Rockenfeller Robert, Günther Michael, Clemente Christofer J, Dick Taylor J M
Mathematical Institute, University of Koblenz, Koblenz, Germany.
School of Biomedical Sciences, University of Queensland, Brisbane, Queensland, Australia.
R Soc Open Sci. 2024 Sep 18;11(9):240037. doi: 10.1098/rsos.240037. eCollection 2024 Sep.
The shape of skeletal muscle varies remarkably-with important implications for locomotor performance. In many muscles, the fibres are arranged at an angle relative to the tendons' line of action, termed the pennation angle. These pennate muscles allow more sarcomeres to be packed side by side, enabling the muscle to generate higher maximum forces for a given muscle size. Historically, the physiological cross-sectional area (PCSA) has been used to capture both the size and arrangement of muscle fibres, and is one of the best predictors of a muscles capacity to produce force. However, the anatomical and mechanical implications of PCSA remain ambiguous as misinterpretations have limited our ability to understand the mechanical advantage of pennate muscle designs. We developed geometric models to resolve the mechanistic and functional impacts of pennation angle across a range of muscle shapes and sizes. Comparisons among model predictions and empirical data on human lower limb muscles demonstrated how a pennate arrangement of fibres allows muscles to produce up to six times more isometric force when compared with non-pennate muscles of the same volume. We show that in muscles much longer than thick, an optimal pennation angle exists at which isometric force is maximized. Using empirically informed geometric models we demonstrate the functional significance of a pennate muscle design and provide a new parameter, pennation mechanical advantage, which quantifies this performance improvement.
骨骼肌的形状差异显著，这对运动表现有着重要影响。在许多肌肉中，肌纤维相对于肌腱的作用线呈一定角度排列，这个角度被称为羽状角。这些羽状肌能使更多肌节并排排列，从而使肌肉在给定的肌肉大小下能够产生更大的最大力量。从历史上看，生理横截面积（PCSA）一直被用于描述肌肉纤维的大小和排列情况，并且是预测肌肉产生力量能力的最佳指标之一。然而，由于误解限制了我们理解羽状肌设计机械优势的能力，PCSA的解剖学和力学意义仍然不明确。我们开发了几何模型，以解析不同形状和大小肌肉中羽状角的机械和功能影响。模型预测结果与人类下肢肌肉的实验数据对比表明，与相同体积的非羽状肌相比，羽状肌纤维排列能使肌肉产生的等长力最多高出六倍。我们发现，在长度远大于厚度的肌肉中，存在一个最佳羽状角，此时等长力达到最大值。通过基于实验数据的几何模型，我们证明了羽状肌设计的功能意义，并提供了一个新参数——羽状机械优势，用以量化这种性能提升。
