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.     

Allometry between length and cross-sectional dimensions of the femur and tibia in Homo sapiens sapiens

Allometric equations relating length and cross-sectional geometric properties of the femur and tibia are generated using skeletal remains from three recent human population samples. Approximate isometry, or geometric similarity, is found both within and between samples. Cross-sectional areas scale to approximately length2, while second moments of area scale to approximately length4. It is shown that this is consistent with the maintenance of equivalent mechanical stress in long bones of different length under dynamic loadings in vivo. Other evidence indicates that bending and torsional loadings are more critical than axial loadings in the determination of lower limb bone cross-sectional dimensions.     

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.     

Sexual dimorphism in human lower limb bone structure: relationship to subsistence strategy and sexual division of labor

Cross-sectional geometric properties of the human femur and tibia are compared in males and females in a number of recent and archaeological population samples extending back to the Middle Paleolithic. There is a consistent decline in sexual dimorphism from hunting-gathering to agricultural to industrial subsistence strategy levels in properties which measure relative anteroposterior bending strength of the femur and tibia in the region about the knee. This trend parallels and is indicative of reductions in the sexual division of labor, in particular differences in the relative mobility of males and females. Sexual dimorphism in mediolateral bending strength near the hip shows no consistent temporal trend, probably reflecting relatively constant sex differences in pelvic structure related to the requirements of childbirth. Upper and Middle Paleolithic samples are indistinguishable in terms of sexual dimorphism from modern huntergatherers, suggesting a similar sexual division of labor. The results illustrate the utility of cross-sectional geometric parameters of long bone diaphyses in reconstructing behavioral differences within and between past populations. Some variations in the accuracy of sexing techniques based on diaphyseal measurements of the lower limb long bones may also be explained by these behavioral and structural factors.     

Relative strength of the tibia and fibula and locomotor behavior in hominoids

The fibula has rarely been considered in comparative morphological studies, probably due to its relatively minor role in carrying mechanical loads. However, some differences in morphology (and inferred function) of the fibula between humans and apes, and within apes, have been noted and related to differences in positional behavior. Therefore, the study of tibiofibular relations may be useful in characterizing such differences. This study examines cross-sectional geometric (CSG) properties (cortical area and polar section modulus, Z(p)) of the tibia and fibula at mid-diaphysis across a sample (n=87) of humans, chimpanzees, gorillas, orangutans, and gibbons. The fibula is compared against the tibia in the different taxa. The results indicate that the robusticity of the fibula relative to that of the tibia can be explained in terms of differences in positional behavior. In particular, hominoids that are more arboreal (i.e., gibbons, orangutans, and chimpanzees) possess a relatively more robust fibula than do hominoids that are more terrestrial (i.e., gorillas and humans). The difference appears to be a consequence of the more mobile fibula and more adducted position of the hindlimb necessary in an arboreal environment. Apart from providing the first CSG data on the fibula, these results may be helpful in reconstructing the locomotor behavior of fossil hominoids.     

Articular-surface-based automatic anatomical coordinate systems for the knee bones

Increasing use of patient-specific surgical procedures in orthopaedics means that patient-specific anatomical coordinate systems (ACSs) need to be determined. For knee bones, automatic algorithms constructing ACSs exist and are assumed to be more reliable than manual methods, although both approaches are based on non-unique numerical reconstructions of true bone geometries. Furthermore, determining the best algorithms is difficult, as algorithms are evaluated on different datasets. Thus, in this study, we developed 3 algorithms, each with 3 variants, and compared them with 5 from the literature on a dataset comprising 24 lower-limb CT-scans. To evaluate algorithms’ sensitivity to the operator-dependent reconstruction procedure, the tibia, patella and femur of each CT-scan were each reconstructed once by three different operators.Our algorithms use principal inertia axis (PIA), cross-sectional area, surface normal orientations and curvature data to identify the bone region underneath articular surfaces (ASs). Then geometric primitives are fitted to ASs, and the ACSs are constructed from the geometric primitive points and/or axes. For each bone type, the algorithm displaying the least inter-operator variability is identified. The best femur algorithm fits a cylinder to posterior condyle ASs and a sphere to the femoral head, average axis deviations: 0.12°, position differences: 0.20 mm. The best patella algorithm identifies the AS PIAs, average axis deviations: 0.91°, position differences: 0.19 mm. The best tibia algorithm finds the ankle AS center and the 1st PIA of a layer around a plane fitted to condyle ASs, average axis deviations: 0.38°, position differences: 0.27 mm.     

Automatic determination of anatomical coordinate systems for three-dimensional bone models of the isolated human knee

The combination of three-dimensional (3-D) models with dual fluoroscopy is increasingly popular for evaluating joint function in vivo. Applying these modalities to study knee motion with high accuracy requires reliable anatomical coordinate systems (ACSs) for the femur and tibia. Therefore, a robust method for creating ACSs from 3-D models of the femur and tibia is required. We present and evaluate an automated method for constructing ACSs for the distal femur and proximal tibia based solely on 3-D bone models. The algorithm requires no observer interactions and uses model cross-sectional area, center of mass, principal axes of inertia, and cylindrical surface fitting to construct the ACSs. The algorithm was applied to the femur and tibia of 10 (unpaired) human cadaveric knees. Due to the automated nature of the algorithm, the within specimen variability is zero for a given bone model. The algorithm’s repeatability was evaluated by calculating variability in ACS location and orientation across specimens. Differences in ACS location and orientation between specimens were low (<1.5 mm and <2.5°). Variability arose primarily from natural anatomical and morphological differences between specimens. The presented algorithm provides an alternative method for automatically determining subject-specific ACSs from the distal femur and proximal tibia.     

Assessment of the bilateral asymmetry of human femurs based on physical,densitometric, and structural rigidity characteristics

The purpose of this study was to perform a comprehensive geometric, densitometric, biomechanical, and statistical analysis of paired femurs for an adult population over a wide age range using three imaging modalities to quantify the departure from symmetry in size, bone mineral density, and cross-sectional structural rigidities.Femur measurements were obtained from 20 pairs of cadaveric femurs. Dimensions of these anatomic sites were measured using calipers directly on the bone and plain radiographs. Dual energy X-ray absorptiometry was used to measure bone mineral density. Bone mineral content and axial and bending rigidities were determined from the CT imaging.No differences were observed between the geometric measurements, DXA based bone mineral density and axial and bending rigidities of left and right femurs (P>0.05 for all cases). Left and right proximal femurs are not significantly different based on geometric, densitometric, and structural rigidity measurements. However, absolute left–right differences for individual patients can be substantial. When using the contralateral femur as a control, the number of femur pairs required to assess significant changes in anatomic dimensions and structural properties induced by a tumor, infection, fracture, or implanted device can range from 3 to 165 pairs depending on the desired effect size or sensitivity (5% or 10% difference).This information is important both for femoral arthroplasty implant design and the use of the contralateral femur as an intra-subject control for clinical assessment and research studies. In addition, our statistical analysis provides sample size estimates for planning future orthopedic research studies.     

Femoral ontogeny and locomotor biomechanics of Dryosaurus lettowvorbecki (Dinosauria, Iguanodontia)

Ontogenetic changes in femoral morphology and locomotion were analysed in the iguanodontian dinosaur Dryosaurus lettowvorbecki using cross-sectional data and applying principles of beam theory. The results presented here suggest that locomotor ontogeny in D. lettowvorbecki was more complicated than has generally been recognized. The percentage cortical area (a measure of the relative amount of bone) increases abruptly over a relatively short period during early ontogeny and then remains uniform during subsequent increases in body size. Modifications in cross-sectional shape also occur with increasing size, as demonstrated by differences in second moment of area ratios. The patterns of change in these properties indicate that the orientation of mechanical loadings acting on the femur of D. lettowvorbecki differed at various stages of growth and development. It is suggested that the alterations in femoral architecture described here reflect a shift from quadrupedality to bipedality early in the ontogeny of this animal.     

Automatic construction of an anatomical coordinate system for three-dimensional bone models of the lower extremities – Pelvis,femur, and tibia

Automated methods for constructing patient-specific anatomical coordinate systems (ACSs) for the pelvis, femur and tibia were developed based on the bony geometry of each, derived from computed tomography (CT). The methods used principal axes of inertia, principal component analysis (PCA), cross-sectional area, and spherical and ellipsoidal surface fitting to eliminate the influence of rater's bias on reference landmark selection. Automatic ACSs for the pelvis, femur, and tibia were successfully constructed on each 3D bone model using the developed algorithm. All constructions were performed within 30 s; furthermore, between- and within- rater errors were zero for a given CT-based 3D bone model, owing to the automated nature of the algorithm. ACSs recommended by the International Society of Biomechanics (ISB) were compared with the automatically constructed ACS, to evaluate the potential differences caused by the selection of the coordinate system. The pelvis ACSs constructed using the ISB-recommended system were tilted significantly more anteriorly than those constructed automatically (range, 9.6–18.8°). There were no significant differences between the two methods for the femur. For the tibia, significant differences were found in the direction of the anteroposterior axis; the anteroposterior axes identified by ISB were more external than those in the automatic ACS (range, 17.5–25.0°).     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials: the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

Variation in fibular robusticity reflects variation in mobility patterns

During hominin plantigrade locomotion, the weight-bearing function of the fibula has been considered negligible. Nevertheless, studies conducted on human samples have demonstrated that, even if less than that of the tibia, the load-bearing function of the fibula still represents a considerable portion of the entire load borne by the leg. The present study assesses whether variation in habitual lower limb loading influences fibular morphology in a predictable manner. To achieve this, both fibular and tibial morphology were compared amongst modern human athletes (field hockey players and cross-country runners) and matched sedentary controls. Peripheral quantitative computed tomography was used to capture two-dimensional, cross-sectional bone images. Geometric properties were measured at the midshaft for each bone. Results show a trend of increased fibular rigidity from control to runners through to field hockey players. Moreover, relative fibular robusticity (fibula/tibia) is significantly greater in hockey players compared with runners. These results are likely the consequence of habitual loading patterns performed by these athletes. Specifically, the repeated directional changes associated with field hockey increase the mediolateral loading on the lower leg in a manner that would not necessarily be expected during cross-country running. The present study validates the use of the fibula in association with the tibia as a mean to provide a more complete picture of leg bone functional adaptations. Therefore, the fibula can be added to the list of bones generally used (tibia and femur) to assess the correspondence between mobility patterns and skeletal morphology for past human populations.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

Genetic and ecological dynamics of species replacement in an arid-land river system

Museum records indicate that Hybognathus placitus was introduced into the Pecos River, New Mexico during the early 1960s. Approximately 10 years later, a congener, Hybognathus amarus, was extirpated from the system. We used microsatellite and mtDNA data, ecological data and modelling, and a computer simulation approach to reconstruct the history of invasion and species replacement. To identify the potential role of hybridization and introgression, we genetically screened H. amarus (n = 389) from the Rio Grande, New Mexico, and H. placitus (n = 424) from the Pecos River, New Mexico using four nuclear microsatellites and a partial fragment of the mtDNA ND4 gene. Assignment tests excluded hybridization as a primary factor in species replacement and suggested a role for interspecific competition. Genetic analyses showed that H. placitus were introduced into the Pecos River from at least two genetically distinct source populations in the Canadian and Red rivers, Oklahoma. Lotka-Volterra models of interspecific competition indicated that the number of founding individuals could have been as few as 20 for H. placitus to have competitively displaced H. amarus in the Pecos River in 10 to 15 generations. Observed differences of allele frequencies between source and founder populations indicated that between 32 and 115 H. placitus individuals founded the Pecos River. Genetic and ecological data suggest that interspecific competition could have led to species replacement in this arid-land river system.     

Cytogenetic studies inSinipta dalmani Stal (Orthoptera: Acrididae). III: Pericentric M4 inversion affecting morphological traits

Three population samples ofSinipta dalmani from Entre Rios Province in Argentina polymorphic for the M₄ inversion were analysed for five body-size-related traits: total body, tegmina, third femur, third tibia and thorax lengths. MANOVA and individual ANOVA revealed that there were significant differences between karyomorphs for total body and thorax lengths. The univariate analyses also revealed significant differences for tibia length, showing an important influence of correlated traits. The influence of the M₄ inversion leads to a significant reduction of body size in the homozygotes for the M₄ inversion. Comparison of mean values for tibia length through Scheffe’s method revealed that (i) heterozygotes were intermediate between homozygotes, and (ii) there were significant differences between homozygotes. These results suggest that the differences between karyomorphs are largely additive. On the contrary, the heterozygote mean value for thorax length differs significantly from the average of the two homozygotes, showing that the dominance effects are mainly related with the differences between karyomorphs. This parametric comparison using total body length data revealed only marginally significant differences. Regression analysis of morphological traits on number of inverted chromosomes revealed that there was a dose effect only for third tibia length.     

Structural and mechanical indicators of limb specialization in primates

The structural mechanics of femora and humeri from primates representing a wide spectrum of habitual locomotor activities were examined to determine how cross-sectional properties vary with functional specializations of the extremities. Average bending rigidities of the midshaft of humerus and femur were measured in 60 individuals of four nonhuman primate species (Macaca nemestrina, Macaca fascicularis, Presbytis cristata, Hylobates lar) using single-beam photon absorptiometry. Linear regression analyses of the loge transformed data were used to assess the relative usage of the forelimb and hindlimb in propulsion and weight bearing, and to evaluate deviations from generalized mammalian quadrupedalism. The results suggest that average bending rigidities of the humerus and femur in primates reflect the extent to which the forelimb and hindlimb are used differently in locomotion; deviations of average bending rigidity from geometric similarity indicate functional variations from generalized mammalian quadrupedalism and the ratio of humeral to femoral bending rigidity can be used to identify trends towards hindlimb or forelimb dominance in locomotion and can be employed in general to determine how the limb was used.     

Effects of joint unloading and reloading on human cartilage morphology and function, muscle cross-sectional areas, and bone density - a quantitative case report

Recent studies have shown that thinning of human cartilage occurs with unloading, but no data are available on the effect of remobilization (after immobilization) on knee joint cartilage status in humans. We examined a 36-year-old patient after 6 weeks of unilateral immobilization. Knee joint cartilage morphology (patella and tibia), patellar cartilage deformation, and thigh muscle cross-sectional areas were assessed with quantitative MR imaging and bone density with peripheral quantitative computed tomography (pQCT) during 24 months of remobilization. The immobilized limb displayed lower muscle cross-sectional areas (MCSA) of the knee extensors (-36%), lower bone density of the femur and tibia (-12/-6%), lower patellar cartilage thickness (-14%), but no side differences of tibial cartilage thickness. During remobilization, side differences decreased to -4% for knee extensor MCSAs, to -6%/-3% for femoral and tibial BMD, and to -8% for patellar cartilage thickness. No change was observed in tibial cartilage. Patellar deformation decreased from 9% to 4% after 15 months. In conclusion, we observed substantial changes of thigh MCSAs, but little (patella) to no (tibia) change in cartilage thickness during remobilization. These preliminary results indicate that human cartilage macro-morphology may be less adaptive to variations of the mechanical loading than muscle and bone.     

Positional cell surface antigens in an insect appendage

Summary Mice were immunized with membrane preparations of epidermal cells taken from different parts (internal and external face of femur and apex and base of tibia) of the metathoracic legs of cockroach larvae. Using indirect immunofluorescence, anti-internal face of femur antibodies were observed to bind preferentially to membranes from the internal face of the femur; similarly, anti-external face of femur antibodies bound preferentially to membranes from the external face of the femur. We also found a preferential binding of anti-apex of tibia antibodies to membranes from the apex of the tibia and anti-base of the tibia antibodies to membranes from the base of the tibia. When anti-tibia sera were tested on membranes from the femur, anti-apex of tibia antibodies bound preferentially to membranes from the apex of the femur, and anti-base of tibia antibodies bound preferentially to membranes from the base of the femur.This demonstrates that epidermal cell membranes from the different parts of the leg differ in their antigenic properties, and that these differences are related to their position around the appendage and along the proximodistal axis of segments.These results are in agreement with those of previous graft experiments and with the concept of ordered sequences in insect appendages.     

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.     

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.