Allometric Scaling of Calcaneal Bone Stiffness in Young Athletes: An Exploratory Study of a Size-Free Index

Background: Bone strength is essential for maintaining athletic performance and preventing stress fractures. However, conventional indicators such as Bone Mineral Density (BMD) and the Osteo Sono-Assessment Index (OSI) are influenced by body size, limiting comparisons between sexes and sports disciplines. This study aimed to develop and validate a body size–independent indicator of calcaneal stiffness using allometric scaling in young athletes. Methods: This cross-sectional study included 295 athletes aged 10–30 years (153 males, 142 females). OSI was measured using quantitative ultrasound, and lean body mass (LBM) was assessed by bioelectrical impedance analysis. Using the scaling exponent (b = 0.199) derived from the log–log regression between OSI and LBM, the size-free OSI (sf_OSI) was calculated as sf_OSI = ln(OSI) − 0.199 × ln(LBM). Sex and sport differences were examined using Welch’s t-test and linear models, with muscle strength evaluated by including knee extension torque as a covariate. Results: Females showed significantly higher OSI values than males (3.31 ± 0.42 vs. 3.18 ± 0.42, p = 0.009), with an even difference for sf_OSI (0.45 ± 0.12 vs. 0.36 ± 0.11, p < 0.001, Hedges’ g = 0.79). Sex (η² = 0.036) and age group (η² = 0.152) exerted independent effects. Sport-specific analysis showed greater female predominance in Court-Jump (+10.3%) and Field-Sprint (+9.5%) sports, with no significant difference in combat sports. Adjustment for knee extension torque reduced the sex difference by up to 13% (ΔR² ≤ 0.04). Conclusions: sf_OSI appears to be a body size–adjusted indicator of calcaneal stiffness that clearly delineates sex- and sport-specific patterns. Although it demonstrated exploratory utility as a monitoring metric, direct causal or fracture risk associations were not established. sf_OSI may serve as a practical, noninvasive tool for monitoring sport-specific bone adaptation and stress fracture risk in field settings. In this study, females consistently exhibited higher sf_OSI values, particularly in Court-Jump and Field-Sprint sports. These sex differences were not fully explained by muscle strength, suggesting that sf_OSI is a useful parameter for evaluating sport-specific bone adaptation and stress fracture risk in young athletes.