Eberhard-Karls-Universität, Institut für Sportwissenschaft, Arbeitsbereich III, Wilhelmstrasse 124, D-72074 Tübingen, Deutschland, Germany.
J Theor Biol. 2010 Apr 21;263(4):407-18. doi: 10.1016/j.jtbi.2009.12.027. Epub 2010 Jan 4.
In this study, we derive the hyperbolic force-velocity relation of concentric muscular contraction, first formulated empirically by A.V. Hill in 1938, from three essential model assumptions: (1) the structural assembly of three well-known elements - i.e. active, parallel damping, and serial - fulfilling a force equilibrium, (2) the parallel damping coefficient explicitly depending on muscle force output and three parameters, and (3) the kinematic gearing ratio between active and serial element being assigned to a parameter. The energy source within the muscle represented by the force of the active element is an additional fifth parameter. As a result we find the Hill "constants" A and B as functions of our five model parameters. Using A and B values from literature on experimental data, we predict heat power release of our model. By calculating enthalpy rate and mechanical efficiency, we compare the model heat power to predictions from another Hill-type model, to Hill's original findings, and to findings from modern muscle heat measurements. We reconsider why the biggest share of heat rate during isometric contractions (maintenance heat) and the velocity-dependent heat rate during concentric contractions in addition to maintenance heat rate (shortening heat rate) may be traced back to the same mechanism represented by the kinematic gearing ratio. Namely, we suggest that the serial element transfers attachment-detachment fluctuations of actin-myosin crossbridges within one sarcomere to others in the same sarcomere and to those in parallel and in series. Numerically, in case of negligible passive muscular damping, we find the ratio between A and isometric force (relative A) to depend exclusively on the kinematic gearing ratio, whereas the maintenance heat rate scales with the square of relative A. Moreover, this mechanical coupling internal to the muscle fibres may also be behind the macroscopic force dependency of the overall parallel damping coefficient.
在这项研究中，我们从三个基本模型假设出发，推导出了同心肌肉收缩的双曲力-速度关系，该关系最初由 A.V. Hill 于 1938 年经验公式化：（1）由三个众所周知的元素——即主动、并联阻尼和串联元素——组成的结构组件，满足力平衡，（2）并联阻尼系数明确取决于肌肉力输出和三个参数，以及（3）主动和串联元素之间的运动学传动比被分配给一个参数。肌肉内由主动元件力代表的能量源是另一个附加的第五个参数。结果，我们发现 Hill“常数”A 和 B 是我们五个模型参数的函数。使用文献中关于实验数据的 A 和 B 值，我们预测了模型的热功率释放。通过计算焓率和机械效率，我们将模型的热功率与另一个 Hill 型模型、Hill 的原始发现以及现代肌肉热测量的发现进行了比较。我们重新考虑为什么在等长收缩（维持热）期间最大份额的热率以及在同心收缩期间除了维持热率之外的速度依赖性热率（缩短热率）可能可以追溯到由运动学传动比代表的相同机制。具体来说，我们建议串联元件将肌动球蛋白横桥在一个肌节内的附着-脱附波动传递到同一肌节中的其他横桥以及平行和串联中的横桥。数值上，在忽略被动肌肉阻尼的情况下，我们发现 A 与等长力（相对 A）的比值仅取决于运动学传动比，而维持热率与相对 A 的平方成正比。此外，这种肌肉纤维内部的机械耦合也可能是整个并联阻尼系数的宏观力依赖性的背后原因。
