1 Environmental interactions
1.1 Hydrodynamics 1.2 Kinematics
2 Musculoskeletal system
2.1 Muscle architecture 2.2 Muscle activity
2.2.1 American eel
3 Neuromuscular system
3.1 Intersegmental coordination
4 Robotics 5 See also 6 References 7 External links
Environmental interactions 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.
Perch filets showing myomere structure
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 produce a higher architectural gear ratio (AGR) (high velocity). However, when subject to a high force, the perpendicular fiber force component overcomes the resistance to width changes and the muscle compresses producing a lower AGR (capable of maintaining a higher force output). Most fishes bend as a simple, homogenous beam during swimming via contractions of longitudinal red muscle fibers and obliquely oriented white muscle fibers within the segmented axial musculature. The fiber strain (εf) experienced by the longitudinal red muscle fibers is equivalent to the longitudinal strain (εx). The deeper white muscle fibers fishes show diversity in arrangement. These fibers are organized into cone-shaped structures and attach to connective tissue sheets known as myosepta; each fiber shows a characteristic dorsoventral (α) and mediolateral (φ) trajectory. The segmented architecture theory predicts that, εx > εf. This phenomenon results in an architectural gear ratio, determined as longitudinal strain divided by fiber strain (εx / εf), greater than one and longitudinal velocity amplification; furthermore, this emergent velocity amplification may be augmented by variable architectural gearing via mesolateral and dorsoventral shape changes, a pattern seen in pennate muscle contractions. A red-to-white gearing ratio (red εf / white εf) captures the combined effect of the longitudinal red muscle fiber and oblique white muscle fiber strains. 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, Azizi et al. studied this phenomenon using a simplified salamander model. Siren lacertian, an aquatic salamander, utilizes swimming motions similar to the aforementioned fishes yet contains hypaxial muscle fibers (which generate bending) characterized by a simpler organization. The hypaxial muscle fibers of S. lacertian are obliquely oriented, but have a near zero mediolateral (φ) trajectory and a constant doroslateral (α) trajectory within each segment. Therefore, the effect of doroslateral (α) trajectory and the distance between a given hypaxial muscle layer and the neutral axis of bending (z) on muscle fiber strain (ε) can be studied. Azizi et al. found that longitudinal contractions of the constant volume hypaxial muscles were compensated by an increase in the dorsoventral dimensions. Bulging was accompanied by fiber rotation as well as an increase in both α hypaxial fiber trajectory and architectural gear ratio (AGR), a phenomenon also seen in pennate muscle contractions. Azizi et al. constructed a mathematical model to predict the final hypaxial fiber angle, AGR and dorsoventral height, where: λx = longitudinal extension ratio of the segment (portortion of final longitudinal length after contraction to initial longitudinal length), β = final fiber angle, γ = initial fiber angle, f = initial fiber length, and εx and εf = longitudinal and fiber strain respectively.
λx = εx + 1 λf = εf + 1 εx = ∆L/Linital Architectural gear ratio = εx / εf = [λf(cos β / cos γ) -1) ]/ (λf – 1) β = sin-1 (y2 / λff)
This relationship shows that AGR increase with an increase in fiber angle from γ to β. In addition, final fiber angle (β) increases with dorsolateral bulging (y) and fiber contraction, but decreases as a function of initial fiber length. The application of the latter conclusions can be seen in S. lacertian. This organism undulates as a homogenous beam (just as in fishes) during swimming; thus the distance of a muscle fiber from the neutral axis (z) during bending must be greater for external oblique muscle layers (EO) than internal oblique muscle layers (IO). The relationship between the strains (ε) experienced by the EO and IO and their respective z values is given by the following equation: where εEO and εIO = strain of the external and internal oblique muscle layers, and zEO and zIO = distance of the external and internal oblique muscle layers respectively from the neutral axis. εEO = εIO (zEO / zIO) Via this equation, we see that z is directly proportional to ε; the strain experienced by the EO exceeds that of the IO. Azizi et al. discovered that the initial hypaxial fiber α trajectory in the EO is greater than that of the IO. Because initial α trajectory is proportional to the AGR, the EO contracts with a greater AGR than the IO. The resulting velocity amplification allows both layers of muscles to operate at similar strains and shortening velocities; this enables the EO and IO to function on comparable portions of the length-tension and force-velocity curves. Muscles recruited for a similar task ought to operate at similar strains and velocities to maximize force and power output. Therefore, variability in AGR within the hypaxial musculature of the Siren lacertian counteracts varying mesolateral fiber distances and optimizes performance. Azizi et al. termed this phenomenon as fiber strain homogeneity in segmented musculature. Muscle activity In addition to a rostral to caudal kinematic wave that travels down the animals body during undulatory locomotion, there is also a corresponding wave of muscle activation that travels in the rostro-caudal direction. However, while this pattern is characteristic of undulatory locomotion, it too can vary with environment. American eel Aquatic Locomotion: Electromyogram (EMG) recordings of the American eel reveal a similar pattern of muscle activation during aquatic movement as that of fish. At slow speeds only the most posterior end of the eel's muscles are activated with more anterior muscle recruited at higher speeds. As in many other animals, the muscles activate late in the lengthening phase of the muscle strain cycle, just prior to muscle shortening which is a pattern believed to maximize work output from the muscle. Terrestrial Locomotion: EMG recordings show a longer absolute duration and duty cycle of muscle activity during locomotion on land. Also, the absolute intensity is much higher while on land which is expected from the increase in gravitational forces acting on the animal. However, the intensity level decreases more posteriorly along the length of the eel's body. Also, the timing of muscle activation shifts to later in the strain cycle of muscle shortening. Energetics Animals with elongated bodies and reduced or no legs have evolved differently from their limbed relatives. 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 associatied 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 (3) there is a lower cost for supporting the body. This hypothesis has been studied further by examining the oxygen consumption rates in the snake during different modes of locomotion: lateral undulation, concertina, 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 consist 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 by 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.
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.
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 maintaince 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
Locomotive Animal locomotion
^ Guo, Z. V.; Mahadeven, L. (2008). "Limbless undulatory propulsion on
land". PNAS. 105 (9): 3179–3184. doi:10.1073/pnas.0705442105.
PMC 2265148 . PMID 18308928.
^ a b McHenry, M. J.; Azizi, E.; Strother, J. A. (2002). "The
hydrodynamics of locomotion at intermediate Reynolds numbers:
undulatory swimming in ascidian larvae (Botrylloides sp.)". J. Exp.
Biol. 206: 327–343. doi:10.1242/jeb.00069.
^ Gray and Hancock, 1955.[full citation needed]
^ Gray and Lissmann, 1964.[full citation needed]
^ a b c Biewener, A. A.; Gillis, G. B. (1999). "Dynamics of Mucscle
Function During Locomotion: Accommodating Variable Conditions". J.
Exp. Biol. 202 (23): 3387–3396.
^ Gillis, G. B. (1998). "Environmental Effects on Undulatory
Locomotion in the American Eel Anguilla Rostrata: Kinematics in Water
and on Land". J. Exp. Biol. 201 (7): 949–961.
^ a b Gillis, G. B. (1998). "Neuromuscular Control of Anguilliform
Locomotion: Patterns of Red and White Muscle Activity During Swimming
in the American Eel Anguilla Rostrata". J. Exp. Biol. 201 (23):
^ a b c d e f Brainerd, E. L.; Azizi, E. (2005). "Muscle Fiber Angle,
Segment Bulging and Architectural Gear Ratio in Segmented
Musculature". Journal of Experimental Biology. 208 (17): 3249–3261.
doi:10.1242/jeb.01770. PMID 16109887.
^ a b c Azizi, E.; Brainerd, E. L.; Roberts, T. J. (2008). "Variable
Gearing in Pennate Muscles". PNAS. 105 (5): 1745–1750.
doi:10.1073/pnas.0709212105. PMC 2234215 .
^ a b c d e Brainerd, E. L.; Azizi, E. (2007). "Architectural Gear
Ratio and Muscle Fiber Strain Homogeneity in Segmented Musculature".
Journal of Experimental Zoology. 307 (A): 145–155.
^ a b c Gans, C. (1975). "Tetrapod Limblessness: Evolution and
Functional Corollaries". Am. Zool. 15 (2): 455–461.
^ a b Goldspink, G. (1977). Mechanics and Energetics of Animal
Locomotion. New York: Wiley. pp. 153–167.
^ a b Walton, M.; Jayne, B. C.; Bennet, A. F. (1990). "The energetic
cost of limbless locomotion". Science. 249 (4968): 524–527.
doi:10.1126/science.249.4968.524. PMID 17735283.
^ Secor, S. M.; Jayne, B. C.; Bennett, A. F. "Locomotor Performance
and energetic Cost of Sidewinging by the Snake Crotalus Cerastes".
Journal of Experimental Biology. 163 (1): 1–14.
^ a b c Hill, Andrew A. V.; Masino, Mark A.; Calabrese, Ronald L.
(2003). "Intersegmental Coordination of Rhythmic Motor Patterns".
Journal of Neurophysiology. 90 (2): 531–538.
doi:10.1152/jn.00338.2003. PMID 12904484.
^ Ijspeert, A. J. (2001). "A Connectionist Central Pattern Generator
for the Aquatic and Terrestrial Gaits of a Simulated Salamander".
Biological Cybernetics. 84 (5): 331–348.
^ Ijspeert, A. J.; Crespi, A.; Ryczko, D.; Cabelguen, J. M. (2007).
"From Swimming to
Biologically Inspired Robotics Group @ EPFL Center for Biologically Inspired Design at Georgia Tech Functional Morphology and Biomechanics Laboratory, Brown University Peristalsis Robot Snake Locomotion Research for this entry was conducted as a part of a Locomotion Neuromechanics course (APPH 6232) offered in the School of Applied Physiology at Georgia Tech
v t e
dermal intramembranous ossification
Cleithrum Chromatophore Fins
branchial arch gill raker gill slit pharyngeal arch pharyngeal slit pseudobranch
hyomandibula pharyngeal jaw
Leydig's organ Mauthner cell Meristics Operculum
Spiral valve Suckermouth Swim bladder
pharyngeal teeth shark teeth
Teleost leptins Digital Library
Sensory systems in fish Ampullae of Lorenzini Barbel Hydrodynamic reception Electrocommunication Electroreception Jamming avoidance response Lateral line Otolith Passive electrolocation Capacity for pain Schreckstoff Surface wave detection Vision Weberian apparatus
Diel vertical migration
Cave Coastal Coldwater Coral reef Deep sea Demersal Euryhaline Freshwater Groundfish Pelagic Tropical
Bait Coarse Diversity Game Genetically modified Hallucinogenic Oily Poisonous Rough Whitefish
Carp Salmonids Tilapia
billfish mackerel salmon tuna
anchovy herring sardine sprats
cod flatfish pollock
chimaeras sharks rays
Prehistoric fish more lists...
Category Portal WikiProject
v t e
Concertina movement Undulatory locomotion Rectilinear locomotion Rolling Sidewinding Other modes
Comparative foot morphology Arthropod leg Digitigrade Plantigrade Unguligrade Uniped Biped (Facultative) Triped Quadruped
Canine gait Horse gait Human gait
v t e
Fins, limbs and wings
Limb development Limb morphology
digitigrade plantigrade unguligrade uniped biped facultative biped triped quadruped
Arthropod Cephalopod Tetrapod
Flying and gliding animals Bat wing Bird wing
keel skeleton feathers
Insect wing Pterosaur wing Wingspan
Evolution of fish Evolution of tetrapods Evolution of birds Origin of birds Origin of avian flight Evolution of cetaceans Comparative anatomy Convergent evolution Analogous structures Homologous structures
Animal locomotion Gait Robot locomotion Samara Terrestrial locomotion Tradeoffs for locomotion in air and water Rotating locomotion Und