Delhaas T, Arts T, Bovendeerd P H, Prinzen F W, Reneman R S
Department of Physiology, Cardiovascular Research Institute Maastricht, University of Limburg, The Netherlands.
Am J Physiol. 1993 May;264(5 Pt 2):H1548-59. doi: 10.1152/ajpheart.1993.264.5.H1548.
In a mathematical model of the mechanics of the left ventricle (LV) by Arts et al. (1), assuming uniformity of fiber stress (sigma f) and fiber strain (delta epsilon f) in the wall during the ejection phase, fiber stress and fiber strain were related to LV cavity pressure (Plv), LV cavity volume (Vlv) and wall volume (Vw) by the following pair of equations: sigma f = Plv (1 + 3 Vlv/Vw) and delta epsilon f = 1/3 delta ln (1 + 3 Vlv/Vw). The ratio of Vlv to Vw appeared to be the most important geometric parameter, whereas the actual LV shape was of minor importance. The relationships on fiber strain and stress were evaluated experimentally in six anesthetized open-chest dogs during normal and elevated (volume loading) end-diastolic LV pressure. Subepicardial fiber strain was measured simultaneously in 16 adjacent regions of the LV anterior wall, using optical markers that were attached to the epicardial surface and recorded on video. Changes in Vlv were measured by use of four inductive coils sutured to the LV in a tetrahedric configuration. Vw was measured postmortem. During control as well as hypervolemia the following results were found. At the anterior free wall of the LV, the slope of the estimated linear relationship between measured and calculated fiber strain was 1.017 +/- 0.168 (means +/- SD), which is not significantly different from unity. Calculated fiber stress corresponded qualitatively and quantitatively with experimental results reported on isolated cardiac muscle. Calculated subepicardial contractile work per unit of tissue volume was not significantly different from global pump work as normalized to Vw. These findings support the assumption of homogeneity of muscle fiber strain and stress in the left ventricular wall during the ejection phase. Furthermore, average values of fiber stress and strain can be estimated on the basis of measured left ventricular pressure and volume.
在阿茨等人（1）建立的左心室（LV）力学数学模型中，假设在射血期壁内纤维应力（σf）和纤维应变（δεf）均匀，纤维应力和纤维应变与左心室腔压力（Plv）、左心室腔容积（Vlv）和壁容积（Vw）通过以下一对方程相关：σf = Plv (1 + 3 Vlv/Vw) 以及 δεf = 1/3 δln (1 + 3 Vlv/Vw)。Vlv与Vw的比值似乎是最重要的几何参数，而左心室的实际形状则不太重要。在六只麻醉开胸犬处于正常和升高（容量负荷）舒张末期左心室压力时，对纤维应变和应力的关系进行了实验评估。使用附着在心外膜表面并记录在视频上的光学标记，同时在左心室前壁的16个相邻区域测量心外膜下纤维应变。通过以四面体构型缝合到左心室的四个感应线圈测量Vlv的变化。Vw在死后测量。在对照以及高血容量期间发现了以下结果。在左心室前游离壁，测量的和计算的纤维应变之间估计的线性关系斜率为1.017±0.168（均值±标准差），与1无显著差异。计算的纤维应力在定性和定量上与关于分离心肌报道的实验结果相符。计算的每单位组织容积的心外膜下收缩功与以Vw归一化的整体泵功无显著差异。这些发现支持了射血期左心室壁内肌纤维应变和应力均匀性的假设。此外，可以根据测量的左心室压力和容积估计纤维应力和应变的平均值。
