Abstract
A fluid-fiber-collagen stress tensor is used to describe the rheology of the left ventricle of the heart. Linear theory is used to find the equilibrium solutions for the end-diastolic and end-systolic states of general axisymmetric shapes that are small perturbations of a thick-walled finite cylinder. The general problem can be studied by superposing the effects of variable midwall radius but constant wall thickness with those of variable wall thickness but constant midwall radius. A Fourier series representation is used to describe the midwall radius and thickness functions. Numerical calculations are performed to determine the deformed geometry and spatial distributions of tissue pressure, stresses, and fiber strains. The calculations proved to be highly accurate when compared to an analytical solution obtained for the special case of no fibers. The results show significant longitudinal differences when compared to results for the cylindrical geometry, with more sensitivity to variation in wall thickness than to variation in midwall radius.
Full text
PDF
Images in this article
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- 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]
- Borg T. K., Caulfield J. B. The collagen matrix of the heart. Fed Proc. 1981 May 15;40(7):2037–2041. [PubMed] [Google Scholar]
- 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]
- Feit T. S. Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle. Biophys J. 1979 Oct;28(1):143–166. doi: 10.1016/S0006-3495(79)85165-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ohayon J., Chadwick R. S. Effects of collagen microstructure on the mechanics of the left ventricle. Biophys J. 1988 Dec;54(6):1077–1088. doi: 10.1016/S0006-3495(88)83044-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ohayon J., Chadwick R. S. Theoretical analysis of the effects of a radial activation wave and twisting motion on the mechanics of the left ventricle. Biorheology. 1988;25(3):435–447. doi: 10.3233/bir-1988-25305. [DOI] [PubMed] [Google Scholar]
- Robinson T. F., Factor S. M., Sonnenblick E. H. The heart as a suction pump. Sci Am. 1986 Jun;254(6):84–91. doi: 10.1038/scientificamerican0686-84. [DOI] [PubMed] [Google Scholar]
- Tözeren A. Static analysis of the left ventricle. J Biomech Eng. 1983 Feb;105(1):39–46. [PubMed] [Google Scholar]