Much of what we know about animal locomotion is derived from studies examining animals moving within a single, homogeneous environment, at a steady speed and along a flat grade. As a result, the issue of how musculoskeletal function might shift to accommodate variability within the external environment has remained relatively unexplored. One possibility is that locomotor muscles are differentially recruited depending upon the environment in which the animal is moving. A second possibility is that the same muscles are recruited, but that they are activated in a different manner so that their contractile function differs according to environment. Finally, it is also possible that, in some cases, animals may not need to alter their musculoskeletal function to move under different external conditions. In this case, however, the mechanical behavior appropriate for one environmental condition may constrain locomotor performance in another. To begin to explore the means by which animals accommodate variable conditions in their environment, we present three case studies examining how musculoskeletal systems function to allow locomotion under variable conditions: (1) eels undulating through water and across land, (2) turkeys running on level and inclined surfaces, and (3) ducks using their limbs to walk and to paddle. In all three of these examples, the mechanical behavior of some muscle(s) involved in locomotion are altered, although to different degrees and in different ways. In the running turkeys, the mechanical function of a major ankle extensor muscle shifts from contracting isometrically on a flat surface (producing little work and power), to shortening actively during contraction on an uphill gradient (increasing the amount of work and power generated). In the ducks, the major ankle extensor undergoes the same general pattern of activation and shortening in water and on land, except that the absolute levels of muscle stress and strain and work output are greater during terrestrial locomotion. In eels, a transition to land elicits changes in electromyographic duty cycles and the relative timing of muscle activation, suggesting some alteration in the functional mechanics of the underlying musculature. Only by studying muscle function in animals moving under more variable conditions can we begin to characterize the functional breadth of the vertebrate musculoskeletal system and understand more fully its evolutionary design.
The present study sought to answer two research questions. First, how distinctive, as a potential osteogenic stimulus, are short-duration bouts of treadmill exercise relative to sedentary background activity? Second, how well does daily effective strain stimulus relate the loading history for one such exercise program, in comparison with other experimental loading programs, to bone formation? In vivo cortical strains were measured in the tibiotarsus of White Leghorn chickens at a late stage of skeletal growth (14-34 weeks old) under the conditions of a previous investigation of bone formation in response to an exercise program (15 min/day, treadmill gait at 60% maximum speed while carrying 20% body mass) that included sedentary background activity. These strain data were compiled into 24-hour loading histories of peak cyclic strain, demonstrating that strains were statistically different for exercise and background activities (p < 0.0001), with both the magnitude and number of cyclic strain events being greater during exercise (generally greater than 500 microstrain, 2,500 cycles/day) than during background activity (generally less than 500 microstrain, mean: 775 cycles/day). Strains during exercise accounted for more than 97% of the daily effective strain stimulus for bone adaptation, despite the fact that exercise comprised only 1% of the daily period (15 min/day). The levels of the daily effective strain stimulus were similar to those calculated for strains engendered by artificial loading of functionally isolated avian ulnae, which either maintained bone mass or resulted in a 15% increase of cortical cross-sectional area in both sets of studies. These results indicate that short-duration bouts of treadmill exercise and sedentary background activity can represent distinct osteogenic stimuli for adaptive bone modeling. They also provide experimental support for the use of a daily effective strain stimulus to quantify skeletal loading histories for differing programs of physical exercise, although the relative importance of other mechanical and nonmechanical factors requires further investigation.
To evaluate the safety factor for flight feather shafts, in vivo strains were recorded during free flight from the dorsal surface of a variety of flight feathers of captive pigeons (Columba livia) using metal foil strain gauges. Strains recorded while the birds flew at a slow speed (approximately 5-6 m s-1) were used to calculate functional stresses on the basis of published values for the elastic modulus of feather keratin. These stresses were then compared with measurements of the failure stress obtained from four-point bending tests of whole sections of the rachis at a similar location. Recorded strains followed an oscillatory pattern, changing from tensile strain during the upstroke to compressive strain during the downstroke. Peak compressive strains were 2.2+/-0. 9 times (mean +/- s.d.) greater than peak tensile strains. Tensile strain peaks were generally not as large in more proximal flight feathers. Maximal compressive strains averaged -0.0033+/-0.0012 and occurred late in the downstroke. Bending tests demonstrated that feather shafts are most likely to fail through local buckling of their compact keratin cortex. A comparison of the mean (8.3 MPa) and maximum (15.7 MPa) peak stresses calculated from the in vivo strain recordings with the mean failure stress measured in four-point bending (137 MPa) yields a safety factor of between 9 and 17. Under more strenuous flight conditions, feather stresses are estimated to be 1.4-fold higher, reducing their safety factor to the range 6-12. These values seem high, considering that the safety factor of the humerus of pigeons has been estimated to be between 1.9 and 3.5. Several hypotheses explaining this difference in safety factor are considered, but the most reasonable explanation appears to be that flexural stiffness is more critical than strength to feather shaft performance.
Moderate to large macropodids can increase their speed while hopping with little or no increase in energy expenditure. This has been interpreted by some workers as resulting from elastic energy savings in their hindlimb tendons. For this to occur, the muscle fibers must transmit force to their tendons with little or no length change. To test whether this is the case, we made in vivo measurements of muscle fiber length change and tendon force in the lateral gastrocnemius (LG) and plantaris (PL) muscles of tammar wallabies Macropus eugenii as they hopped at different speeds on a treadmill. Muscle fiber length changes were less than +/-0.5 mm in the plantaris and +/-2.2 mm in the lateral gastrocnemius, representing less than 2 % of total fiber length in the plantaris and less than 6 % in the lateral gastrocnemius, with respect to resting length. The length changes of the plantaris fibers suggest that this occurred by means of elastic extension of attached cross-bridges. Much of the length change in the lateral gastrocnemius fibers occurred at low force early in the stance phase, with generally isometric behavior at higher forces. Fiber length changes did not vary significantly with increased hopping speed in either muscle (P>0.05), despite a 1. 6-fold increase in muscle-tendon force between speeds of 2.5 and 6.0 m s-1. Length changes of the PL fibers were only 7+/-4 % and of the LG fibers 34+/-12 % (mean +/- S.D., N=170) of the stretch calculated for their tendons, resulting in little net work by either muscle (plantaris 0.01+/-0.03 J; gastrocnemius -0.04+/-0.30 J; mean +/- s.d. ). In contrast, elastic strain energy stored in the tendons increased with increasing speed and averaged 20-fold greater than the shortening work performed by the two muscles. These results show that an increasing amount of strain energy stored within the hindlimb tendons is usefully recovered at faster steady hopping speeds, without being dissipated by increased stretch of the muscles' fibers. This finding supports the view that tendon elastic saving of energy is an important mechanism by which this species is able to hop at faster speeds with little or no increase in metabolic energy expenditure.
For the first time, we report in vivo measurements of pectoralis muscle length change obtained using sonomicrometry combined with measurements of its force development via deltopectoral crest strain recordings of a bird in free flight. These measurements allow us to characterize the contractile behavior and mechanical power output of the pectoralis under dynamic conditions of slow level flight in pigeons Columba livia. Our recordings confirm that the pigeon pectoralis generates in vivo work loops that begin with the rapid development of force as the muscle is being stretched or remains nearly isometric near the end of the upstroke. The pectoralis then shortens by a total of 32 % of its resting length during the downstroke, generating an average of 10.33.6 J kg-1 muscle (mean s.d.) of work per cycle for the anterior and posterior sites recorded among the five animals. In contrast to previous kinematic estimates of muscle length change relative to force development, the sonomicrometry measurements of fascicle length change show that force declines during muscle shortening. Simultaneous measurements of fascicle length change at anterior and posterior sites within the same muscle show significant (P<0.001, three of four animals) differences in fractional length (strain) change that averaged 1912 %, despite exhibiting similar work loop shape. Length changes at both anterior and posterior sites were nearly synchronous and had an asymmetrical pattern, with shortening occupying 63 % of the cycle. This nearly 2:1 phase ratio of shortening to lengthening probably favors the ability of the muscle to do work. Mean muscle shortening velocity was 5.381.33 and 4.881.27 lengths s-1 at the anterior and posterior sites respectively. Length excursions of the muscle were more variable at the end of the downstroke (maximum shortening), particularly when the birds landed, compared with highly uniform length excursions at the end of the upstroke (maximum lengthening). When averaged for the muscle as a whole, our in vivo work measurements yield a mass-specific net mechanical power output of 70. 2 W kg-1 for the muscle when the birds flew at 5-6 m s-1, with a wingbeat frequency of 8.7 Hz. This is 38 % greater than the value that we obtained previously for wild-type pigeons, but still 24-50 % less than that predicted by theory.
The stresses acting in muscle-tendon units and ligaments of the forelimb and hindlimb of horses were determined over a range of speed and gait based on recordings of ground reaction forces and limb kinematics. Maximum stresses of 40-50 MPa were calculated to act in several of the principal forelimb (superficial digital flexor (SDF), deep digital flexor (DDF), ulnaris lateralis (UL) and flexor carpi ulnaris/radialis (FCU/R)) and hindlimb tendons (plantaris, DDF) at the fastest galloping speeds recorded (up to 7.4 m s-1). Smaller stresses were found for the gastrocnemius (GAST) tendon (30 MPa) and suspensory ligaments (S-Ligs) (18-25 MPa). Average peak muscle stresses reached 200-240 kPa during galloping. Tendon and muscle stresses increased more steeply with changes of gait and during galloping, than during trotting. Calculations of elastic strain energy storage based on tendon stress showed similar patterns of increase with change of speed and gait, with the greatest contribution to elastic savings by the DDF tendons of the forelimb and hindlimb. In general, the hindlimb contributed two-thirds and the forelimb one-third to overall energy storage. Comparison of tendon elastic energy savings with mechanical work showed a maximum 40% recovery of mechanical work by elastic savings when the horses changed gait from a walk to a slow trot. Percentage of recovery then decreased with increased trotting speed, but increased again with a change of gait to a gallop, reaching 36% recovery at the fastest measured galloping speed (7.4 m s-1). The long length of horse tendons in relation to extremely short pennate muscle fibers suggests a highly specialized design for economical muscle force generation and enhanced elastic energy savings. However, elastic energy savings in terms of percentage of recovery of mechanical work and metabolic energy is less than that observed in wallabies and kangaroos during hopping, but similar to that in humans during running, and greater than that for dogs during trotting and galloping.
Principal strains and their orientation, determined from in vivo and in situ strains recorded from the lateral cortical surface of the calcaneus of potoroos (a small marsupial) during treadmill exercise and tension applied via the Achilles tendon, were compared with the underlying trabecular architecture and its alignment to test Wolff's "trajectorial theory" of trabecular alignment. In vivo and in situ principal compressive strains (-800 to -2000 mu e) were found to be aligned (mean 161 +/- 7 degrees) close to the preferred alignment (160 degrees) of underlying trabeculae within the calcaneal metaphysis [a second trabecular arcade was closely aligned (70 degrees) with the direction (71 degrees) of principal tensile strain]. This finding represents quantitative verification of Wolff's trajectorial theory of trabecular alignment. These trabecular alignments, as measured by trabecular anisotropy (TbAn, the ratio of horizontal: vertical intercepts), remained unchanged (p > 0.05) after 8 weeks of disuse. However, trabecular bone volume fraction (BV/TV, -35%), trabecular thickness (TbTh, -25%), and trabecular number (TbN, -16%) were reduced for the tenotomized calcaneii relative to their contralateral controls (p < 0.001 to < 0.003). The reduction in trabecular number was associated with a corresponding increase in trabecular spacing (TbSp, +30%). Together, these results suggest that once trabecular alignment is established during growth (along the directions of principal strain during locomotion), it is not altered when functional strains are removed.
The limbs of growing chicks (2-12 wk of age) were subjected to differing conditions of mechanical use to examine the effect of extrinsic loading on bone modeling early in postnatal growth. One group of chicks was subjected to intensive exercise by running on a treadmill 5 days/wk at 60% maximum speed while carrying on their trunk a load equal to 20% of body weight (EXER). In a second group, weight-bearing function was eliminated by sciatic denervation of one hindlimb at 2 wk of age (DNV). A third group grew under sedentary conditions (SED). Comparisons among groups were made on the basis of bone mass and length, cortical cross-sectional area and second moment of area, cortical thickness, longitudinal curvature, and % ash. After normalizing for growth-related differences in body mass among the three groups, we found that exercise led to an overall 16 +/- 13% increase in cortical cross-sectional area and a 26 +/- 21% increase in second moment of area measured at proximal, midshaft, and distal levels of the bone compared with values of SED animals. These increases in cortical geometry corresponded to a 10% increase in total bone mass and were generally established by 8 wk of age (6 wk of training) and maintained to 12 wk of age. When deprived of functional use, the growing bones of DNV animals were reduced in mass (-19%), cortical area (-8 +/- 7%), and second moment of area (-11 +/- 9%) compared with SED animals. DNV tibiotarsi were also significantly shorter (7% at 8 wk and 14% at 12 wk); however, the contralateral load-bearing tibiotarsus of the DNV animals was similarly reduced compared with SED and EXER animals, suggesting a general reduction of growth in the DNV group. Even more pronounced than the reductions in bone mass and area, however, were the loss of normal longitudinal curvature and an increase in the variability of cross-sectional shape and cortical thickness of the DNV tibiotarsi compared with SED and EXER animals.
Bones are believed to alter their shape in response to changes in tissue strains produced by physical activity and the goal of this study is to examine whether modeling responses of a growing bone to changes in physical exercise are adjusted to maintain a uniform distribution of functional strains. We test this idea by comparing in vivo strains recorded in the tibiotarsus of white leghorn chicks during 'intensive' treadmill exercise (60% of maximum speed, carrying a weight equal to 20% body weight on the trunk: 60%/L) with strains that had been recorded previously during 'moderate' treadmill exercise (35% of maximum speed, unloaded: 35%/UNL) at similar bone sites. Our hypothesis is that modeling adjustments of bones subjected to the intensive load-carrying exercise should re-establish strains recorded in the bones subjected to moderate exercise. At each exercise level, the animals were exercised for 5 days per week (2500 loading cycles per day) from 2 to 12 weeks of age. As in the moderate exercise group studied earlier, strains measured at six functionally equivalent sites on the tibiotarsus of the 60%/L group were consistently maintained during growth from 4 to 12 weeks of age. In addition, the pattern of strain recorded at these sites was uniformly maintained over the full range of speeds recorded (from 0.48 to 2.70 m s-1 at 12 weeks of age). Peak strains measured at 4 weeks of age in the load-carrying exercise group were initially elevated by 57% overall compared with peak strains recorded in the moderate exercise group. At 8 weeks of age, strain levels in the 60%/L group differed by only 4% overall compared with those recorded in the 35%/UNL group. The nature of strain (tensile versus compressive) and the orientation of principal strain at corresponding sites were also similar in the two groups. At 12 weeks of age, however, bone strain levels in the 60%/L group were again elevated (47% overall) compared with those recorded in the 35%/UNL group, although the general pattern and orientation of strains remained similar. This finding suggests a transient modeling response of the bone to the onset of exercise training, which was lost during subsequent growth, possibly because the normal pattern of functional strain was not altered significantly by the faster load-carrying exercise.
Functional in vivo strain data are examined in relation to bone material properties in an attempt to evaluate the relative importance of osteoporotic bone loss versus fatigue damage accumulation as factors underlying clinical bone fragility. Specifically, does the skeleton have a sufficiently large safety factor (ratio of bone failure strain to maximum functional strain) to require that fatigue damage accumulation is the main factor contributing to increased risk of fracture in the elderly? Existing methods limit in vivo strain measurements to the surfaces of cortical bone. Peak principal compressive strains measured at cortical sites during strenuous activity in various mammalian and avian species range from -1700 to -5200 mu epsilon, averaging -2500 mu epsilon (-0.0025 strain). Much of this threefold variation reflects differences in the intensity of physical activity, as well as differences among species and bones that have been studied. Peak strains can also vary as much as tenfold at different cortical sites within the same bone. No data exist for cortical bone strain during strenuous activity in humans, but it is likely that human bones experience a similar range of peak strain levels. Compact bone fails in longitudinal compression at strains as high as -14,000 to -21,000 mu epsilon, but begins to yield at strains between -6000 and -8000 mu epsilon. Given that yielding involves rapid accumulation of microdamage within the bone, it seems prudent to base skeletal safety factors on the yield strain, rather than the ultimate failure strain of bone tissue. Safety factors to yield failure therefore range from 1.4 to 4.1.(ABSTRACT TRUNCATED AT 250 WORDS)
In order to assess the mechanical properties of xenarthrous vertebrae, and to evaluate the role of xenarthrae as fossorial adaptations, in vitro bending tests were performed on posterior thoracic and lumbar vertebral segments excised from specimens of the armadillo Dasypus novemcinctus and the opossum Didelphis virginiana, the latter being used to represent the primitive mammalian condition. The columns of the two species were subjected to dorsal, ventral, and lateral bending, as well as torsion, in order to determine their stiffness in each of these directions. During these tests, bone strains in the centra of selected vertebrae were determined using rosette strain gages. Overall stiffness of the armadillo backbone at physiologically relevant displacement levels was significantly higher than that of the opossum for both dorsal and lateral bending. The two species also exhibited significant differences in angular displacement of individual vertebrae and in vertebral strain magnitudes and orientations in these two directions. No significant differences were observed when the columns of the two species were subjected to torsion or to ventral bending. Our results suggest that some, but not all, of the mechanical differences between the two species are due to the presence of xenarthrae. For example, removal of the xenarthrae from selected vertebrae (L2-L4) changes strain orientation and shear, but not strain magnitudes. Comparisons with functional data from other digging mammals indicate that the modified mechanical properties of the Dasypus column are consistent with an interpretation of xenarthrae as digging adaptations and lend support to the idea that the order Xenarthra represents an early offshoot of placental mammals specialized for fossoriality.
Irrespective of body size and phylogenetic diversity, the skeletal systems of terrestrial mammals are built of tissue components having similar mechanical properties and material organization. Because of scale effects on skeletal form, therefore, larger mammals increase the effective mechanical advantage of their limbs to decrease mass-specific forces associated with the support of gravitational loads imposed during locomotion to maintain a similar safety factor. Larger animals accomplish this by adopting a more upright posture while running, which aligns their limb joints more closely with the resultant ground reaction force, thereby decreasing the mass-specific force that their muscles must generate to support externally applied joint moments. As a result, peak (compressive) bone stresses determined from in vivo bone strain recordings and force platform and kinematic analyses of the limb generally range from -40 to -80 MPa (mean: -55 +/- 23 MPa), corresponding to a safety factor to compressive bone failure of about three to four. The decrease in mass-specific muscle force indicates that the maximum stresses developed in limb muscles of different sized species are also similar at equivalent levels of performance. Stresses developed in the midshafts of most long bones are primarily the result of bending, often engendered by axial forces transmitted about the bone's longitudinal curvature. The consistency of bending-induced skeletal strain over a range of physical activity and the associated expense of increased strain magnitude that this form of loading incurs suggest that functional strain patterns developed through bending may be a desirable architectural objective of most long bones. Alteration of a bone's normal functional strain distribution, therefore, is likely a key factor underlying adaptive remodeling in response to changes in mechanical loading.
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.