Static analysis of the left ventricle is developed to estimate the local stresses and deformations that occur during the heart cycle. The left ventricle is represented as a thick hollow tube composed of solid fibers embedded in an inviscid fluid matrix. A finite deformation analysis is developed to estimate the variation of the pressure, fiber tension and fiber extension across the thickness of the left ventricle. Pressure-volume relations are obtained for the diastolic and the systolic peak isovolumetric phases. The fiber stress distribution and pressure variation are estimated as a function of the initial fiber orientation distribution, relative thickness of the ventricle, inner volume of the ventricle and the various tension-extension relations proposed for the fibers of the heart muscle. It is concluded that the diastolic pressure-volume relation is not very sensitive to either the fiber orientation distribution or the thickness of the ventricle. However, the pumping efficiency of the modeled ventricle is shown to increase with increasing thickness of the modeled left ventricle and with increasing contractility of the heart muscle fibers.

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