Streeter D D, Vaishnav R N, Patel D J, Spotnitz H M, Ross J, Sonnenblick E H
Biophys J. 1970 Apr;10(4):345-63. doi: 10.1016/S0006-3495(70)86306-8.
A model is proposed for stress analysis of the left ventricular wall (LV wall) based on the realistic assumption that the myocardium is essentially composed of fiber elements which carry only axial tension and vary in orientation through the wall. Stress analysis based on such a model requires an extensive study of muscle fiber orientation and curvature through the myocardium. Accordingly, the principal curvatures were studied at a local site near the equator in ten dog hearts rapidly fixed in situ at end diastole and end systole; the fiber orientation for these hearts had already been established in a previous study. The principal radii of curvature were (a) measured by fitting templates to the endocardial and epicardial wall surfaces in the circumferential and longitudinal directions and (b) computed from measured lengths of semiaxes of ellipsoids of revolution representing the LV wall ("ellipsoid" data). The wall was regarded as a tethered set of nested shells, each having a unique fiber orientation. Results indicate the following. (a) Fiber curvature, k, is maximum at midwall at end systole; this peak shifts towards endocardium at end diastole. (b) The pressure or radial stress through the wall decreases more rapidly near the endocardium than near the epicardium at end diastole and at end systole when a constant tension is assumed for each fiber through the wall. (c) At end diastole the curve for the circumferential stress vs. wall thickness is convex with a maximum at midwall. In the longitudinal direction the stress distribution curve is concave with a minimum at midwall. Similar distributions are obtained at end systole when a constant tension is assumed for each fiber through the wall. (d) The curvature and stress distributions obtained by direct measurements at a selected local site agree well with those computed from "ellipsoid" data.
基于心肌本质上由仅承受轴向张力且贯穿心室壁方向变化的纤维单元组成这一实际假设，提出了一种用于左心室壁（LV壁）应力分析的模型。基于此类模型的应力分析需要对贯穿心肌的肌纤维方向和曲率进行广泛研究。因此，在舒张末期和收缩末期原位快速固定的十只犬心脏赤道附近的局部位置研究了主曲率；这些心脏的纤维方向在先前的研究中已经确定。主曲率半径通过以下方式确定：(a) 将模板拟合到圆周和纵向方向的心内膜和心外膜壁表面进行测量，以及(b) 根据代表LV壁的旋转椭球体半轴的测量长度计算得出（“椭球体”数据）。心室壁被视为一组相互嵌套的栓系壳，每个壳都有独特的纤维方向。结果表明如下：(a) 纤维曲率k在收缩末期的壁中部最大；该峰值在舒张末期向心内膜移动。(b) 当假设贯穿壁的每条纤维的张力恒定时，舒张末期和收缩末期时贯穿壁的压力或径向应力在心内膜附近比在心外膜附近下降得更快。(c) 在舒张末期，圆周应力与壁厚的曲线是凸形的，在壁中部有最大值。在纵向方向上，应力分布曲线是凹形的，在壁中部有最小值。当假设贯穿壁的每条纤维的张力恒定时，收缩末期也会得到类似的分布。(d) 在选定局部位置通过直接测量获得的曲率和应力分布与从“椭球体”数据计算得出的结果非常吻合。
