Updated lower limb stature estimation equations for a South African population group

FUNDING: Carnegie Corporation (NY, USA); National Research Foundation (South Africa) One of the main steps in the identification of an unknown person, from their skeletal remains, is the estimation of stature. Measurements of intact long bones of the upper and lower extremities are widely used for this purpose because of the high correlation that exists between these bones and stature. In 1987, Lundy and Feldesman presented regression equations for stature estimation for the black South African population group based on measurements of bones from the Raymond A. Dart Collection of Human Skeletons. Local anthropologists have questioned the validity of these equations. Living stature measurement and magnetic resonance imaging scanograms of 58 adult volunteers (28 males and 30 females) representing the modern black South African population group were obtained. Physiological length of the femur (FEPL) and physiological length of the tibia (TPL) were measured on each scanogram and substituted into appropriate equations of Lundy and Feldesman (S Afr J Sci. 1987;83:54–55) to obtain total skeletal height (TSHL&F). Measured total skeletal height (TSHMeas) for each subject from scanograms was compared with TSHL&F. Both FEPL and TPL presented with significantly high positive correlations with TSHMeas. A comparison between TSHL&F and TSHMeas using a paired t-test, showed a statistically significant difference – an indication of non-validity of Lundy and Feldesman’s equations. New regression equations for estimation of living stature were formulated separately for male and female subjects. The standard error of estimate was low, which compared well with those reported for other studies that used long limb bones.


Introduction
Estimation of stature from complete skeletons (anatomical method) or from individual/combination measurements of bones (mathematical method) forms a necessary part of the process of establishing the biological profile of an individual from recovered or discovered skeletons. The former method has been reported to produce accurate estimates of stature and is neither population nor sex-specific. [1][2][3] However, it has the disadvantages of being time consuming and very tedious. 2 In addition, the anatomical method can be used for estimation of stature only if an intact and complete skeleton is available, which is considered a luxury in forensic cases. Consequently, the latter method, i.e. the mathematical method, is the most often used method in the absence of a complete skeleton or when bones are recovered in fragmentary states.
The mathematical method is based mainly on a statistical theorem known as regression analysis. This involves the formulation of regression equations from individual measurements or combinations of measurements of intact and fragmentary bones of the skeleton and percutaneous bones. This method is less time-consuming and tedious than the anatomical method and is considered more applicable in most forensic cases. However, the mathematical method is both population and sex specific. It therefore requires that equations for the estimation of stature need to be formulated for different population groups and at appropriate intervals in order to account for temporal changes. 4 There has been a plethora of studies on stature reconstruction using measurements of long bones of upper and lower limbs in different parts of the world following the publication of arguably the largest study on stature reconstruction by Trotter and Gleser 4 in 1958. Regression equations have been formulated for populations including, but not limited to, the Portuguese 5 , Germans 6 , Bulgarian 7 , Polish 8 , Turks 9 , Croatians 10 , Mexicans 11 , Spaniards 12 , Koreans 13 and Japanese 14 . Regression equations have also been formulated from measurements of fragments of long bones for stature reconstruction 15 and other bony elements (e.g. clavicle 16 , skull 17 , scapulae 18 , metacarpals, 19 vertebrae 20 , sacrum 21 , calcaneus 22 and metatarsals 23 ) as long limb bones are often recovered in forensic and archaeological practice in fragmentary states.
In South Africa, a country with a high crime rate, similar regression equations have been formulated from intact long bones 24,25 , fragments of long bones 26 , the skull 27 , sacrum 28 , metatarsals 29 and calcaneus 30 . In 1983, Lundy 31 conducted the first ever study on stature reconstruction in South Africa. Lundy 31 used Fully's 1 method in calculating total skeletal height (TSH) which was later regressed on maximum lengths of humeri, radii, ulnae, femora, tibiae and fibulae. Regression equations were derived separately for male and female black South Africans. 31 Lundy and Feldesman 24 revised the regression equations due to some errors in the computer program handling some data. The regression equations developed by Lundy and Feldesman 24 are the most frequently used stature estimation equations when dealing with black South African skeletal remains; however, results from an unpublished study by Arendse 32 highlighted the need to re-examine these equations, specifically in modern black South Africans. The validity of these equations on a contemporary black South African population has been questioned, as these equations were derived more than three decades ago, using skeletal remains housed in the Raymond A. Dart Collection of Human Skeletons. Regrettably, many skeletal collections do not represent the populations from which they were derived as collections often have an over-representation of the elderly and individuals from lower socio-economic strata. 33,34 Additionally, the effects of secular trends on populations also often render skeletal collections unrepresentative of their modern counterparts. 35,36 As such, many studies are using modern image modalities of living individuals to study skeletonised remains. 12,18,20,37,38 Because there has not been any attempt to test the validity of these equations on living individuals, the aim of this study was to investigate the validity of some of Lundy and Feldesman's equations 24 on a sample of living black South Africans using data collected from magnetic resonance imaging (MRI) scanograms and to calculate new equations, if necessary.

Participants
Prior to the commencement of the study, ethics approval was obtained from the Human Research Ethics Committee of the University of the Witwatersrand, Johannesburg, South Africa (clearance certificate number M180788) to access data collected in two previous studies by Bidmos and Manger 37 and Brits et al. 38 Data used in the current study and how they were obtained have been described in previous studies. 37,38 Participants in these studies 37,38 were individuals from diverse South African black ethnological groups. As previous studies 31, 39 have shown little intertribal variations amongst black South Africans, they were considered a single homologous group. Furthermore, Franklin et al. 40 reported the disappearance of tribal subdivisions, possibly due to inter-marriage between individuals of different groups. More than 88 individuals were approached to participate in both studies. 37,38 However, only data from a final sample of 58 participants (28 males and 30 females) were analysed. The individual measurements of each participant are provided in Supplementary table 1.

Measurements
Living stature of participants was measured, and thereafter, full body MRI scans were collected. Measurement of the living stature (LSM) of each of the participants was taken with a stadiometer on the morning of the MRI scan. This procedure became necessary because of the documented loss of stature during the day. 41 Full body MRI scans were carried out at the Wits Donald Gordon Medical Centre in Johannesburg, South Africa. Each participant was scanned in a supine position as documented in previous studies 37,38 and the scanned images were then transferred to a DVD. A suite of measurements as described in previous studies 37,38 was taken on each scanogram using OsiriX 42 . These measurements are height of cranium, height of axis (C2), height of vertebrae (C3 to L5), height of first sacral vertebra, physiological (bicondylar) length of the femur, physiological length of tibia and talus-calcaneal height. The sum total of these measurements gave the measured total skeletal height (TSH Meas ). Two of these measurements defined and illustrated below were used in the assessment of the validity of Lundy and Feldesman equations 24 : 1. Physiological (bicondylar) length of the femur (FEPL): The linear measurement between the most superior projecting point of the head of the femur and a line connecting the most inferior aspects of the femoral condyles 38 ( Figure 1). This measurement was taken on coronal images.

Physiological length of the tibia (TPL):
The physiological length of the tibia as described by Lundy 43 was measured by excluding the intercondylar eminence of the tibia while including the medial malleolus. In the female sample, the physiological length of the tibia was measured between the tip of the medial malleolus and a line drawn parallel to the superior aspect of the lateral tibial condyle 38 ( Figure 2a). For the male sample, the physiological length of the tibia was measured from the tip of the medial malleolus to the superior aspect of the medial condyle 37 (Figure 2b). This measurement was taken on coronal images. As no guidelines are available for osteometric data collection from MRI scans, the two studies explored various ways to collect the tibial length as reliably and accurately as possible.
Updated stature estimation equations for South Africans Page 2 of 7 Scale = 5 cm The FEPL and TPL measurements were summed to produce an additional skeletal measurement. These measurements were used in conjunction with the stature estimation equations for the femur and tibia developed by Lundy

Data analysis
Prior to data collection for the current study, a test of intra-observer repeatability was performed using Lin's concordance co-efficient of reproducibility. 44 A total of 20 individuals were measured for this purpose and after confirming that the measuring technique was satisfactory (Lin's concordance correlation coefficients for all measurements were between 0.95 and 0.99), data were collected separately for males and females and captured into MS Excel sheets. Thereafter, descriptive statistics were obtained separately for male and female samples using IBM SPSS (version 24). In addition, normality of data was tested and verified for both sexes.

Results
The ages of female subjects ranged between 19 and 60 years, with a mean of 38 years (s.d.=11.2). Male subjects were of a similar agebetween 18 and 56 years with a mean age of 35 years (s.d.=10.5).
The majority of male and female subjects (70%) fell within the 21-45-year age bracket. There is no statistically significant difference between the mean ages of both sexes ( Table 1). The means and standard deviations for LSM, TSH Meas , FEPL and TPL are also shown in Table 1. Mean values of all measurements of male subjects were statistically significantly higher than those for female subjects (Table 1).
Measured values of FEPL, TPL and the combined measurement of FEPL and TPL were substituted into the appropriate sex-specific regression equations of Lundy and Feldesman 24 to estimate total skeletal height (TSH L&F ). TSH L&F was compared with TSH Meas using a paired t-test. Table 2 shows that a statistically significant difference exists between TSH Meas and calculated TSH L&F using Lundy and Feldesman's 24 equations for FEML, TPL and the sum of FEML and TPL. These results indicate that regression equations previously derived for skeletal height estimation by Lundy and Feldesman 24 using FEPL, TPL and a combination of these measurements are no longer valid for male and female black South Africans (Table 2).
Therefore, new regression equations specific for the direct estimation of living stature were calculated from FEPL, TPL and the sum thereof for black South Africans. The correlations between LSM and each of the measured variables -namely FEPL, TPL and a combination of FEPL and TPL -were strong and statistically significant (p<0.0001; Table 3).
In the female sample, FEPL displayed the strongest correlation with LSM (r=0.879, r 2 =0.773) while the lowest correlation was obtained for the regression equation generated for TPL (r=0.792, r 2 =0.627). The SEE for the equations ranged between 2.56 and 3.28 cm (Table 3). In the male   (Table 3).

Discussion
In the current study, MRI was used to study the components of the skeletons that constitute stature of living individuals. MRI was selected as the imaging modality as it does not expose participants to high doses of harmful ionising radiation as is the case with X-ray and computed tomography (CT). 45 Although MRI is not usually used to examine skeletal remains, it has been found that measurements obtained from these scans are comparable to those obtained from CT and dry bones. 45 Furthermore, as is evident from the intra-observer repeatability scores, MRI measurements are easily reproducible. By studying living individuals, the researchers were able to measure living stature as opposed to relying on often overreported statures 46 or questionable cadaveric lengths reported in skeletal collections 31 . It has been shown that cadaveric length is greater than living stature 47 and therefore stature estimation methods using cadaveric length tends to overestimate living stature 48 . To adjust for this, a correction factor of 25 mm was proposed by Trotter and Gleser 49 . However, a recent study by Cardoso et al. 47 showed that the difference between cadaveric length and living stature is greater than initially proposed with an average difference of about 40 mm, and, as such, there is no consensus yet on the adjustment factor required.
By using measured living stature, researchers also did not have to make use of estimates of living stature produced using the anatomical (Fully 1 ) method. This method is considered to be an accurate method for the estimation of skeletal height because it takes into account all the skeletal elements that constitute stature. 2 It remains the most extensively used method in the formulation of regression equations for stature estimation in South Africa. 24 The mean femoral and tibial length measurements from scanograms were 45.2 cm (±2.3 cm) and 38.2 cm (±2.1 cm) for males and 43.3 cm (±2.0 cm) and 36.5 cm (±2.1 cm) for females. The mean femoral measurement from the current study for males was smaller compared to those of black and white North Americans 49 , Spanish 12 and white South Africans 25 but slightly larger than that reported for Japanese 14 .
The mean femoral measurement for the current sample was comparable to that of black South Africans reported by Lundy 43 . The mean femoral measurement for females was larger than those reported for Japanese 14 but smaller than the average recorded by Lundy 43 . The measurement is comparable to that of black North Americans 49 , white South Africans 25 and Spaniards 12 . In addition, mean tibial measurement for females was longer than those reported for black 43 and white South Africans 25 while the mean tibial measurement for males was comparable to that reported for black 24,43 and white South Africans 25 . A direct comparison of bone lengths with other studies were difficult as some studies report cutaneous bone measurements 11 , measurements with cartilage 7 or maximum measurements as opposed to physiological/bicondylar measurements 10,11 . Comparisons of tibial measurements were also limited due to variations in the way in which the tibiae were measured. 52,53 Furthermore, tibial differences or the lack thereof can also be contributed to the MRI techniques used to measure the bone. No standards for the measurement of skeletal remains from MRI scanograms or other image modalities are currently available or are yet to be validated. However, a pilot study has found no significant difference between the tibial lengths measured from MRI scans and the corresponding dry bone measurement. 54 As such, efforts were made to collect data in line with current standard osteometric practices. The differences highlighted above between the various population groups support the need for population-specific equations. All measurements for male subjects were significantly greater than those for female subjects, thus confirming the need for sex-specific regression equations.
Of importance are the differences noted between the femoral and tibial measurements of female black South Africans in the current study compared to those presented by Lundy 43 . These differences hint at secular trends. Secular trends are often associated with changes in environmental conditions such as nutrition, health and medical care 55 and in South Africa could also be related to the abolishment of apartheid. Previously, a lack of secular change in stature and measurements of the femur and tibia were noted in black South African individuals from the early 20th century. 56 However, more recent results have found a positive secular increase in stature in black South Africans along with an increase in lower limb lengths in relation to stature. 57 The reason for the lack of secular change in males is not fully understood and warrants further research; however, it could in part be related to the small sample sizes in the study. Further supporting secular changes are the statistically significant differences observed between measured total skeletal height and all estimates of total skeletal height using Lundy and Feldesman's 24 stature estimation equations. Therefore, as suggested by Meadows and Jantz 35 and Myburgh 57 , new stature estimation equations from lower limb bone measurements of modern black South Africans were calculated in the current study.
All measured variables along with associated regression equations had very strong statistically significant correlations with measured living stature ( Table 3). The correlation between stature and the bicondylar length of the femur was similar between males and females; however, the correlation between the physiological length of the tibia and stature was stronger in males. The association between the femoral and tibial measurements, and stature had an equivalent correlation in males; however, the femur had a stronger association with stature in females. The association between the femur and stature in males in the current study was stronger than that reported for black and white Americans 49 , Spaniards 12 and Koreans 13 , but weaker than that noted for white South Africans 25 and black South Africans 24 ( Table 4). The relationship between the femur and stature in females was stronger than that reported for White Americans 49 and Spaniards 12 , but weaker than associations reported for black South Africans 24 , white South Africans 25 and Koreans 13 ( Table 4).
The association between the tibia and stature in the current male sample was comparable to that reported for Spaniards 12 and white South Africans 25 but stronger than that previously noted by Lundy and Feldesman 24 for black South Africans (Table 4). The correlation between stature and the tibia in females was weaker than that documented for Spaniards 12 and white South Africans 25 and that of black South Africans noted by Lundy and Feldesman 24 (Table 4). Interestingly, the correlation of the combined femur and tibia measurement and stature in females was not stronger than that of the femur alone, while the combined measurement in males showed the strongest correlation to stature. Many studies have reported very strong associations between lower limb long bones and stature (Table 4), because these bones directly contribute to the overall height of a person. 58 The SEE of equations are considered as a measure of accuracy of regression equations. 49 The SEE for stature estimation equations derived from the femoral and tibial measurements in the current male sample was smaller than that reported by various authors for different populations, including that reported for black South Africans by Lundy and Feldesman 24 (Table 4). This was also true for female femoral measurements with the exception of the SEE reported for white South Africans. 25 Interestingly, SEEs from other populations were smaller than the SEE noted for the stature estimation regression equations derived from the tibia in the current female sample ( Table 4). The higher SEE related to the female tibial regression equation is not fully understood and could in part be related to secular trends that have been observed in the distal limb of female black South Africans 57 or could be associated with the slightly larger standard deviation observed for the female tibial measurement, which might hint at greater variation in this measurement in females. Table 3 are equations for the estimation of living stature as opposed to the estimation of total skeletal height which is often the case in South Africa. 24,25,27,29 Lundy and Feldesman 24 derived their total skeletal height estimation equations using the anatomical method in conjunction with soft tissue correction factors proposed by Fully 1 to provide an estimate of stature. A number of researchers 3,37,38 have questioned the accuracy and applicability of Fully's 1 soft tissue correction factors. Consequently, alternative soft tissue correction factors have been proposed by various authors 3,37,38 but there is no consensus on the validity of these factors.

Presented in
In conclusion, we provide regression equations for the estimation of living stature of black South Africans from measurements of the femur and tibia. These equations, with reasonably low SEEs, do not require the addition of soft tissue correction factors. Regrettably, the sample size of this study was very small due to expenses associated with the collection of full body MRI scans as well as difficulties related to the recruitment of willing participants. As the regression equations proposed here were derived from a small sample size, future studies are encouraged to explore larger sample sizes to validate these equations and also to generate additional stature estimation equations from various skeletal elements, as research has shown that secular trends affect all limbs, especially in black South African populations. 57