Undulatory locomotion

In limbless locomotion, forward locomotion is generated by propagating flexural waves along the length of the animal's body. Forces generated between the animal and surrounding environment lead to a generation of alternating sideways forces that act to move the animal forward. These forces generate thrust and drag. Hydrodynamics Simulation predicts that thrust and drag are dominated by viscous forces at low Reynolds numbers and inertial forces at higher Reynolds numbers. When the animal swims in a fluid, two main forces are thought to play a role: • Skin friction: Generated due to the resistance of a fluid to shearing and is proportional to speed of the flow. This dominates undulatory swimming in spermatozoa and the nematode. • Form force: Generated by the differences in pressure on the surface of the body and it varies with the square of flow speed. At low Reynolds number (Re~100), skin friction accounts for nearly all of the thrust and drag. For those animals which undulate at intermediate Reynolds number (Re~101), such as the Ascidia larvae, both skin friction and form force account for the production of drag and thrust. At high Reynolds number (Re~102), both skin friction and form force act to generate drag, but only form force produces thrust. (see muscle activation patterns below). In terrestrial locomotion, all points along the body move on approximately the same path and, therefore, the lateral displacements along the length of the eel's body is approximately the same. However, in aquatic locomotion, different points along the body follow different paths with increasing lateral amplitude more posteriorly. In general, the amplitude of the lateral undulation and angle of intervertebral flexion is much greater during terrestrial locomotion than that of aquatic. ==Musculoskeletal system==

Muscle architecture A typical characteristic of many animals that utilize undulatory locomotion is that they have segmented muscles, or blocks of myomeres, running from their head to tails which are separated by connective tissue called myosepta. In addition, some segmented muscle groups, such as the lateral hypaxial musculature in the salamander are oriented at an angle to the longitudinal direction. For these obliquely oriented fibers the strain in the longitudinal direction is greater than the strain in the muscle fiber direction leading to an architectural gear ratio greater than 1. A higher initial angle of orientation and more dorsoventral bulging produces a faster muscle contraction but results in a lower amount of force production. It is hypothesized that animals employ a variable gearing mechanism that allows self-regulation of force and velocity to meet the mechanical demands of the contraction. When a pennate muscle is subjected to a low force, resistance to width changes in the muscle cause it to rotate which consequently produces a higher architectural gear ratio (AGR) (high velocity). Simple bending behavior in homogenous beams suggests ε increases with distance from the neutral axis (z). This poses a problem to animals, such as fishes and salamanders, which undergo undulatory movement. Muscle fibers are constrained by the length-tension and force-velocity curves. Furthermore, it has been hypothesized that muscle fibers recruited for a particular task must operate within an optimal range of strains (ε) and contractile velocities to generate peak force and power respectively. Non-uniform ε generation during undulatory movement would force differing muscle fibers recruited for the same task to operate on differing portions of the length-tension and force-velocity curves; performance would not be optimal. Alexander predicted that the dorsoventral (α) and mediolateral (φ) orientation of the white fibers of the fish axial musculature may allow more uniform strain across varying mesolateral fiber distances. Unfortunately, the white muscle fiber musculature of fishes is too complex to study uniform strain generation; however, Brainerd and Azizi studied this phenomenon using a simplified salamander model. In the past, some have speculated that this evolution was due to a lower energetic cost associated with limbless locomotion. The biomechanical arguments used to support this rationale include that (1) there is no cost associated with the vertical displacement of the center of mass typically found with limbed animals, (2) there is no cost associated with accelerating or decelerating limbs, and sidewinding. The net cost of transport (NCT), which indicates the amount of energy required to move a unit of mass a given distance, for a snake moving with a lateral undulatory gait is identical to that of a limbed lizard with the same mass. However, a snake utilizing concertina locomotion produces a much higher net cost of transport, while sidewinding actually produces a lower net cost of transport. Therefore, the different modes of locomotion are of primary importance when determining energetic cost. The reason that lateral undulation has the same energetic efficiency as limbed animals and not less, as hypothesized earlier, might be due to the additional biomechanical cost associated with this type of movement due to the force needed to bend the body laterally, push its sides against a vertical surface, and overcome sliding friction. ==Neuromuscular system==

Intersegmental coordination Wavelike motor pattern typically arise from a series of coupled segmental oscillator. Each segmental oscillator is capable of producing a rhythmic motor output in the absence of sensory feedback. One such example is the half center oscillator which consists of two neurons that are mutually inhibitory and produce activity 180 degrees out of phase. The phase relationships between these oscillators are established by the emergent properties of the oscillators and the coupling between them. Forward swimming can be accomplished by a series of coupled oscillators in which the anterior oscillators have a shorter endogenous frequency than the posterior oscillators. In this case, all oscillators will be driven at the same period but the anterior oscillators will lead in phase. In addition, the phase relations can be established by asymmetries in the couplings between oscillators or by sensory feedback mechanisms. • Leech The leech moves by producing dorsoventral undulations. The phase lags between body segments is about 20 degrees and independent of cycle period. Thus, both hemisegments of the oscillator fire synchronously to produce a contraction. Only the ganglia rostral to the midpoint are capable of producing oscillation individually. There is U-shaped gradient in endogenous segment oscillation as well with the highest oscillations frequencies occurring near the middle of the animal. Although the couplings between neurons spans six segments in both the anterior and posterior direction, there are asymmetries between the various interconnections because the oscillators are active at three different phases. Those that are active in the 0 degree phase project only in the descending direction while those projecting in the ascending direction are active at 120 degrees or 240 degrees. In addition, sensory feedback from the environment may contribute to resultant phase lag. (also called swimmerets) • Lamprey The lamprey moves using lateral undulation and consequently left and right motor hemisegments are active 180 degrees out of phase. Also, it has been found that the endogenous frequency of the more anterior oscillators is higher than that of the more posterior ganglia. In addition, inhibitory interneurons in the lamprey project 14-20 segments caudally but have short rostral projections. Sensory feedback may be important for appropriately responding to perturbations, but seems to be less important for the maintenance of appropriate phase relations. ==Robotics==

Based on biologically hypothesized connections of the central pattern generator in the salamander, a robotic system has been created which exhibits the same characteristics of the actual animal. Electrophysiology studies have shown that stimulation of the mesencephalic locomotor region (MLR) located in the brain of the salamander produce different gaits, swimming or walking, depending on intensity level. Similarly, the CPG model in the robot can exhibit walking at low levels of tonic drive and swimming at high levels of tonic drive. The model is based on the four assumptions that: • Tonic stimulation of the body CPG produces spontaneous traveling waves. When the limb CPG is activated it overrides the body CPG. • The strength of the coupling from the limb to the body CPG is stronger than that from body to limb. • Limb oscillators saturate and stop oscillating at higher tonic drives. • Limb oscillators have lower intrinsic frequencies than body CPGs at the same tonic drive. This model encompasses the basic features of salamander locomotion. == See also ==