Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Friedrich-Schiller-Universität, 07737 Jena, Germany.
Mathematisches Institut, Universität Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany.
J Theor Biol. 2021 Aug 21;523:110714. doi: 10.1016/j.jtbi.2021.110714. Epub 2021 Apr 20.
The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.
动物的最大奔跑速度是进化选择的一个明显因素——无论是捕食者还是猎物。因此，人们已经在从最小的螨虫到最大的大象，甚至是已经灭绝的恐龙的整个动物体型范围内研究了这一速度。最近对动物体重（大小）与最大奔跑速度之间关系的分析表明，似乎存在一个最佳的体重范围，在这个范围内可以达到最高的陆地奔跑速度。然而，从该分析中得出的结论——即最大速度受到白色肌肉纤维在加速体重达到理论上可能的最大速度时的疲劳的限制——是基于代谢原因的粗略推理，这种推理忽略了重要的生物力学因素和基本的肌肉代谢参数。在这里，我们提出了一个通用的生物力学模型来研究腿部奔跑的最大速度的比例关系。该模型包含了一些生物力学上重要的概念：地面反作用力与空气阻力相抗衡，腿部通过肌肉将其长度变化和地面反作用力相连接，以及最大肌肉收缩速度，其中包括肌肉-肌腱动力学和肌肉惯性——所有这些都与体重成比例。总之，这些概念的特征及其相互作用为腿部奔跑最大速度的比例关系提供了一个机械解释。这伴随着对经验上发现的整体最大速度的解释：在比猎豹或叉角羚大的动物中，任何腿部伸展肌肉从等长状态开始，在达到最高速度所需的向心收缩速度下开始伸展所需的时间变得太长，以至于在腿部从中立位置移动到离地的时间段内无法实现。基于我们的生物力学模型，我们因此建议考虑整体速度最大值来指示肌肉惯性在动物运动中具有功能意义。此外，该模型使得我们能够深入了解生物设计原则，例如猫和蜘蛛的腿部概念之间的差异，以及多足（哺乳动物：四足，昆虫：六足，蜘蛛：八足）身体设计和新兴步态的相关性。此外，我们提出了一个全新的考虑，即肌肉在加速到最大速度和稳定状态运动过程中的代谢能量消耗。
