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.     

Built for speed: strain in the cartilaginous vertebral columns of sharks

In most bony fishes vertebral column strain during locomotion is almost exclusively in the intervertebral joints, and when these joints move there is the potential to store and release strain energy. Since cartilaginous fishes have poorly mineralized vertebral centra, we tested whether the vertebral bodies undergo substantial strain and thus may be sites of energy storage during locomotion. We measured axial strains of the intervertebral joints and vertebrae in vivo and ex vivo to characterize the dynamic behavior of the vertebral column. We used sonomicrometry to directly measure in vivo and in situ strains of intervertebral joints and vertebrae of Squalus acanthias swimming in a flume. For ex vivo measurements, we used a materials testing system to dynamically bend segments of vertebral column at frequencies ranging from 0.25 to 1.00 Hz and a range of physiologically relevant curvatures, which were determined using a kinematic analysis. The vertebral centra of S. acanthias undergo strain during in vivo volitional movements as well as in situ passive movements. Moreover, when isolated segments of vertebral column were tested during mechanical bending, we measured the same magnitudes of strain. These data support our hypothesis that vertebral column strain in lateral bending is not limited to the intervertebral joints. In histological sections, we found that the vertebral column of S. acanthias has an intracentral canal that is open and covered with a velum layer. An open intracentral canal may indicate that the centra are acting as tunics around some sections of a hydrostat, effectively stiffening the vertebral column. These data suggest that the entire vertebral column of sharks, both joints and centra, is mechanically engaged as a dynamic spring during locomotion.     

Vertebral function during tadpole locomotion

Most anuran larvae show large lateral oscillations at both the tip of the tail and the snout while swimming in a straight line. Although the lateral deflections at the snout have long been considered an inefficient aspect of tadpole locomotion, a recent hydrodynamic model suggests that they may in fact help generate thrust. It is not clear though exactly where this bending takes place. The vertebral column is extremely short and seemingly inflexible in anurans, and any axial flexion that might occur there is hidden within the globose body of the tadpole. Here we test the hypothesis that lateral deflections of the snout correlate with bending of the vertebral column within the torso of tadpoles. To quantify vertebral curvature, three sonomicrometry crystals were surgically implanted along the dorsal midline in locations corresponding to the anterior, middle, and posterior region of the presacral vertebral column. Swimming trials were conducted in a flume where synchronized video recordings were collected in dorsal view. Our results confirm that cyclic lateral bending occurs along the vertebral column during swimming and indicate that vertebral curvature is temporally in phase with lateral oscillation of the snout. Lateral oscillation of the snout increased significantly with increasing vertebral curvature. Similarly, tail beat amplitude also increases significantly with increasing vertebral curvature. Our results suggest that cyclic lateral flexion of the vertebral column, activated by the axial muscle within the torso of tadpoles contributes to snout oscillations and the generation of thrust during undulatory swimming in anuran larvae.     

Vertebrae in compression: Mechanical behavior of arches and centra in the gray smooth‐hound shark (Mustelus californicus)

In swimming sharks, vertebrae are subjected, in part, to compressive loads as axial muscles contract. We currently have no information about which vertebral elements, centra, arch cartilages, or both, actually bear compressive loads in cartilaginous vertebrae. To address this issue, the goal of this experiment was to determine the load‐bearing ability of arch and centrum cartilages in compression, to determine the material properties of shark vertebrae, and to document fracture patterns in the centra with and without the arches. Intact vertebrae and vertebrae with the arch cartilages experimentally removed (centra alone) were subjected to compressive loading to failure at a single strain rate. The maximum compressive forces sustained by the vertebrae and the centra are statistically indistinguishable. Thus we conclude that under these testing conditions the arch does not bear appreciable loads. Independent evidence for this conclusion comes from the fact that vertebrae fail in compression at the centra, and not at the arches. Overall, the results of these mechanical tests suggest that the neural arches are not the primary load‐bearing structure during axial compression. J. Morphol. 2010. © 2009 Wiley‐Liss, Inc.     

Elastic properties of structures in the tails of cetaceans (Phocaena and Lagenorhynchus) and their effect on the energy cost of swimming

A swimming whale must do work against hydrodynamic forces, to move its fluke through the water. In addition, it must do positive work at some stages of the swimming cycle and negative work at others, to accelerate and decelerate the fluke. The energy cost of swimming could be reduced by means of elastic elements in the tail.
A mathematical model predicts the work required of the muscles, when they have elastic compliances in series with them. It is shown that there is an optimum compliance that minimizes the energy cost of swimming, for any given ratio of peak hydrodynamic force to peak inertial force.
Anatomical measurements have been made on flukes, tail muscles and tendons of Phocaena and Lagenorhynchus . Mechanical tests have been made on the tendons, fluke and vertebral column. It is shown that the important compliances are those of the tendons, and the axial compliance of the vertebral column, and that these compliances should be regarded as being in series with the muscles.
Calculations using these data, and Lang & Daybell's (1963) observations of a Lagenorhynchus swimming at 5 m/s, seem to show that the compliances greatly exceed the optimum value for this swimming speed. They increase the energy cost of swimming, rather than decreasing it.     

Morphology,mechanics, and locomotion: the relation between the notochord and swimming motions in sturgeon

Synopsis To examine the relation between morphology and performance, notochordal morphology was correlated with notochordal mechanics and with steady swimming motions in white sturgeon, Acipenser transmontanus. In a still-water tank, motions of four sturgeon varied with changes in swimming speed and axial position along the body. For a 1..34 m sturgeon, slow and fast swimming modes were distinguished, with speeds at the fast mode more than two times those at the slow mode without changes in tailbeat frequency. This increase in speed is correlated with an increase in the body's maximal midline curvature (m^–1), suggesting a role for curvature-related mechanical properties of the notochord. Maximal midline curvature also varied with axial position, and surprisingly was uncorrelated with axial changes in the notochord's cross-sectional shape - as measured by height, width, inner diameter, and lateral thickness of the sheaths. On the other hand, maximal midline curvature was negatively correlated with the axial changes in the notochord's angular stiffness (N m rad^–1) and change in internal pressure (% change from baseline of 58.6 kPa), both of which were measured during in vitro bending tests. In vivo curvature and in vitro angular stiffness were then used to estimate the bending moments (Nm) in the notochord during swimming. In the precaudal notochord, the axial pattern of maximal stiffness moments was congruent with the pattern of maximal notochordal curvature in the precaudal region, but in the caudal notochord maximal angular stiffness was located craniad to maximal curvature. One interpretation of this pattern is that the precaudal notochord resists bending moments generated by the muscles and that the caudal notochord resists bending moments generated by hydrodynamic forces acting on the tail.     

Axial allometry in a neutrally buoyant environment: effects of the terrestrial‐aquatic transition on vertebral scaling

Ecological diversification into new environments presents new mechanical challenges for locomotion. An extreme example of this is the transition from a terrestrial to an aquatic lifestyle. Here, we examine the implications of life in a neutrally buoyant environment on adaptations of the axial skeleton to evolutionary increases in body size. On land, mammals must use their thoracolumbar vertebral column for body support against gravity and thus exhibit increasing stabilization of the trunk as body size increases. Conversely, in water, the role of the axial skeleton in body support is reduced, and, in aquatic mammals, the vertebral column functions primarily in locomotion. Therefore, we hypothesize that the allometric stabilization associated with increasing body size in terrestrial mammals will be minimized in secondarily aquatic mammals. We test this by comparing the scaling exponent (slope) of vertebral measures from 57 terrestrial species (23 felids, 34 bovids) to 23 semi‐aquatic species (pinnipeds), using phylogenetically corrected regressions. Terrestrial taxa meet predictions of allometric stabilization, with posterior vertebral column (lumbar region) shortening, increased vertebral height compared to width, and shorter, more disc‐shaped centra. In contrast, pinniped vertebral proportions (e.g. length, width, height) scale with isometry, and in some cases, centra even become more spool‐shaped with increasing size, suggesting increased flexibility. Our results demonstrate that evolution of a secondarily aquatic lifestyle has modified the mechanical constraints associated with evolutionary increases in body size, relative to terrestrial taxa.     

Importance of mechanics and kinematics in determining the stiffness contribution of the vertebral column during body-caudal-fin swimming in fishes

Whole-body stiffness in fishes has important consequences for swimming mode, speed and efficiency, but the contribution of vertebral column stiffness to whole-body stiffness is unclear. In our opinion, this lack of clarity is due in part to the lack of studies that have measured both in vitro mechanical properties of the vertebral column as well as in vivo vertebral kinematics in the same species. Some lack of clarity may also come from real variation in the mechanical role of the vertebral column across species. Previous studies, based on either mechanics or kinematics alone, suggest species-specific variation in vertebral column locomotor function that ranges from highly stiff regimes that contribute greatly to whole-body stiffness, and potentially act as a spring, to highly compliant regimes that only prohibit excessive flexion of the intervertebral joints. We review data collected in combined investigations of both mechanics and kinematics of three species, Myxine glutinosa, Acipenser transmontanus, and Morone saxatilis, to illustrate how mechanical testing within the context of the in vivo kinematics more clearly distinguishes the role of the vertebral column in each species. In addition, we identify species for which kinematic data are available, but mechanical data are lacking. We encourage further investigation of these species to fill these mechanical data gaps. Finally, we hope these future combined analyses will identify certain morphological, mechanical, or kinematic parameters that might be associated with certain vertebral column functional regimes with respect to body stiffness.     

Tail development and regeneration throughout the life cycle of the four-toed salamander Hemidactylium scutatum

The salamander tail displays different functions and morphologies in the aquatic and terrestrial stages of species with complex life cycles. During metamorphosis the function of the tail changes; the larval tail functions in aquatic locomotion while the juvenile and adult tail exhibits tail autotomy and fat storage functions. Because tail injury is common in the aquatic environment, we hypothesized that mechanisms have evolved to prevent altered larval tail morphology from affecting normal juvenile tail morphology. The hypothesis that injury to the larval tail would not affect juvenile tail morphology was investigated by comparing tail development and regeneration in Hemidactylium scutatum (Caudata: Plethodontidae). The experimental design included larvae with uninjured tails and with cut tails to simulate natural predation. The morphological variables analyzed to compare normally developing and regenerating tails were 1) tail length, 2) number of caudal vertebrae, and 3) vertebral centrum length. Control and experimental groups do not differ in time to metamorphosis or snout-vent length. Tails of experimental individuals are shorter than controls, yet they display a significantly higher rate of tail growth and less resorption of tail tissue. Anterior to the site of tail injury, caudal vertebrae in juveniles display greater average centrum lengths. Results suggest that regenerative mechanisms are functioning not only to produce structures, but also to influence growth of existing structures. Further investigation of juvenile and adult stages as well as comparative analyses of tail morphology in salamanders with complex life cycles will enhance our understanding of amphibian development and of the evolution of amphibian life cycles. J Morphol 233:15–29, 1997. © 1997 Wiley-Liss, Inc.     

Jumping sans legs: does elastic energy storage by the vertebral column power terrestrial jumps in bony fishes?

Despite having no obvious anatomical modifications to facilitate movement over land, numerous small fishes from divergent teleost lineages make brief, voluntary terrestrial forays to escape poor aquatic conditions or to pursue terrestrial prey. Once stranded, these fishes produce a coordinated and effective “tail-flip” jumping behavior, wherein lateral flexion of the axial body into a C-shape, followed by contralateral flexion of the body axis, propels the fish into a ballistic flight-path that covers a distance of multiple body lengths. We ask: how do anatomical structures that evolved in one habitat generate effective movement in a novel habitat? Within this context, we hypothesized that the mechanical properties of the axial skeleton play a critical role in producing effective overland movement, and that tail-flip jumping species demonstrate enhanced elastic energy storage through increased body flexural stiffness or increased body curvature, relative to non-jumping species. To test this hypothesis, we derived a model to predict elastic recoil work from the morphology of the vertebral (neural and hemal) spines. From ground reaction force (GRF) measurements and high-speed video, we calculated elastic recoil work, flexural stiffness, and apparent material stiffness of the body for Micropterus salmoides (a non-jumper) and Kryptolebias marmoratus (adept tail-flip jumper). The model predicted no difference between the two species in work stored by the vertebral spines, and GRF data showed that they produce the same magnitude of mass-specific elastic recoil work. Surprisingly, non-jumper M. salmoides has a stiffer body than tail-flip jumper K. marmoratus. Many tail-flip jumping species possess enlarged, fused hypural bones that support the caudal peduncle, which suggests that the localized structures, rather than the entire axial skeleton, may explain differences in terrestrial performance.     

Inertial properties and loading rates affect buckling modes and injury mechanisms in the cervical spine

Cervical spine injuries continue to be a costly societal problem. Future advancements in injury prevention depend on improved physical and computational models which, in turn, are predicated on a better understanding of the responses of the neck during dynamic loading. Previous studies have shown that the tolerance of the neck is dependent on its initial position and its buckling behavior. This study uses a computational model to examine the mechanical factors influencing buckling behavior during impact to the neck. It was hypothesized that the inertial properties of the cervical spine influence the dynamics during compressive axial loading. The hypothesis was tested by performing parametric analyses of vertebral mass, mass moments of inertia, motion segment stiffness, and loading rate. Increases in vertebral mass resulted in increasingly complex kinematics and larger peak loads and impulses. Similar results were observed for increases in stiffness. Faster loading rates were associated with higher peak loads and higher-order buckling modes. The results demonstrate that mass has a great deal of influence on the buckling behavior of the neck, particularly with respect to the expression of higher-order modes. Injury types and mechanisms may be substantially altered by loading rate because inertial effects may influence whether the cervical spine fails in a compressive mode, or a bending mode.     

Embryonic development of the axial column in the little skate,Leucoraja erinacea

The morphological patterns and molecular mechanisms of vertebral column development are well understood in bony fishes (osteichthyans). However, vertebral column morphology in elasmobranch chondrichthyans (e.g., sharks and skates) differs from that of osteichthyans, and its development has not been extensively studied. Here, we characterize vertebral development in an elasmobranch fish, the little skate, Leucoraja erinacea , using microCT, paraffin histology, and whole‐mount skeletal preparations. Vertebral development begins with the condensation of mesenchyme, first around the notochord, and subsequently around the neural tube and caudal artery and vein. Mesenchyme surrounding the notochord differentiates into a continuous sheath of spindle‐shaped cells, which forms the precursor to the mineralized areolar calcification of the centrum. Mesenchyme around the neural tube and caudal artery/vein becomes united by a population of mesenchymal cells that condenses lateral to the sheath of spindle‐shaped cells, with this mesenchymal complex eventually differentiating into the hyaline cartilage of the future neural arches, hemal arches, and outer centrum. The initially continuous layers of areolar tissue and outer hyaline cartilage eventually subdivide into discrete centra and arches, with the notochord constricted in the center of each vertebra by a late‐forming “inner layer” of hyaline cartilage, and by a ring of areolar calcification located medial to the outer vertebral cartilage. The vertebrae of elasmobranchs are distinct among vertebrates, both in terms of their composition (i.e., with centra consisting of up to three tissues layers—an inner cartilage layer, a calcified areolar ring, and an outer layer of hyaline cartilage), and their mode of development (i.e., the subdivision of arch and outer centrum cartilage from an initially continuous layer of hyaline cartilage). Given the evident variation in patterns of vertebral construction, broad taxon sampling, and comparative developmental analyses are required to understand the diversity of mechanisms at work in the developing axial skeleton of vertebrates. J. Morphol. 278:300–320, 2017. © 2017 Wiley Periodicals, Inc.     

The composition of the caudal skeleton of teleosts (Actinopterygil: Osteichthyes)

The diural caudal skeleton of teleostean actinopterygians develops phylogeneticaily and ontogenetically from a polyural skeleton. The reduction of the polyural anlage to four, three, two or fewer centra in the adult caudal skeleton takes different pathways in different genera (e.g. compare Elops and Albula) and groups of teleosts. As a result, ural centra are not homologous throughout the teleosts. By numbering the ural centra in a homocercal tail in polyural fashion, one can demonstrate these and the following differences. The ventral elements (hypurals) always occur in sequential series, whereas the dorsal elements (epurals and uroneurals) may alter like the ural centra. The number of epurals, five or four in fossil primitive teleosts, is reduced in other primitive and advanced teleosts, but the same epurals are not always lost. The number of uroneurals, seven in fossil teleosts, is reduced in living teleosts, but it has not been demonstrated that the first uroneural is always derived from the neural arch of the same ural centrum. The landmark in the homocercal tail is the preural centrum I which can be identified by (1) bifurcation of the caudal artery and vein in its ventral element, the parhypural, (2) its position directly caudal to the preural centrum (PU2) which supports the lowermost principal caudal ray with its haemal spine, (3) carrying the third hypaxial element ventral to the course of arteria and vena pinnalis, and (4) by carrying the first haemal spine (parhypural) below the dorsal end of the ventral cartilage plate. The study of the development of the vertebral column reveals that teleosts have different patterns of centrum formation. A vertebral centrum is a complete or partial ring of mineralized, cartilaginous or bony material surrounding at least the lateral sides of the notochord. A vertebral centrum may be formed by arcocentrum alone, or arcocentral arcualia and chordacentrum, or arco-, chorda- and autocentrum, or arcocentral arcualia and autocentrum. This preliminary research demonstrates that a detailed ontogenetic interpretation of the vertebral centra and of the caudal skeleton of different teleosts may be useful tools for further interpretations of teleostean interrelationships.     

Modular evolution of the Cetacean vertebral column

Modular theory predicts that hierarchical developmental processes generate hierarchical phenotypic units that are capable of independent modification. The vertebral column is an overtly modular structure, and its rapid phenotypic transformation in cetacean evolution provides a case study for modularity. Terrestrial mammals have five morphologically discrete vertebral series that are now known to be coincident with Hox gene expression patterns. Here, I present the hypothesis that in living Carnivora and Artiodactyla, and by inference in the terrestrial ancestors of whales, the series are themselves components of larger precaudal and caudal modular units. Column morphology in a series of fossil and living whales is used to predict the type and sequence of developmental changes responsible for modification of that ancestral pattern. Developmental innovations inferred include independent meristic additions to the precaudal column in basal archaeocetes and basilosaurids, stepwise homeotic reduction of the sacral series in protocetids, and dissociation of the caudal series into anterior tail and fluke subunits in basilosaurids. The most dramatic change was the novel association of lumbar and anterior caudal vertebrae in a module that crosses the precaudal/caudal boundary. This large unit is defined by shared patterns of vertebral morphology, count, and size in all living whales (Neoceti).     

Morphology and Function of the Vertebral Column in Remingtonocetus domandaensis (Mammalia, Cetacea) from the Middle Eocene Domanda Formation of Pakistan

The archaeocete family Remingtonocetidae is a group of early cetaceans known from the Eocene of India and Pakistan. Previous studies of remingtonocetids focused primarily on cranial anatomy due to a paucity of well-preserved postcranial material. Here we describe the morphology of the known vertebral column in Remingtonocetus domandaensis based largely on a single well-preserved partial skeleton recovered from the upper Domanda Formation of Pakistan. The specimen preserves most of the precaudal vertebral column in articulation and includes seven complete cervical vertebrae, ten partial to complete thoracic vertebrae, six complete lumbar vertebrae, and the first three sacral vertebrae. Cervical centra are long and possess robust, imbricating transverse processes that stabilized the head and neck. Lumbar vertebrae allowed for limited flexibility and probably served primarily to stabilize the lumbar column during forceful retraction of the hind limbs. Vertebral evidence, taken together with pelvic and femoral morphology, is most consistent with interpretation of Remingtonocetus domandaensis as an animal that swam primarily by powerful movement of its hind limbs rather than dorsoventral undulation of its body axis.     

Features of the Changes in External Morphology and Axial Skeleton in Juvenile Salmonid Fishes (Salmonidae) Associated with Smoltification

Journal of Ichthyology - Changes in external morphological characters and relative lengths of vertebral centra from different regions of the vertebral column are analyzed during smoltification in...     

Caudal vertebral development and morphology in three salamanders with complex life cycles (Ambystoma jeffersonianum, Hemidactylium scutatum, and Desmognathus ocoee)

We describe caudosacral and caudal vertebral morphology across life history stages in three caudate amphibians: Ambystoma jeffersonianum (Ambystomatidae), Desmognathus ocoee (Plethodontidae: Desmognathinae), and Hemidactylium scutatum (Plethodontidae: Plethodontinae). All three species have aquatic larvae, but adults differ in habitat and predator defense strategy. Predator defense includes tail autotomy in D. ocoee and H. scutatum but not A. jeffersonianum. Of the species that autotomize, H. scutatum has a specialized constriction site at the tail base. We investigated whether aquatic larvae exhibit vertebral features similar to those previously described for aquatic adults and examined the effect of metamorphosis, if any, on vertebral morphology and the ontogeny of specialized vertebral features associated with tail autotomy. Interspecific comparisons of cleared-and-stained specimens indicate that vertebral morphology differs dramatically at hatching and that caudosacral and caudal vertebrae undergo continuous ontogenetic change throughout larval, metamorphic, and juvenile periods. Larvae and juveniles of H. scutatum do not exhibit adult vertebral features associated with constricted-base tail autotomy. The pond-type larvae of A. jeffersonianum and H. scutatum have tapering centrum lengths posterior to the sacrum. This pattern is functionally associated with aquatic locomotion. The stream-type larvae of D. ocoee undergo enhanced regional growth in the anterior tail such that the anterior caudal centra become longer than the preceding caudosacral centra. With the exception of the first two caudal vertebrae, a similar growth pattern occurs in H. scutatum adults. We hypothesize that enhanced growth of the anterior caudal segments is associated with tail elongation and autotomy.