Robert G. Root

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.

Biomimetic evolutionary analysis: Robotically-simulated vertebrates in a predator-prey ecology

To test adaptation hypotheses about the evolution of animals, we need information about the behavior of phenotypically-variable individuals in a specific environment. To model behavior of ancient fish-like vertebrates, we previously combined evolutionary robotics and software simulations to create autonomous biomimetic swimmers in a simple aquatic environment competing and foraging for a single source of food. This system allowed us to test the hypothesis that selection for improved forage navigation drove the evolution of stiffer tails. In this paper, we extend our framework to evaluate more complex environments and hypotheses. Specifically, we test the hypothesis that predatorprey dynamics and the need for effective foraging strategies, operating simultaneously, were key selection pressures driving the evolution of morphological and sensory traits in early, fish-like vertebrates. Three evolvable traits were chosen because of their importance in propulsion and predator avoidance: (1) the number of vertebrae in the axial skeleton, (2) the trailing edge span of the caudal fin, and (3) the sensitivity of the sensory lateral line. To produce variable offspring, we used a genetic algorithm that rewarded parents with high fitness, allowing them to mate randomly and combine their mutated gametes. Offspring were then instantiated as autonomous embodied robots, the prey. These prey were chased by a non-evolving autonomous predator. Both kinds of robots were surface swimmers. The prey used a control architecture based on that of living fish: a two-layer subsumption architecture with predator escape over-riding steady swimming during foraging. The performance of six different prey robots in each generation was judged with a relative fitness function that rewarded a combination of high speed, rapid escape acceleration, escape responses, and the ability to stay away from the predator while at the same time staying close to the food source. This approach, which we call biomimetic evolutionary analysis, shows promise for investigators seeking new ways to test evolutionary hypotheses about biological systems.

Comparative equilibrium mechanical properties of bovine and lamprey cartilaginous tissues.

SUMMARY 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.

Modeling a swimming fish with an initial boundary value problem: Unsteady maneuvers of an elastic plate with internal force generation

In order to model unsteady maneuvers in swimming fish, we develop an initial-boundary value problem for a fourth-order hyperbolic partial differential equation in which the fishs body is treated as an inhomogeneous elastic plate. The model is derived from the three-dimensional equations of elastic dynamics, and is essentially a simple variant of the classical Kirchhoff model for a dynamic plate. The model incorporates body forces generating moment to simulate muscle force generation in fish. The initial-boundary value problem is reduced to a beam model in one spatial dimension and formulated computationally using finite differences. Interaction with the surrounding water is represented by nonlinear viscous damping. Two example applications using simple but physically reasonable physiological parameters are presented and interpreted. One models the acceleration from rest to steady swimming, the other a rapid turn from rest.

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.

Using Artificial Organisms To Study The Evolution of Backbones in Fish

This paper describes the use of both robotic and digital organisms to help in the study and understanding of the evolution of biological structures. Our premise in this paper is that simulations using robotic and digital organisms are an effective methodology for studying how some features evolved in swimming fish. Experiments with the artificial organisms allow us to evaluate the hypothesis that backbones evolved in fish in part because they result in higher velocity, acceleration and maneuverability. The use of both robotic and digital organisms provides the ability to (1) use computers to efficiently explore a very large search space of possibilities, (2) validate (using the robotic organisms) that the digital models accurately reflect the physical constraints of the environment