Loading Rate Has Little Influence on Tendon Fascicle Mechanics.

Mechanically, tendons behave like springs and store energy by stretching in proportion to applied stress. This relationship is potentially modified by the rate at which stress is applied, a phenomenon known as viscosity. Viscoelasticity, the combined effects of elasticity and viscosity, can affect maximum strain, the amount of stored energy, and the proportion of energy recovered (resilience). Previous studies of tendons have investigated the functional effects of viscoelasticity, but not at the intermediate durations of loading that are known to occur in fast locomotor events. In this study, we isolated tendon fascicles from rat tails and performed force-controlled tensile tests at rates between ∼10 MPa s-1 to ∼80 MPa s-1. At high rates of applied stress, we found that tendon fascicles strained less, stored less energy, and were more resilient than at low rates of stress (p = 0.007, p = 0.040, and p = 0.004, respectively). The measured changes, however, were very small across the range of strain rates studied. For example, the average strain for the slowest loading rate was 0.637% while it was 0.614% for the fastest loading. We conclude that although there is a measurable effect of loading rate on tendon mechanics, the effect is small and can be largely ignored in the context of muscle-actuated locomotion, with the possible exception of extreme muscle-tendon morphologies.

Playing with Power: Mechanisms of Energy Flow in Organismal Movement.

Across multiple evolutionary clades and size scales, organismal movement requires controlling the flow of energy through the body to enhance certain functions. Whether energy is released or absorbed by the organism, proper function hinges on the ability to manipulate both where and when energy is transferred. For example, both power amplification and power attenuation rely on the use of springs for the intermediate storage of energy between the body and the environment; but variation in function is the result of the path and timing of energy flow. In this symposium, we have invited speakers that demonstrate the diversity of mechanisms used to control the flow of energy through the body and into the environment. By bringing together researchers investigating movements in the context of power and energy flow, the major goal of this symposium is to facilitate fresh perspectives on the unifying mechanical themes of energy transfer in organismal movement.

Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement.

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.

How do baleen whales stow their filter? A comparative biomechanical analysis of baleen bending.

Bowhead and right whale (balaenid) baleen filtering plates, longer in vertical dimension (≥3-4 m) than the closed mouth, presumably bend during gape closure. This has not been observed in live whales, even with scrutiny of video-recorded feeding sequences. To determine what happens to the baleen during gape closure, we conducted an integrative, multifactorial study including materials testing, functional (flow tank and kinematic) testing and histological examination. We measured baleen bending properties along the dorsoventral length of plates and anteroposterior location within a rack of plates via mechanical (axial bending, composite flexure, compression and tension) tests of hydrated and air-dried tissue samples from balaenid and other whale baleen. Balaenid baleen is remarkably strong yet pliable, with ductile fringes, and low stiffness and high elasticity when wet; it likely bends in the closed mouth when not used for filtration. Calculation of flexural modulus from stress/strain experiments shows that the balaenid baleen is slightly more flexible where it emerges from the gums and at its ventral terminus, but kinematic analysis indicates plates bend evenly along their whole length. Fin and humpback whale baleen has similar material properties but less flexibility, with no dorsoventral variation. The internal horn tubes have greater external and hollow luminal diameter but lower density in the lateral relative to medial baleen of bowhead and fin whales, suggesting a greater capacity for lateral bending. Baleen bending has major consequences not only for feeding morphology and energetics but also for conservation given that entanglement in fishing gear is a leading cause of whale mortality.

Hydration affects the physical and mechanical properties of baleen tissue.

Baleen, an anisotropic oral filtering tissue found only in the mouth of mysticete whales and made solely of alpha-keratin, exhibits markedly differing physical and mechanical properties between dried or (as in life) hydrated states. On average baleen is 32.35% water by weight in North Atlantic right whales (Eubalaena glacialis) and 34.37% in bowhead whales (Balaena mysticetus). Baleen's wettability measured by water droplet contact angles shows that dried baleen is hydrophobic whereas hydrated baleen is highly hydrophilic. Three-point flexural bending tests of mechanical strength reveal that baleen is strong yet ductile. Dried baleen is brittle and shatters at about 20-30 N mm-2 but hydrated baleen is less stiff; it bends with little force and absorbed water is squeezed out when force is applied. Maximum recorded stress was 4× higher in dried (mean 14.29 N mm-2) versus hydrated (mean 3.69 N mm-2) baleen, and the flexural stiffness was >10× higher in dried (mean 633N mm-2) versus hydrated (mean 58 N mm-2) baleen. In addition to documenting hydration's powerful effects on baleen, this study indicates that baleen is far more pliant and malleable than commonly supposed, with implications for studies of baleen's structure and function as well as its susceptibility to oil or other hydrophobic pollutants.

Joined at the hip: linked characters and the problem of missing data in studies of disparity.

Paleontological investigations into morphological diversity, or disparity, are often confronted with large amounts of missing data. We illustrate how missing discrete data affect disparity using a novel simulation for removing data based on parameters from published datasets that contain both extinct and extant taxa. We develop an algorithm that assesses the distribution of missing characters in extinct taxa, and simulates data loss by applying that distribution to extant taxa. We term this technique "linkage." We compare differences in disparity metrics and ordination spaces produced by linkage and random character removal. When we incorporated linkage among characters, disparity metrics declined and ordination spaces shrank at a slower rate with increasing missing data, indicating that correlations among characters govern the sensitivity of disparity analysis. We also present and test a new disparity method that uses the linkage algorithm to correct for the bias caused by missing data. We equalized proportions of missing data among time bins before calculating disparity, and found that estimates of disparity changed when missing data were taken into account. By removing the bias of missing data, we can gain new insights into the morphological evolution of organisms and highlight the detrimental effects of missing data on disparity analysis.

Gearing for speed slows the predatory strike of a mantis shrimp.

The geometry of an animal's skeleton governs the transmission of force to its appendages. Joints and rigid elements that create a relatively large output displacement per unit input displacement have been considered to be geared for speed, but the relationship between skeletal geometry and speed is largely untested. The present study explored this subject with experiments and mathematical modeling to evaluate how morphological differences in the raptorial appendage of a mantis shrimp (Gonodactylus smithii) affect the speed of its predatory strike. Based on morphological measurements and material testing, we computationally simulated the transmission of the stored elastic energy that powers a strike and the drag that resists this motion. After verifying the model's predictions against measurements of strike impulse, we conducted a series of simulations that varied the linkage geometry, but were provided with a fixed amount of stored elastic energy. We found that a skeletal geometry that creates a large output displacement achieves a slower maximum speed of rotation than a low-displacement system. This is because a large displacement by the appendage causes a relatively large proportion of its elastic energy to be lost to the generation of drag. Therefore, the efficiency of transmission from elastic to kinetic energy mediates the relationship between the geometry and the speed of a skeleton. We propose that transmission efficiency plays a similar role in form-function relationships for skeletal systems in a diversity of animals.