Journal of Forensic Science and Medicine

: 2021  |  Volume : 7  |  Issue : 1  |  Page : 1--8

Virtual determination of sex: Estimating cut off value of digital metric traits of foramen magnum on three-dimensional computed tomography with receiver operating characteristic and logistic regression analysis

Harish Kumar S Agarwal1, Pardaman Singh Setia2, Suryamani Pandey3,  
1 Department of Forensic Medicine and Toxicology, Maharaja Agrasen Medical College, Hisar, Haryana, India
2 Department of Radiodiagnosis, Maharaja Agrasen Medical College, Hisar, Haryana, India
3 Department of Community Medicine, Maharaja Agrasen Medical College, Hisar, Haryana, India

Correspondence Address:
Harish Kumar S Agarwal
Department of Forensic Medicine and Toxicology, Maharaja Agrasen Medical College, Agroha, Hisar - 125 047, Haryana


Background: Radiological imaging plays a pivotal role in forensic anthropology. As have the imaging techniques advances, so have the digital skeletal measurements inched towards precision. Secular trends of the population keep on changing in modern times. Hence, finding the precise technique of bone measurement, with greater reproducibility, in modern population is always needed in making population specific biological profile. Aim and Objective: The aim of this study was to estimate the accuracy of the foramen magnum measurement, obtained by three dimensional multi-detector computed tomography using volume rendering technique with the cut off value of each variable, in sex determination of an individual. Materials and Methods: Two metric traits, an antero-posterior diameter (APD) and transverse diameter (TD), were measured digitally in an analysis of 130 radiological images having equal proportion of male and female samples. Foramen magnum index and area of foramen magnum (Area by Radinsky's [AR], Area by Teixeira's ORIGINAL ARTICLE) were derived from APD and TD. Results: Descriptive statistical analysis, using unpaired t-test, showed significant higher value in males in all the variables. Using Pearson correlation analysis, maximum correlation was observed between area (AT and AR r = 0.999) and between area and TD (AR r = 0.955 and AT r = 0.945 respectively). When used individually, TD had the highest predictive value (67.7%) for sex determination among all the parameters followed by AT (65.4%) and AR (64.6%). Cutoff value of variables TD,AR and AT were 29.9 mm, 841.80 mm2 and 849.70 mm2 respectively. Receiver operating characteristic curve predicted male and female sex with 96.2% and 89.2% accuracy respectively. The overall accuracy of the model was 92.7%. Conclusion: Measurements from 3D CT using volume rendering technique were precise, and the application of logistic regression analysis predicted the sex with more accuracy.

How to cite this article:
Agarwal HK, Setia PS, Pandey S. Virtual determination of sex: Estimating cut off value of digital metric traits of foramen magnum on three-dimensional computed tomography with receiver operating characteristic and logistic regression analysis.J Forensic Sci Med 2021;7:1-8

How to cite this URL:
Agarwal HK, Setia PS, Pandey S. Virtual determination of sex: Estimating cut off value of digital metric traits of foramen magnum on three-dimensional computed tomography with receiver operating characteristic and logistic regression analysis. J Forensic Sci Med [serial online] 2021 [cited 2021 Apr 12 ];7:1-8
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The identification of human remains is of major importance in investigation of criminal cases and civil cases. Extreme decomposition, effect of animals, fire, or even the hiding efforts of the perpetrator, prevent positive identification. In such cases, skeletal remains due to their resistant nature are helpful in establishing the identity of the person.[1]

In forensic anthropology, sex determination in human skeletal remains can be achieved by morphological (descriptive/qualitative) or metric (quantitative) methods. Morphological methods rely on expertise and judgment of the observer and lack statistical analysis, hence are subjective. Metric methods remove the subjectivity and produce the same results as of morphological, but these are population specific.[2]

Base of the cranium withstands, both physical insults and inhumation, somewhat more successfully than many other areas of the cranium because of its thickness and its relatively protected anatomical position.[3] Therefore, there is considerable merit in investigating the value of this region in the process of sex determination.

In decomposed and charred remains, special techniques, like maceration, are needed to carry out the standard osteometric techniques. In such cases, image-processing techniques like radiography or computed tomography (CT) could be of substantial help.[4]

Franklin et al.,[5] in their comparison study, found statistically insignificant difference between scans of volume render three-dimensional (3D) multi-detector CT of the skull and actual physical specimen.

In modern era, populations are not stationary in a specific geographic area with relation to time so the size in the skeleton or its respective parts also changes rapidly. This influences the applicability of the older methods used in sex determination.[6] Limited dry bone collection of modern population and rapid secular changes in populations and easy reproducibility of data pave the way for many researchers to publish the radiological data on sexual dimorphism of foramen magnum with varied accuracy applying different statistical test.[7]

The most popular statistical model of sex determination is a discriminant function analysis (DFA) which encouraged many forensic scientists to assess their anthropometric data accordingly.[8] However, researchers proved that logistic regression analysis is better than DFA.[9],[10]

The objective of the present study was to contribute classification functions which help to determine sex based on foramen magnum dimension in North Indian region and to indicate accuracy of the classification with determination of cut off value in sex determination for each significant parameter.


With the permission of the Institutional Ethical Committee, image analysis was done on the data obtained from radiological department of past 6 months at the tertiary care medical and teaching hospital. Data comprising of a soft copy image of CT head of the patients with known sex who had visited the institute for their ailments other than the purpose of identification. Scan image showing any pathology of cranial vault, fracture of skull, congenital malformations were excluded from the study. A total image of 130 patients consisting of equal proportion of males and females were included in the study.

Technical specification of machine

Axial sections using helical CT scan (Somatom Emotion, Siemens, AG, Erlangen, Germany) with 5 mm thickness, 130 kVp, 200–230 mAs, 1800 AU window levels and 35–45s scan time. All sections selected were parallel to the plane of the FM to select the best image of the foramen magnum. All images were retrieved on the Osirix X (v. 4.1.1. 64 bit) CT workstation with a resolution of 1280 × 1042 full-screen format and picture size of 360 × 288 mm. Dimensions were measured using multiplanar reconstruction and 3D volume-rendered images. For accuracy, dots cursors for measuring on the 3D volume-rendered image were placed in identical portions on corresponding axial and sagittal images using rotation and translation of the reconstructed image. The distances were measured on the axial image passing from the points established on the level of sagittal image. For the axial measurements, the reviewer scrolled through the axial image to select the optimal location to measure diameter. The starting and ending points of distance for linear measurements on the axial images were determined with the internal digital caliper of the workstation.

The following measurements were recorded:

Anterior-posterior diameter (APD): Was measured from the basion (the midpoint of the anterior margin of the FM) to the opisthion (the midpoint of the posterior margin of the FM)Transverse diameter (TD), i.e., width of the foramen: Was measured between the lateral margins of the FM at the point of greatest lateral curvature [Figure 1]The foramen magnum index (FMI): Ratio of TD to APDArea of the foramen magnum by Teixeira's Formula[11] Area by Teixeira's (AT) = π ([Sagittal diameter + TD]/4)[2]Area of the foramen magnum by Radinsky's formula[12] Area by Radinsky's (AR) = ¼ × π × TD × APL.{Figure 1}

APD, TD and Area (both AT and AR) were recorded in millimeters up to two decimal points.

All the data were first entered into Microsoft Excel 2016 than transferred to SPPS. A descriptive statistic was completed on the linear measurements to ascertain the mean, maximum and minimum values, dividing the results by sex. An unpaired t-test was performed to know statistically significant differences (p < 0.05) between the variables. Linear correlation was performed to know their association to each other, bearing in mind sex. Sensitivity and specificity at different cut off points were obtained by receiver operating characteristic (ROC) curve and last of all, a logistic regression analysis was performed using backward stepping method to ascertain the effectiveness of the model used significant variables in combination for sex determination. Statistical Package of Social Science (SPSS 23 IBM, Armonk, New York, USA) was used for analysis.


The mean value of all the dimensions (APD, TD, Index, AR, and AT) were more for male. The area calculated by Teixeira's Formula was more than Radinsky's formula in each sex. The values were statistically significant among all the parameters studied (p = 0.001) except the FM index (p = 0.157). Therefore, the FMI was not used for further sex discriminant analysis [Table 1].{Table 1}

Relation between different variables in male and female shown in regression scatter plots [Figure 2], [Figure 3], [Figure 4],[Figure 5],[Figure 6],[Figure 7]. Significant correlation was present more in female. Maximum correlation was observed between area obtained by AR and AT (r = 0.999) followed by TD with area (AR r = 0.955, AT r = 0.945). Correlation between APD and TD was 0.787 in female.{Figure 2}{Figure 3}{Figure 4}{Figure 5}{Figure 6}{Figure 7}

The discriminatory analysis of each variable was calculated by measuring area under the curve on ROC curve [Figure 8]. The cut off value for sex differentiation of each variable were computed using the point of highest sensitivity and specificity in ROC curve. According to the results each value equal or greater than the cut-off value for each variable classifies the specimen as male while less value as a female [Table 2].{Figure 8}{Table 2}

The regression analysis done to the estimated the odds ratio (OR) of each parameters in sex determination. Code 1 given for the male and code 2 for the female. On entering the variables into a backward stepwise analysis and controlling the confounding factors, only TD (OR = 0.001), AR (OR = 2.092), and AT (OR =0.250), were selected in the analysis as the most significant (p < 0.05) independent predictors [Table 3].{Table 3}

Sensitivity, specificity, accuracy of final regression model were calculated using the ROC curve [Figure 9] and were compared with value of each independent variable [Table 4].{Figure 9}{Table 4}


The foramen magnum is a prominent structure in the base of the skull, and it shows a morphometric difference between males and females. These differences are unique to each population and thought to be influenced by genetic, environmental, and socio-economic factors.[13] It is therefore necessary to study its expression in as many geographically and temporally diverse populations as possible.

The present study supported the view that sexual dimorphism existed in the foramen magnum. The correct prediction percentage demonstrated in this study will provide a statistically useful guide in incomplete human skull or a fragment of the cranial base with intact foramen magnum. The “cut off” analysis observed in present study can be used as the base reference of the population in north Indian population.

From a medico-legal point of view, the work on “virtual skeletons” can bring many advantages. Like, in case of decomposition if anthropological examination is required than, time-consuming maceration of the bones can be avoided using imaging techniques. The data can also be stored in a database to constitute a digital library for future comparison.[14]

The obtained metric traits of the foramen magnum were comparable with the value presented by most of the other authors [Table 5]. The samples of listed studies were consisting of both dry skulls and radiological images.{Table 5}

The comparative table clearly indicated that value of all the foramen magnum parameters was more in male. This difference was statistically significant except in FMI. Very few authors[15],[16],[17] studied the FMI. Burdan et al.[15] and Jain and Jasuja[16] were also not found any statistical difference (p = 0.05) in FMI which was in consonance with present study while result of Aghakhani et al.[17] was contrary.

Variation present in many studies could be due to ethnic differences of the tested populations, sample size, differences between the anatomic and radiographic techniques, different variables included in study and different statistical methods.[18]

In a present forensic environment, it is not always possible to recover the full sample, and therefore there are cases in which very few skeletal remains are available. In these cases, it is necessary to obtain the greatest possible information to create specific classification functions for a population in order to determine sex in a reliable manner, or at least with awareness of the margins of error.[19]

Documenting the morphometric values of foramen magnum in original populations is important. This variation advocates the need of a morphometric analysis of foramen magnum so that interested regions should be known in detail.[20]

Researchers used statistical analysis such as Discriminant Function Analysis (DFA), Logistic Regression Analysis (LRA), and Receiver Operating Characteristic Curve (ROC) which allows a fast data processing which is evident by the amount of publications devoted to sex estimation based on FM in recent years with divided suggestions about applicability in forensic practice.

The overall accuracy in sex determination using TD, AR, and AT by logistic regression and ROC analysis was 92.70% with predicted probability of 96.20% for male and 89.20% for female demonstrates that a logistic regression analysis identifies males more often than females.

Jain and Jasuja[16] in their study on 140 dry skull from north India in 2015, found the breadth of foramen magnum, i.e., TD as the highest predictor of sex having 75.7% accuracy followed by area 68.6% through stepwise discriminant analysis and the combined accuracy was 76.5% using the same parameters as of the present study.

Aghakhani et al.[17] in their study of 100 cranial CT image analysis by regression method found 96% of samples predicted the sex with 86% accuracy however accuracy of individual parameters was found between 92% and 100%.

Gapert et al.[21] done a study in British ethnic group using DFA and logistic regression analysis on 158 dry adult skulls in 2008 observed that with DFA the predicted value for male, female, and overall sex was 65.9%, 68.4%, and 67%, respectively. Sex prediction by LRA was better (66%, 70%, and 68%). They concluded that width of foramen magnum and circumference (area) are the two parameters best used for sex determination.

Uthman et al.[22] studied 43 males and 45 females on CT, predicted the correct sex in male by 90.7% while prediction for female was 73.3% on DFA.

Raghavendra Babu et al.[23] in 2012 investigated 90 dry Indian skulls and analyses the results using binary logistic regression found the anteroposterior diameter as the most reliable variable for sex estimation (86.5%) followed by the area of FM (AR 81.6% and AT 82.2%), while TD showed the least predictability (65.4%), and 88% overall predictability using APD and TD.

Kamath et al.[24] in their study on 72 dry skull found anterior posterior diameter to predict the sex with 69.6% accuracy which was more than TD (66.4%) but less than area (70.3%) on ROC curve using binary logistic regression analysis. The overall accuracy was same as of Raghavendra Babu et al.,[20] They concluded that the sexing potential is limited due to considerable overlapping of male and female values.

A study done by Singh and Talwar[25] on 50 dry skulls from Punjab in 2013 reported, that length of foramen magnum was insignificant in predicting sex. They were able to predict the sex with 70% overall accuracy with DFA. They used six parameters and did not measure area of foramen magnum in their study.

Meral et al.[26] analyzed 600 (300 males and 300 females) CT images of Turkish individuals aged between 21 and 50 using the same four parameters as in the present study. All measurements in males were significantly greater than in females. The area of the foramen magnum calculated by Radinsky's formula was the best measurement for sex estimation with a 75% accuracy rate.

Mehta et al.[27] in their CT study on 553 adult individuals (Male = 291, Female = 262) of Gujarati origin with age range 18–60 years, found significant difference in all variables except FMI. Although their sexing accuracy was 69.1% using multivariate discriminant analysis.

Zanutto et al.[28] studied cone beam CT images of 309 individuals (162 females; 147 males). As with present study, all the measurements except FM index were reported higher in males and strongest correlation was seen between FM areas for both sexes (r = 0.999). The overall accuracy rate of sex estimation was 84.8%, which was less than present study.

The result of the present study was more accurate than other study[15],[16],[18],[19],[20],[21],[22],[26],[27],[28] and marginally legs the results of Aghakhani et al.[17]

The present study has the potential to serve as a data base for sexual dimorphism from foramen magnum in north Indian region. More research on a wider scale of adult population will be useful in preparation of biological profile of modern population of this region.


The database of various parameters of the skull images from the same region is not available, comparison with such data could have been valuableInclusion of more data from various age groups could have been helpful to suggest any relation of age with respect to sex discrimination of foramen magnum. Later, comparative studies with other populations will be necessary to determine the variability between population.


Measurements from 3D CT using volume rendering technique were precise, and the application of logistic regression analysis predicted the sex with more accuracy. Significant sexual dimorphism was presented in the used morphometric traits of foramen magnum. Anteroposterior diameter was more than TD, so the resulting FMI was <1. Significant correlation was present among all the independent variable except FMI. TD was the most single predictor of sex followed by AT and AR while the role of APD in predicting the sex was insignificant. This observation should only be used as a corroborative in predicting sex in case of fragmented cranial bases and not recommended as sole indicators for sexing complete skulls.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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