Estimating human long bone cross-sectional geometric properties: a comparison of noninvasive methods

Cross-sectional properties (areas, second moments of area) have been used extensively for reconstructing the mechanical loading history of long bone shafts. In the absence of a fortuitous break or available computed tomography (CT) facilities, the endosteal and/or periosteal boundaries of a bone may be approximated using alternative noninvasive methods. The present study tests whether cross-sectional geometric properties of human lower limb bones can be adequately estimated using two such techniques: the ellipse model method (EMM), which uses biplanar radiography alone, and the latex cast method (LCM), which involves molding of the subperiosteal contour in combination with biplanar radiography to estimate the contour of the medullary canal. Results of both methods are compared with "true" cross-sectional properties calculated by direct sectioning. The study sample includes matched femora and tibiae of 50 Pecos Pueblo Amerindians. Bone areas and second moments of area were calculated for the midshaft femur and tibia and proximal femoral diaphysis in each individual. Percent differences between methods were derived to evaluate directional (systematic) and absolute (random) error. Multiple regression was also used to investigate the sources of error associated with each method. The results indicate that while the LCM shows generally good correspondence to the true cross-sectional properties, the EMM generally overestimates true parameters. Regression equations are provided to correct this overestimation, and, when applied to another sample, are shown to significantly improve estimates for the femoral midshaft, although corrections are less successful for the other section locations. Our results suggest that the LCM is an adequate substitute for estimating cross-sectional properties when direct sectioning and CT are not feasible. The EMM is a reasonable alternative, although the bias inherent in the method should be corrected if possible, especially when the results of the study are to be compared with data collected using different methods.     

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.     

Periosteal versus true cross‐sectional geometry: A comparison along humeral,femoral, and tibial diaphyses

Cross‐sectional geometric (CSG) properties of human long bone diaphyses are typically calculated from both periosteal and endosteal contours. Though quantification of both is desirable, periosteal contours alone have provided accurate predictions of CSG properties at the midshaft in previous studies. The relationship between CSG properties calculated from external contours and “true” (endosteal and periosteal) CSG properties, however, has yet to be examined along the whole diaphysis. Cross‐sectional computed tomography scans were taken from 21 locations along humeral, femoral, and tibial diaphyses in 20 adults from a late prehistoric central Illinois Valley cemetery. Mechanical properties calculated from images with (a) artificially filled medullary cavities (“solid”) and (b) true unaltered cross‐sections were compared at each section location using least squares regression. Results indicate that, in this sample, polar second moments of area (J), polar section moduli (Z_p), and cross‐sectional shape (I_max/I_min) calculated from periosteal contours correspond strongly with those calculated from cross‐sections that include the medullary cavity. Correlations are high throughout most of the humeral diaphysis and throughout large portions of femoral and tibial diaphyses (R² = 0.855–0.998, all P < 0.001, %SEE ≤ 8.0, %PE ≤ 5.0), the major exception being the proximal quarter of the tibial diaphysis for J and Z_p. The main source of error was identified as variation in %CA. Results reveal that CSG properties quantified from periosteal contours provide comparable results to (and are likely to detect the same differences among individuals as) true CSG properties along large portions of long bone diaphyses. Am J Phys Anthropol, 2013. © 2013 Wiley Periodicals, Inc.     

Structural changes in the femur with the transition to agriculture on the Georgia coast

Structural characteristics of the femur are compared in preagricultural (2200 B.C.–A.D. 1150) and agricultural (A.D. 1150–1550) subsistence strategy groups from the Georgia coast. Using an automated technique, cross-sectional geometric properties used in structural analyses (areas, second moments of area) were determined at midshaft and distal to the lesser trochanter in 20 adults from each group. A significant decline in magnitude of almost every geometric property occurs in the agricultural group. The differences between groups are reduced but still significant for many properties after standardizing for bone length differences. In addition, a remodeling of the femoral cortex to one of relatively smaller medullary and subperiosteal diameter, as well as a more circular cross-sectional shape, is characteristic of agricultural femora. Thus, while the relative cross-sectional area of bone remains the same, the spatial distribution of bone area is different in the two groups. The results strongly suggest a relative reduction in mechanical loadings of the femur in the agricultural group, implying different levels and possibly types of activity involving the lower limb in the two groups. The data are also compared with similar data available for the Pecos Pueblo (agricultural) sample. The comparison indicates that types of activity may have been more similar in the two agricultural samples, but that general levels of activity were more similar in the Pecos Pueblo and Georgia coast preagricultural samples.     

The physical and mechanical effects of suspension-induced osteopenia on mouse long bones.

The present investigation addresses the extent of tail-suspension effects on the long bones of mice. The effects are explored in both sexes, in both forelimb and hindlimb bones, and in both diaphyseal and metaphyseal/epiphyseal bones. Two weeks of suspension provided unloading of the femora and tibiae and an altered loading of the humeri. Whole-bone effects included lower mass (approximately 10%) and length (approximately 4%) in the bones of suspended mice compared to controls. The geometric and material properties of the femora were considered along the entire length of the diaphysis and in the metaphysis/epiphysis portions as a unit. Geometric effects included lower cross-sectional cortical area (16%), cortical thickness (25%) and moment of inertia (21%) in the femora of suspended mice; these differences were observed in both distal and proximal portions of the femur diaphysis. The relative amount of bone comprising the middle 8 mm of the diaphysis was greater (3%) in the control mice than in the suspended mice. Significant mass differences between the group in the metaphysis/epiphysis were not observed. Material effects included lower %ash (approximately 2%) in the femora and tibiae as well as in the humeri of suspended mice compared to controls. With respect to the measured physical and material properties, suspension produced similar bone responses in male and female mice. The effects of suspension are manifested largely through geometric rather than through material changes.     

Hindlimb unloading has a greater effect on cortical compared with cancellous bone in mature female rats.

This study was designed to determine the effects of 28 days of hindlimb unloading (HU) on the mature female rat skeleton. In vivo proximal tibia bone mineral density and geometry of HU and cage control (CC) rats were measured with peripheral quantitative computed tomography (pQCT) on days 0 and 28. Postmortem pQCT, histomorphometry, and mechanical testing were performed on tibiae and femora. After 28 days, HU animals had significantly higher daily food consumption (+39%) and lower serum estradiol levels (-49%, P = 0.079) compared with CC. Proximal tibia bone mineral content and cortical bone area significantly declined over 28 days in HU animals (-4.0 and 4.8%, respectively), whereas total and cancellous bone mineral densities were unchanged. HU animals had lower cortical bone formation rates and mineralizing surface at tibial midshaft, whereas differences in similar properties were not detected in cancellous bone of the distal femur. These results suggest that cortical bone, rather than cancellous bone, is more prominently affected by unloading in skeletally mature retired breeder female rats.     

Ash content modulation of torsionally derived effective material properties in cortical mouse bone

The purpose of this study was to evaluate the effects of isolated alterations in mineral content on mouse bone torsional properties. The femora and tibiae from 25 eight-week-old male A/J strain mice were divided into five groups and selectively decalcified from 5% to 20%. The right femora were then tested to failure in torsion while the tibiae were ashed to determine final mineral content of the decalcified bones. Contralateral femora were serially cross-sectioned to determine geometric properties, and effective material properties were then calculated from the geometric and structural properties of each femoral pair. We found that the relationship between ash content and effective shear modulus or maximum effective shear stress could best be characterized through a power law, with an exponential factor of 6.79 (R2 = 0.85) and 4.04 (R2 = 0.67), respectively. This indicates that in a murine model, as with other species, small changes in ash content significantly influence effective material properties. Furthermore, it appears that (in adolescent A/J strain mice) effective shear modulus is more heavily affected by changes in mineralization than is maximum effective shear stress when these properties are derived from whole bone torsional tests to failure.     

The influence of body proportions on femoral and tibial midshaft shape in hunter‐gatherers

Variation in femoral and tibial diaphyseal shape is used as an indicator of adaptation to patterns of terrestrial mobility. Recent experimentation has implied that lower limb diaphyseal shape may be primarily influenced by lower limb length, and less so by mobility patterns. If valid, this would, at most, render previous interpretations of mobility patterns based on analyses of diaphyseal shape questionable, and, at least, require additional standardization that considers the influence of limb length. Although the consequences could be profound, this implication has yet to be directly tested. Additionally, the influence of body breadth on tibial shape (and to a lesser extent femoral shape) remains uncertain. Tibial and femoral cross‐sectional midshaft shape measurements, taken from nine Pleistocene and Holocene skeletal populations, were compared against lower limb length, limb segment length, and bi‐iliac breadth. Generally, limb length and limb segment length do not significantly influence femoral or tibial midshaft shape. After controlling for body mass greater bi‐iliac breadth is associated with a relative mediolateral strengthening of the femoral midshaft, while the influence of a wider body shape (BIB/length) is associated with a relative M‐L strengthening of the tibia and femur of males, and the tibia of females. We conclude that; (1) mechanical interpretations of lower limb diaphyseal shape are most parsimonious due to the lack of evidence for a consistent relationship between segment length and shape; however, (2) further work is required to investigate the influence of bi‐iliac breadth on both femoral and tibial midshaft shape. Am J Phys Anthropol, 2010. © 2010 Wiley‐Liss, Inc.     

Site specific bone adaptation response to mechanical loading

Over 25 million Americans suffer from osteoporosis. Bone size and strength depends both upon the level of adaptation due to physical activity (applied load), and genetics. We hypothesized that bone adaptation to loads differs among mice breeds and bone sites. Forty-five adult female mice from three inbred strains (C57BL/6 [B6], C3H/HeJ [C3], and DBA/2J [D2]) were loaded at the right tibia and ulna in vivo with non-invasive loading devices. Each loading session consisted of 99 cycles at a force range that induced approximately 2000 microstrain (microepsilon) at the mid-shaft of the tibia (2.5 to 3.5 N force) and ulna (1.5 to 2 N force). The right and left ulnae and tibiae were collected and processed using protocols for histological undecalcified cortical bone slides. Standard histomorphometry techniques were used to quantify new bone formation. The histomorphometric variables include percentage mineralizing surface (%MS), mineral apposition rate (MAR), and bone formation rate (BFR). Net loading response [right-left limb] was compared between different breeds at tibial and ulnar sites using two-way ANOVA with repeated measures (p<0.05). Significant site differences in bone adaptation response were present within each breed (p<0.005). In all the three breeds, the tibiae showed greater percentage MS, MAR and BFR than the ulna at similar in vivo load or mechanical stimulus (strain). These data suggest that the bone formation due to loading is greater in the tibiae than the ulnae. Although, no significant breed-related differences were found in response to loading, the data show greater trends in tibial bone response in B6 mice as compared to D2 and C3 mice. Our data indicate that there are site-specific skeletal differences in bone adaptation response to similar mechanical stimulus.     

Femoral expansion in the adult male rat

The length, total and cortical widths at midshaft, and robusticity of femora were measured in growing and mature male Holtzman rats. Analysis of covariance revealed significant differences in the regression coefficients (slopes) between young rats (1-4 months) and adult rats (5-16 months), indicating that, for a given increment in femoral length, young rats have a smaller increment in total femoral width than do adult rats. In addition, the results indicated that femoral expansion occurs in adult male Holtzman rats (5-16 months of age) without cortical thinning or loss of bone mass.     

Radiographic estimation of long bone cross-sectional geometric properties

Because of their biomechanical significance, cross-sectional geometric properties of long bone diaphyses (areas, second moments of area) have been increasingly used in a number of form/function studies, e.g., to reconstruct body mass or locomotor mode in fossil primates or to elucidate allometric scaling relationships among extant taxa. In the present study, we test whether these biomechanical section properties can be adequately estimated using biplanar radiographs, as compared to calculations of the same properties from computer digitization of cross-sectional images. We are particularly interested in smaller animals, since the limb bone cortices of these animals may not be resolvable using other alternative noninvasive techniques (computed tomography). The test sample includes limb bones of small (25–5,000 g) relatively generalized quadrupedal mammals—mice, six species of squirrels, and Macaca fascicularis. Results indicate that biplanar radiographs are reasonable substitutes for digitized cross-sectional images for deriving areas and second moments of area of midshaft femora and humeri of mammals in this size range. Potential application to a variety of questions relating to mechanical loading patterns in such animals is diverse. © 1993 Wiley-Liss, Inc.     

Hunter-gatherer postcranial robusticity relative to patterns of mobility, climatic adaptation, and selection for tissue economy

Human skeletal robusticity is influenced by a number of factors, including habitual behavior, climate, and physique. Conflicting evidence as to the relative importance of these factors complicates our ability to interpret variation in robusticity in the past. It remains unclear how the pattern of robusticity in the skeleton relates to adaptive constraints on skeletal morphology. This study investigates variation in robusticity in claviculae, humeri, ulnae, femora, and tibiae among human foragers, relative to climate and habitual behavior. Cross-sectional geometric properties of the diaphyses are compared among hunter-gatherers from southern Africa (n = 83), the Andaman Islands (n = 32), Tierra del Fuego (n = 34), and the Great Lakes region (n = 15). The robusticity of both proximal and distal limb segments correlates negatively with climate and positively with patterns of terrestrial and marine mobility among these groups. However, the relative correspondence between robusticity and these factors varies throughout the body. In the lower limb, partial correlations between polar second moment of area (J(0.73)) and climate decrease from proximal to distal section locations, while this relationship increases from proximal to distal in the upper limb. Patterns of correlation between robusticity and mobility, either terrestrial or marine, generally increase from proximal to distal in the lower and upper limbs, respectively. This suggests that there may be a stronger relationship between observed patterns of diaphyseal hypertrophy and behavioral differences between populations in distal elements. Despite this trend, strength circularity indices at the femoral midshaft show the strongest correspondence with terrestrial mobility, particularly among males.     

A simple univariate technique for determining sex from fragmentary femora: its application to a Scottish short cist population

A simple univariate technique for sexing individuals represented by fragmentary skeletal remains is described. The results obtained were highly consistent (about 90%) with those obtained by conventional analysis of pelvic and cranial morphology. It is suggested that using maximum anteroposterior diameter of the femoral shaft as a sex discriminator has advantages over midshaft circumference even when intact femora are available.     

Technical note: A novel geometric morphometric approach to the study of long bone shape variation

Procrustes‐based geometric morphometrics (GM) is most often applied to problems of craniofacial shape variation. Here, we demonstrate a novel application of GM to the analysis of whole postcranial elements in a study of 77 hominoid tibiae. We focus on two novel methodological improvements to standard GM approaches: 1) landmark configurations of tibiae including 15 epiphyseal landmarks and 483 semilandmarks along articular surfaces and muscle insertions along the tibial shaft and 2) an artificial affine transformation that sets moments along the shaft equal to the sum of the moments estimated in the other two anatomical directions. Diagrams of the principal components of tibial shapes support most differences between human and non‐human primates reported previously. The artificial affine transformation proposed here results in an improved clustering of the great apes that may prove useful in future discriminant or clustering studies. Since the shape variations observed may be related to different locomotor behaviors, posture, or activity patterns, we suggest that this method be used in functional analyses of tibiae or other long bones in modern populations or fossil specimens. Am J Phys Anthropol, 2012. © 2012 Wiley Periodicals, Inc.     

The importance of accounting for the area of the medullary cavity in cross‐sectional geometry: A test based on the femoral midshaft

In cross‐sectional geometric (CSG) studies, both the subperiosteal and endosteal contours are considered important factors in determining bone bending rigidity. Recently, regression equations predicting CSG properties from a section's external dimensions were developed in a world‐wide sample of human long bones. The results showed high correlations between some subperiosteally derived and actual CSG parameters. We present a theoretical model that further explores the influence of endosteal dimensions on CSG properties. We compare two hypothetical femoral midshaft samples with the same total subperiosteal area but with percentages of cortical bone at the opposite ends of published human variation for population sample means. Even in this relatively uncommon scenario, the difference between the samples in the resultant means for predicted femoral polar second moment of area (J) appears to be modest: power analysis indicates that a minimum sample size of 61 is needed to detect the difference 90% of the time via a t‐test. Moreover, endosteal area can be predicted—although with substantial error—from periosteal area. Despite this error, including this relationship in subperiosteally derived estimates of J produces sample mean estimates close to true mean values. Power analyses reveal that when similar samples are used to develop prediction equations, a minimum sample of hundreds or more may be needed to distinguish a predicted mean J from the true mean J. These results further justify the use of regression equations estimating J from periosteal contours when analyzing behaviorally induced changes in bone rigidity in ancient populations, when it is not possible to measure endosteal dimensions. However, in other situations involving comparisons of individual values, growth trends, and senescence, where relative cortical thickness may vary greatly, inclusion of endosteal dimensions is still important. Am J Phys Anthropol, 2010. © 2010 Wiley‐Liss, Inc.     

The line of action in the tibia during axial compression of the leg

Compression of the leg induces bending in the tibia, which can lead to tensile failure of the bone in the midshaft. The purpose of this study was to determine the orientation of the compressive load vector in the human tibia. Five cadaveric lower extremities were instrumented with in situ 6-axis tibial and fibular load cells and subjected to quasistatic axial leg compression tests in two knee positions and nine ankle positions. For each test, the location and angle of the line of action were calculated at the tibial midshaft. The line of action was extended to the bone ends in order to determine the locations of the effective centers of pressure on the tibial plafond and tibial plateau. The effective center of pressure on the tibial plafond consistently migrated anteriorly in dorsiflexion, laterally in eversion, posteriorly in plantarflexion, and medially in inversion. An opposite pattern was observed on the tibial plateau. When the knee was flexed, the effective center of pressure was generally isolated to a small area in the posterior portion of the medial tibial condyle. The percentage of the axial load borne by the fibula varied from -8% to 19%, and was related to the inversion/eversion angle of the ankle (p<0.02), as well as the distance between the fibula and the axial load path at the midshaft (p<0.001). The line of action through the tibia appeared to follow the external load path to the extent allowed by the available joint contact surfaces.     

Cortical remodeling data are affected by sampling location

It has been argued that techniques for estimating adult ageat-death from cortical histology are deleteriously affected by sampling location. This study uses nine complete femoral midshaft cross-sections to test the effect of sampling site on measurement of a standard histological variable, percent remodeled bone. Circumferential periosteal fields from four anatomically defined locations (anterior, posterior, medial, lateral) and four mechanically defined locations (maximum and minimum moments of area) were evaluated. Locations deviating from the periosteal surface toward the endosteal surface were also compared. Significant differences were found for both location and field placement. The anatomical axes exhibited greater variability than the mechanical axes, in particular the anterior location, a standard sampling site for age-at-death estimation techniques. More endosteal fields tended to show elevated levels of percent remodeled bone. This study demonstrates that circumferential and radial sampling locations are important considerations in deriving and applying predictive equations based on cortical remodeling. © 1995 Wiley-Liss, Inc.     

The functionally-related signatures characterizing the endostructural organisation of the femoral shaft in modern humans and chimpanzee

Within the limits imposed by a number of developmental and rheological factors, endostructural arrangement of the appendicular skeleton is consistent with the functional patterns of stress, where cortical bone topographic thickness variation in long bones primarily reflects the nature, direction, intensity, and frequency of the locomotion-related biomechanical loads. By applying techniques of cross-sectional geometric analysis and 3D morphometric mapping to a (micro)tomographic record consisting of 12 modern human and 10 chimpanzee adult femora, we have shown two distinct patterns (functional “signatures”) of cortical bone arrangement along the shaft (20–80% portion of the biomechanical length) specifically associated to the bipedal (Homo) and the quadrupedal modes (Pan). In particular, the inner structure of the human femoral diaphysis is adapted to antero-posterior loadings and presents a greater rigidity against posterior bending, while that of Pan is characterized by the presence of strong medial and lateral bony reinforcements positioned above its femoral midshaft.     

Continual measurement of intramedullary blood perfusion with laser Doppler flowmetry in intact and ostectomized tibiae of rabbits

Blood flow is important for the healing of bone fractures. Until now, however, there have been no publications on the daily, continual measurement of intramedullary blood perfusion using laser Doppler flowmetry (LDF) in the conscious animal. In this study, a model for the daily, continual measurement of intramedullary blood perfusion by LDF and the temperature near the cortex both in intact and ostectomized tibiae in the conscious rabbit is described. The probes for blood perfusion and temperature measurement were implanted permanently at three different localizations into the right tibia of 10 adult New Zealand White rabbits. The probes were held in place by a bilateral, single-plane external fixator. In five of these animals, a midshaft tibial ostectomy was created in order to simulate a fracture. Intramedullary blood perfusion and temperature were measured daily over 49 days. While in intact tibiae no significant (P > 0.05) differences were found in blood perfusion readings taken at various time points, for mean values or for blood perfusion over time, in ostectomized tibiae the differences were significant: various time points (P = 0.0056), mean values (P = 0.0034) and blood perfusion over time (P = 0.0337). Blood perfusion readings at the centre probe were elevated compared with those at the proximal and distal probes. Thus, a revascularization in the ostectomy gap during the fracture healing was proven by means of the LDF. No influence of the blood perfusion on the temperature in the ostectomy area could be determined during healing of the ostectomy. The described model seems suitable for the continual measurement of intramedullary blood perfusion both in intact and ostectomized tibiae in the conscious rabbit.