An investigation of the interactions between lower-limb bone morphology, limb inertial properties and limb dynamics

A comparative study of trabecular bone mass distribution in cursorial and non-cursorial limb joints

Skeletal design among cursorial animals is a compromise between a stable body that can withstand locomotor stress and a light design that is energetically inexpensive to grow, maintain, and move. Cursors have been hypothesized to reduce distal musculoskeletal mass to maintain a balance between safety and energetic cost due to an exponential increase in energetic demand observed during the oscillation of the distal limb. Additionally, experimental research shows that the cortical bone in distal limbs experiences higher strains and remodeling rates, apparently maintaining lower mass at the expense of a smaller safety factor. This study tests the hypothesis that the trabecular bone mass in the distal limb epiphyses of cursors is relatively lower than that in the proximal limb epiphyses to minimize the energetic cost of moving the limb. This study utilized peripheral quantitative computed tomography scanning to measure the trabecular mass in the lower and upper limb epiphyses of hominids, cercopithecines, and felids that are considered cursorial and non-cursorial. One-way ANOVA with Tukey post hoc corrections was used to test for significant differences in trabecular mass across limb epiphyses. The results indicate that overall, both cursors and non-cursors exhibit varied trabecular mass in limb epiphyses and, in certain instances, conform to a proximal-distal decrease in mass irrespective of cursoriality. Specifically, hominid and cercopithecine hind limb epiphyses exhibit a proximal-distal decrease in mass irrespective of cursorial adaptations. These results suggest that cursorial mammals employ other energy saving mechanisms to minimize energy costs during running.

Intracortical remodeling parameters are associated with measures of bone robustness

Prior work identified a novel association between bone robustness and porosity, which may be part of a broader interaction whereby the skeletal system compensates for the natural variation in robustness (bone width relative to length) by modulating tissue-level mechanical properties to increase stiffness of slender bones and to reduce mass of robust bones. To further understand this association, we tested the hypothesis that the relationship between robustness and porosity is mediated through intracortical, BMU-based (basic multicellular unit) remodeling. We quantified cortical porosity, mineralization, and histomorphometry at two sites (38% and 66% of the length) in human cadaveric tibiae. We found significant correlations between robustness and several histomorphometric variables (e.g., % secondary tissue [R(2)  = 0.68, P < 0.004], total osteon area [R(2)  = 0.42, P < 0.04]) at the 66% site. Although these associations were weaker at the 38% site, significant correlations between histological variables were identified between the two sites indicating that both respond to the same global effects and demonstrate a similar character at the whole bone level. Thus, robust bones tended to have larger and more numerous osteons with less infilling, resulting in bigger pores and more secondary bone area. These results suggest that local regulation of BMU-based remodeling may be further modulated by a global signal associated with robustness, such that remodeling is suppressed in slender bones but not in robust bones. Elucidating this mechanism further is crucial for better understanding the complex adaptive nature of the skeleton, and how interindividual variation in remodeling differentially impacts skeletal aging and an individuals' potential response to prophylactic treatments.

Structural analysis of the human tibia by tomographic (pQCT) serial scans

This study analyses the evaluation of tomographic indicators of tibia structure, assuming that the usual loading pattern shifts from uniaxial compression close to the heel to a combined compression, torsion and bending scheme towards the knee. To this end, pQCT scans were obtained at 5% intervals of the tibia length (S5-S95 sites from heel to knee) in healthy men and women (10/10) aged 20-40 years. Indicators of bone mass [cortical area, cortical/total bone mineral content (BMC)], diaphyseal design (peri/endosteal perimeters, cortical thickness, circularity, bending/torsion moments of inertia - CSMIs), and material quality [(cortical vBMD (bone mineral density)] were determined. The longitudinal patterns of variation of these measures were similar between genders, but male values were always higher except for cortical vBMD. Expression of BMC data as percentages of the minimal values obtained along the bone eliminated those differences. The correlative variations in cortical area, BMC and thickness, periosteal perimeter and CSMIs along the bone showed that cortical bone mass was predominantly associated with cortical thickness toward the mid-diaphysis, and with bone diameter and CSMIs moving more proximally. Positive relationships between CSMIs (y) and total BMC (x) showed men's values shifting to the upper-right region of the graph and women's values shifting to the lower-left region. Total BMC decayed about 33% from S5 to S15 (where minimum total BMC and CSMI values and variances and maximum circularity were observed) and increased until S45, reaching the original S5 value at S40. The observed gender-related differences reflected the natural allometric relationships. However, the data also suggested that men distribute their available cortical mass more efficiently than women. The minimum amount and variance of mass indicators and CSMIs, and the largest circularity observed at S15 reflected the assumed adaptation to compression pattern at that level. The increase in CSMIs (successively for torsion, A-P bending, and lateral bending), the decrease in circularity values and the changes in cortical thickness and periosteal perimeter toward the knee described the progressive adaptation to increasing torsion and bending stresses. In agreement with the biomechanical background, the described relationships: (i) identify the sites at which some changes in tibial stresses and diaphyseal structure take place, possibly associated with fracture incidence; (ii) allow prediction of mass indicators at any site from single determinations; (iii) establish the proportionality between the total bone mass at regions with highly predominant trabecular and cortical bone of the same individual, suitable for a specific evaluation of changes in trabecular mass; and (iv) evaluate the ability of bone tissue to self-distribute the available cortical bone according to specific stress patterns, avoiding many anthropometric and gender-derived influences.

Bone modeling response to voluntary exercise in the hindlimb of mice

The functional adaptation of juvenile mammalian limb bone to mechanical loading is necessary to maintain bone strength. Diaphyseal size and shape are modified during growth through the process of bone modeling. Although bone modeling is a well-documented response to increased mechanical stress on growing diaphyseal bone, the effect of proximodistal location on bone modeling remains unclear. Distal limb elements in cursorial mammals are longer and thinner, most likely to conserve energy during locomotion because they require less energy to move. Therefore, distal elements are hypothesized to experience greater mechanical loading during locomotion and may be expected to exhibit a greater modeling response to exercise. In this study, histomorphometric comparisons are made between femora and tibiae of mice treated with voluntary exercise and a control group (N = 20). We find that femora of exercised mice exhibit both greater bone growth rates and growth areas than do controls (P < 0.05). The femora of exercised mice also have significantly greater cortical area, bending rigidity, and torsional rigidity (P < 0.05), although bending and torsional rigidity are comparable when standardized by bone length. Histomorphometric and cross-section geometric properties of the tibial midshaft of exercised and control mice did not differ significantly, although tibial length was significantly greater in exercised mice (P < 0.05). Femora of exercised mice were able to adapt to increased mechanical loading through increases in compressive, bending, and torsional rigidity. No such adaptations were found in the tibia. It is unclear if this is a biomechanical adaptation to greater stress in proximal elements or if distal elements are ontogenetically constrained in a tradeoff of bone strength of distal elements for bioenergetic efficiency during locomotion.

Variation in cortical bone histology within the human femur and its impact on estimating age at death

Histological methods for the estimation of age at death using cortical bone are based on the evaluation of microstructural changes over time. Since histological analysis is a destructive method, most techniques attempt to limit the amount of cortical bone needed for analysis. Sample location, however, can have a significant effect on the accuracy of these methods. Furthermore, research demonstrates that both intersection and intrasection variation is present at the midshaft of the femur, which is the primary location for estimating age at death in humans. This research determines the extent of regional variation within the adult human femur and its effect on age estimation. Secondary osteon lamellae and Haversian canal ratio and cortical thickness were quantified. Thompson's All Males Left Femur regression equation was used to estimate age. Results show that significant regional variation occurs in the estimated ages derived from the posterior aspect of the femoral shaft and significant intrasection variation occurs in age estimates from the mid and mid-distal cross-sections. Thus, the inter and intrasection variation that occurs in bone remodeling within the femoral cortex has the potential to produce significant differences amongst age estimates taken from various femoral diaphyseal locations compared to the age estimated from the standard location used in Thompson's core method (1978). The results indicate that the use of this histological method is dependant on the ability to correctly identify the four anatomical locations, but the extracted core used for age estimation is not necessarily confined to the anterior midshaft.

Modeling and remodeling responses to normal loading in the human lower limb

Limb bones are designed to be strong enough to support the body and yet be energetically conservative during locomotion. Bones of the distal segment, which are relatively costly to move, are often more slender than bones of the proximal segments, even though they must sustain proportionally greater loads. As a result, they are expected to experience a higher incidence of microdamage. With this constraint in mind, Lieberman and Crompton (1998 Principles of Animal Design, Cambridge: Cambridge University Press, p. 78-86) proposed that bones response to strain varies along the proximo-distal axis of the limb. In order to avoid fatigue fractures due to the accumulation of microdamage, the distal segment, in comparison to the proximal segment, will have an increase in remodeling events to replace damaged bone. In this paper, we test the hypothesis of Lieberman and Crompton (1998) with respect to the human lower limb. With a sample of adult individuals, we compare tibiae and femora for mid-diaphyseal cross-sectional geometry and Haversian remodeling differences. Our results indicate that the human limb is not designed like that of quadrupedal cursorial animals. The tibia is not less resistant in bending and torsion, and does not remodel more than the femur. Our findings fail to support the hypothesis of Lieberman and Crompton (1998) and suggest, instead, that the human lower limb is not designed like a cursorial animal limb. In addition, our results support previous observations that remodeling is not uniform within the cross section of a bone, probably a reflection of different loading histories within the different regions of the cross section.

Effects of limb mass distribution on mechanical power outputs during quadrupedalism

Many researchers have suggested that cursorial mammals concentrate limb muscle mass proximally to reduce energy costs during locomotion. Although supported by experiments where mass is added to an individual's limbs, mammals with naturally occurring distally heavy limbs such as primates have similar energy costs compared with other mammals. This study presents a new hypothesis to explain how animals with distally heavy limbs maintain low energy costs. Since distal mass should increase energy costs due to higher amounts of muscular power outputs, this hypothesis is based on the divergent effects of stride frequency on internal and external power outputs (the power output to move the limbs and the body center of mass, respectively). The use of low stride frequencies reduces limb velocities and therefore decreases internal power, while associated long strides increase the vertical displacement of the body center of mass and therefore increase external power. Total power (the sum of internal and external power) may therefore not differ among mammals with different limb mass distributions. To test this hypothesis, I examined a sample of infant baboons (Papio cynocephalus) during ontogeny and compared them with more cursorial mammals. Limb mass distribution changes with age (from distal to more proximally concentrated) in baboons, and the infants used shorter strides and higher stride frequencies when limb mass was most proximally concentrated. Compared with non-primates who have more proximally concentrated limb mass, the infants used longer strides and lower stride frequencies. Relatively low internal power was associated with low stride frequencies in both the intra- and inter-specific samples. However, only in the inter-specific comparison were relatively long strides associated with high external power outputs. In both the intra-specific and the inter-specific samples, total power did not differ between groups who differed in limb mass distribution. The results of this study suggest that a trade-off mechanism is available to quadrupeds with distally heavy limbs allowing them to maintain similar total power outputs (and likely similar energy costs) compared with mammals with more proximally concentrated limb mass.

The Effects of Changing Bone and Muscle Size on Limb Inertial Properties and Limb Dynamics: A Computer Simulation

The magnitude and distribution of bone and muscle mass within limbs affect limb inertial properties, maximum movement speed and the energy required to maintain submaximal movements. Musculoskeletal modeling and movement simulations were used to determine how changes in bone and muscle cross-sectional area (and thus mass) affect human thigh and shank inertial properties, the maximum speed of unloaded single-leg cycling and the energy required to sustain submaximal single-leg cycling. Depending on initial conditions, shank moments of inertia increased 61-72 kg cm2 per kg added bone and 72-100 kg cm2 per kg added muscle. Thigh moments of inertia increased 46-63 kg cm2 per kg bone and 180-225 kg cm2 per kg muscle. Maximum unloaded cycling velocity increased with increased muscle mass (approximately 2.2-2.9 rpm/kg muscle), but decreased with increased cortical bone mass (approximately 2.0-2.8 rpm/kg bone). The internal work associated with unloaded submaximal cycling increased with increased muscle mass (approximately 0.42-0.48 J/kg muscle) and bone mass (approximately 0.18-0.22 J/kg bone).