Force transmission via axial tendons in undulating fish: a dynamic analysis

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra- and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.