**4. Discussion**

The objective of this study was to reveal the humeral asymmetry patterns of East Asian modern humans with diverse backgrounds, by evaluating the biomechanical performance across complete humeral diaphysis rather than individual cross-sections only, as well as to identify the reliability of torsional rigidity at the 35% and 50% cross-sections (J35 and J50) in bilateral asymmetry analysis.

By quantifying the overall bending rigidity asymmetry of humeral proximodistal diaphysis using morphometric mapping of SMA asymmetry values, the variation range and pattern of humeral asymmetry in East Asian modern humans represented by our samples were investigated. In all the sub-groups, male humeri are more asymmetrical than female humeri. The Henan population has lower humeral asymmetry overall compared to the Hubei and Xinjiang populations. Although three populations show unique distributions of bending rigidity asymmetry, the inter-group differences are not significant in MANOVA. This suggests that, at least for the samples used in this study, the behavioral differences among different populations and between different sexes are not significant enough to generate discernable differences in bilateral asymmetry. The relatively small sample size of the present study might be a factor in this result. Future studies with larger sample sizes and populations from more varied backgrounds may reveal significant differences.

Overall, the mean morphometric maps of most the sub-groups and pooled samples show the following common distribution pattern: the asymmetry of the proximal section is reinforced anteroposteriorly, connecting it to another relatively asymmetrical area between the mid-proximal and middle diaphysis, mediolaterally, and finally extending to the distal end in the anterolateral posteromedial aspect. Previous research found that humeral asymmetry was most prominent at the midshaft and decreased towards both the proximal and distal diaphyseal ends, and this pattern can be attributed to the general mechanical model that bending loads should be the greatest at mid-diaphyseal regions [55]. However, as revealed in the present study, the proximal to middle diaphysis tends to have a higher asymmetrical level than the distal half, and the differences tend to be more prominent among different anatomical directions than between different sections along the humeral diaphysis. This asymmetry pattern emphasizes the necessity of examining multiple anatomical directions when analyzing bilateral asymmetry, and suggests that the mechanism regulating the response of the long bone to external stimuli might be more complicated than previously understood.

As some highly asymmetrical regions correspond with the positions of major muscle attachments, such as deltoid tuberosity and the crest of the greater tubercle [56], the distribution of areas with reinforced asymmetry might reflect adaptions to muscle loadings, which were proved to be an important determinant of upper-limb strength [57–59]. In our study, factors such as genetic regulation and health condition can be excluded from the elements influencing the bilateral asymmetry because the analysis was based on paired humeri from the same individual. However, more experimental evidences are needed to verify this hypothesis in future studies.

According to the results of the CV morphometric maps, the variability in bilateral asymmetry is not consistent across the humeral diaphysis. Highly variable regions are restricted to the distal half of humeral diaphysis in the anteromedial posterolateral aspect, corresponding to the medial/lateral border and medial/lateral supracondylar. Since this feature is shared by all the sub-groups as well as the pooled data, it may represent a generality of East Asian modern humans. It is noteworthy that highly variable regions on the humeral diaphysis tend to overlap with areas presenting a low asymmetrical level, which may be a signal of relative insensitivity to lateralized mechanical stimuli (see previous paragraph). Previous studies found that humeral distal articular properties, such as articular surface area, did not just respond to mechanical loadings, but were also ontogenetically constrained and genetically canalized [60]. As the structure of the medial/lateral border and medial/lateral supracondylar are closely related to the distal articular morphology, according to their anatomical adjacency [56], one possible interpretation for the high variability of asymmetry is that these regions might present fluctuating asymmetry that is attributable to genetic, nutrient, and health factors instead of the mechanical environment alone [60–62].

This study supports the previous perspective that torsional rigidity at a specific crosssection (35% or 50% of the humeral biomechanical length) can be used to indicate the overall biomechanical asymmetry of humeral diaphysis, because the multivariate regression model built on all the specimens is effective, and a positive correlation exists between the SMA asymmetry and J asymmetry at most diaphyseal locations. However, we should also note that a single J asymmetry value cannot convey the complexity of the entire humerus' asymmetry. The correlation between overall SMA asymmetry and J asymmetry is moderate, because J35 and J50 asymmetry can only explain about half of the total variation in humeral bilateral asymmetry. In addition, the degree of correlation between SMA asymmetry and J asymmetry varies across the humeral diaphysis, and is only strong in specific regions.
