Publications

Mammalian skeletons experience peak locomotor stresses (force per area) that are 25 to 50% of their failure strength, indicating a safety factor of between two and four. The mechanism by which animals achieve a constant safety factor varies depending on the size of the animal. Over much of their size (0.1 to 300 kilograms), larger mammals maintain uniform skeletal stress primarily by having a more upright posture, which decreases mass-specific muscle force by increasing muscle mechanical advantage. At greater sizes, increased skeletal allometry and decreased locomotor performance likely maintain stresses constant. At smaller sizes, skeletal stiffness may be more critical than strength. The decrease in mass-specific muscle force in mammals weighing 0.1 to 300 kilogram indicates that peak muscle stresses are also constant and correlates with a decrease in mass-specific energy cost of locomotion. The consistent pattern of locomotor stresses developed in long bones at different speeds and gaits within a species may have important implications for how bones adaptively remodel to changes in stress.

We measured the lengths and diameters of four long bones from 118 terrestrial carnivoran species using museum specimens. Though intrafamilial regressions scaled linearly, nearly all intraordinal regressions scaled non-linearly. The observed non-linear scaling of bone dimensions within this order results from a systematic decrease in intrafamilial allometric slope with increasing body size. A change in limb posture (more upright in larger species) to maintain similar peak bone stresses may allow the nearly isometric scaling of skeletal dimensions observed in smaller sized mammals (below about 100 kg). However, strong positive allometry is consistently observed in a number of large terrestrial mammals (the largest Carnivora, the large Bovidae, and the Ceratomorpha). This suggests that the capacity to compensate for size increases through alteration of limb posture is limited in extremely large-sized mammals, such that radical changes in bone shape are required to maintain similar levels of peak bone stress.

The slender elongated form that is characteristic of the forelimb long bones of gibbons (Hylobates) has long been attributed to their functional adaptation to habitual armswinging locomotion, although potential selective advantages of this morphology for brachiation have yet to be demonstrated. If the forces exerted on the limb skeleton during brachiation indeed differ greatly from those of other locomotor modes, then the changes in skeletal loading accompanying a shift in locomotor behaviour could favour alterations in skeletal morphology in brachiating lineages. In vivo skeletal strain patterns recorded by using radiotelemetry during brachiation indicate that the forelimb bones of the gibbon are loaded in substantial tension and show reduced bending and compression in comparison with those of other mammals. We suggest that this unique loading regime could have contributed to the evolution of the distinctive morphology of hylobatid limbs.

The scaling of bone and muscle geometry in mammals suggests that peak stresses (ratio of force to cross-sectional area) acting in these two support elements increase with increasing body size. Observations of stresses acting in the limb bones of different sized mammals during strenuous activity, however, indicate that peak bone stress is independent of size (maintaining a safety factor of between 2 and 4). It appears that similar peak bone stresses and muscle stresses in large and small mammals are achieved primarily by a size-dependent change in locomotor limb posture: small animals run with crouched postures, whereas larger species run more upright. By adopting an upright posture, large animals align their limbs more closely with the ground reaction force, substantially reducing the forces that their muscles must exert (proportional to body mass) and hence, the forces that their bones must resist, to counteract joint moments. This change in limb posture to maintain locomotor stresses within safe limits, however, likely limits the maneuverability and accelerative capability of large animals.

Terrestrial animals have 'preferred speeds' within each gait, that are used much more frequently than others for moving along the ground. Energy costs reach minimal values at these speeds within each gait. In this study we asked whether these speeds are mechanically equivalent among different animals (i.e. speeds where the same levels of peak muscle stress occur). If so, this would help in establishing a link between the energetics and the mechanics of the active muscles at these speeds, providing a first step in understanding why energy costs are minimal. We also asked whether peak muscle stress reaches a similar fraction of the maximal isometric stress at these speeds. If so, this would suggest that muscles are structured so that a similar reserve capacity remains, with a similar safety factor for avoidance of injury in response to prolonged repetitive loading. We compared two species that use quite different locomotory methods at their preferred speeds: white rats that gallop and kangaroo rats that hop. We measured peak stress in the ankle extensor muscles of these two species, as they moved at their preferred speeds, using a force platform/cine analysis technique. We also measured the maximum isometric force that this muscle group could develop in situ in the same individuals. We found the ankle extensors of white rats and kangaroo rats developed virtually identical levels of peak stress at their preferred speeds (70 +/- 6 kPa and 69 +/- 6 kPa, respectively, mean +/- S.E.), despite a fourfold difference in peak ground reaction force per unit body mass exerted on each limb. The values of peak isometric stress in situ were also virtually identical (206 +/- 17 kPa and 200 +/- 9 kPa, respectively). Our finding that the peak muscle stress is about one-third of maximum isometric stress at the preferred speeds is consistent with the idea that these are mechanically equivalent speeds, where the same fraction of available muscle fibres is recruited. Finding nearly identical values in two species that move in such different ways (galloping vs hopping), and have such large differences in ground reaction force exerted by each limb, suggests this may be true more generally for terrestrial vertebrates.

Mechanical stresses (force/cross-sectional area) acting in muscles, tendons and bones of the hindlimbs of kangaroo rats (Dipodomys spectabilis) were calculated during steady-speed hops and vertical jumps. Stresses were determined from both high-speed cine films (light and X-ray) and force plate recordings, as well as from in vivo tendon force recordings. Stresses in each hindlimb support element during hopping (1.6-3.1 m s-1) were generally only 33% of those acting during jumping (greater than or equal to 40 cm height): ankle extensor muscles, 80 +/- 12 (S.D.) versus 297 +/- 42 kPa; ankle extensor tendons, 7.9 +/- 1.5 versus 32.7 +/- 4.8 MPa; tibia, -29 +/- 5 versus -110 +/- 25 MPa (all values are for hopping versus jumping). The magnitude of stress in each structure during these locomotor activities was similarly matched to the strength of each element, so that a consistent safety factor to failure is achieved for the hindlimb as a whole (1.5-2.0). The large stresses during jumping were correlated with a three-fold increase in ground reaction forces exerted on the ground compared with the fastest steady hopping speeds. We conclude that, for its size, the kangaroo rat has disproportionately large hindlimb muscles, tendons and bones to withstand the large forces associated with rapid acceleration to avoid predation, which limits their ability to store and recover elastic strain energy. Middle ear morphology and behavioural observations of kangaroo rats jumping vertically to avoid predation by owls and rattlesnakes support this view.

The muscle forces and stresses occurring during normal locomotor activity in kangaroo rats are compared with the peak isometric force developed by the same muscles in situ. Two methods were used simultaneously to determine the stresses (force/cross-sectional area) acting in the ankle extensors during steady-speed hopping and during jumps when animals were startled: a direct measurement using a force buckle surgically implanted around a tendon; and an indirect measurement using a force platform/cine analysis technique. We obtained essentially the same values with the two techniques. We found that at slow speeds (0.7 m s-1) the ankle extensor muscles of kangaroo rats exerted 20% of the maximum isometric force developed when the muscles were stimulated via the tibial nerve. This increased to 53% at higher speeds (1.9 m s-1). At the animals's preferred hopping speed (1.5 m s-1), peak force was approximately 40% of maximum isometric force. In jumps when animals were startled, peak forces as high as 175% of the maximal elicited isometric force were recorded. These high forces always occurred when the muscles were being stretched. It appears that kangaroo rats utilize nearly the entire range of muscle force possible during normal locomotor events (i.e. up to 175% of maximum isometric force when muscles are stretched).

Nearly all long bones of terrestrial mammals that have been studied are loaded in bending. Yet bending requires greater bone mass than axial compression for effective support of equivalent static loads. Most long bones, in fact, are curved along their length; their curvature augmenting rather than diminishing stresses developed due to bending. The most "efficient" design of a bone (maximal strength per unit mass) should be a form which is straight and resists axial compression. Bone curvature and the bending developed in the long bones of most species studied, therefore, poses a paradox in design. However, under natural conditions an animal's skeleton must support a range of dynamic loads that vary in both direction and magnitude. Thus, improved predictability of dynamic loading should represent an important feature in the design of the bone, in addition to its absolute strength. We present an explanation of long bone curvature, based on the conditions of stability for bending vs. axial compression in a column, that describes this apparent design paradox as a mechanism for improving the predictability of loading direction (and, consequently, the pattern of stresses within the bone). Our hypothesis argues that in order to understand the design "effectiveness" of long bone shape the role of the bone as a structural unit must be redefined to one in which bone strength is optimized concurrently with loading predictability. In agreement with our hypothesis, bone curvature appears to meet this requirement.

Bone loading was quantified, using in vivo strain recordings, in the tibiotarsus of growing chicks at 4, 8, 12, and 17 weeks of age. The animals were exercised on a treadmill at 35% of their maximum running speed for 15 minutes/day. In vivo bone strains were recorded at six sites on the tibiotarsus. Percentages of the bone's length and a percentage of top running speed were used to define functionally equivalent sites on the bone, and a consistent exercise level over the period of growth was studied. The pattern of bone strain defined in terms of strain magnitude, sign, and orientation remained unchanged from 4-17 weeks of age, a period when bone mass and length increased 10-fold and threefold, respectively. Our findings support the hypothesis that bones model (and remodel) during growth to achieve and maintain a similar distribution of dynamic strains at functionally equivalent sites. Because strain magnitude and sign (tensile versus compressive) differed among recording sites, these data also suggest that cellular responses to strain-mediated stimuli differ from site to site within a bone.

Principal strains were recorded in vivo from the radial and tibial midshafts of three goats as they increased speed and changed gait. These data were compared with strain data measured for the radius and tibia of the dog (Rubin & Lanyon, 1982) and the horse (Biewener, Thomason & Lanyon, 1983b) in order to test the hypothesis that similar peak bone strains (stresses) occur at functionally equivalent points in the gaits of different species. Multiple recordings of in vivo strain along the caudal diaphyses of the radius and tibia of one goat were made to test the validity of this technique for measuring peak locomotor stress. Measured strains were extremely consistent over the animal's full range of speed (coefficient of variation for the radius 0.05-0.08, and for the tibia 0.06-0.11). The data from the three gauges, which were spaced 15 mm apart, demonstrated that maximal strains act at the midshaft, substantiating the use of this technique to measure peak locomotor bone strains. Strain levels recorded at the trot-gallop transition and top galloping speeds of the goat were similar to the values reported for the dog and horse, despite large differences in absolute speed (goat, 4.3 ms-1; dog, 6.9 ms-1; horse, 7.5 ms-1 at maximum gallop). The second moments of area of the tibia and radius (+ ulna) of the dog are 29% and 113% greater than for goats of equal size, explaining how similar strains are achieved in the dog at higher speeds than the goat. Furthermore, peak bone strains recorded at the fastest trotting speed were similar to those recorded at the fastest galloping speed for each species. Peak strains recorded for the goat at a maximum gallop correspond to stresses of +37.9 MPa (cranial) and -47.7 MPa (caudal) in the radius and +36.3 MPa (cranial) and -50.3 MPa (caudal) in the tibia, representing a safety factor to yield failure of three.

Cineradiographic study of the movement patterns of oropharyngeal and laryngeal structures during breathing and panting in dogs, correlated with recordings of expiratory and inspiratory airflow patterns (via thermocouples) at the nose and mouth show that the soft palate is the principal structural component regulating the path of respiratory in these animals. Cyclical movements of the soft palate during panting are accompanied by complementary movements of the posterior dorsum of the tongue (and epiglottis) to open and to close alternately the oropharynx and nasopharynx. The epiglottis appears to play a passive role during changes in airflow direction; its movements at this time being closely coupled to movements of the posterior tongue and hyoid. The dogs did not breathe during lapping or mastication, indicating the loss of functional separation of respiratory and feeding activities - a role traditionally held for the evolution of a secondary palate in mammals. Food stored in the posterior region of the oral cavity was observed to obstruct airflow via the nasopharynx during food transport and breakdown. Respiration commenced only after the food bolus had been swallowed. We suggest that specializations of the soft palate and epiglottis in dogs for thermal panting appear to restrict the formation of an adequate oropharyngeal seal during feeding.

Longitudinal stresses acting in the cranial and caudal cortices of the radius and the dorsal and palmar cortices of the metacarpus in the horse were determined using two independent methods simultaneously. One approach involved the use of rosette strain gauges to record in vivo bone strain; the other involved filming the position of the horse's forelimb as it passed over a force plate. Agreement between the two analyses was better for the radius than for the metacarpus. Both methods showed the radius to be loaded primarily in sagittal bending, acting to place the caudal cortex in compression and the cranial cortex in tension. At each gait the magnitude of peak stress in each cortex based on the film/force analysis was 1.5-2 times higher than that determined from the bone strain recordings. In the metacarpus, the magnitude of stress in each cortex calculated from the film/force method was 2-3 times greater at each gait than that shown by the bone strain recordings. However, whereas the film/force analysis indicated that the metacarpus was loaded in sagittal bending (acting to place the palmar cortex in compression and the dorsal cortex in tension), the bone strain recordings showed the metacarpus to be loaded primarily in axial compression at each gait. Because the film/force method depends on an accurate measure of limb segment orientation relative to the direction of ground reaction force, comparatively small errors in calculations of bending moments may lead to a significant difference in the level and distribution of stress determined to act in the bone's cortices. The discrepancy in metacarpal loading obtained by the two methods may be explained in part by the simplicity of the biomechanical model which, for instance, neglected the force exerted by the sesamoids on the distal end of the metacarpus. The records of stress determined from the in vivo bone strain recordings showed that each bone was subjected to a consistent loading regime despite changes of gait. Such a consistent strain distribution should allow these bones to maximize economy in the use of tissue required to support the dynamic loads applied. Peak stresses measured from the bone strain recordings in the radius during locomotion at constant speed (-40.8 +/- 4.1 MN m-2) were significantly larger than those in the metacarpus (-25.1 +/- 2.8 MN m-2), regardless of speed and gait. During acceleration and deceleration, however, peak stress rose dramatically in the metacarpus (-40.6 +/- 3.4 MN m-2) but remained constant in the radius (-37.8 +/- 5.8 MN m-2).(ABSTRACT TRUNCATED AT 400 WORDS)

Peak stresses acting in limb bones should increase with increasing size if the forces acting on the bones increase in direct proportion to the animal's body weight. This is a direct consequence of the scaling of limb bone geometry over a wide range in size in mammals. In addition, recent work has shown that the material strength of bone is similar in large and small animals. If the assumptions in this analysis are correct, large animals would have a lower safety factor to failure than small animals. The purpose of this study was to measure peak stresses acting in the limb bones of small animals during locomotion and compare the results with similar measurements available for larger animals. Locomotory stresses acting in the fore and hindlimb bones of two rodents, the ground squirrel (Spermophilus tridecemlineatus) and chipmunk (Tamais striatus), were calculated using ground force recordings and measurements of limb position taken from high speed x-ray cine films. Peak (compressive) stresses calculated to act in the bones of these animals (-31 to -86 MN/m2) are similar in magnitude to those determined for much larger mammals. The more proximal bones of the fore and hindlimb, the humerus and femur, were found to develop stresses (-31 to -42 MN/m2) significantly lower than those acting in the more distal bones of each limb: the radius, ulna and tibia (-58 to -86 MN/m2). All of the long bones from both species, except their femora, were found to be loaded principally in bending. The caudal cortices of each bone developed a peak compressive stress, whereas the cranial cortices were loaded in tension. Various features of the musculo-skeletal organization and manner of locomotion of these rodents are considered to explain how animals of different size maintain a uniform safety factor to failure.

Measurements of the chord length (alpha M0.31) and diameter (alpha M0.35) of the femora, tibiae, humeri and radii from 32 species of mammals, ranging in approximate body mass from 0.020-3500 kg, support previous data which show that mammalian long bones scale close to geometric similarity. Scaling of peak stresses based on these measurements of limb bone geometry predicts that peak stress increases alpha M0.28, assuming that the forces acting on a bone are directly proportional to an animal's weight. Peak locomotory stresses measured in small and large quadrupeds contradict this scaling prediction, however, showing that the magnitude of peak bone stress is similar over a range of size. Consequently, a uniform safety factor is maintained. Bone curvature (alpha M-0.09) and limb bone angle relative to the direction of ground force (alpha M-0.07) exhibit a slight, but significant, decrease with increasing body mass. Duty factor measured at the animal's trot--gallop transition speed does not change significantly with body size. The moment arm ratio of ground force to muscular force exerted about a joint was found to decrease dramatically for horses as compared to ground squirrels and chipmunks. This six-fold decrease (alpha M-0.23) provides preliminary data which appear to explain, along with the decrease in bone curvature and angle, the similar magnitudes of peak bone stress developed during locomotion in different sized animals. The crouched posture adopted by small quadrupeds while running may allow greater changes in momentum (when accelerating or decelerating) or a decrease in the forces exerted on their limbs.

Measurements of the cross-sectional geometry and length of bones from animals of different sizes suggest that peak locomotory stresses might be as much as nine times greater in the limb bones of a 300 kg horse than those of a 0.10 kg chipmunk. To determine if the bones of larger animals are stronger than those of small animals, the bending strength of whole bone specimens from the limbs of small mammals and bipedal birds was measured and compared with published data for large mammalian cortical bone (horses and bovids). No significant difference (P greater than 0.2) was found in the failure stress of bone over a range in size from 0.05-700 kg (233 +/- 53 MN/m2 for small animals compared to 200 +/- 28 MN/m2 for large animals). This finding suggests that either the limb bones of small animals are much stronger than they need to be, or that other aspects of locomotion (e.g. duty factor and limb orientation relative to the direction of the ground force) act to decrease peak locomotory stresses in larger animals.