3D computational models explain muscle activation patterns and energetic functions of internal structures in fish swimming
Authors: Ming Tingyu , Jin Bowen , Song Jialei , Luo Haoxiang , Du Ruxu , Ding Yang 
Published: February 2019

How muscles are used is a key to understanding the internal driving of fish swimming. However, the underlying mechanisms of some features of the muscle activation patterns and their differential appearance on different species are still obscure. In this study, we explain the muscle activation patterns by using 3D computational fluid dynamics models coupled to the motion of fish with prescribed deformation and examining the torque and power required along the fish body with two primary swimming modes. We find that the torque required by the hydrodynamic forces and body inertia exhibits a wave pattern that travels faster than the curvature wave in both anguilliform and carangiform swimmers, which can explain the traveling wave speeds of the muscle activations. Most interestingly, intermittent negative power (i.e., power delivered by the fluid to the body) on the posterior part, along with a timely transfer of torque and energy by tendons, explains the decrease of the duration of muscle activation towards the tail. The torque contribution from the body elasticity further solves the mystery of the wave speed increase or the reverse of the wave direction of the muscle activation on the posterior part of a carangiform swimmer. For anguilliform swimmers, the absence of the changes mentioned above in the muscle activation on the posterior part is in line with our torque prediction and the absence of long tendons from experimental observations. These results provide novel insights into the function of muscles and tendons as an integrative part of the internal driving system, especially from an energy perspective, and highlight the differences in the internal driving systems between the two primary swimming modes.

Author summary

For undulatory swimming, fish form posteriorly traveling waves of body bending by activating their muscles sequentially along the body. However, experimental observations have showed that the muscle activation wave does not simply match the bending wave. Researchers have previously computed the torque required for muscles along the body based on classic hydrodynamic theories and explained the higher wave speed of the muscle activation compared to the curvature wave. However, the origins of other features of the muscle activation pattern and their variation among different species are still obscure after decades of research. In this study, we use 3D computational fluid dynamics models to compute the spatiotemporal distributions of both the torque and power required for eel-like and mackerel-like swimming. By examining both the torque and power patterns and considering the energy transfer, storage, and release by tendons and body viscoelasticity, we can explain not only the features and variations in the muscle activation patterns as observed from fish experiments but also how tendons and body elasticity save energy. We provide a mechanical picture in which the body shape, body movement, muscles, tendons, and body elasticity of a mackerel (or similar) orchestrate to make swimming efficient.