Russell P. Main

Biomechanics of quadrupedal walking: how do four-legged animals achieve inverted pendulum-like movements?

SUMMARY Walking involves a cyclic exchange of gravitational potential energy and kinetic energy of the center of mass. Our goal was to understand how the limbs of walking quadrupeds coordinate the vertical movements of the fore and hind quarters to produce these inverted pendulum-like movements. We collected kinematic and ground reaction force data from dogs walking over a range of speeds. We found that the fore and hind quarters of dogs behaved like two independent bipeds, each vaulting up and over its respective support limb. The center of mass moved up and down twice per stride, like a single walking biped, and up to 70% of the mechanical energy required to lift and accelerate the center of mass was recovered via the inverted pendulum mechanism. To understand how the limbs produce these center of mass movements, we created a simple model of two independent pendulums representing the movements of the fore and hind quarters. The model predicted that the fore and hind quarter movements would completely offset each other if the fore limb lagged the hind limb by 25% of the stride time and body mass was distributed equally between the fore and hind quarters. The primary reason that dogs did not walk with a flat trajectory of the center of mass was that each fore limb lagged its ipsilateral hind limb by only 15% of the stride time and thereby produced time periods when the fore and hind quarters moved up or down simultaneously. The secondary reason was that the fore limbs supported 63% of body mass. Consistent with these experimental results, the two-pendulum model predicts that the center of mass will undergo two fluctuations per stride cycle if limb phase is less than 25% and/or if the total mass is not distributed evenly between the fore or hind quarters.

The evolution and function of thyreophoran dinosaur scutes: implications for plate function in stegosaurs

Abstract The evolution of scutes in thyreophoran dinosaurs, based on Scutellosaurus, Scelidosaurus, Stegosaurus, and several ankylosaurs, began with small rounded or ovoid structures that typically had slight, anteroposteriorly oriented keels. These scutes were elaborated in two general and overlapping ways: they could flare laterally and asymmetrically beneath the keels that mark the anteroposterior axis, and they could be hypertrophied in their distal growth to produce plates, spikes, and other kinds of ornamentation. Stegosaurus plates and spikes are thus primarily hypertrophied keels of primitive thyreophoran scutes, sometimes with elaboration of dermal bone around their pustulate bases. Histologically, most thyreophoran scute tissues comprise secondary trabecular medullary bone that is sandwiched between layers of compact primary bone. Some scutes partly or mostly comprise anatomically metaplastic bone, that is, ossified fibrous tissue that shows incremental growth. The “plumbing” of Stegosaurus plates was not apparently built to support a “radiator” system of internal blood vessels that communicated with the outside of the plates and coursed along their external surfaces to return heated or cooled blood to the body core. Possibly a purely external system supported this function but there is no independent evidence for it. On the other hand, many of the vascular features in stegosaurian plates and spikes reflect bautechnisches artifacts of growth and production of bone. Surface vascular features likely supported bone growth and remodeling, as well as the blood supply to a keratinous covering. When the gross and microstructural features of the plates and spikes are viewed in phylogenetic context, no clear pattern of thermoregulatory function emerges, though an accessory role cannot be eliminated in certain individual species. It seems more likely, as in other groups of dinosaurs, that the variation of dermal armor form in stegosaurs was primarily linked to species individuation and recognition, perhaps secondarily to inter- and intraspecific display, and rarely to facultative thermoregulation.

Skeletal strain patterns and growth in the emu hindlimb during ontogeny

SUMMARY Most studies examining changes in mechanical performance in animals across size have typically focused on inter-specific comparisons across large size ranges. Scale effects, however, can also have important consequences in vertebrates as they increase in size and mass during ontogeny. The goal of this study was to examine how growth and development in the emu (Dromaius novaehollandiae) hindlimb skeleton reflects the demands placed upon it by ontogenetic changes in locomotor mechanics and body mass. Bone strain patterns in the femur and tibiotarsus (TBT) were related to ontogenetic changes in limb kinematics, ground reaction forces, and ontogenetic scaling patterns of the cross-sectional bone geometry, curvature and mineral ash content over a 4.4-fold increase in leg length and 65-fold increase in mass. Although the distribution of principal and axial strains remained similar in both bones over the ontogenetic size range examined, principal strains on the cranial femur and caudal femur and TBT increased significantly during growth. The ontogenetic increase in principal strains in these bones was likely caused by isometry or only slight positive allometry in bone cross-sectional geometry during growth, while relative limb loading remained similar. The growth-related increase in bone strain magnitude was likely mitigated by increased bone mineralization and decreased curvature. Throughout most of ontogeny, shear strains dominated loading in both bones. This was reflected in the nearly circular cross-sectional geometry of the femur and TBT, suggesting selection for resistance to high torsional loads, as opposed to the more eccentric cross-sectional geometries often associated with the bending common to tetrapods with parasagittal limb orientations, for which in vivo bone strains have typically been measured to date.

Diminished response to in vivo mechanical loading in trabecular and not cortical bone in adulthood of female C57Bl/6 mice coincides with a reduction in deformation to load☆

Bone loss occurs during adulthood in both women and men and affects trabecular bone more than cortical bone. The mechanism responsible for trabecular bone loss during adulthood remains unexplained, but may be due at least in part to a reduced mechanoresponsiveness. We hypothesized that trabecular and cortical bone would respond anabolically to loading and that the bone response to mechanical loading would be reduced and the onset delayed in adult compared to postpubescent mice. We evaluated the longitudinal adaptive response of trabecular and cortical bone in postpubescent, young (10 week old) and adult (26 week old) female C57Bl/6J mice to axial tibial compression using in vivo microCT (days 0, 5, 10, and 15) and dynamic histomorphometry (day 15). Loading elicited an anabolic response in both trabecular and cortical bone in young and adult mice. As hypothesized, trabecular bone in adult mice exhibited a reduced and delayed response to loading compared to the young mice, apparent in trabecular bone volume fraction and architecture after 10 days. No difference in mechanoresponsiveness of the cortical bone was observed between young and adult mice. Finite element analysis showed that load-induced strain was reduced with age. Our results suggest that trabecular bone loss that occurs in adulthood may in part be due to a reduced mechanoresponsiveness in this tissue and/or a reduction in the induced tissue deformation which occurs during habitual loading. Therapeutic approaches that address the mechanoresponsiveness of the bone tissue may be a promising and alternate strategy to maintain trabecular bone mass during aging.

Tibial compression is anabolic in the adult mouse skeleton despite reduced responsiveness with aging

The ability of the skeleton to adapt to mechanical stimuli diminishes with age in diaphyseal cortical bone, making bone formation difficult for adults. However, the effect of aging on adaptation in cancellous bone, tissue which is preferentially lost with age, is not well characterized. To develop a model for early post-menopausal women and determine the effect of aging on cancellous bone adaptation in the adult mouse skeleton, in vivo tibial compression was applied to adult (26 week old) osteopenic female mice using loading parameters, peak applied load and peak diaphyseal strain magnitude, that were previously found to be osteogenic in young, growing (10 week old) mice. A Load-Matched group received the same peak applied loads (corresponding to +2100 με at the medial diaphysis of the tibia) and a Strain-Matched group received the same peak diaphyseal strains (+1200 με, requiring half the load) as the young mice. The effects of mechanical loading on bone mass and architecture in adult mice were assessed using micro-computed tomography and in vivo structural stiffness measures. Adaptation occurred only in the Load-Matched group in both the metaphyseal and diaphyseal compartments. Cancellous bone mass increased 54% through trabecular thickening, and cortical area increased 41% through medullary contraction and periosteal expansion. Adult mice were able to respond to an anabolic stimulus and recover bone mass to levels seen in growing mice; however, the adaptive response was reduced relative to that in 10 week old female mice for the same applied load. Using this osteogenic loading protocol, other factors affecting pathological bone loss can be addressed using an adult osteopenic mouse model.

Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius

SUMMARY As tetrapods increase in size and weight through ontogeny, the limb skeleton must grow to accommodate the increases in body weight and the resulting locomotor forces placed upon the limbs. No study to date, however, has examined how morphological changes in the limb skeleton during growth reflect ontogenetic patterns of limb loading and the resulting stresses and strains produced in the limbs. The goal of this study was to relate forelimb loads to in vivo bone strains in the radius of the domestic goat (Capra hircus) across a range of gaits and speeds through ontogeny while observing how the growth patterns of the bone relate to the mechanics of the limb. In vivo bone strains in the radius were recorded from two groups of juvenile goats (4 kg, 6 weeks and 9 kg, 15 weeks) and compared with previously reported strain data for the radius of adult goats. Ontogenetic strain patterns were examined in relation to peak forelimb ground reaction forces, ontogenetic scaling patterns of cross-sectional geometry and bone curvature, and percentage mineral ash content. Peak principal longitudinal tensile strains on the cranial surface and compressive strains on the caudal surface of the radius increased during ontogeny but maintained a uniform distribution, resulting in the radius being loaded primarily in bending through ontogeny. The increase in strain occurred despite uniform loading (relative to body weight) of the forelimb through ontogeny. Instead, the increase in bone strain resulted from strong negative growth allometry of the cross-sectional area (∝M0.53) and medio-lateral and cranio-caudal second moments of area (IML∝M1.03, ICC∝M0.84) of the radius and only a small increase (+2.8%) in mineral ash content. Even though bone strains increased with growth and age, strains in the younger goats were small enough to suggest that they maintain safety factors at least comparable with adults when moving at similar absolute speeds. Increased variability of loading in juvenile animals may also favor the more robust dimensions of the radius, and possibly other limb bones, early in growth.

Cancellous bone adaptation to tibial compression is not sex dependent in growing mice

Mechanical loading can be used to increase bone mass and thus attenuate pathological bone loss. Because the skeletons adaptive response to loading is most robust before adulthood, elucidating sex-specific responses during growth may help maximize peak bone mass. This study investigated the effect of sex on the response to controlled, in vivo mechanical loading in growing mice. Ten-week-old male and female C57Bl/6 mice underwent noninvasive compression of the left tibia. Peak loads of -11.5 N were applied, corresponding to +1,200 microepsilon at the tibial midshaft in both sexes. Cancellous bone mass, architecture, and dynamic formation in the proximal metaphysis were compared between loaded and control limbs via micro-computed tomography and histomorphometry. The strain environment of the proximal metaphysis during loading was characterized using finite element analysis. Both sexes responded to tibial compression through increased bone mass and altered architecture. Cancellous bone mass and tissue density were enhanced in loaded limbs relative to control limbs in both sexes through trabecular thickening and reduced separation. Changes in mass were due to increased cellular activity in loaded limbs compared with control limbs. Adaptation to loading increased the proportion of load transferred by the cancellous bone in the proximal metaphysis. For all cancellous measures, the response to tibial compression did not differ between male and female mice. When similar strains are engendered in males and females, the adaptive response in cancellous bone to mechanical loading does not depend on sex.

Female mice lacking estrogen receptor-alpha in osteoblasts have compromised bone mass and strength.

Reduced bioavailability of estrogen increases skeletal fracture risk in postmenopausal women, but the mechanisms by which estrogen regulates bone mass are incompletely understood. Because estrogen signaling in bone acts, in part, through estrogen receptor alpha (ERα), mice with global deletion of ERα (ERαKO) have been used to determine the role of estrogen signaling in bone biology. These animals, however, have confounding systemic effects arising from other organs, such as increased estrogen and decreased insulin‐like growth factor 1 (IGF‐1) serum levels, which may independently affect bone. Mice with tissue‐specific ERα deletion in chondrocytes, osteoblasts, osteocytes, or osteoclasts lack the systemic effects seen in the global knockout, but show that presence of the receptor is important for the function of each cell type. Although bone mass is reduced when ERα is deleted from osteoblasts, no study has determined if this approach reduces whole bone strength. To address this issue, we generated female osteoblast‐specific ERαKO mice (pOC‐ERαKO) by crossing mice expressing a floxed ERα gene (ERαfl/fl) with mice transgenic for the osteocalcin‐Cre promoter (OC‐Cre). Having confirmed that serum levels of estrogen and IGF‐1 were unaltered, we focused on relating bone mechanics to skeletal phenotype using whole bone mechanical testing, microcomputed tomography, histology, and dynamic histomorphometry. At 12 and 18 weeks of age, pOC‐ERαKO mice had decreased cancellous bone mass in the proximal tibia, vertebra, and distal femur, and decreased cortical bone mass in the tibial midshaft, distal femoral cortex, and L5 vertebral cortex. Osteoblast activity was reduced in cancellous bone of the proximal tibia, but osteoclast number was unaffected. Both femora and vertebrae had decreased whole bone strength in mechanical tests to failure, indicating that ERα in osteoblasts is required for appropriate bone mass and strength accrual in female mice. This pOC‐ERαKO mouse is an important animal model that could enhance our understanding of estrogen signaling in bone cells in vivo.

In vivo cranial suture function and suture morphology in the extant fish Polypterus: implications for inferring skull function in living and fossil fish.

SUMMARY This study describes the mechanical role that cranial sutures play in fish during feeding. The long-term goal of our work is to establish relationships between suture form and function, so that functional inferences can be made from suture morphology in fossil taxa. To this end, strain gauges were surgically implanted across selected sutures in the skull roof of four individuals of Polypterus endlicherii. After surgery, bone and suture strains during feeding were recorded along with high-speed video of the feeding events. Each trial was designated as a suction feeding or biting on prey trial, and neurocranial elevation, hyoid position and gape were quantified to aid in interpreting the strain data. The strains due to suction feeding are different from those observed during biting. Suction feeding results in a fairly stereotyped strain pattern, with the interfrontal and frontoparietal sutures experiencing tension, while the interparietal suture is compressed. Biting causes much more variable strain patterns. However, both suction and biting result in compression in the back of the skull, and tension between the frontals. Peak strains, and the time at which they occur in the feeding cycle, were compared between suction and biting. In general, peak suture strains are higher during suction than during biting, but not all of these differences are significant. Peak suture and bone strains occur at or near maximum gape during both suction and biting, suggesting that these strains are caused by muscle contraction involved in mouth opening and closing. Micro-computed tomography (microCT) scans of the experimental specimens indicate that the interfrontal and frontoparietal sutures, typically loaded in tension, are less interdigitated in cross section than the interparietal suture, which experiences compression. This is consistent with published correlations of suture form and function in mammals, where interdigitated sutures indicate compression and lack of interdigitation is associated with tension.

Characterization of cancellous and cortical bone strain in the in vivo mouse tibial loading model using microCT-based finite element analysis

The in vivo mouse tibial loading model has been increasingly used to understand the mechanisms governing the mechanobiological responses of cancellous and cortical bone tissues to physical stimuli. Accurate characterization of the strain environment throughout the tibia is fundamental in relating localized mechanobiological processes to specific strain stimuli in the skeleton. MicroCT-based finite element analysis, together with diaphyseal strain gauge measures, was conducted to quantify the strain field in the tibiae of 16-wk-old female C57Bl/6 mice during in vivo dynamic compressive loading. Despite a strong correlation between the experimentally-measured and computationally-modeled strains at the gauge site, no correlations existed between the strain at the gauge site and the peak strains in the proximal cancellous and midshaft cortical bone, indicating the limitations of using a single diaphyseal strain gauge to estimate strain in the entire tibia. The peak compressive and tensile principal strain magnitudes in the proximal cancellous bone were 10% and 34% lower than those in the midshaft cortical bone. Sensitivity analyses showed that modeling bone tissue as a heterogeneous material had a strong effect on cancellous strain characterization while cortical strain and whole-bone stiffness were primarily affected by the presence of the fibula and the proximal boundary conditions. These results show that microCT-based finite element analysis combined with strain gauge measures provides detailed resolution of the tissue-level strain in both the cancellous and cortical bones of the mouse tibia during in vivo compression loading, which is necessary for interpreting localized patterns of modeling/remodeling and, potentially, gene and protein expression in skeletal mechanobiology studies.