  7. Mirsky, I. 1970. “Effects of Anisotropy and Nonhomogeneity on Left Ventricular Stresses in the Intact Heart.”Bull. Math. Biophysics,32, 197–213.Google Scholar
  8. Ninomiya, I. and M. F. Wilson. 1965. “Analysis of Ventricular Dimensions in the Unanesthetized Dog.”Circulation Res.,16, 249–260.Google Scholar
  9. Rushmer, R. F., D. L. Frankin and R. M. Ellis. 1956. “Left Ventricular Dimensions Recorded by Sonocardiometry.”Circulation Res.,4, 684–688.Google Scholar
  10. Streeter, D. D. and D. L. Bassett. 1966. “An Engineering Analysis of the Myocardial Fiber Orientation in Pig's Left Ventricle in Systole.”Anatomical Rec.,155, 503–512.CrossRefGoogle Scholar
  11. ——, S. M. Spotnitz, D. P. Patel, J. Ross and E. H. Sonnenblick. 1969. “Fiber Orientation in the Canine Left ventricle During Diastole and Systole.”Circulation Res.,24, 339–347.Google Scholar
  12. Timoshenko, S. and S. Woinowsky-Krieger. 1959.Theory of Plates and Shells, New York, Toronto, London: McGraw-Hill Book Co. Inc.MATHGoogle Scholar
  13. Voukydis, P. C. 1970a. “The Effect of Distension of the Left Ventricle of the Heart on the Length of the Individual Myocardial Fibers.”Bull. Math. Biophysics,32, 45–58.Google Scholar
  14. —— 1970b. “Preload of the Individual Myocardial Fibers.” —Ibid.,32, 323–325.Google Scholar
  15. —— 1972. “Geometrical Parameters of the Individual Myocardial Fibers.” —Ibid.,34, 205–211.Google Scholar
  16. Wong, A. Y. K. and P. M. Rautaharju. 1968. “Stress Distribution Within the Left Ventricular Wall Approximated as a Thick Ellipsoidal Shell.”Am. Heart J.,75, 649–622.CrossRefGoogle Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • P. C. Voukydis
    • 1
  1. 1.Cardiac UnitBeth Israel HospitalBoston

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