



ORIGINAL ARTICLE 

Year : 2021  Volume
: 70
 Issue : 4  Page : 209215 

Estimation of humerus length by measuring the dimensions of its lower fragments
KU Prashanth^{1}, Mangala M Pai^{2}, BV Murlimanju^{2}, Latha V Prabhu^{2}, MD Prameela^{2}
^{1} Department of Anatomy, A. J. Institute of Medical Sciences and Research, Kuntikana, Mangalore, Karnataka, India ^{2} Department of Anatomy, Kasturba Medical College, Mangalore, Manipal Academy of Higher Education, Manipal, Karnataka, India
Date of Submission  22Oct2021 
Date of Acceptance  08Sep2021 
Date of Web Publication  21Dec2021 
Correspondence Address: Prof. Mangala M Pai Mangala M. Pai, Department of Anatomy, Kasturba Medical College, Mangalore  575 004, Karnataka India
Source of Support: None, Conflict of Interest: None
DOI: 10.4103/jasi.jasi_174_21
Introduction: The aim was to obtain the dimensions of the distal fragments of humerus bone, and the objective was to derive the formulae of regression, which will assist us to estimate the humeral length. Material and Methods: In this cadaveric research, 166 adult dried humeri from the department of anatomy were utilized. The measurements were performed by using the osteometric board and digital Vernier caliper. The seven distal humeral fragments were measured. Results: We were able to associate the dimensions of the distal humeral fragments with the humeral length (P = 0.00). The distances between the radial summit of the capitulum to the ulnar part of the medial epicondyle (right side Pearson's coefficient, 0.70 and left side, 0.78) and the radial side of the lateral condyle to the ulnar most side of the medial epicondyle (right side Pearson's coefficient, 0.69 and left side, 0.77) were the finest parameters, which can predict the length of humerus. Discussion and Conclusion: The regression calculations can be of help in estimating the humeral length. Such equations could be utilized during the examinations of forensic cases, where the estimation of height of an individual is required to be predicted, when only a few distal fragments of humerus are available. The figures of this investigation can also help in anthropology and archaeological research.
Keywords: Anthropology, archaeology, humerus, regression analysis
How to cite this article: Prashanth K U, Pai MM, Murlimanju B V, Prabhu LV, Prameela M D. Estimation of humerus length by measuring the dimensions of its lower fragments. J Anat Soc India 2021;70:20915 
How to cite this URL: Prashanth K U, Pai MM, Murlimanju B V, Prabhu LV, Prameela M D. Estimation of humerus length by measuring the dimensions of its lower fragments. J Anat Soc India [serial online] 2021 [cited 2022 May 24];70:20915. Available from: https://www.jasi.org.in/text.asp?2021/70/4/209/333186 
Introduction   
The different structural components or segments of bone are in certain proportion to each other and with the bone as a whole. It should be possible to reconstruct the individual skeleton from a single bone or a single bone from any of its parts. If the cranium and pelvis are not available, the long bone fragments are used in the anthropology and forensic science investigations.^{[1]} The height of an individual can be determined with the full length of a long bone.^{[2]} Identification of human remains and providing the stature of a person is a difficult process. This is a very imperative phase in estimating the human proportion and dimorphic features in relation to the gender.^{[3],[4]} Krishan^{[5]} described that the physique of an individual can be estimated to a desired level of accuracy, from the available individual bones. He also noted that the long bones give the best results for the stature determination.^{[5]} The humeral fragments were utilized, which used their articular surfaces.^{[6]} Steele^{[2]} noted that calculating the human stature is possible with the determination of humeral length if the best bones such as femur and tibia are not available.
This makes the relevance of developing a set of morphometric data, which will be of immense value in forensic science. It was reported that the normative data are essential for a population.^{[7]} There are a wide variety of methods, which can be applied to assess the stature of a person. The method which is of high degree of precision and reliability is the regression analysis.^{[8],[9]} This method is reliable in determining the relationship between the size of the bony segments and the length of the bone as a whole.^{[9] }The goal of this investigation was to measure the proportions of the distal end humeral fragments and define the humeral length by using them. The objective was to obtain the equation of regression by using the humeral length.
Material and Methods   
In this anatomical research, 166 human adult cadaveric humeri were utilized. They were dried humeri, and among them, 82 were right sided and 84 belonged to the left side. They were obtained from the departments of anatomy of our university. Only intact adult humeri, which had normal ossification of the lower end of humerus, were included in this present research. The humeri which had congenital variations and pathological changes were excluded from this study. The humeri belonged to the adult age group (above 20 years), and they belonged to the subjects who lived on earth during the 20^{th}–21^{st} century. However, the age and gender of the specimens were not taken into consideration in this study. We are not sure that the right and leftsided humeri were from the same individuals, because this is a crosssectional study from the collections at the anatomy laboratory. All the measurements were conducted by the same researcher, thus preventing the interobserver error. The dimension of each fragment was measured three consecutive times, and the average of it was considered, which prevented the intraobserver error. We state that this present anatomical research has the permission of the ethics committee of our college.
The maximum length of humerus (MHL) is the distance from the utmost superior aspect of the humeral head to the furthermost inferior aspect of the trochlea. The osteometric board was utilized to collect these data, and it was recorded in centimeters. The following lowerend segments of humerus were measured [Figure 1] in this study with the help of Digital Vernier Caliper (Mitutoyo, Japan):  Figure 1: Schematic representation of the measurements of lower end humerus segments in this study
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 S1 – Vertical distance among the distal extents of medial flange of trochlea and inferior edge of the medial epicondyle
 S2 – Distance between the two flanges of the posterior aspect of trochlea at the level of distal limit of olecranon fossa
 S3 – Largest breadth of the olecranon fossa in a horizontal plane
 S4 – Total combined width of the trochlea and capitulum
 S5 – From the lateral extent of capitulum to the medial limit of medial epicondyle
 S6 – From the medial limit of trochlea to the lateral extent of lateral epicondyle
 S7 – From the lateral edge of lateral condyle to the most medial part of medial epicondyle.
The statistical comparison for the right and leftsided specimens was performed with the help of independent samples ttest. The SPSS software (version 15, companySPSS Inc., city Chicago, state Illinois, country  United States of America was utilized for the statistical analysis, and the mean and standard deviations were tabulated for each of the measurements. The comparison was considered as statistically significant if P < 0.05. Pearson's correlation coefficient (R) was used to correlate the proportions of the distal humeral fragments and the length of humerus. The regression coefficient (COE) was obtained by the simple linear regression for the data of the right and leftsided distal fragments. The Pearson's correlation coefficient between the dependent and independent variables was considered. Various fragments of humerus are correlated with the humeral length, and the Pearson's coefficient helped in finding the power of relation among the variable fragments. The regression equations were then determined from these parameters, which will calculate the expected MHL from its various distal segments.
The prototype of the formula is, MHL = constant + A × fragment length ± standard error of estimate, where “MHL” is the dependent variable (full length of humerus), and “A” is an unstandardized coefficient (multiplication factor). The “fragment length” is an independent variable (measurement of distal fragment of humerus). The SPSS software offered the “constant.” The regression equation which has the largest multiplying factor was considered as the best.
Results   
The mean length of humerus was 30.7 ± 2 cm and 30.3 ± 2.3 cm over the right and left sides. The dimensions of distal segments of humerus are represented in [Table 1]. The data were compared over the left and rightsided humeri, but the significant difference was not observed statistically (P > 0.05). However, the vertical space between the distal extent of the medial flange of the trochlea and the inferior edge of the medial epicondyle (S1 segment) was greater [Table 1] on the right humerus than the left humerus (P < 0.05). The Pearson's coefficient of the fragments is represented in a descending order in [Table 2]. [Table 3] shows the Pearson's coefficient, the coefficient of determination (R^{2}), and “P” value over the left and right sides, separately. Association between the proportions of distal humeral segments and humeral length were relative, as observed in this study. This association was highly significant as it was not happened with chance (P > 0.05).  Table 1: Sidewise comparison of the dimensions of the distal humeral fragments
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 Table 2: Pearson's coefficient for the distal fragments of humerus in descending sequence
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 Table 3: Pearson coefficient for the right and leftsided distal fragments of humerus
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The best parameters are the S5 segment on the right side and S7 segment on the left side. The Pearson's coefficient was 0.70 (S5) and 0.69 (S7) over the right side and 0.78 (S5) and 0.77 (S7) over the left side. The least value of Pearson coefficient was observed in S1 segment, irrespective of the sides, Pearson coefficient being 0.26 and 0.25 for the right side and left side, respectively.
These regression equations to the lowerend segments of the humerus over the right and left sides are represented in [Table 4]. Among them, the regression formula for S2 segment appears to be the best, the multiplying factor being 6.06 for the left side and 4.79 for the right side. The linear regression of the different lowerend segments (S1–S7) of the right and left humeri is represented in scatter diagrams [Figure 2], [Figure 3], [Figure 4], [Figure 5].  Table 4: Regression equations for determining total length of humerus (maximum length of humerus) by utilizing the dimensions of distal fragments of humerus
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 Figure 2: Scatter diagrams showing the linear regression of right and left humeri with S1 and S2 segments
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 Figure 3: Scatter diagrams showing the linear regression of right and left humeri with S3 and S4 segments
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 Figure 4: Scatter diagrams showing the linear regression of right and left humeri with S5 and S6 segments
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 Figure 5: Scatter diagrams showing the linear regression of right and left humeri with S7 segment
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Discussion   
The formulae developed by Pearson in 1899 were revised in 1951, because of the objection that this was based on the measurements taken on a population of fairly short stature. This was inadequate for estimating the living heights of the taller people. Hence, question was raised about its compatibility for the other races.^{[1]} The equation for height determination from the long bone lengths was used in the identification of American people remains following the war in Korea.^{[10]} The stature of a person can be figured out with some amount of accuracy, if a long bone measurement is available.^{[11],[12]} The delinquent lies with the archaeological excavation sites, which yield the remains of both adult and subadult population.^{[3]} There were some regression formulae available for the adult remains, and there was none for the subadult bones. The regression equations are globally accepted for the stature determination.^{[13],[14]} Mysorekar^{[15]} determined that the regression formula by using the femur and radius was also utilized.^{[16]} Rao et al.^{[17]} deducted a formula to determine the sizes of fragmented skeletons of the higher extremity, which in turn is used to determine the stature of the individual. Singhal and Rao^{[18]} stated that the new equations are needed for the shorter fragments. Somesh et al.^{[19]} highlighted the use of formulae in forensic, anatomic, archaeological, and orthopedic surgeries. Prashanth et al.^{[20]} reported the regression formulae for measuring the length of humerus by upper fragments of humerus. The length of humerus is important to define the population as a whole.^{[21]} The length of the humerus of the present study is comparable to the figures from a Turkey and Spain study.^{[22]} However, it was reported that ancestral variations seemed to exist.^{[13],[23]}
In the present study, Pearson's coefficient of the horizontal segments measured, had good averages, which is better than the study by Somesh et al.^{[19]} in which most of the segments measured were vertical segments. The present study from distal segments of humerus observed that, in the right side, S5, S7, S6, S3, S2, S4, and S1 are the best for the estimation of length of humerus as per their decreasing order of Pearson's coefficient. In the left side, they were S7, S5, S4, S2, S3, S6, and S1. However, the best values were from S5, S7, S3, and S2, irrespective of the side. This means that the above segments would be more appropriate in using to determine the maximum humeral length. It is observed that most of the parameters match well among the right and left sides, with respect to the correlation coefficients. However, few were different as the humeri in the samples could not be matched as right and left from the same individual. The humeri in this study were randomly selected from the disarticulated skeleton.
The S4 segment is the total width of trochlea and capitulum, which had a mean of 3.8 ± 0.4 cm and 3.9 ± 0.5 cm for the left and right sides in this investigation. The values for similar segment in Brazilian samples^{[24]} were 3.9 ± 0.4 cm and 4 ± 0.4 cm for the left and right sides, which is slightly higher. The distance from the lateral extent of the capitulum to the medial limit of the medial epicondyle (S5) in this study for the right and left side were 5.3 ± 0.5 cm and 5.2 ± 0.5 cm individually. The previous Brazilian study^{[24]} reported these data as 5.8 ± 0.5 cm and 5.6 ± 0.4 cm, respectively. In the present study, the distance from the lateral edge of lateral condyle to the most medial point of medial epicondyle (S7) was 5.6 ± 0.5 cm and 5.7 ± 0.5 cm at the left and right sides. This is comparable to the data by Salles et al.,^{[24]} as the values were 5.8 ± 0.6 cm and 5.7 ± 0.4 cm. These values were marginally on the upper side than the data of our study. These findings compare very well with our present study.
The present study observed that all the segments of humerus had a significance value (P < 0.05), which is statistically significant. It was observed that the horizontal segments showed greater Pearson's coefficient of correlation values, suggesting that the horizontal segments were in better ratio relationship with the total humeral length. It was observed that there were some sidebased variations. This may not be considered significant as the sample bones are not paired as such. However, the regression formula is applied to the best five of the parameters on either side. In the present study, the regression equation involves a constant, multiplying factor, and the standard error of estimate. The regression formulae, which are derived here, can approximately estimate the humeral length, whenever an incomplete bone is found or need to be studied. The formulae cater to some of the welldemarcated segments of the distal end of humerus.
The data of the present study are of use when only a few fragments of lower end of humerus are available for the medicolegal investigation. The dimensions of the distal humeral fragments can assist in determining the identity of the corpses throughout the medicolegal inquiry. By knowing the humeral length, one can plan to evaluate the height and built of a person. It was reported that the regression formulae of one population cannot be applied to another, as the stature of an individual can vary depending on their ethnicity.^{[19]} The morphological data of distal humeral fragments are important in the orthopedic surgery. The orthopedicians can utilize the morphometric data during the management of distal humeral fractures and reconstructive surgeries.^{[19]} The data are also helpful during the designing of prosthesis in terms of size and positioning. However, the present study has some limitations like the age and gender of the humeri were not taken into consideration. In the present study, the specimens were randomly selected, and it was not possible to confirm the relation among the humeral length and the height of the person, because of the deficiency of data in this anatomical collection of dried humeri.
Conclusion   
This study adds to the present data concerning the dimensions of the distal fragments of humerus. The equations, which are derived in this research, may be utilized in medicolegal examinations, where the stature of an individual has to be determined and there are only a few bony fragments of humerus are available for the medicolegal examination. The dimensions are also required in anthropological and archaeological surveys.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3], [Table 4]
