Curvature of Swimming Fish Midlines as an Index of Muscle Strain Suggests Swimming Muscle Produces Net Positive Work

The axial muscle used in steady swimming by fish is geometrically complex and this has required the study ofin vivomuscle swimming mechanics to be done with largely inferential techniques. Currently there is some debate concerning the variation in muscle function in different regions of the body, and the importance of negative work production by muscles in posterior locations. We have used video taped kinematics of steady swimming in mackerel and then analysed the lateral flexion of the body that is thought to reflect the cycle of length change in the axial muscles. A comparison of several of the techniques used in the past to estimate muscle length changes are shown not to be equivalent. Specifically, we find that peak values of lateral deflection of the body are not correlated in time or axial position with peaks in curvature of the body midline. This is important because the timing of the muscle strain cycle is often inferred from such information. Having documented this observation in a swimming mackerel, we use analytical geometry to show that this result is a consequence of the curves that describe swimming fish midlines. Since this observation is shown to be the geometric consequence of an amplitude envelope that is not constant, it should therefore apply to other animals that propel themselves with axial undulations of increasing amplitude. Our minor result is that care must be taken when estimating the phase of swimming muscle strain from kinematics. Our major results is that appreciation of the geometric character of the kinematics these fish adopt may resolve much of the current debate concerning the mechanical performance of swimming muscle in fish. Specifically, using our estimate of the phase of muscle shortening and data on EMG timing in the mackerel we conclude that all axial muscles are activated before peak length and in a manner that should produce net positive work within each shortening cycle.