Sex estimation is a fundamental component of establishing the biological profile in forensic anthropology, particularly in cases involving unidentified skeletal remains from mass disasters or medico-legal investigations(1).Accurate determination of sex is essential for narrowing down missing persons databases, with the os coxae traditionally regarded as the most reliable indicator due to its pronounced sexual dimorphism (2). However, in fragmented skeletons, long bones of the lower limb, such as the tibia and fibula, serve as viable alternatives through metric analyses(3).The fibula exhibits dimorphic features at its distal end, including the articular surface and lateral malleolus, reflecting biomechanical adaptations influenced by body size and hormonal factors (4). Early studies demonstrated the utility of discriminant function analysis for classifying sex based on fibular metrics, achieving accuracies of 70-90% (5). Vedapriya and Rajasree reported 75-85% accuracy using fibular length and midshaft circumference in a southern Indian sample, while Tabencki achieved up to 91% for the distal articular surface in a U.S. cohort (6,7). The present study aimed to evaluate sexual dimorphism in distal fibula parameters like total length, midshaft circumference, distal articular surface height and width, and lateral malleolus length in adult dry bones from Maharashtra, India.

This cross-sectional osteometric study was conducted on dry adult fibulae of known sex, sourced from bone banks at medical colleges in Maharashtra, India. The study was carried out in the Department of Anatomy over a period of 18 months following approval from the Institutional Ethics Committee (IEC No: BJGMC/IEC/D-1019131-131; Dated:15.10.2019). As the investigation involved archived skeletal material with no identifiable personal information, informed consent was not required, in accordance with ethical guidelines for osteological research (8). Sample Selection A total of 85 dry fibulae (55 male, 30 female) from adult individuals (aged >18 years) were included. Bones were selected based on the following criteria: Inclusion Criteria: • Fully ossified adult fibulae. • Free of pathological deformities, fractures, or surgical modifications. • Known sex, derived from documented donor records. Exclusion Criteria: • Bones with fractures or replaced by implants. • Evidence of congenital or acquired deformities. • Incomplete or damaged specimens unsuitable for accurate measurement. Samples were randomly selected from available collections to minimize selection bias, ensuring a balanced representation of left and right sides where possible. No significant age-related effects on measurements were anticipated, based on prior studies (7). Osteometric Measurements Measurements were performed by a single observer to ensure consistency, using standardized instruments calibrated prior to use. All dimensions were recorded to the nearest 0.01 cm. The following parameters were assessed, focusing on the distal fibula for its diagnostic potential in sex estimation: 1. Total Length of Fibula: Measured as the maximum distance from the apex of the styloid process to the tip of the lateral malleolus using an osteometric board. 2. Mid-Shaft Circumference at Dominant Nutrient Foramen: The circumference at the level of the dominant nutrient foramen on the shaft, determined using a flexible thread and subsequently measured with a scale. 3. Height of Distal Articular Surface: The vertical distance from the most distal point of the articular surface to its most proximal extent, measured with vernier calipers. 4. Maximum Antero-Posterior (AP) Width of Distal Articular Surface: The greatest breadth in the antero-posterior direction across the distal articular surface, using vernier calipers. 5. Length of Lateral Malleolus: The distance from the apex of the distal articular surface to the tip of the lateral malleolus, measured with vernier calipers. Instruments employed were osteometric board, digital vernier calipers (accuracy 0.01 mm), flexible measuring tape, scale, thread, chalk for marking, marker pens, and disposable gloves for handling. Statistical Analysis Data were analysed using SPSS software (version 25.0; IBM Corp., Armonk, NY, USA). Descriptive statistics (mean, standard deviation, range) were calculated for each parameter by sex. Independent t-tests assessed differences between male and female means, with statistical significance set at p < 0.05. For sex classification, univariate discriminant function analysis was applied to individual parameters, evaluating discriminatory power via Wilks' lambda (Λ) and F-ratio. Multivariate analyses included direct discriminant function analysis (using all five variables) and stepwise discriminant function analysis (forward selection with F-to-enter = 3.84 and F-to-remove = 2.71). Assumptions of normality and homogeneity of variance were verified using Shapiro-Wilk and Levene's tests, respectively (9).

A total of 85 adult fibulae (55 male and 30 female) were analysed, with no significant differences observed between left and right sides (p > 0.05). All measured parameters demonstrated statistically significant sexual dimorphism, with males exhibiting larger mean values across the board (p < 0.001 for all except height of distal articular surface, p < 0.0001). Descriptive statistics revealed greater variability in female samples for most parameters, potentially attributable to sample heterogeneity. The total length of the fibula was the most dimorphic linear dimension, followed by the length of the lateral malleolus and maximum antero-posterior (AP) width of the distal articular surface. In contrast, the height of the distal articular surface showed considerable overlap between sexes, limiting its univariate discriminatory utility. Univariate discriminant function analysis (DFA) confirmed significant separation for four of the five parameters, with Wilks' lambda values ranging from 0.57 to 0.89 and corresponding F-ratios indicating strong discriminatory power, particularly for the maximum AP width (F = 90.42). Classification accuracies varied from 73.3% to 81.75% overall, with the maximum AP width achieving the highest combined accuracy (81.75%; 79.2% for males, 85.42% for females). The total length provided robust male classification (87.5%) but lower female accuracy (66.67%), while mid-shaft circumference and lateral malleolus length offered balanced performance (overall 73.3-78.3%).Multivariate DFA, incorporating all parameters, yielded an overall classification accuracy of 83.5%, with improved specificity for females (92.3%). Stepwise DFA further refined the model by sequentially selecting the three most predictive variables: maximum AP width (Step 1), length of lateral malleolus (Step 2), and mid-shaft circumference (Step 3). This reduced model terminated after Step 3 due to non-significant F-ratios for remaining variables (F < 2.71). The final stepwise function achieved 91.7% overall accuracy (87.5% males, 100% females), outperforming both univariate and direct multivariate approaches. Canonical correlation analysis within the stepwise model highlighted strong correlations between the selected variables and the discriminant function (structure coefficients > 0.70 for maximum AP width and lateral malleolus length), underscoring their primacy in sex prediction. The derived sectioning point for classification was Z = -1.23, with the discriminant score calculated as Z = constant + (raw coefficient × variable value) for the three predictors. Tables Table-1: Descriptive Statistics for Morphometric Parameters of the Fibula by Sex Parameter Males (n=55) Mean ± SD (Range, cm) Females (n=30) Mean ± SD (Range, cm) t-value p-value Total length 36.68 ± 1.44 (34.6–39.8) 33.40 ± 5.09 (30.6–36.7)* 4.52 <0.001 Mid-shaft circumference at dominant nutrient foramen 4.38 ± 0.28 (3.8–4.9) 3.95 ± 0.33 (3.2–4.5) 6.12 <0.001 Height of distal articular surface 2.18 ± 0.19 (1.8–2.6) 2.38 ± 0.26 (1.7–2.4)** -3.21 <0.0001 Maximum AP width of distal articular surface 2.26 ± 0.26 (1.7–2.7) 1.85 ± 0.17 (1.6–2.2) 9.51 <0.001 Length of lateral malleolus 2.70 ± 0.27 (2.2–3.3) 2.26 ± 0.24 (1.8–2.8) 7.89 <0.001 Table -2: Summary of Univariate Discriminant Function Analysis for Fibula Parameters Parameter Wilks' Lambda (Λ) F-ratio Overall Accuracy (%) Male Accuracy (%) Female Accuracy (%) Total length 0.72 45.23 79.2 87.5 66.67 Mid-shaft circumference at dominant nutrient foramen 0.66 59.17 73.3 76.4 68.75 Height of distal articular surface 0.89 12.34 62.4 56.9 73.3** Maximum AP width of distal articular surface 0.57 90.42 81.75 79.2 85.42 Length of lateral malleolus 0.58 84.04 78.3 77.8 79.2 Table - 3: Stepwise Discriminant Function Analysis: Variable Selection Summary Step Variable Entered Wilks' Lambda (Λ) F-ratio (to Enter) Cumulative Accuracy (%) 1 Maximum AP width of distal articular surface 0.57 90.42 81.75 2 Length of lateral malleolus 0.58 84.04 85.9 3 Mid-shaft circumference at dominant nutrient foramen 0.66 59.17 91.7 Table - 4: Canonical Discriminant Function Coefficients for Stepwise Model Variable Raw Coefficient Standardized Coefficient Structure Coefficient Constant -15.24 - - Maximum AP width of distal articular surface 4.12 0.44 0.74 Length of lateral malleolus 5.67 0.39 0.71 Mid-shaft circumference at dominant nutrient foramen 3.89 0.51 0.65

The present study confirms the presence of significant sexual dimorphism in the morphometric parameters of the distal fibula among an adult Maharashtra population, aligning with established principles in forensic osteology that emphasize the role of long bones in sex estimation when pelvic or cranial elements are unavailable (10). Males consistently displayed larger dimensions across all measured variables, a pattern attributable to greater overall skeletal robusticity influenced by genetic, hormonal, and biomechanical factors during growth and maturation (11). Notably, the total fibula length (mean 36.68 cm in males vs. 33.40 cm in females) exhibited the greatest absolute dimorphism (Δ mean = 3.28 cm), corroborating findings from Vedapriya and Rajasree's southern Indian cohort, where male fibular lengths averaged 35.2 cm compared to 32.1 cm in females, yielding a similar dimorphic gap of approximately 3.1 cm (6). This consistency suggests that fibular length remains a reliable univariate discriminator in Indian populations, though its classification accuracy (79.2% overall) was slightly lower than reported in East Asian samples (e.g., 85% in Hanihara's study of Japanese long bones) (20), potentially due to nutritional and socioeconomic variations affecting stature in South Asia (12).The mid-shaft circumference at the dominant nutrient foramen (4.38 cm males vs. 3.95 cm females) also demonstrated robust dimorphism (p < 0.001), with an overall accuracy of 73.3%, mirroring Vedapriya and Rajasree's observations where this parameter achieved 80% male classification in a smaller sample of 80 fibulae (6). Such circumferential measures reflect diaphyseal robusticity linked to muscle attachment sites and load-bearing, and their utility is enhanced in fragmented remains where full length cannot be obtained (13). In contrast, the height of the distal articular surface showed paradoxical results, with females exhibiting a slightly larger mean (2.38 cm vs. 2.18 cm; p < 0.0001) and substantial overlap (62.4% accuracy), challenging expectations of uniform male enlargement. This anomaly may stem from measurement variability or population-specific adaptations, as Tabencki reported no significant height differences in a U.S. sample but emphasized transverse widths for discrimination (7). Our maximum antero-posterior (AP) width of the distal articular surface (2.26 cm males vs. 1.85 cm females) emerged as the strongest univariate predictor (81.75% accuracy, F = 90.42), closely paralleling Tabencki's 91% accuracy for left fibular articular surfaces, where AP dimensions were prioritized over height due to clearer dimorphic boundaries (7). Similarly, the lateral malleolus length (2.70 cm males vs. 2.26 cm females) provided balanced accuracy (78.3%), consistent with broader lower limb studies like Kranioti et al.'s analysis of Greek-Cypriot tibiae, which noted malleolar dimorphism contributing 75-80% to sex classification (23).Multivariate approaches substantially improved discriminatory power, with stepwise discriminant function analysis (DFA) achieving 91.7% overall accuracy using just three variables (maximum AP width, lateral malleolus length, and mid-shaft circumference), outperforming the direct multivariate model (83.5%) and all univariate metrics. This stepwise selection—prioritizing variables with the lowest Wilks' lambda (0.57 for AP width)—echoes Fisher's foundational framework for maximizing group separation through correlated predictors (11), and aligns with Robinson and Bidmos's South African study, where stepwise fibular models reached 88% accuracy by excluding overlapping parameters like articular height (14). The derived function (Z = -15.24 + 4.12 × AP width + 5.67 × malleolus length + 3.89 × mid-shaft circumference; sectioning point -1.23) offers a practical tool for forensic practitioners, particularly in medico-legal cases involving dismembered lower limbs from Maharashtra. Compared to Tabencki's univariate focus (91% for left sides only) (7), our multivariate integration mitigates side bias and enhances generalizability, though female-specific accuracy (100%) may reflect sample imbalance (30 vs. 55 males), warranting caution in diverse ancestries (15).These population-specific standards address a critical gap in South Asian forensic anthropology, where generalized equations from Western cohorts often yield 10-15% misclassification rates due to inter-regional variability in body proportions (16). For instance, while Vedapriya and Rajasree's southern Indian data overlap with ours in length and circumference means (Δ < 1 cm), northern populations like those in Srivastava et al.'s tibial study show 5-7% larger dimensions, underscoring the need for Maharashtra-tailored norms (24). The high F-ratios in our fibular analysis (up to 90.42) further indicate its complementary role to tibial metrics, as tibia-fibula combined models in prior Indian research elevated accuracies to 95% (19), though fibula's distal features prove invaluable in talocrural joint isolations. Limitations The modest female sample size (n=30), which may inflate specificity, and the unilateral focus without bilateral comparisons, despite no side effects noted (p > 0.05). Additionally, ancestry was not stratified beyond Maharashtra origins, potentially confounding results in multi-ethnic cases (17). Age data, while known, were not analysed for interactions, though prior evidence suggests minimal impact post-ossification (7,25). Future research should incorporate larger, balanced cohorts, 3D morphometrics via CT scanning, and validation against living populations to refine these equations for broader Indian forensic applications(18).

The distal fibular morphometry, particularly via stepwise DFA, provides a reliable, population-specific method for sex estimation with 91.7% accuracy, enhancing the toolkit for unidentified remains in medico-legal contexts. These findings affirm the fibula's forensic value, especially in fragmented scenarios, and advocate for regionally calibrated standards to improve identification efficacy in South Asia.

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