Computational and mathematical modeling of the effects of tailbeat frequency and flexural stiffness in swimming fish.

In this paper we describe how we combine computational and mathematical models to form virtual fish to explore different hypotheses about the impact of centra. We show how we create simulation models using a combination of a mathematical model of a fish-like robot using caudal fin propulsion, a propulsion model, and an optimizer, to explore the impact of centra under various scenarios. The optimizer uses the mathematical model to construct valid configurations of the digital robot and uses the utility function and propulsion model to evaluate the performance of each configuration. The evaluations are used to explore the adaptive landscape and find high-performing configurations. Our results show that the high-performing configurations have both increased (flexural) stiffness of the tail and higher tailbeat frequencies.

Go reconfigure: how fish change shape as they swim and evolve.

The bodies of fish change shape over propulsive, behavioral, developmental, and evolutionary time scales, a general phenomenon that we call "reconfiguration". Undulatory, postural, and form-reconfiguration can be distinguished, studied independently, and examined in terms of mechanical interactions and evolutionary importance. Using a combination of live, swimming fishes and digital robotic fish that are autonomous and self-propelled, we examined the functional relation between undulatory and postural reconfiguration in forward swimming, backward swimming, and yaw turning. To probe how postural and form reconfiguration interact, the yaw turning of leopard sharks was examined using morphometric and kinematic analyses. To test how undulatory reconfiguration might evolve, the digital robotic fish were subjected to selection for enhanced performance in a simulated ecology in which each individual had to detect and move towards a food source. In addition to the general issue of reconfiguration, these investigations are united by the fact that the dynamics of undulatory and postural reconfigurations are predicted to be determined, in part, by the structural stiffness of the fish's body. Our method defines undulatory reconfiguration as the combined, point-by-point periodic motion of the body, leaving postural reconfiguration as the combined deviations from undulatory reconfiguration. While undulatory reconfiguration appears to be the sole or primary propulsive driver, postural reconfiguration may contribute to propulsion in hagfish and it is correlated with differences in forward, and backward, swimming in lamprey. Form reconfigures over developmental time in leopard sharks in a manner that is consistent with an allometric scaling theory in which structural stiffness of the body is held constant. However, correlation of a form proxy for structural stiffness of the body suggests that body stiffness may scale in order to limit maximum postural reconfiguration during routine yaw turns. When structural stiffness and undulatory frequency are modeled as determining the tail's undulatory wave speed, both factors evolve under selection for enhanced foraging behavior in the digital fish-like robots. The methods used in making these distinctions between kinds of reconfiguration have broad applicability in fish biology, especially for quantifying complex motor behaviors in the wild and for simulating selection on behavior that leads to directional evolution of functional phenotypes.

Comparative equilibrium mechanical properties of bovine and lamprey cartilaginous tissues.

In contrast to all other vertebrate cartilages, the major extracellular matrix protein of lamprey cartilages is not collagen. Instead, there exists a unique family of noncollagenous structural proteins, the significance of which is not completely understood. A custom-built uniaxial testing apparatus was used to quantify and compare equilibrium stress-relaxation behavior (equilibrium moduli, stress decay behavior, recovery times and relaxation times) of (1) lamprey pericardial cartilages with perichondria tested in tension (young adult and aged), (2) annular cartilages without perichondria tested in compression (young adult and aged) and (3) bovine auricular cartilage samples without perichondria tested in both tension and compression. Results of this study demonstrated that all cartilages were highly viscoelastic but with varying relaxation times; approximately 120 min for annular and pericardial cartilages and 30 min for bovine auricular cartilages. For mean equilibrium moduli, young adult lamprey annular cartilages (0.71 MPa) and pericardial cartilages (2.87 MPa) were found to be statistically different. The mean moduli of all bovine auricular cartilages were statistically identical to lamprey cartilages except in the case of aged adult pericardial cartilages, which were statistically larger than all other cartilages at 4.85 MPa. Taken together, the results of this study suggest that lamprey cartilages are able to exhibit mechanical properties largely similar to those of mammalian cartilages despite unique structural proteins and differences in extracellular matrix organization.

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.