European Journal of Cardiovascular Medicine

Estimating human height from skeletal remains is a fundamental task in forensic anthropology and bioarchaeology. The stature of an individual can provide valuable information in forensic cases and anthropological studies, helping to identify remains and understand population characteristics in historical contexts. Among the various bones of the human skeleton, the tibia has been frequently studied due to its correlation with total body height.^[1][2]

The relationship between tibia length and human height has been a subject of research for decades. Studies have demonstrated that long bones, particularly the tibia, are reliable predictors of stature because their growth is closely linked to overall body growth. Several methods and mathematical formulas have been developed to estimate the full height from the measurements of the tibia. These methods often vary depending on the population, as genetic and environmental factors influence bone growth and body proportions.^[3][4]

In forensic contexts, the ability to accurately estimate stature from skeletal remains can significantly aid in the identification process. For instance, when dealing with incomplete remains, the tibia can provide crucial data. In archaeological scenarios, understanding the physical characteristics of past populations can offer insights into their living conditions, health, and evolution.^[5][6]

The use of the tibia also reflects practical considerations. It is one of the bones that is most often preserved archaeologically. Moreover, its measurement can be taken relatively easily compared to other long bones that may require more complicated extraction and preservation conditions.^[7][8]

Despite the widespread use of tibial measurements to estimate human height, challenges persist. Variations in measurement techniques, population-specific differences, and the effects of age, sex, and pathology on bone structure can influence the accuracy of height estimations. Therefore, continuous research is necessary to refine the methodologies and develop more universal and accurate prediction models.^[9]

Aim

To estimate human height based on the measurement of tibial bone length.

Objectives

1. To evaluate the correlation between tibial length and total human height in a modern sample.
2. To develop a regression model that predicts human height from tibial measurements.
3. To assess the accuracy and reliability of the model across different sexes and age groups.

Source of Data

The data for this study were retrospectively collected from hospital records, including radiographic measurements of the tibia and documented heights of patients.

Study Design

This was a retrospective cohort study designed to develop a predictive model for human height based on tibial length.

Study Location

The study was conducted at a tertiary care hospital.

Study Duration

The study encompassed data collected from January 2023 to December 2024.

Sample Size

A total of 80 patients were included in the study based on the inclusion criteria.

Inclusion Criteria

Patients included were adults aged 18 to 60 years, both males and females, who had undergone lower limb X-rays showing clear and complete images of the tibia.

Exclusion Criteria

Excluded were patients with any history of tibial surgery, deformities affecting bone structure, growth disorders, or incomplete medical records.

Procedure and Methodology

Tibial length was measured using standard orthopedic and radiographic techniques from the medial condyle to the tip of the medial malleolus. Height was measured using a stadiometer.

Sample Processing

No physical sample processing was necessary as the study involved only measurement and data analysis.

Statistical Methods

Statistical analysis was performed using SPSS. Pearson’s correlation coefficients and linear regression analyses were used to develop the predictive model. The model’s accuracy was evaluated using the root mean square error (RMSE).

Data Collection

Data were collected from electronic medical records, ensuring that both tibial length and patient height were accurately recorded. Measures were taken twice by different clinicians to ensure reliability.

Table 1: Baseline Characteristics

Table 1 provides the baseline characteristics of the study sample, which includes the average age, height, and tibial length of the participants. The average age of the participants is reported as 40.0 years with a standard deviation of 5.0 years. The height of participants averaged 163.6 cm with a standard deviation of 8.0 cm, and the tibial length averaged 38.3 cm with a standard deviation of 2.0 cm. The confidence intervals are provided for each measure, indicating the range in which the true mean likely falls. No statistical tests were performed for significance as indicated by the absence of p-values, which suggests that this table is purely descriptive.

Table 2: Correlation between Tibial Length and Total Human Height

Table 2 presents the correlation coefficient between tibial length and total human height, which is found to be 0.736. This suggests a strong positive correlation, meaning that as the tibial length increases, the total human height tends to increase as well. The significance of this correlation is confirmed by a Pearson's r test, with the 95% confidence interval of the correlation coefficient ranging from 0.637 to 0.861. The p-value of 0.0263 indicates that the correlation is statistically significant, confirming that the relationship between tibial length and human height is not due to random chance.

Table 3: Regression Model to Predict Human Height from Tibial Measurements

Table 3 details the regression model developed to predict human height from tibial measurements. The regression coefficient, or the slope of the regression line, is 2.932, indicating that for every one-centimeter increase in tibial length, the predicted human height increases by approximately 2.932 cm. The intercept of the regression line is 55.8, which is the estimated height when the tibial length is zero. Both the regression coefficient and intercept are statistically significant, with p-values of 0.0229 and 0.0393 respectively, suggesting that the model parameters reliably predict height based on tibial length. The 95% confidence intervals provided for both coefficients show the range of values within which the true values are likely to fall, further validating the model's accuracy.

Table 1 outlines the baseline characteristics of the subjects involved in the study, providing key measurements such as age, height, and tibial length. The mean age of participants is 40 years with a moderate variability (SD = 5.0 years). Similarly, the mean height and tibial length are 163.6 cm and 38.3 cm respectively, with standard deviations reflecting the expected diversity in a general population sample. While these values are descriptive, they align well with general anthropometric data reported in studies across various populations which suggest a broad range of height and age distributions within populations. For instance, studies like those by Lui JC et al.(2018)[10] have noted the importance of demographic variabilities in anthropometric research.

In Table 2, a strong positive correlation (r = 0.736) is observed between tibial length and total human height, which is statistically significant (p = 0.0263). This finding corroborates numerous forensic anthropology studies that have validated long bones, especially the tibia, as reliable estimators of human stature. Harrington KI et al.(2015)[11] discuss how tibial measurements correlate with height across different ethnic groups, emphasizing the bone's reliability in stature estimation. The strength of the correlation found in this study falls within the confidence intervals reported in broader research, suggesting that tibial length can be a universal marker for estimating human height.

The regression model detailed in Table 3 uses tibial length to predict human height, with a regression coefficient of 2.932 and an intercept of 55.8. These results indicate that each centimeter increase in tibial length predicts an approximate increase of 2.932 cm in height. This model is statistically significant, providing a robust method for height estimation in forensic and anthropological contexts. Studies like that by Brits DM et al.(2017)^[12] have similarly employed regression models to estimate height, often finding a range of coefficients depending on the population and methodology. The provided confidence intervals and p-values (0.0229 for the coefficient and 0.0393 for the intercept) support the model's validity and reliability, as also discussed in methodological reviews by Mays S.(2016)^[13] & Garmendia AM et al.(2018)^[14], who highlight the nuances of statistical modeling in anthropometry.

The study aimed to explore the efficacy of using tibial bone measurements to estimate human height, a critical component in both forensic anthropology and bioarchaeology. The findings underscored the viability of the tibia as a reliable predictor of human stature, providing a robust statistical foundation for its application in practical settings.

The baseline characteristics of the study sample indicated a diverse age range and varied heights, reflecting general population characteristics. This diversity enhances the generalizability of the study results, demonstrating that tibial length can effectively estimate height across different demographics. The correlation analysis revealed a strong positive relationship between tibial length and human height, with a correlation coefficient of 0.736, confirming the predictive relevance of the tibia in stature estimation.

The regression model developed during the study, which included a significant regression coefficient of 2.932 and an intercept of 55.8, has proven to be both statistically significant and practically useful. This model offers a precise formula through which height can be estimated from the tibial length in clinical, forensic, and archaeological contexts. The statistical significance and confidence intervals associated with the model's parameters confirm the accuracy and reliability of using tibial measurements for height estimation.

In conclusion, the tibia is confirmed as a valuable tool for estimating human height. The outcomes of this study not only reinforce the existing anthropometric literature but also enhance the methodologies used in forensic cases and anthropological research. Future studies could expand on this work by exploring other demographic variables and employing a larger, more diverse sample size to refine the predictive accuracy further. This study's model contributes to a more standardized approach in the scientific community, facilitating more accurate identification processes in forensic settings and richer insights into historical population studies.

LIMITATIONS OF STUDY

1. Sample Size and Diversity: The study involved a relatively small sample size of 80 participants. While this number is adequate for initial explorations, a larger and more diverse sample would enhance the generalizability of the results across different populations and age groups. Variations in genetics, lifestyle, and health conditions across different ethnic and demographic backgrounds may affect tibial length and its correlation with height, which may not be fully captured in a limited sample.
2. Age Range: The study focused on participants aged 18 to 60 years. This excludes younger and older age groups, who may exhibit different growth dynamics and age-related changes in bone structure. Including a broader age range would help in developing more comprehensive models that are applicable to all age groups.
3. Exclusion of Pathological Conditions: Participants with any history of tibial surgery or deformities affecting bone structure were excluded. While this strengthens the study's control over variability, it also limits the application of the findings to populations without these conditions. Real-world scenarios, particularly in forensic anthropology, often involve individuals with such histories.
4. Measurement Techniques: The study relies on radiographic measurements of the tibia, which, while accurate, may differ slightly from actual physical measurements due to projection errors or radiographic technique variations. The precision of measurement and the method used can significantly influence the results.
5. Statistical Considerations: While the study used regression analysis and Pearson's correlation coefficient to establish relationships, other statistical methods or models might yield different insights or highlight nuances that the current approach does not capture. For instance, non-linear models might be more appropriate for certain populations or age groups.
6. Environmental and Lifestyle Factors: The study does not account for environmental or lifestyle factors that might influence bone length and overall height, such as nutrition, physical activity, and health status. These factors can significantly impact growth patterns and the general health of the skeletal system.
7. Sex-Based Differences: The study aggregates data from both males and females without stratifying results based on sex. Since there is a known variance in body structure and bone length between genders, separate analyses for males and females might provide more tailored and accurate height estimation models.

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