Rethinking the physiological cross-sectional area of skeletal muscle reveals the mechanical advantage of pennation

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.