华南地区男性成年人由长骨长度推算身长的回归方程

从近年来收集的华南地区汉族成年男性50具已知生前身长的骨骼材料,算出从各长骨推算身长的常数(a)及回归系数(b),并算出长骨长度与身高的相关系数(r)数值在0.516—0.913之间,表明相关度较为密切,在此基础上算出10个由各长骨的估计身长的回归方程。并采用校正值:0.6毫米×(年龄—30),校正因年龄所造成的身长误差。从肱骨、腓骨及肱骨加桡骨、股骨加胫骨的长度推算身长最为理想。本文所得的回归方程,适用于华南人。     

中国汉族女性长骨碎片的身高推断

本文作者通过对69副有生前确切资料的中国汉族女性四肢长骨的研究,在女性四肢长骨推断身高的基础上,参考国内外学者的研究方法,选择左右侧肱骨,尺骨,桡骨,股骨,胫骨,腓骨的局部测量项目,其中肱骨8项,尺骨3项,桡骨3项,股骨14项,胫骨8项,腓骨3项,用SPSS软件包对测量项目进行统计分析,建立了中国汉族女性破碎长骨推断身高的回归方程。本文所建方程可以用于中国汉族女性破碎长骨的身高推断,其中肱骨,股骨,胫骨碎片推断身高的效果较好。     

Estimation stature from X-rays of metacarpals in the Turkish population

Determination of stature is as important as the determination of sex and age when analyzing and identifying the remains of skeletons. Stature, in an approximate and widespread manner, is determined by the femur and tibia, i.e. those long bones that affect stature directly. However, when long bones are not available or when they are found in a very badly preserved condition that does not permit any estimation on stature, then other bones of the body can also be used for this purpose. The aim of this study is to determine stature with the help of metacarpals in the Turkish population. In this study, by using the X-ray films of metacarpal bones of 100 females and 100 males, regression equations have been set up for 5 metacarpal bones. The coefficients of correlation existing between the metacarpal bones and stature, together with the standard errors of these equations, have been intensively examined in this study. The results of studies conducted by other researchers such as Musgrave & Harneja (1978) and Meadows & Jantz (1992) have been compared with the results of our study. As a result of this comparison, the difference existing between them has been found to be significant according to the results of the t-test (p < 0.05, p < 0.01 and p < 0.001). The significance of such results proves that the general body characteristics and body proportions of populations are differing from each other and therefore specific regression equations for the different populations have to be set up.     

Calcaneal measurement in estimation of stature of South African blacks

Stature (height) is an important factor in establishing the identity of a person in the living as well as in the skeletonized state. When stature is estimated from the bones of the limbs, regression equations, which estimate the ratios of the lengths of bones to the height of the individual, are generated. The majority of bones that were used previously were the long bones. The calcaneus was used for estimating stature only in American whites and blacks (Holland [1995] Am. J. Phys. Anthropol. 96:315-320). The regression equations that he generated were found to be useful for stature estimation in these population groups. Since the calcaneus has not been used for the same purpose in South Africa, the aim of this study was to derive regression equations that will allow this bone to be used for stature estimation in South African blacks. In total, 116 complete skeletons (60 males and 56 females) were selected from the Raymond A. Dart Collection of Human Skeletons, School of Anatomical Sciences, University of the Witwatersrand (Johannesburg, South Africa). The skeletal heights of these sets of skeletons were calculated using the anatomical method of Fully ([1956] Ann. Med. Leg. 35:266-273). Nine parameters of the calcaneus were measured and matched against skeletal heights, using univariate and multivariate regression methods. Regression equations were obtained for estimation of the stature of the South African black population from the calcaneus. The standard error of estimate that was obtained with univariate regression analysis was higher than the corresponding values using multivariate regression analysis. In both cases, the standard errors of estimate compared well with the values obtained for fragmentary long bones by previous authors.     

Determination of adult stature from metatarsal length

The results of a study to determine the value of foot bones in reconstructing stature are presented. The data consist of length measurements taken on all ten metatarsals as well as on cadaver length from a sample of 130 adults of documented race, sex, stature, and, in most cases, age. Significant correlation coefficients (.58-.89) are shown between known stature and foot bone lengths. Simple and multiple regression equations computed from the length of each of these bones result in standard errors of estimated stature ranging from 40-76 mm. These errors are larger than those for stature calculated from complete long bones, but are approximately the same magnitude for stature calculated from metacarpals and fragmentary long bones. Given that metatarsals are more likely to be preserved unbroken than are long bones and given the ease with which they are accurately measured, the formulae presented here should prove useful in the study of historic and even prehistoric populations.     

Body mass and stature estimation based on the first metatarsal in humans

Archaeological assemblages often lack the complete long bones needed to estimate stature and body mass. The most accurate estimates of body mass and stature are produced using femoral head diameter and femur length. Foot bones including the first metatarsal preserve relatively well in a range of archaeological contexts. In this article we present regression equations using the first metatarsal to estimate femoral head diameter, femoral length, and body mass in a diverse human sample. The skeletal sample comprised 87 individuals (Andamanese, Australasians, Africans, Native Americans, and British). Results show that all first metatarsal measurements correlate moderately to highly (r = 0.62-0.91) with femoral head diameter and length. The proximal articular dorsoplantar diameter is the best single measurement to predict both femoral dimensions. Percent standard errors of the estimate are below 5%. Equations using two metatarsal measurements show a small increase in accuracy. Direct estimations of body mass (calculated from measured femoral head diameter using previously published equations) have an error of just over 7%. No direct stature estimation equations were derived due to the varied linear body proportions represented in the sample. The equations were tested on a sample of 35 individuals from Christ Church Spitalfields. Percentage differences in estimated and measured femoral head diameter and length were less than 1%. This study demonstrates that it is feasible to use the first metatarsal in the estimation of body mass and stature. The equations presented here are particularly useful for assemblages where the long bones are either missing or fragmented, and enable estimation of these fundamental population parameters in poorly preserved assemblages.     

Estimation of height from the length of long bones in a Portuguese adult population

Research was undertaken on 200 individuals (100 males and 100 females) from the northern districts of Portugal, all Caucasian, between the ages of 20 and 59. Height and bones were measured directly. Estimation of stature is obtained by applying a mathematical method based on a multivariable linear regression between the height of the cadaver and the lengths of humerus and femur. Humerus is measured on full length; femur is measured on both physiological and maximum lengths. Regression formulae and tables for males and females are produced for application in forensic anthropology when studying human skeletal remains. Comparisons are made between these tables and those of earlier authors, allowing us to verify important differences. One of the conclusions concerns the application of regression formulae based on some segment measurements. Due to the extremely high values of standard deviations, these may have no practical application.     

On the allometry of long bones in dogs (Canis familiaris)

The allometric relations of diameter and length of humerus, ulna, femur, and tibia of 108 specimens, from 63 different breeds of dogs and 12 specimens of wolves, were calculated by means of model II of regression or major axis method. Only for the tibia were the values of wolves included in the cluster formed for dog breeds. Consequently, separate lines of regression were calculated for the other bones. Results agree in general with the exponents predicted by the theory of geometric similarity; however, the slope obtained for femur (0.865) differed significantly from this. Morphology of the long bones of the legs does not differentiate dogs and wolves; this probably reflects secondary convergence among wolves with relatively modern breeds of dogs.     

掌骨X线测量推断身高的研究

随机选取在校健康大学生186人(男90人, 女96人, 年龄18—27岁), 拍摄双手后前位372侧X线片, 测量身高和掌骨的长与宽。通过掌骨和身高的测量, 分析掌骨各参数与身高的关系, 为人类学和法医学的身高推断积累研究资料。掌骨长与身高的相关性明显高于掌骨宽, 其中男性第2掌骨长与身高相关性最高, 其线性回归方程为Ym=1097.320+9.337X; 女性第3掌骨长与身高的相关性最高, 其线性回归方程为Yf=1016.752+9.878X。男性第2掌骨长和女性第3掌骨长与身高的相关性最高, 可分别作为推断身高的依据。     

Allometry and curvature in the long bones of quadrupedal mammals

The allometric relationships between basic structural proportions in long bones are examined in the humerus, radius, femur and tibia for a diverse group of 42 terrestrial quadrupedal mammals that span a size range from 0.02–6000 kg. Non-linear scaling is found for length vs. diameter in the tibia and radius, suggesting that the mechanical constraints on the skeleton differ within large and small body-size mammals. Curvature normalized to mid-shaft radius scales differently in the different long bones. Curvature is poorly related to size in the proximal limb bones (humerus and femur) while it decreases systematically with size in the tibia (mass exponent −0.13). The scaling of normalized curvature in the radius is unique among long bones. Variability of curvature in the radius is reduced at any size in comparison to that found in the other long bones. Normalized curvature is constant within the small body size group (0.02 to approximately 100 kg) while it decreases sharply with size within animals over 100 kg body mass. The unusual scaling found in the radius is probably the result of this bone's close alignment with the extrinsic forces which act on it during locomotion. The change in scaling within the radius for animals of different size may be indicative of more general size-dependent mechanical trade-offs which are masked by the complex loading circumstances of the other long bones.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex, and neck length. In this study, we measured the length, mediolateral (ML) diameter, craniocaudal (CC) diameter and circumference of the humerus, radius, metacarpus, femur, tibia, and metatarsus in 10 fetuses, 21 females, and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340 ± 50 mm at birth to 700 ± 120 mm at maturity, while average diameters increased from 30 ± 3 to 70 ± 11 mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso‐ or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones, ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically, respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments. We concluded that the patterns of bone growth in males and females are identical. In fetuses, the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution. Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture. J. Morphol. 276:503–516, 2015. © 2014 Wiley Periodicals, Inc.     

Stature in Holocene foragers of North India

The Ganga Plain of North India provides an archaeological and skeletal record of semi‐nomadic Holocene foragers in association with an aceramic Mesolithic culture. Prior estimates of stature for Mesolithic Lake Cultures (MLC) used inappropriate equations from an American White reference group and need revision. Attention is given to intralimb body proportions and geo‐climatic provenance of MLC series in considering the most suitable reference population. Regression equations from ancient Egyptians are used in reconstructing stature for MLC skeletal series from Damdama (DDM), Mahadaha (MDH), and Sarai Nahar Rai (SNR). Mean stature is estimated at between 174 (MDH) and 178 cm (DDM and SNR) for males, and between 163 cm (MDH) and 179 cm (SNR) for females. Stature estimates based on ancient Egyptian equations are significantly shorter (from 3.5 to 7.1 cm shorter in males; from 3.2 to 7.5 cm shorter in females) than estimates using the American White reference group. Revised stature estimates from tibia length and from femur + tibia more accurately estimate MLC stature for two reasons: a) these elements are highly correlated with stature and have lower standard estimates of error, and b) uncertainty regarding methods of measuring tibia length is avoided. When compared with Holocene samples of native Americans and Mesolithic Europeans, MLC series from North India are tall. This aspect of their biological variation confirms earlier assessments and results from the synergistic influence of balanced nutrition from broad‐spectrum foraging, body‐proportions adapted to a seasonally hot and arid climate, and the functional demands of a mobile, semi‐nomadic life‐style. Am J Phys Anthropol 153:408–416, 2014. © 2013 Wiley Periodicals, Inc.     

A comparison of mechanical properties derived from multiple skeletal sites in mice

Laboratory mice provide a versatile experimental model for studies of skeletal biomechanics. In order to determine the strength of the mouse skeleton, mechanical testing has been performed on a variety of bones using several procedures. Because of differences in testing methods, the data from previous studies are not comparable. The purpose of this study was to determine which long bone provides the values closest to the published material properties of bone, while also providing reliable and reproducible results. To do this, the femur, humerus, third metatarsal, radius, and tibia of both the low bone mass C57BL/6H (B6) and high bone mass C3H/HeJ (C3H) mice were mechanically tested under three-point bending. The biomechanical tests showed significant differences between the bones and between mouse strains for the five bones tested (p < 0.05). Computational models of the femur, metatarsal, and radius were developed to visualize the types of measurement error inherent in the three-point bending tests. The models demonstrated that measurement error arose from local deformation at the loading point, shear deformation and ring-type deformation of the cylindrical cross-section. Increasing the aspect ratio (bone length/width) improved the measurement of Young's modulus of the bone for both mouse strains (p < 0.01). Bones with the highest aspect ratio and largest cortical thickness to radius ratio were better for bending tests since less measurement error was observed in the computational models. Of the bones tested, the radius was preferred for mechanical testing because of its high aspect ratio, minimal measurement error, and low variability.     

Using scapular measurements in regression formulae for the estimation of stature

There are very few papers in forensic literature in which scapular dimensions have been used for estimation of living stature. Allowing the forensic duty to estimate the living stature of skeletal remains, using intact or fragmented scapulae, the Authors have performed multiple regression analysis between the measurements taken from 80 scapula (40 male and 40 female) belonging to a skeletal collection with anthropometric known data. Seven parameters (max length, max breadth, max acrocoracoid distance, length of acromion, max length of coracoid, length of glenoid cavity, width of glenoid cavity) have been recorded. By statistical analysis multiple and linear regressions have been obtained. The results show that living stature may be determined by using regression formulae of single or associated parameters taken from whole or fragmented scapulae. In absence of intact or fragmented long limb bones, scapula sample can be reliably employed for the estimation of stature in forensic practice.     

Estimating stature in fossil hominids: which regression model and reference sample to use?

coResearchers have long appreciated the significant relationship between body size and an animal's overall adaptive strategy and life history. However, much more emphasis has been placed on interpreting body size than on the actual calculation of it. One measure of size that is especially important for human evolutionary studies is stature. Despite a long history of investigation, stature estimation remains plagued by two methodological problems: (1) the choice of the statistical estimator, and (2) the choice of the reference population from which to derive the parameters.This work addresses both of these problems in estimating stature for fossil hominids, with special reference to A.L. 288-1 (Australopithecus afarensis) and WT 15000 (Homo erectus). Three reference samples of known stature with maximum humerus and femur lengths are used in this study: a large (n=2209) human sample from North America, a smaller sample of modern human pygmies (n=19) from Africa, and a sample of wild-collected African great apes (n=85). Five regression techniques are used to estimate stature in the fossil hominids using both univariate and multivariate parameters derived from the reference samples: classical calibration, inverse calibration, major axis, reduced major axis and the zero-intercept ratio model. We also explore a new diagnostic to test extrapolation and allometric differences with multivariate data, and we calculate 95% confidence intervals to examine the range of variation in estimates for A.L. 288-1, WT 15000 and the new Bouri hominid (contemporary with [corrected] Australopithecus garhi). Results frequently vary depending on whether the data are univariate or multivariate. Unique limb proportions and fragmented remains complicate the choice of estimator. We are usually left in the end with the classical calibrator as the best choice. It is the maximum likelihood estimator that performs best overall, especially in scenarios where extrapolation occurs away from the mean of the reference sample. The new diagnostic appears to be a quick and efficient way to determine at the outset whether extrapolation exists in size and/or shape of the long bones between the reference sample and the target specimen.     

Estimation of australopithecine stature from long bones: A.L.288-1 as a test case

Regression equations for the estimation of stature from long bones, although derived from modern human populations, are frequently applied to early hominids. In fact, some of these equations have even been recommended or especially created to be applied to Australopithecus remains. In this study, 45 sets of regression and correlation formulae, recurrent in anthropological and medico-legal literature, are applied to long bones of the Pliocene hominid A.L.288-1 ('Lucy'), in order to assess which, if any, could be considered suitable for stature reconstruction in 'gracile' australopithecines. Virtually every method based on regression equations overestimates stature as compared with the estimate based on reconstruction of all the preserved skeletal parts. In addition, most methods failed to give consistent results with data from different limb segments. None of the sets of regression formulae tested here can be recommended as a reliable means of stature estimation in 'gracile' australopithecines.     

Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.     

Methods for estimating missing human skeletal element osteometric dimensions employed in the revised fully technique for estimating stature

One of the greatest limitations to the application of the revised Fully anatomical stature estimation method is the inability to measure some of the skeletal elements required in its calculation. These element dimensions cannot be obtained due to taphonomic factors, incomplete excavation, or disease processes, and result in missing data. This study examines methods of imputing these missing dimensions using observable Fully measurements from the skeleton and the accuracy of incorporating these missing element estimations into anatomical stature reconstruction. These are further assessed against stature estimations obtained from mathematical regression formulae for the lower limb bones (femur and tibia). Two thousand seven hundred and seventeen North and South American indigenous skeletons were measured, and subsets of these with observable Fully dimensions were used to simulate missing elements and create estimation methods and equations. Comparisons were made directly between anatomically reconstructed statures and mathematically derived statures, as well as with anatomically derived statures with imputed missing dimensions. These analyses demonstrate that, while mathematical stature estimations are more accurate, anatomical statures incorporating missing dimensions are not appreciably less accurate and are more precise. The anatomical stature estimation method using imputed missing dimensions is supported. Missing element estimation, however, is limited to the vertebral column (only when lumbar vertebrae are present) and to talocalcaneal height (only when femora and tibiae are present). Crania, entire vertebral columns, and femoral or tibial lengths cannot be reliably estimated. Further discussion of the applicability of these methods is discussed.     

Geometry and evolutionary parallelism in the long bones of cavioid rodents and small artiodactyls

Morphological parallelism between South American cavioid rodents and small artiodactyls from the Old World has been postulated for a long time. Our study deals with this question from the point of view of biomechanical characteristics of the long bones. For this, cross-sectional area, second moment of the area, polar moment, athletic ability indicators and strength were calculated for the long bones (i.e. humerus, radius, femur and tibia) of five species of cavioids and two species of artiodactyls. Regressions of all these variables to body mass were established. Regarding the cross-sectional area, the confidence intervals show that the exponents calculated are not significantly different from the geometrical predicted value. The exponents obtained for the second moment of area and the polar moment are not significantly different from the geometrical prediction, except for the humerus. The two indicators of athletic ability scaled as expected, but the bending indicator of athletic ability of the femur was not correlated to body mass. The exponent calculated for femur strength is not different from zero, while the strength of the humerus decreases slightly with the body mass. Additional statistical tests (ANCOVAs) showed no difference between the values of these variables calculated for the samples studied of artiodactyls and rodents. The present results are consistent with the hypothesis that there is significant evolutionary parallelism between cavioid rodents and small artiodactyls.