Takeda K, Shimizu T, Yamamoto H, Yagi S
Department of Medicine, Dokkyo University School of Medicine, Tochigi, Japan.
Jpn Heart J. 1988 Sep;29(5):689-707. doi: 10.1536/ihj.29.689.
The relationship between myocardial total force and length at the end of systole appears to be linear, and the slope of this relationship is considered to be an appropriate index of myocardial contractile state, independent of preload and afterload. However, direct measurements of this relation may be impossible in the intact human heart, and thus, alternative indices such as the left ventricular end-systolic stress-length, stress-strain, pressure-volume, and pressure-dimension slopes have been proposed to evaluate myocardial contractility in the intact heart. However, the mathematical relationship between the myocardial end-systolic total force-length relation and any of these left ventricular end-systolic relations remains unclear. In this study, assuming a linear myocardial end-systolic total force-length relation in an intact ventricle, we obtained mathematical formulae for the left ventricular end-systolic stress-strain, pressure-radius, and pressure-volume relations, using a cylinder model of the left ventricle. The results obtained using these formulae and the cylinder model were found to match accurately findings obtained from earlier experimental and clinical studies of these left ventricular end-systolic relations. Thus, this model could mathematically account for the relationships between the slopes of the myocardial end-systolic total force-length relation and these left ventricular end-systolic relations.
心肌总力与收缩末期长度之间的关系似乎呈线性，且这种关系的斜率被认为是心肌收缩状态的一个合适指标，不受前负荷和后负荷的影响。然而，在完整的人体心脏中可能无法直接测量这种关系，因此，人们提出了诸如左心室收缩末期应力 - 长度、应力 - 应变、压力 - 容积以及压力 - 维度斜率等替代指标，以评估完整心脏中的心肌收缩力。然而，心肌收缩末期总力 - 长度关系与这些左心室收缩末期关系中的任何一种之间的数学关系仍不清楚。在本研究中，假设完整心室中心肌收缩末期总力 - 长度关系呈线性，我们使用左心室的圆柱模型得出了左心室收缩末期应力 - 应变、压力 - 半径和压力 - 容积关系的数学公式。使用这些公式和圆柱模型获得的结果被发现与早期关于这些左心室收缩末期关系的实验和临床研究结果精确匹配。因此，该模型可以从数学上解释心肌收缩末期总力 - 长度关系的斜率与这些左心室收缩末期关系之间的关系。
