The Ability to Determine the Length of the Human Body by the Parameters of the Skull

Introduction

Personal identification in forensic medicine continues to be one of the urgent tasks [1, 2, 3]. The presence of the skull, or even its large fragments, allows the forensic expert to determine most of the group personality traits [4, 5].

However, regarding the establishment of the length of the human body by the size of the skull, there is extremely little information in the forensic literature. While working on the project for the development of diagnostic methods for identifying a person (adapted for the population of Azerbaijan), we also did some work to study the possibility of calculating the length of an individual’s body using craniometric parameters. We present a summary of this study below.

Materials and Methods

The craniological collection of Azerbaijanis of known height, sex and age from different regions of the republic, which is stored in the medical forensic department of the Person of Public Law, the Association of SME and PA of the Ministry of Health of the Republic of Azerbaijan, served as the material. The craniological series was collected in the 70s of the last century and includes more than 200 skulls. This collection of skulls adequately reflects the craniological characteristics of the modern population of Azerbaijan, has been introduced into scientific discussion since 1995 and has repeatedly become material for various studies [3, 5]. From this collection, taking into account the craniometric representativeness of objects, as well as population homogeneity, 120 skulls (70 males; 50 females) were selected. 120 craniometric features were studied on each skull. Standard craniometry procedures were used according to well-known recommendations [6]. Most of the parameters were measured from skulls mounted on a Mollison stand in the Frankfurt horizontal plane. Of the studied skull sizes, 80 features were taken from standard craniometric programs previously proposed by various authors [6, 7]. The remaining 40 craniometric dimensions are either proposed by us or mentioned in studies by various authors, as having a correlation with body length. Of these parameters, 17 are used in the equations we present in this article. Therefore, we present their detailed description and measurement technique: S1 - The sum of the sagittal curve (Mart25) and the transverse curve (Mart24) on the skull (hereinafter, the abbreviation “Mart” and the number denote the number of the feature from the standard craniometric program R.Martin [6]). S2 – The sum of the length of the foramen magnum (Mart7) and the width of the foramen magnum (Mart16). S3 - The sum of the values of the longitudinal diameter of the skull (Mart1) and the length of the foramen magnum (Mart7). M3 - Length of linea nuchalis superior. It is measured with a soft cloth tape or a curvimeter along the surface of the line itself on the skull from the left border of the occipital bone to its right border, through the inion point. M6 - Length of linea nuchalis inferior. Also measured as size M3. S4 - Sum of dimensions M3 and M6. M7 - Length of crista occipitalis externa. The shortest distance along the surface of the skull from the point of inion to the point of opistion. It is measured with a soft cloth tape or a curvimeter along the surface on the skull. S7 - The sum of the greatest distance between the margo articularis condylus occipitalis (between the most lateral points on the margo articularis condylus occipitalis) and the smallest distance between the articular edges of the occipital condyles (between the most medial points of the margo articularis of the right and left condylus). The articular edges of the condyles were marked with a pencil, and measurements were taken with a digital caliper. M8 - The average value of the largest dimensions of the foramen rotundum (right and left). Measured with a digital caliper. The legs of the caliper are inserted into the hole and moved apart, then, moving the legs along the perimeter of the hole, the largest diameter is found. The diameters on the right and left are summed and then divided by two. M9 - Length of the anterior section of the inner base of the neurocrane. Distance from the most protruding point of the endocran on the border with the cranial vault to the middle of tuberculum sellae turcica. S9 - The sum of the length and width of the posterior cranial fossa. The length of the fossa is measured from the base of the dorsum sellae turcica to the protuberantia occipitalis interna. The width of the fossa is the distance between the bases of the two temporal pyramids (the point of intersection of the upper edge of the sulcus sinus sigmoidei with the sutura occipitomastoidea was marked as reference points on the right and left). M11 - The smallest distance between the foramina ovalia on the outer base of the skull. The legs of the digital caliper are inserted into the foramen ovale (each into one) and shifted, the value of the attribute is the index of the compass with the legs maximally shifted in this position. M12 - The smallest distance between the foramen canalis caroticus on the outer base of the skull. It was determined similarly to M11. M14 - Length parameter of the left processus mastoideus. As a long-length characteristic of the mastoid process, a chord is used, which is a perpendicular restored from the mastoid point to a conditional line on the lateral surface of the skull. This line is drawn parallel to the Frankfurt horizontal through the highest point at the transition point of the upper edge of the external auditory opening to the root of the zygomatic process of the temporal bone. The technique of taking this size is described in the work of Galli G., Galli S. [8]. M16 - Arithmetic mean of the length of the left processus mastoideus and the length of the right processus mastoideus. The length of the right processus mastoideus is measured similarly to M14. M17 - The greatest distance between the foramen canalis opticus. The size was measured between the most distant points of the upper edges of the openings of the visual channels. A sliding compass is used. M18 - The smallest distance between the foramen rotundum from the side of the middle cranial fossa. Using a caliper, the minimum distance between the medial walls of the right and left round holes is fixed.

As we noted above, all other skull sizes that we present in this work were taken from standard craniometric programs. To analyze the results of craniometry, we used standard methods of variation statistics, as well as correlation and regression analysis [9].

Mathematical modeling and calculations were performed using the MATLAB statistical software package (version 8.6).

Research Results

After the skulls were selected from the collection (a blind method was used, focused only on the absence of defects on the skulls), we considered the order of their distribution by age and body length. Since the archival collection of skulls was studied, the age of individuals and their lifetime body length (we are talking about people who owned the studied skulls) were known. Tables 1 and 2 provide data on the distribution by sex, age, and height of individuals whose skulls made up the studied craniological series. Age periodization and body length rubrication in the tables are conditional and correspond to our arbitrary ranking.

As can be seen from the tables, the skulls of individuals whose age was in the range of 16-80 years were studied. However, we note that, in general, there were very few skulls of elderly and senile age (in the combined group of men and women, the proportion of skulls corresponding to the age of over 60 did not exceed 14%). Also unevenly distributed were data on the lifetime length of the body of individuals whose skulls were the objects of study. Individuals who had high or low growth during their lifetime turned out to be less than 25% of the total. That is, in the study sample, there were mainly men and women of average height.

After the measurement procedure, the obtained numerical indicators of craniometric signs were grouped in tables separately for male and female. Here we present the statistical parameters of some of these features (these are the features that were included in the regression equations we modeled). Statistical characteristics of the studied craniometric parameters on male skulls are presented in Table No. 3, and in Table No. 4, statistical characteristics of the dimensions of female skulls.

Next, we conducted a correlation analysis, which showed that among the studied craniometric dimensions, more than 60 parameters had a good or moderate relationship (r = 0.3-0.7) with body length. At the same time, craniometric parameters that correlate well with body length in men did not always show the same relationship in the sample of female skulls. Having a sufficiently large number of features that have a relationship of medium and above average degree with body length, we began to develop equations of multiple linear regression, which could to a certain extent predict the growth of an individual by the size of his skull.

The method of stepwise linear regression was used, the essence of which is to sequentially introduce features into the regression model depending on the degree of their correlation with the predicted factor. At the same time, the criterion for selecting features (regressors) in the format of a specific diagnostic model is their maximum correlation with the predicted parameter and weak among themselves. This condition is fundamental in mathematical models similar in structure and functions, since it minimizes the phenomenon of multicollinearity. Without dwelling in detail on the relevant theoretical aspects, we note that compliance with this rule increases the reliability of the equations being created. Taking into account this factor, we calculated the correlation coefficients of the traits we studied for all possible combinations in pairs (separately for the skulls of men and women).

In total, r values were obtained for 2278 pairs of traits in the male sample, and 2211 pairs of traits for the female series. The analysis of correlation matrices to determine the compatibility of craniometric dimensions as part of a specific regression equation made it possible to predict the construction of a very large number of equations (for example, using only two features more than 110 for each sex). However, in mathematical constructions, similar to the equations of multiple linear regressions, the quality of the forecast increases significantly when the integral consideration of factors related to the reconstructed value is taken into account. Therefore, associating as many regressor features as possible into the format of one specific model is an extremely effective approach. The focus on the heterogeneity of the composition of dynamic models was dictated by practical considerations related, for example, to the examination of a fragmented skull, when the presence of a defect automatically excludes some of the craniometric features from the general flow of potential determinants of body length. In such situations, equations with slightly different regressors, which are measured in the perimeter of the skull destruction zone, lose their operational life in a complex way.

In accordance with these considerations, by means of mathematical modeling, we constructed regression equations separately for the skulls belonging to the male (total 34) and female (total 37) sex. After the procedure for calculating the statistical parameters of the equations and evaluating the forecast, the designed models were implemented into functioning ones. A brief review of the work and the entire package of proposed equations, as well as recommendations for their application, are presented in a separate monograph [10]. Below we present 12 equations from our set (equations with the abbreviation K are for the study of male skulls, equations with the abbreviation Q for the study of female skulls): K1. L = 23,9254 + 0,7876хM16 + 0,0816хZ12 + 0,2475хZ33 + 0,0783хM3 + 0,1768хZ2 + 0,7233хZ22 + 3,966 K2. L = – 10,4004 + 0,3518xZ1 + 0,2179xZ67 + 0,2436xZ46 + 0,5522xM11 + 0,4285xZ43 + 0,1383xZ16 + 0,1951xZ72 + 0,0921xM6 + 4,01 K3. L = 27,0135 + 0,6371хM14 + 0,0754хZ12 + 0,2672хZ33

+ 0,0931хM3 + 0,1678хZ2 + 1,3861хM8 + 0,6325хZ22 + 4,018 K4. L = 50,5189 + 0,8644хM16 + 0,0571хS1 + 0,1049хS4 – 0,0128хZ24 + 0,0461хZ70 + 0,2944хZ44 + 1,5371хM8 + 4,151 K5. L = 26,1981 + 0,1352хZ25 + 0,5237хS2 + 0,325хZ67 + 0,2129хZ15 + 0,234хZ7 + 0,1332хM7 + 4,374 K6. L = – 3,5717 + 0,3717хZ1 + 0,1863хZ3 + 0,0457хZ24 + 0,5645хZ43 + 0,1612хS9 + 0,1285хM6 + 4,387 Q1. L = – 79,391 + 0,4776xZ28 + 1,6073xZ72 + 0,3862xZ1 + 0,1286xS4 + 0,4392xM18 + 5,321 Q2. L = – 123,8375 + 0,7412xS3 + 1,473xZ72 + 0,1727xM6 + 0,4752xM18 + 0,2227xZ3 + 5,333 Q3. L = – 42,8738 + 0,2078xZ10 + 0,9852xM14 + 1,1887xZ50 + 0,108xS4 + 0,1093xM18 + 0,1513xS7 + 5,391 Q4. L = – 51,9107 + 1,0246xM14 + 0,116xZ12 + 0,8135xZ50 + 0,3527xM3 + 0,0387xZ11 + 0,2629xM18 + 0,2372xS7 + 0,3467xZ5 + 5,536 Q5. L = – 36,8554 + 0,4131xZ28 + 0,1772xM17 + 0,345xZ26 + 0,5862xZ4 + 0,263xZ15 + 0,3206xM9 + 6,139 Q6. L = – 66,7968 + 1,6412xZ72 + 0,227xZ12 + 0,4086xM18 + 0,4706xZ27 + 0,1411xZ5 + 0,0995xZ3 + 6,155 In these equations, “L” is the parameter being set (i.e. body length), all other numbers are the equation constant, regressor coefficients (craniometric features) and the standard error of the equation. Information about the craniometric features used and the technique for measuring them are given in the text.

Discussion of the Research Results

As we indicated, a total of 34 equations were developed for diagnosing growth on male skulls and 37 equations for corresponding examinations of female skulls. In each of these equations, from 5 to 8 regressors are used, and the errors in determining the length of an individual’s body during life range in these equations from 4 cm to 6.2 cm. To verify our equations, we used the cross-validation method. The material submitted for examinations of personality identification was examined (out of context) using the proposed equations. With a positive outcome of identification, we checked the accuracy of the coincidence of the real height of a person with the data obtained by our equations. We were able to conduct such cross-checking in 20 cases. Note that the correlation between real data on human height and predicted data was about r=0.8. Starting work on studying the possibility of predicting body length from the skull, we understood that this was an unpromising direction. In the literature, we found very few works that provide at least some information about determining the height of the skull, or the size of the head [11, 12, 13, 14]. However, in our case, practice required at least some scientific data in this matter due to the presence of a military conflict on the territory of our country [15]. After this conflict, about 4,000 people were listed as missing. Most of these people are soldiers whose remains will have to be identified. Since people who disappeared in the war are mostly young men, when analyzing mass graves and completing skeletons, taking into account body length becomes of paramount importance in segregation (compared to sex and age).

However, regarding the accuracy of the proposed equations, we note that we have no right to expect perfect results. Using all the proposed equations (easily implemented in Excel) and determining the average value from them turns out to be the closest to the true growth value (within an error of 4-5 cm). That is, relatively speaking, the equations clearly recognize the difference, for example, between a body length of 175cm and 185cm. At the same time, the solution of the problem, when it is necessary to classify the skull as an individual with a body length of 170 cm, or 175 cm, will have a less reliable answer. It should also be borne in mind that our equations were developed on the basis of osteological material from people of average height, so our diagnostic method will probably be less accurate when studying short or tall populations. Regarding populations, we also note that in the anthropology of the modern population of Azerbaijan, 4 anthropological types are distinguished: Caspian, Pontic, Western Asian and the type of population of the Caucasus mountains [5]. However, the most common is the Caspian type (more than 65%), and we studied precisely the skulls from this group. Perhaps that is why the equations we designed turned out to be a little more accurate, because it is known that body proportions are more stable within anthropological types.

Thus, the above analysis shows that the developed equations for determining the length of the body from the skull have some limitations for their unconditional application in forensic practice. This diagnostic method has the best prospects in the study of bone remains from the territory of Azerbaijan. At the same time, in the absence of a legal incident and a setting for undoubted accuracy (for example, in archeology, during historical restoration work, etc.), for an approximate calculation of the length of an individual’s body, the equations may turn out to be quite acceptable.

Conclusion

Some craniometric indicators studied on the skulls of modern Azerbaijanis are interconnected by correlation- regression relationships with body length. This relationship can be described using multiple linear regression equations. Taking into account these mathematical prerequisites, the corresponding diagnostic equations for practical application have been developed. But according to modern standards for making expert decisions in forensic medicine, they cannot be unconditionally recommended for widespread use, since verification of the used of these prediction equations on other population groups is necessary. Nevertheless, under certain circumstances (some works in anthropology, archeology, etc.), the proposed equations are of practical value as an independent method for diagnosing the lifetime body length.