Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 1991 Jan;59(1):93–102. doi: 10.1016/S0006-3495(91)82201-9

Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall.

T Arts 1, P H Bovendeerd 1, F W Prinzen 1, R S Reneman 1
PMCID: PMC1281121  PMID: 2015392

Abstract

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).

Full text

PDF
93

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Arts T., Reneman R. S. Dynamics of left ventricular wall and mitral valve mechanics--a model study. J Biomech. 1989;22(3):261–271. doi: 10.1016/0021-9290(89)90093-6. [DOI] [PubMed] [Google Scholar]
  2. Arts T., Reneman R. S., Veenstra P. C. A model of the mechanics of the left ventricle. Ann Biomed Eng. 1979;7(3-4):299–318. doi: 10.1007/BF02364118. [DOI] [PubMed] [Google Scholar]
  3. Arts T., Veenstra P. C., Reneman R. S. Epicardial deformation and left ventricular wall mechanisms during ejection in the dog. Am J Physiol. 1982 Sep;243(3):H379–H390. doi: 10.1152/ajpheart.1982.243.3.H379. [DOI] [PubMed] [Google Scholar]
  4. Beyar R., Sideman S. A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity. Circ Res. 1984 Sep;55(3):358–375. doi: 10.1161/01.res.55.3.358. [DOI] [PubMed] [Google Scholar]
  5. Chadwick R. S. Mechanics of the left ventricle. Biophys J. 1982 Sep;39(3):279–288. doi: 10.1016/S0006-3495(82)84518-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Falsetti H. L., Mates R. E., Grant C., Greene D. G., Bunnell I. L. Left ventricular wall stress calculated from one-plane cineangiography. Circ Res. 1970 Jan;26(1):71–83. doi: 10.1161/01.res.26.1.71. [DOI] [PubMed] [Google Scholar]
  7. Feigl E. O., Simon G. A., Fry D. L. Auxotonic and isometric cardiac force transducers. J Appl Physiol. 1967 Oct;23(4):597–600. doi: 10.1152/jappl.1967.23.4.597. [DOI] [PubMed] [Google Scholar]
  8. Huisman R. M., Sipkema P., Westerhof N., Elzinga G. Comparison of models used to calculate left ventricular wall force. Med Biol Eng Comput. 1980 Mar;18(2):133–144. doi: 10.1007/BF02443288. [DOI] [PubMed] [Google Scholar]
  9. Janz R. F. Estimation of local myocardial stress. Am J Physiol. 1982 May;242(5):H875–H881. doi: 10.1152/ajpheart.1982.242.5.H875. [DOI] [PubMed] [Google Scholar]
  10. Kim H. C., Min B. G., Lee M. K., Seo J. D., Lee Y. W., Han M. C. Estimation of local cardiac wall deformation and regional wall stress from biplane coronary cineangiograms. IEEE Trans Biomed Eng. 1985 Jul;32(7):503–512. doi: 10.1109/TBME.1985.325567. [DOI] [PubMed] [Google Scholar]
  11. Mirsky I. Left ventricular stresses in the intact human heart. Biophys J. 1969 Feb;9(2):189–208. doi: 10.1016/S0006-3495(69)86379-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Mirsky I. Ventricular and arterial wall stresses based on large deformation analyses. Biophys J. 1973 Nov;13(11):1141–1159. doi: 10.1016/S0006-3495(73)86051-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. PUFF A. [The morphology of the motion process of the heart ventricle (A study of reciprocal modification of the contraction process in the right and left ventricle)]. Anat Anz. 1960 Dec 27;108:342–350. [PubMed] [Google Scholar]
  14. Pao Y. C., Robb R. A., Ritman E. L. Plane-strain finite-element analysis of reconstructed diastolic left ventricular cross section. Ann Biomed Eng. 1976 Sep;4(3):232–249. doi: 10.1007/BF02584517. [DOI] [PubMed] [Google Scholar]
  15. Perl M., Horowitz A., Sideman S. Comprehensive model for the simulation of left ventricle mechanics. Part 1. Model description and simulation procedure. Med Biol Eng Comput. 1986 Mar;24(2):145–149. doi: 10.1007/BF02443927. [DOI] [PubMed] [Google Scholar]
  16. Regen D. M. Effects of chamber shape and fiber orientation on relations between fiber dynamics and chamber dynamics. Ann Biomed Eng. 1988;16(6):589–607. doi: 10.1007/BF02368017. [DOI] [PubMed] [Google Scholar]
  17. Regen D. M. Myocardial stress equations: fiberstresses of the prolate spheroid. J Theor Biol. 1984 Jul 21;109(2):191–215. doi: 10.1016/s0022-5193(84)80003-x. [DOI] [PubMed] [Google Scholar]
  18. Skalak R. Approximate formulas for myocardial fiber stresses. J Biomech Eng. 1982 May;104(2):162–163. doi: 10.1115/1.3138332. [DOI] [PubMed] [Google Scholar]
  19. Streeter D. D., Jr, Hanna W. T. Engineering mechanics for successive states in canine left ventricular myocardium. II. Fiber angle and sarcomere length. Circ Res. 1973 Dec;33(6):656–664. doi: 10.1161/01.res.33.6.656. [DOI] [PubMed] [Google Scholar]
  20. Waldman L. K., Nosan D., Villarreal F., Covell J. W. Relation between transmural deformation and local myofiber direction in canine left ventricle. Circ Res. 1988 Sep;63(3):550–562. doi: 10.1161/01.res.63.3.550. [DOI] [PubMed] [Google Scholar]
  21. Woods R H. A Few Applications of a Physical Theorem to Membranes in the Human Body in a State of Tension. J Anat Physiol. 1892 Apr;26(Pt 3):362–370. [PMC free article] [PubMed] [Google Scholar]
  22. Yin F. C. Ventricular wall stress. Circ Res. 1981 Oct;49(4):829–842. doi: 10.1161/01.res.49.4.829. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES