Some implications of a constant fiber stress hypothesis in the diastolic left ventricle |
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Authors: | R F Janz R J Waldron |
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Institution: | (1) The Aerospace Corporation, 90009 Los Angeles, California, U.S.A. |
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Abstract: | A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial
nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall.
The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the
context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased
monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function
of transmural pressure above a pressure of 6 g/cm2. It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which
differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm2, fiber stress in the nonhomogenous model was equal to 17 g/cm2 while fiber stress in the homogeneous model varied between 100 g/cm2 at the endocardial surface and 2 g/cm2 at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also
tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural
pressure. |
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