Relative fibular strength and locomotor behavior in KNM-WT 15000 and OH 35.

Relative fibular/tibial strength has been demonstrated to vary with locomotor behavior among anthropoid primates. In this study fibular/tibial strength was determined in KNM-WT 15000, a juvenile Homo erectus individual (1.5 Ma), and in OH 35, a Homo habilis (or possibly Paranthropus boisei) individual (1.8 Ma), and compared to that of adult modern humans (n = 79), chimpanzees (n = 16), gorillas (n = 16) and orangutans (n = 11). Ontogenetic changes in fibular/tibial strength were also analyzed due to KNM-WT 15000's juvenile status. Cross-sectional properties at midshaft were derived from multi-plane radiography and external contours, or CT scanning. Comparisons of log-transformed fibular/tibial polar second moment of area and anteroposterior (A-P) and mediolateral (M-L) second moments of area were carried out between extant species. Fossil deviations from each extant taxon's mean proportion were calculated in standard deviation (SD) units for that taxon. Great apes differ significantly from modern humans, with relatively stronger fibulae, particularly in the M-L plane. KNM-WT 15000 is more than 2 SD from all great apes (≥3 SD in the M-L plane) and within 1 SD of modern humans for almost all variables. This is not a result of its age, as fibular/tibial strength slightly decreases with age (i.e., becomes less like that of great apes) in humans. OH 35 falls within 1 SD of chimpanzees and orangutans for the majority of cross-sectional proportions, but more than 1 SD from humans. KNM-WT 15000 is demonstrated to be fully modern, complimenting other indications of complete terrestrial bipedality and possibly showing adaptations for endurance running. OH 35 has some human-like features; however, the relative strength of the two bones aligns the specimen with great apes, consistent with a significant degree of arboreality, in particular, vertical climbing.

Influence of surface modifications on the degradation of standard-sized magnesium plates and healing of mandibular osteotomies in miniature pigs.

Biodegradable magnesium alloys are suitable osteosynthesis materials. Despite the alloy composition, surface modifications appear to have an influence on the degradation process and biocompatibility. The aim of this study was to investigate the impact of hydrogenation and fluoridation of the surface in a mandibular osteotomy model. Standard-sized plates and screws were implanted in an osteotomy at the mandibular angle in nine miniature pigs. The plates and screws were harvested together with the adjacent tissues at 8 weeks after surgery and were investigated by micro-computed tomography and histological analysis. The bone healing of the osteotomy was undisturbed, independent of the surface properties. The adjacent bone tissue showed new bone formation at the implant surface; however, formation of some lacunae could be observed. The corrosion was between 9.8% and 11.6% (fluoridated

Subperiosteal expansion and cortical remodeling of the human femur and tibia with aging.

Increases with aging in subperiosteal dimensions and second moments of area (measures of bending and torsional rigidity) in femoral and tibial cross sections are documented in an archeological sample from the American Southwest. Significant differences between cross-sectional sites and between sexes in the pattern of cortical remodeling with age are also present. These differences appear to be related to variations in the stress or strain levels in different regions of the femur and tibia which result from in vivo mechanical loadings of the lower limb.

Mechanical determinants of bone form: insights from skeletal remains.

Analysis of skeletal remains from humans living in the past forms an important complement to observational and experimental studies of living humans and animal models. Including earlier humans in such analyses increases the range of variation in both behavior and body size and shape that are represented, and can provide insights into the adaptive potential of the modern human skeleton. I review here a variety of studies of archaeological and paleontological remains that have investigated differences in skeletal structure from a mechanical perspective, focusing in particular on diaphyseal strength of the limb bones. Several conclusions can be drawn from these studies: 1) there has been a decline in overall skeletal strength relative to body size over the course of human evolution that has become progressively steeper in recent millennia, probably due to increased sedentism and technological advancement; 2) differences in pelvic structure and hip mechanical loadings affect femoral shape; 3) activity patterns affect overall strength and shape of both the lower and upper limb bones; and 4) responsiveness to changes in mechanical loading varies between skeletal features (e.g., articulations versus diaphyses) and by age.

Structural trends in the aging femoral neck and proximal shaft: analysis of the Third National Health and Nutrition Examination Survey dual-energy X-ray absorptiometry data.

Hip scans of U.S. adults aged 20-99 years acquired in the Third National Health and Nutrition Examination Survey (NHANES III) using dual-energy X-ray absorptiometry (DXA) were analyzed with a structural analysis program. The program analyzes narrow (3 mm wide) regions at specific locations across the proximal femur to measure bone mineral density (BMD) as well as cross-sectional areas (CSAs), cross-sectional moments of inertia (CSMI), section moduli, subperiosteal widths, and estimated mean cortical thickness. Measurements are reported here on a non-Hispanic white subgroup of 2,719 men and 2,904 women for a cortical region across the proximal shaft 2 cm distal to the lesser trochanter and a mixed cortical/trabecular region across the narrowest point of the femoral neck. Apparent age trends in BMD and section modulus were studied for both regions by sex after correction for body weight. The BMD decline with age in the narrow neck was similar to that seen in the Hologic neck region; BMD in the shaft also declined, although at a slower rate. A different pattern was seen for section modulus; furthermore, this pattern depended on sex. Specifically, the section modulus at both the narrow neck and the shaft regions remains nearly constant until the fifth decade in females and then declined at a slower rate than BMD. In males, the narrow neck section modulus declined modestly until the fifth decade and then remained nearly constant whereas the shaft section modulus was static until the fifth decade and then increased steadily. The apparent mechanism for the discord between BMD and section modulus is a linear expansion in subperiosteal diameter in both sexes and in both regions, which tends to mechanically offset net loss of medullary bone mass. These results suggest that aging loss of bone mass in the hip does not necessarily mean reduced mechanical strength. Femoral neck section moduli in the elderly are on the average within 14% of young values in females and within 6% in males.

Dual-energy X-ray absorptiometry derived structural geometry for stress fracture prediction in male U.S. Marine Corps recruits.

A total of 626 U.S. male Marine Corps recruits underwent anthropometric measurements and dual-energy X-ray absorptiometry (DXA) scans of the femoral midshaft and the distal third of the tibia prior to a 12 week physical training program. Conventionally obtained frontal plane DXA scan data were used to measure the bone mineral density (BMD) as well as to derive the cross-sectional area, moment of inertia, section modulus, and bone width in the femur, tibia, and fibula. During training, 23 recruits (3.7%) presented with a total of 27 radiologically confirmed stress fractures in various locations in the lower extremity. After excluding 16 cases of shin splints, periostitis, and other stress reactions that did not meet fracture definition criteria, we compared anthropometric and bone structural geometry measurements between fracture cases and the remaining 587 normals. There was no significant difference in age (p = 0.8), femur length (p = 0.2), pelvic width (p = 0.08), and knee width at the femoral condyles (p = 0.06), but fracture cases were shorter (p = 0.01), lighter (p = 0.0006), and smaller in most anthropometric girth dimensions (p < 0.04). Fracture case bone cross-sectional areas (p < 0.001), moments of inertia (p < 0.001), section moduli (p < 0.001), and widths (p < 0.001) as well as BMD (p < 0.03) were significantly smaller in the tibia and femur. After correcting for body weight differences, the tibia cross-sectional area (p = 0.03), section modulus (p = 0.05), and width (p = 0.03) remained significantly smaller in fracture subjects. We conclude that both small body weight and small diaphyseal dimensions relative to body weight are factors predisposing to the development of stress fractures in this population. These results suggest that bone structural geometry measurements derived from DXA data may provide a simple noninvasive methodology for assessing the risk of stress fracture.

Structural adaptation to changing skeletal load in the progression toward hip fragility: the study of osteoporotic fractures.

Longitudinal, dual-energy X-ray absorptiometry (DXA) hip data from 4187 mostly white, elderly women from the Study of Osteoporotic Fractures were studied with a structural analysis program. Cross-sectional geometry and bone mineral density (BMD) were measured in narrow regions across the femoral neck and proximal shaft We hypothesized that altered skeletal load should stimulate adaptive increases or decreases in the section modulus (bending strength index) and that dimensional details would provide insight into hip fragility. Weight change in the approximately 35 years between scan time points was used as the primary indicator of altered skeletal load. "Static" weight was defined as within 5% of baseline weight, whereas "gain" and 'loss" were those who gained or lost >5%, respectively. In addition, we used a frailty index to better identify those subjects undergoing changing in skeletal loading. Subjects were classified as frail if unable to rise from a chair five times without using arm support. Subjects who were both frail and lost weight (reduced loading) were compared with those who were not frail and either maintained weight (unchanged loading) or gained weight (increased loading). Sixty percent of subjects (n = 2,559) with unchanged loads lost BMD at the neck but not at the shaft, while section moduli increased slightly at both regions. Subjects with increasing load (n = 580) lost neck BMD but gained shaft BMD; section moduli increased markedly at both locations. Those with declining skeletal loads (n = 105) showed the greatest loss of BMD at both neck and shaft; loss at the neck was caused by both increased loss of bone mass and greater subperiosteal expansion; loss in shaft BMD decline was only caused by greater loss of bone mass. This group also showed significant declines in section modulus at both sites. These results support the contention that mechanical homeostasis in the hip is evident in section moduli but not in bone mass or density. The adaptive response to declining skeletal loads, with greater rates of subperiosteal expansion and cortical thinning, may increase fragility beyond that expected from the reduction in section modulus or bone mass alone.

Stress fracture in military recruits: gender differences in muscle and bone susceptibility factors.

A total of 693 female U.S. Marine Corps recruits were studied with anthropometry and dual-energy X-ray absorptiometry (DXA) scans of the midthigh and distal third of the lower leg prior to a 12 week physical training program. In this group, 37 incident stress fracture cases were radiologically confirmed. Female data were compared with male data from an earlier study of 626 Marine recruits extended with additional cases for a total of 38 stress fracture cases. Using DXA data, bone structural geometry and cortical dimensions were derived at scan locations and muscle cross-sectional area was computed at the midthigh. Measurements were compared within gender between pooled fracture cases and controls after excluding subjects diagnosed with shin splints. In both genders, fracture cases were less physically fit, and had smaller thigh muscles compared with controls. After correction for height and weight, section moduli (Z) and bone strength indices (Z/bone length) of the femur and tibia were significantly smaller in fracture cases of both genders, but patterns differed. Female cases had thinner cortices and lower areal bone mineral density (BMD), whereas male cases had externally narrower bones but similar cortical thicknesses and areal BMDs compared with controls. In both genders, differences in fitness, muscle, and bone parameters suggest poor skeletal adaptation in fracture cases due to inadequate physical conditioning prior to training. To determine whether bone and muscle strength parameters differed between genders, all data were pooled and adjusted for height and weight. In both the tibia and femur, men had significantly larger section moduli and bone strength indices than women, although women had higher tibia but lower femur areal BMDs. Female bones, on average, were narrower and had thinner cortices (not significant in the femur, p = 0.07). Unlike the bone geometry differences, thigh muscle cross-sectional areas were virtually identical to those of the men, suggesting that the muscles of the women were not relatively weaker.

Predicting femoral neck strength from bone mineral data. A structural approach.

An interactive computer program was developed to derive femoral neck geometry from raw bone mineral image data for an estimate of hip strength using single plane engineering stress analysis. The program, which we call Hip Strength Analysis (HSA), was developed as an attempt to improve the predictive value of hip bone mineral data for osteoporosis fracture risk assessment. We report a series of experiments with an aluminum phantom and with cadaver femora, designed to test the accuracy of derived geometric measurements and strength estimates. Using data acquired with both Lunar DP3 (DPA) and Hologic QDR-1000 (x-ray) scanners, HSA computed femoral neck cross-sectional areas (CSA) and cross-sectional moments of inertia (CSMI) on an aluminum phantom were in excellent agreement with actual values (r greater than .99). Using Lunar DP3 data, CSA and CSMI measurements at mid-femoral necks of 22 cadaver specimens were in good general agreement with literature values. HSA computed cross-sectional properties of three of these specimens were compared with measurements derived from sequential CT cross-sectional images. Discrepancy between the two methods averaged less than 10% along the length of the femoral neck. Finally, breaking strengths of 20 of the femora were measured with a materials testing system, showing better agreement with HSA predicted strength (r = .89, percent standard of the estimate (%SEE) = 21%) than femoral neck bone mineral density (r = .79, %SEE = 28%).

Effects of long-term treatment with estradiol or clomiphene citrate on bone maintenance, and pituitary and uterine weights in ovariectomized rats.

Long-term estrogen replacement therapy in postmenopausal women can bring relief to hot flushes and reduce loss of bone mass due to osteoporosis, however, such treatment often can cause uterine hyperplasia and other undesirable effects. This study compared changes in bone mineral content (BMC), uterine weight, pituitary weight and pituitary gonadotropin content in the ovariectomized rat model following treatment with estradiol (E2) or two levels of clomiphene citrate (CC), an estrogen agonist/antagonist. Groups (n = 8-12) of adult ovariectomized (OVX) rat were implanted with E2 pellets (5 micrograms/day) or injected subcutaneously with CC at 1 mg/kg body wt (CC-1) or 5 mg/kg body wt (CC-5) twice weekly for 12 months. Placebo implanted OVX and intact (INT) female rats served as negative and positive controls, respectively. Following treatment, the uterus, pituitary gland and right femur were collected from each animal. E2 treatment increased (P less than 0.05) uterine weight compared to all other treatment groups, while both CC doses increased uterine weight over the OVX group only (E2, 0.24 +/- 0.03; INT, 0.14 +/- 0.01; CC-1, 0.06 +/- 0.01; CC-5, 0.07 +/- 0.01; and OVX, 0.02 +/- 0.01 g per 100 g body wt). Pituitary weight was increased 15-fold (P less than 0.05) by E2 treatment over all other treatment groups (E2, 65.7 +/- 13.9; INT, 4.0 +/- 0.5; CC-1, 3.3 +/- 0.03; CC-5, 2.7 +/- 0.02; and OVX, 2.9 +/- 0.02 mg per 100 g body wt). Both E2 and CC treatments reduced pituitary luteinizing hormone and follicle stimulating hormone content (micrograms/pit) to INT levels and were lower (P less than 0.05) than OVX levels. Mean BMC of E2, CC-1- or CC-5-treated rats was greater (P less than 0.05) than that of either the INT or OVX groups, while INT animals had a higher BMC compared to OVX animals (E2, 0.027 +/- 0.003; CC-1, 0.026 +/- 0.001; CC-5, 0.028 +/- 0.001; INT, 0.021 +/- 0.001; and OVX, 0.017 +/- 0.001 g/cm per 100 g body wt). These data indicate that CC has the potential to reduce bone mineral loss without causing other undesirable effects, including uterine hyperstimulation, and thus needs to be further investigated.

Sex differences in age-related remodeling of the femur and tibia.

Changes with age in cross-sectional geometry of the lower limb bones were investigated in a large sample of cadaveric skeletal material from U.S. white adults. Section properties (areas and second moments of area) were determined at 11 locations by sectioning and direct measurement of 103 femora and 99 tibiae. All properties were standardized for body size differences by dividing by powers of bone length, and age trends were determined through linear regression analysis. Results indicate that while both men and women undergo endosteal resorption of bone and medullary expansion with aging, only men exhibit concurrent subperiosteal bone apposition and expansion. As a consequence, men show little change in cortical area and some increase in second moments of area with age, while women show decreases in both cortical area and second moments of area. Thus, only men appear to remodel bone in a way that would tend to compensate for loss of bone material strength with aging. In a previous study of a preindustrial sample with high activity levels, both men and women exhibited bone subperiosteal expansion and increase in second moments of area with aging. Together with observed differences in fracture incidence among living populations, these findings suggest that relatively low activity levels may not stimulate optimal bone remodeling throughout life and thus may contribute to higher risk of fracture in old age.

A quantitative assessment of cross-sectional cortical bone remodeling in the femoral diaphysis following hip arthroplasty in elderly females.

A quantitative assessment of cross-sectional cortical bone remodeling in the femoral diaphysis following hip arthroplasty was made by direct in vitro measurements of cross-sectional geometric properties. We obtained eight femora from four female cadavers ranging in age from 77 to 96 years. In three cases unilateral uncemented Austin Moore implants were used, and in one case a unilateral cemented Thompson prosthesis had been implanted. The time of implantation in the two specimens where this information could be obtained was greater than 40 months. Sections were made at 12 diaphyseal locations from the superior aspect of the lesser trochanter through the distal diaphysis. Section properties (areas and second moments of area, or area moments of inertia) were determined by tracing photographs of the cross-sections with a digitizer. In this sample of prosthetic femora, we found reductions in both total subperiosteal area (TA) and endosteal area (ENDA) relative to the contralateral unoperated side in most sections distal to the lesser trochanter. The average pairwise reduction in ENDA for this region was 21.1 mm2, reaching statistical significance in one distal diaphyseal section. The average decline in TA in this region was 10.2 mm2. Because the reduction in endosteal dimensions was generally greater than the reduction in subperiosteal dimensions, cortical area (CA) was maintained or increased throughout the distal 80% of this region in prosthetic femora with an average increase in CA of 9.3 mm2, reaching statistical significance in one mid-diaphyseal section. A completely different pattern of remodeling occurred in the two most proximal sections through the lesser trochanter and base of the femoral neck.(ABSTRACT TRUNCATED AT 250 WORDS)

Curved beam model of the proximal femur for estimating stress using dual-energy X-ray absorptiometry derived structural geometry.

The investigation of individual differences in hip strength requires a method to measure structural geometry in vivo and a valid analytical approach to calculate mechanical stress. We developed a method for deriving structural geometry of the femur from the proximal shaft through the femoral neck, using data from dual energy X-ray absorptiometry. The geometric properties are employed in a two-dimensional curved beam model of the proximal femur to estimate stresses on the lateral and medial bone surfaces. Stresses calculated by this method are compared with those from the conventional flexure formula and with results produced from a cadaver femur with use of three-dimensional finite element analysis of computed tomography data. Loading conditions simulating a one-legged stance and a fall on the greater trochanter are employed. Stresses calculated by curved beam theory are in much better agreement with three-dimensional finite element analysis than are those for which the conventional straight beam formula was used. In simulation of a fall on the greater trochanter, all three methods show peaks of stress at the femoral neck but only the curved beam and finite element analysis methods show an additional peak at the medial intertrochanteric margin. Both neck and trochanter regions correspond to common failure sites for hip fractures in the elderly. The curved beam treatment of hip structure derived from dual-energy X-ray absorptiometry provides an approach for the in vivo engineering analysis of hip structure that is not practical by other methods.

Experimental testing of a DEXA-derived curved beam model of the proximal femur.

This study was designed to test whether, using curved beam theory, a structural model of the proximal femur derived from two-dimensional dual energy x-ray absorptiometry could be used to predict femoral strength in an experimental simulation of a fall on the greater trochanter. A set of 22 fresh cadaveric femoral specimens were scanned with use of two-dimensional dual energy x-ray absorptiometry and then were tested to failure in a materials testing system, under three-point loading, with the ground impact vector aligned within the plane and along the bisector of the femoral neck-shaft angle. Failure locations generally corresponded to stress peak locations predicted by the curved beam model. Predicted failure loads correlated well with measured failure loads for femoral neck fractures (r=0.89; percent SE of estimate=23%) and some-what less well for intertrochanteric fractures (r=0.83; percent SE of estimate=29%). Overall predictions for failure load calculated from the maximum stress peak value over both locations corresponded to measured failure loads with an r value of 0.91 (percent SE of estimate=21%). This kind of structural approach to the analysis of data for hip bone mass has the potential to provide mechanistic interpretations of the statistical associations frequently shown between conventional bone mineral measures and either hip fracture risk in vivo or bone strength in vitro.

Bone-mineral content in the lower limb. Relationship to cross-sectional geometry.

For this study, bone-mineral content and bone-mineral width were measured using photon absorptiometry at eleven locations in forty excised femora and tibiae obtained from an archaeological sample. An additional seventy-nine femora were scanned at the middle of the shaft and through the femoral neck. After scanning, the bones were sectioned at each location and cross-sectional areas and other geometrical properties were determined directly from section tracings. The results indicated that locational, sex, and age-related differences in bone-mineral content were largely determined by variation in cortical area. Due to differences in bone geometry, variation in bone width does not reflect variation in cortical area, and as a consequence the use of bone width to standardize for volumetric or bone "size" differences produces misleading results in sex and age comparisons. In this study, decreases with age in the bone-mineral content and bone-mineral content:bone width ratio were similar to those observed in living populations. However, the bone-mineral content:cortical area ratio showed no significant decline with age for any cross section. Thus, the age-related changes in compact cortical bone appeared to be mainly volumetric, not densitometric.

Body mass prediction from skeletal frame size in elite athletes.

Body mass can be estimated from measures of skeletal frame size (stature and bi-iliac (maximum pelvic) breadth) fairly accurately in modern human populations. However, it is not clear whether such a technique will lead to systematic biases in body mass estimation when applied to earlier hominins. Here the stature/bi-iliac method is tested, using data available for modern Olympic and Olympic-caliber athletes, with the rationale that these individuals may be more representative of the general physique and degree of physical conditioning characteristic of earlier populations. The average percent prediction error of body mass among both male and female athletes is less than 3%, with males slightly underestimated and females slightly overestimated. Among males, the ratio of shoulder to hip (biacromial/bi-iliac) breadth is correlated with prediction error, while lower limb/trunk length has only a weak inconsistent effect. In both sexes, athletes in "weight" events (e.g. , shot put, weight-lifting), which emphasize strength, are underestimated, while those in more endurance-related events (e.g., long distance running) are overestimated. It is likely that the environmental pressures facing earlier hominins would have favored more generalized physiques adapted for a combination of strength, speed, agility, and endurance. The events most closely approximating these requirements in Olympic athletes are the decathlon, pentathlon, and wrestling, all of which have average percent prediction errors of body mass of 5% or less. Thus, "morphometric" estimation of body mass from skeletal frame size appears to work reasonably well in both "normal" and highly athletic modern humans, increasing confidence that the technique will also be applicable to earlier hominins.

New approaches to structural evolution of limb bones in primates.

Structural analysis of primate limb bones using engineering beam theory can reduce complex biological forms to a few readily interpretable and functionally relevant parameters. Several methods of obtaining and analyzing these structural parameters are described, including computed tomography, multiple plane radiography, photon absorptiometry, and automated digital analysis. Examples of applications of these data to problems in primate adaptation and evolution include improved estimation of body mass in fossil species, investigation of relative fore- and hindlimb mechanical loadings ('dominance'), and study of more subtle within and between species differences in behavior as reflected in variations in limb bone shape. In addition, it is shown that combined analyses of diaphyseal and articular structure can provide information on aspects of structural evolution of primate limb bones not evident from independent analysis of either type of characteristic alone.

Biomechanics of the hip and birth in early Homo.

A complex of traits in the femur and pelvis of Homo erectus and early "erectus-like" specimens has been described, but never satisfactorily explained. Here the functional relationships between pelvic and femoral structure in humans are explored using both theoretical biomechanical models and empirical tests within modern samples of diverse body form (Pecos Amerindians, East Africans). Results indicate that a long femoral neck increases mediolateral bending of the femoral diaphysis and decreases gluteal abductor and hip joint reaction forces. Increasing biacetabular breadth along with femoral neck length further increases M-L bending of the femoral shaft and maintains abductor and joint reaction forces at near "normal" levels. When compared to modern humans, Homo erectus and early "erectus-like" specimens are characterized by a long femoral neck and greatly increased M-L relative to A-P bending strength of the femoral shaft, coupled with no decrease in hip joint size and a probable increase in abductor force relative to body size. All of this strongly suggests that biacetabular breadth as well as femoral neck length was relatively large in early Homo. Several features preserved in early Homo partial hip bones also indicate that the true (lower) pelvis was very M-L broad, as well as A-P narrow. This is similar to the lower pelvic shape of australopithecines and suggests that nonrotational birth, in which the newborn's head is oriented transversely through the pelvic outlet, characterized early Homo as well as Australopithecus. Because M-L breadth of the pelvis is constrained by other factors, this may have limited increases in cranial capacity within Homo until rotational birth was established during the late Middle Pleistocene. During or after the transition to rotational birth biacetabular breadth decreased, reducing the body weight moment arm about the hip and allowing femoral neck length (abductor moment arm) to also decrease, both of which reduced M-L bending of the proximal femoral shaft. Variation in femoral structural properties within early Homo and other East African Early Pleistocene specimens has several taxonomic and phylogenetic implications.

The contribution of cancellous bone to long bone strength and rigidity.

A recent article (Burr and Piotrowski, 1982) suggested that structural analyses of long bone cross-sectional geometry will be inaccurate and should be considered inappropriate when cancellous bone accounts for 10-15% or more of the cross-sectional area. Consideration of material property differences between compact and cancellous bone, however, indicates that even significant proportions of cancellous bone (10-40% of total cross-sectional area) will very likely have negligible effects on bone strength and rigidity, and can be effectively ignored in geometrical analyses of diaphyseal sections. In metaphyseal and epiphyseal regions, however, geometric analyses of section properties such as area moments of inertia are inappropriate, both because of significant trabecular bone effects, and because of the inherent constraints of mechanical beam models.

Body size, body shape, and long bone strength in modern humans.

To identify behaviorally significant differences in bone structure it is first necessary to control for the effects of body size and body shape. Here the scaling of cross-sectional geometric properties of long bone diaphyses with different "size" measures (bone length, body mass, and the product of bone length and body mass) are compared in two modern human populations with very different body proportions: Pecos Pueblo Amerindians and East Africans. All five major long bones (excluding the fibula) were examined. Mechanical predictions are that cortical area (axial strength) should scale with body mass, while section modulus (bending/torsional strength) should scale with the product of body mass and moment arm length. These predictions are borne out for section moduli, when moment arm length is taken to be proportional to bone length, except in the proximal femoral diaphysis, where moment arm length is proportional to mediolateral body breadth (as would be expected given the predominance of M-L bending loads in this region). Mechanical scaling of long bone bending/torsional strength is similar in the upper and lower limbs despite the fact that the upper limb is not weight-bearing. Results for cortical area are more variable, possibly due to a less direct dependence on mechanical factors. Use of unadjusted bone length alone as a "size" measure produces misleading results when body shape varies significantly, as is the case between many modern and fossil hominid samples. In such cases a correction factor for body shape should be incorporated into any "size" standardization.