Multidimensional models for predicting muscle structure and fascicle pennation

Pennation angles change during muscle contraction and must be tracked by muscle models. When muscles contract they can change in depth (distance between the bounding sheets of aponeurosis) or width, and this is related to pennation angle and muscle fascicle length. As a simplification to these relationships, many models of pennate muscle assume a constant distance between aponeuroses during contraction (constant depth). It is possible that these 1D models do not recreate the internal structure of muscles adequately, whereas 2D panel models that assume a constant panel area, or 3D models that assume a constant muscle volume may better predict the structural changes that occur within muscle during contraction. However, these ideas have never been validated in man. The purpose of this study was to test the accuracy with which 1D, 2D or 3D structural models of muscle could predict the pennation and muscle depth within the medial gastrocnemius (MG) and lateral gastrocnemius (LG) in man during ankle plantarflexions. The 1D model, by definition, was unable to account for changes in muscle depth. The 2D model predicted change in depth as the aponeurosis was loaded, but could only allow a decrease in depth as the aponeurosis is stretched. This was not sufficient to predict the increases in depth that occur in the LG during plantarflexion. The 3D model had the ability to predict either increases or decreases in depth during the ankle plantarflexions and predicted opposing changes in depth that occurred between the MG and LG, whilst simultaneously predicting the pennation more accurately than the 1D or 2D models. However, when using mean parameters, the 3D model performed no better than the more simple 1D model, and so if the intent of a model is purely to establish a good relation between fascicle length and pennation then the 1D model is a suitable choice for these muscles.