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The axisymmetric model described represents myocardial tissue as a spongy anisotropic viscoelastic material. It includes torsion around the axis of symmetry of the ventricle, transmural variation of fiber angle, and redistribution of intracoronary blood in the myocardial wall. In simulations, end-systolic principal strains were equal to 0.45, -0.01, and -0.24 at two-thirds of the wall thickness from the epicardium and 0.26, 0.00, and -0.19 at one-third of the wall thickness from the epicardium. The direction of maximal shortening varied by less than 30 degrees from epicardium to endocardium, whereas fiber direction varied by greater than 100 degrees from epicardium to endocardium. During a normal cardiac cycle peak, equatorial intramyocardial pressure differed by less than 5% from peak intraventricular pressure. When redistribution of intracoronary blood in the ventricular wall was suppressed, peak equatorial intramyocardial pressure was found to exceed peak intraventricular pressure by greater than 30%. Simulated contraction of an unloaded left ventricle (left ventricular pressure = 0 kPa) produced similar magnitude for systolic intramyocardial pressures as the normal cardiac cycle. Transmural systolic fiber stress distribution was very sensitive to the chosen transmural fiber angle distribution.

Abstract-The strain of muscle fibers in the heart is likely to be distributed uniformly over the cardiac walls during the ejection period of the cardiac cycle. Mathematical models of left ventricular ͑LV͒ wall mechanics have shown that the distribution of fiber strain during ejection is sensitive to the orientation of muscle fibers in the wall. In the present study, we tested the hypothesis that fiber orientation in the LV wall is such that fiber strain during ejection is as homogeneous as possible. A finite-element model of LV wall mechanics was set up to compute the distribution of fiber strain at the beginning ͑BE͒ and end ͑EE͒ of the ejection period of the cardiac cycle, with respect to a middiastolic reference state. The distribution of fiber orientation over the LV wall, quantified by three parameters, was systematically varied to minimize regional differences in fiber shortening during ejection and in the average of fiber strain at BE and EE. A well-defined optimum in the distribution of fiber orientation was found which was not significantly different from anatomical measurements. After optimization, the average of fiber strain at BE and EE was 0.025 Ϯ0.011 (meanϮstandard deviation) and the difference in fiber strain during ejection was 0.214Ϯ0.018. The results indicate that the LV structure is designed for maximum homogeneity of fiber strain during ejection.

Abstract-The influence of variations of fiber direction on the distribution of stress and strain in the left ventricular wall was investigated using a finite element model to simulate the mechanics of the left ventricle. The commonly modelled helix fiber angle was defined as the angle between the local circumferential direction and the projection of the fiber path on the plane perpendicular to the local radial direction. In the present study, an additional angle, the transverse fiber angle, was used to model the continuous course of the muscle fibers between the inner and the outer layers of the ventricular wall. This angle was defined as the angle between the circumferential direction and the projection of the fiber path on the plane perpendicular to the local longitudinal direction.First, a reference simulation of left ventricular mechanics during a cardiac cycle was performed, in which the transverse angle was set to zero. Next, we performed two simulations in which the spatial distribution of either the transverse or the helix angle was varied with respect to the reference situation, the spatially averaged variations being about 3 and 14", respectively. The changes in fiber orientation hardly affected the pressure-volume relation of the ventricle, but significantly affected the spatial distribution of active muscle fiber stress (up to 50% change) and sarcomere length (up to 0

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