Osteology: Estimating Femur Length from the Diameter of the Femoral Shaft

Abstract
Bone lengths can be used to provide stature estimations in case of unidentified skeletal remains, an important tool in forensic and bioarchaelogical cases. Where the bones are broken or fragmented, regression equations can be used to estimate total bone length from its fragments, which in turn can be used to estimate stature.
The aim of this study was to test 2 new measurements of the femoral shaft to see if they could be used as predictors of maximum femoral length. The minimum transverse femoral shaft diameter and the minimum anterior-posterior femoral shaft where measured on a small sample of an archaeological population from Poulton, Cheshire, along with the maximum femur length for each sample. Simple linear regression analysis was performed and the results showed that the minimum transverse femoral shaft diameter correlated significantly in both males (R2=. 635, p=0. 006) and females (R2=0. 8, p=? 0. 001) with maximum femur length. The minimum anterior-posterior femoral shaft diameter showed no significant correlation with maximum femur length. Subsequently, regression equations were presented for the significant correlations. Further research is needed to validate the results and to improve the accuracy of the method. 1. Introduction The role of a forensic anthropologist in forensic and archaeological cases is to establish demographics (population affinity, age, sex and stature), time since death and cause of death from an individual’s remains (Chibba et al, 2006).

The use of stature as a biological characteristic of identity can significantly contribute to the identification of unknown skeletal remains. Numerous areas of the skeleton have been used to try and determine an individual’s living height such as the upper limb bones (Rao et al. 1989), lower limb bones (Trotter and Gleeson, 1952), the metatarsals (Cordiero et al, 2009) and the skull (Ryan and Bidmos, 2007). Hauser et al. (2005) provide a good review of the past research in the area of stature estimation. One of the methods used in the estimation of stature is the formulation of regression equations from measurements of various bone lengths.
Pearson (1899) was the first to derive regression equations for estimating stature, and since then it has grown to be the method of choice among most anthropologists. Many of the methods used to approximate stature require complete or near complete bones, so consequently few studies have been done on incomplete or fragmentary bones (Bidmos, 2008). Forensic anthropologists are often confronted with fragmented bones and in these cases it is impossible to derive regression equations directly from bone length (Rao et al. 989). Wright and Vasquez (2003) state the problems they faced in Guatemala in which they were often unable to estimate stature from bone length due to the rapid deterioration of bone in the tropical environment. This is only one of many factors that lead to the all too frequent recovery of broken or fragmented remains. Therefore it is beneficial to have equations available for bone length or stature derived from measurements of smaller segments or landmarks on the chosen bone.
The femur is the favoured bone of use among anthropologists in estimating stature, due to its high correlation with height in addition to the fact that it is one of bones most often recovered (Simmons et al. 1990). A number of measurements of the femur have already been reported to have good correlations with femur length. Many of these measurements focus on the proximal and distal ends of the femur such as the upper epicondylar length, epicondylar breath, vertical neck diameter and the bicondylar breathe (Brauer, 1988), yet few have focused on measurements of the femoral shaft.
This pilot study looks to test the validity of 2 measurements from the femoral shaft as predictors of maximum femoral length. The points of reference chose on the femur are the minimum transverse femoral shaft diameter (TRD) and the minimum anterior-posterior diameter (APD) of the femoral shaft. The samples being used are that of an archaeological population recovered from a medieval cemetery in Poulton, Cheshire. The aim is to use linear regression analysis to test the assumption that there is a significant correlation between these measurements and the maximum femoral length.
A further aim is to produce regression equations that can be used on other skeletal remains from the Poulton collection for estimating maximum femur length.
Materials and Methods
Samples
The samples used in this study were obtained from the Poulton collection housed at Liverpool John Morres University. Due to the small size of the collection at present and the poor condition of some of the bones, a total number of 18 left sided femora were selected for use in the study. These femora were chosen on the basis of completeness and measurability.
All the samples were obtained from adults skeletal remains and the number of male and females femora was 10 and 8 respectively.
Measurements
The following 3 measurements were taken on each of the 18 samples: i. Maximum length of the femur (MAXL) ii. Minimum anterior-posterior femoral shaft diameter (APD) iii. Minimum transverse femoral shaft diameter (TRD) The MAXL measurement was taken as described by Brauer (1988). The APD and TRD measurements were taken as described by Ziylin and Mursid (2002). The MAXL was measured using an osteometric board.
The APD and TRD were measured using a sliding callipers with an accuracy of 0. 1 mm. Linear regression analysis was carried using the SPSS statistic program to see if any correlation existed between the measurements taken of the femoral shaft (APD and TRD) and the maximum length of the femur. All analysis was carried out separately for males and females on the advice of Trotter and Gleser (1952) who state the specificity of such measurements in relation to sex.
Results
The descriptive statistics for males and females are shown in Table 1. Males showed the highest mean values of each of the 3 measurements taken.
Males also showed the higher standard deviations in respect to MAXL and APD, with females showing a higher standard deviation for TRD. Table 1 Descriptive statistics for measurements of male and female left femora. All descriptive values are given in mm.
Table 2 shows the results of the linear regression analysis that was performed. Both APD and TRD were regressed against MAXL according to sex.
The analysis showed that the variable APD showed no significant correlation to MAXL for males (R2=0. 154, P=0. 262) or females (R2=0. 044, P=0. 619). TRD provided more positive results showing a moderate significant correlation in respect to males (R2=0. 635, P=0. 006), and a strong significant correlation in respect to females (R2=0. 88, P=<0. 001). Scatter plots (Figure 1. and Figure 2. ) show the distribution of the TRD among males and females along the line of regression. These graphs add weight to the correlations presented in Table 3 in that it is clear the females fit line of regression better than the males.
Regression equations for estimating MAXL from measurements of TRD are provided in Table 3. The standard error of the estimates is also shown in Table 3, which is considerably lower in females. Due to this lack any significant correlation for the APD measurement it was decided that it would be irrelevant to perform multiple regression analysis using both the TRD and APD variables. As a result no regression equations were computed for APD. Table 2 Results of linear regression analysis of MAXL (dependant value) against TRD (independent value) and MAXL (dependant value) and APD (independent value) for males and females.
Significance is reported at the 5% level.
B – Slope of the regression line Sig (B) – Signification of the slope in relation to zero. <0. 05 = slope significantly different from zero. Table 3 Regression equations for estimation of the MAXL from measurement of the TRD. Separate equations for males and females. Measurement| Male | Female|
TRD| MAXL=9. 91(TRD) +190. 1 (SEE* =10. 865mm)| MAXL=6. 234(TRD) +274. 990 (SEE* =4. 365)| * SEE – Standard error of the estimate Figure 1 Regression of minimum transverse femoral shaft diameter on maximum length of the femur in females. Figure 2 Regression of minimum transverse femoral shaft diameter on maximum length of the femur in males. 4. Discussion The analysis performed on the 2 measurements taken from the femoral shaft gave very contrasting results. It is clear that APD is not a reliable indicator of femur length with equally poor correlation shown for both males (0. 54) and females (0. 044). A contributing factor to this is the differences among individuals in the size and pronunciation of the linea aspera, a morphological feature of the femur that runs along the posterior shaft of the femur.
Since the linea aspera is a point of attachment for a number of muscles, it can be presumed that intrapopulation variation in muscle mass and activity contributes to the low correlation obtained (Wright and Vasquez, 2003). On the other hand the significant correlations (Table 2) show that TRD is a good predictor of maximum femur length in both males (0. 635) and females (0. 8) in cases where the femora are broken or incomplete. Therefore the equations (Table 3) obtained can be used to estimate maximum femur length and thereafter stature using the appropriate equations/tables/ multiplication factors available in the literature (Trotter and Gleser 1952, 1958) (Simmons et al. 1990). Some authors have argued that it is more accurate to calculate stature directly from bone measurements (direct method), rather than the 2-step approach of first estimating the bone length and then using that value to obtain an estimation of stature which is known as the indirect method (Simmons et al. 1990).
Bidmos (2009) compared the 2 methods using measurements of the femur and found the direct method to be more accurate; in contrast to earlier work by Steel (1970), who found the opposite to be the case. Bidmos (2009) commented on the fact that both steps of the indirect method incur standard errors, hence increasing the overall error value. His results reflect this observation. Since this study is only focused on determining the validity of femoral shaft measurements as predictors of femoral length it is thought that concentrating on the direct method in future studies of the Poulton collection may provide more accurate stature estimations.
Other factors also need to be taken into consideration before using the results obtained in this study. The number of samples used is considerably low due to the current size of the Poulton collection and the damage some of the individual skeletons have incurred. For these reasons it is impossible to tell whether the results accurately represent the Poulton population. For instance, in Table 1 it can be seen that standard deviations for MAXL is higher in males than females, indicating that there is a greater variability in the maximum femur length among males.
This explains lower correlation obtained in the males samples when MAXL was regressed against TRD. A repeat of this study with a greater number of samples may further improve the accuracy of the derived equations (Table 3), particularly in males. Another area of concern is the population specificity of such regression equations. Ethnicity, heredity, climate and nutrition status are known to affect length of long bones (Prasad et al, 1996), which in turn affects stature.
From this, one could conclude that the equations in Table 3 are specific to the Poulton collection and any attempt at using them on a different population should be approached with caution. In light of this remark it is also advised that equations for estimating stature from maximum femur length be produced specifically for the Poulton collection, as any of the existing equations may prove unreliable due to these population biases.
Conclusions
This study shows that the TRD measurements taken from the femur is a good predictor of MAXL. This is confirmed in the results with the correlations eing >0. 6 (Table 2), P-values being >0. 01 (Table 2) and the standard error of the estimated being <11mm (Table 3). However it is advised that caution should be taken in using the results until further efforts are made to validate and improve the given regression equations (Table 3) with the use of large sample sizes and different populations. It can also be assumed that these equations are population specific and may prove misleading if used on populations other than that used in this study. The APD measurements of the femur showed to be a very poor predictor of MAXL (Table 2 and Table 3).
This has been contributed to the morphological differences between individuals in the linea aspera. It is unclear whether further analysis could yield contrasting results but on the evidence of the results gathered from this study it is advised that the APD variable be disregarded in future research on stature and bone length estimation. Acknowledgments I would like to thank Professor Alan turner for help in choosing the topic. I would also like to thank Colin Armstrong of the LJMU technical staff for his help in accessing the materials necessary for completing this research.
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