Biomechanical Evaluation on the Bilateral Asymmetry of Complete Humeral Diaphysis in Chinese Archaeological Populations

: Diaphyseal cross-sectional geometry (CSG) is an effective indicator of humeral bilateral asymmetry. However, previous studies primarily focused on CSG properties from limited locations to represent the overall bilateral biomechanical performance of humeral diaphysis. In this study, the complete humeral diaphyses of 40 pairs of humeri from three Chinese archaeological populations were scanned using high-resolution micro-CT, and their biomechanical asymmetries were quantiﬁed by morphometric mapping. Patterns of humeral asymmetry were compared between sub-groups deﬁned by sex and population, and the representativeness of torsional rigidity asymmetry at the 35% and 50% cross-sections (J 35 and J 50 asymmetry) was testiﬁed. Inter-group differences were observed on the mean morphometric maps, but were not statistically signiﬁcant. Analogous distribution patterns of highly asymmetrical regions, which correspond to major muscle attachments, were observed across nearly all the sexes and populations. The diaphyseal regions with high variability of bilateral asymmetry tended to present a low asymmetrical level. The J 35 and J 50 asymmetry were related to the overall humeral asymmetry, but the correlation was moderate and they could not reﬂect localized asymmetrical features across the diaphysis. This study suggests that the overall asymmetry pattern of humeral diaphysis is more complicated than previously revealed by individual sections. diaphyseal cross-sections, and morphometric map exhibiting bending rigidity asymmetry. Abbreviations for anatomical terms are as follows: prox: proximal; mid: middle; dist: distal; lat: lateral; post: posterior; med: medial; ant: anterior. maps SMA asymmetry values of all specimens.


Introduction
Humeral bilateral asymmetry has been extensively studied in orthopedics, forensics, and paleo/archaeological anthropology [1][2][3]. Handedness can be inferred from the bilateral asymmetry of the upper limb [4][5][6]. Evidence from living athletes of unilaterally dominated sports (such as tennis and cricket) suggests a close relationship between humeral bilateral asymmetry and behavioral laterality [7][8][9]. A combined study of endocranial and humeral asymmetry can shed light on how the human body responds to dependent asymmetrical stimuli across biologically independent anatomical regions [10]. These applications make humeral bilateral asymmetry an effective approach for reconstructing the behaviors of past human populations [11][12][13][14][15][16].

Data Collecting and Processing
All humeri were scanned by a 450 kV micro-CT scanner (designed by Institute of High Energy Physics, Chinese Academy of Sciences) located in Key Laboratory of Vertebrate Evolution and Human Origins, Institute of Vertebrate Paleontology and Paleoanthropology, Chinese Academy of Sciences. The scanning was performed under a voltage of 380 kV, current of 1.5 mA, 360 • rotation with a step of 0.5 • , and an isometric voxel size of 160 µm. Raw data were virtually reconstructed and segmented in VGStudio Max 3.0. Volume renderings of all humeri were aligned to anatomical position using the standard protocol defined by Ruff [26]. To ensure that the humeri were consistently aligned and to avoid inter-observer error, all alignments were made by one author (Y.Z.). Paired humeri were always aligned synchronously. Three-dimensional meshes of each aligned humerus were generated and saved as PLY files in Avizo 8.1 for the following analyses.

Cross-Sectional Geometric Parameters Calculation
Customized in-house scripts, mainly sourced from R package 'morphomap', were applied to calculate the CSG parameters [52]. For each humerus, the single-layer periosteum and endosteum surface meshes were firstly detached from the original humeral mesh. Second, 61 equidistant cross-sections were extracted from the surface meshes along the proximodistal diaphysis (between 20 and 80% of the biomechanical length). Third, 360 equiangular landmarks were placed along both the inner and outer contours on each cross-section. Finally, J values of the cross-sections at 35% and 50% of biomechanical length (J 35

Bilateral Asymmetry Quantification
Commonly used practices for assessing bilateral asymmetry are absolute asymmetry ([(max − min)/((max + min)/2)] × 100%) and directional asymmetry ([(right − left)/((right + left)/2)] × 100%). However, absolute asymmetry is not appropriate in this study, as the magnitude relationship between the left and right side is not consistent among different landmarks at humeral diaphysis. However, our study still focuses on absolute information of overall bilateral asymmetry, so directional asymmetry is also not suitable, because it does not eliminate the impact of handedness as well as behavioral laterality, which is not the issue this study attempts to investigate and may bring about bias to the conclusion. Therefore, bilateral asymmetry was quantified using dominant asymmetry ([(dominant − non-dominant)/((dominant + non-dominant)/2)] × 100%). The dominant side was decided according to the magnitude of J 50 , given that it is a valid indicator of handedness [5].

Morphometric Mapping
The SMA asymmetry values were obtained using the dominant asymmetry equation for all 21,960 (360 × 61) landmarks, and the results for each paired humeri were deposited in a matrix with 61 rows (sorted by the order of cross-sections) and 360 columns (sorted by the order of directions). These matrices were then visualized as morphometric maps to display the distribution characteristics of bending rigidity asymmetry along the proximodistal humeral diaphysis (Figures 1 and A1). The asymmetry values of J 35 and J 50 for all individuals were also calculated using the same equation.
the proximodistal diaphysis (between 20 and 80% of the biomechanical length). Third, 360 equiangular landmarks were placed along both the inner and outer contours on each cross-section. Finally, J values of the cross-sections at 35% and 50% of biomechanical length (J35 and J50), and SMA values of 360 directions on 61 cross-sections were calculated based on the landmark coordinates.

Bilateral Asymmetry Quantification
Commonly used practices for assessing bilateral asymmetry are absolute asymmetry ([(max − min)/((max + min)/2)] × 100%) and directional asymmetry ([(right − left)/((right + left)/2)] × 100%). However, absolute asymmetry is not appropriate in this study, as the magnitude relationship between the left and right side is not consistent among different landmarks at humeral diaphysis. However, our study still focuses on absolute information of overall bilateral asymmetry, so directional asymmetry is also not suitable, because it does not eliminate the impact of handedness as well as behavioral laterality, which is not the issue this study attempts to investigate and may bring about bias to the conclusion. Therefore, bilateral asymmetry was quantified using dominant asymmetry ([(dominant − non-dominant)/((dominant + non-dominant)/2)] × 100%). The dominant side was decided according to the magnitude of J50, given that it is a valid indicator of handedness [5].

Morphometric Mapping
The SMA asymmetry values were obtained using the dominant asymmetry equation for all 21,960 (360 × 61) landmarks, and the results for each paired humeri were deposited in a matrix with 61 rows (sorted by the order of cross-sections) and 360 columns (sorted by the order of directions). These matrices were then visualized as morphometric maps to display the distribution characteristics of bending rigidity asymmetry along the proximodistal humeral diaphysis (Figures 1 and A1). The asymmetry values of J35 and J50 for all individuals were also calculated using the same equation.

Methods to Estimate the Variation of Humeral Biomechanical Asymmetry
To explore the variation in humeral asymmetry patterns in modern humans, 40 individuals were divided into sub-groups defined by sex and population. The three populations, which varied in geographic location, chronological age, and subsistence pattern, were supposed to vary in their habitual behaviors, so population was set as one variable. Sexual division of labor is an important issue when discussing historical populations, and the sexual dimorphism of humeral asymmetry can be affected by nonbehavioral factors such as genetics or hormones [27]. Therefore, sex was set as another variable. Mean morphometric maps exhibiting SMA asymmetry values for each sub-group were qualitatively compared. Additionally, a two-way multivariate analysis of variance (MANOVA) was conducted to quantitatively test whether sex and/or population were significant sources of variation. When fitting the regression model for MANOVA, SMA asymmetry values at all landmarks were set as the dependent variables, while sex and population were set as the independent variables with interaction. Customized in-house scripts, mainly sourced from R package 'geomorph' and 'RRPP', were utilized to conduct MANOVA [53,54]. In addition, the coefficients of variation (CV) for SMA asymmetry values at all landmarks were calculated in sub-groups and visualized by morphometric maps to exhibit intra-group variation characteristics. Only sub-groups defined by sex or by population were included in this analysis to reduce the impact of outliers.

Methods to Test the Representativeness of J 35 or J 50 Asymmetry
The reliability of using J 35 or J 50 asymmetry to represent the overall humeral asymmetry was tested using several statistical methods. First, a multivariate regression model was built on all specimens to statistically test the degree of correlation between overall SMA asymmetry and J asymmetry. When fitting the model, the SMA asymmetry values at all landmarks were set as the dependent variables, and the J 35 or J 50 asymmetry value as the independent variable. Customized in-house scripts, mainly sourced from R package 'geomorph' and 'RRPP', were utilized to carry out this fitting [53,54]. Second, to investigate the association of every SMA asymmetry value and J asymmetry value across the entire humeral diaphysis, the correlation coefficients between each SMA asymmetry value and J 35 or J 50 asymmetry value (CC 35 and CC 50 ) were calculated within sub-groups. The same protocols for visualizing SMA asymmetry values were applied to CC results to generate morphometric maps. The CC morphometric maps of sub-groups were qualitatively compared to reveal inter-group variations.

Pattern of Humeral Biomechanical Asymmetry in Modern Humans
The mean morphometric maps exhibiting SMA asymmetry values for each sub-group and pooled samples are presented in Figure 2. Hubei females and males are more asymmetrical in the near-anterolateral posteromedial aspect along the entire proximodistal diaphysis. The degree of asymmetry is transversely uniform around the mid-distal diaphysis for Hubei females, and around the midshaft for Hubei males. Hubei males have higher anteroposterior asymmetry from the proximal to mid-proximal diaphysis. Henan females have a restricted area of relatively higher anteroposterior asymmetry around the midproximal diaphysis, while Henan males are more asymmetrical in the near-anterolateral posteromedial aspect spanning the mid-proximal to distal diaphysis. Both Xinjiang females and males have reinforced anteroposterior asymmetrical areas around the proximal diaphysis, as well as the region between the proximal to mid-proximal diaphysis, mediolaterally. The region with a relatively higher asymmetry of Xinjiang males extends from the midshaft to the distal diaphysis in the near-anterolateral posteromedial aspect.
For the mean morphometric maps that are defined only by population, Hubei is more asymmetrical across the entire proximodistal diaphysis in the near-anterolateral posteromedial aspect, with a reinforcement of anteroposterior asymmetry along the proximal to mid-proximal diaphysis. The region with high asymmetry for Henan is located in the anterolateral posteromedial aspect between the mid-proximal to distal diaphysis. Xinjiang has higher anteroposterior asymmetry around the proximal diaphysis, connecting with another area with high mediolateral asymmetry around the mid-proximal diaphysis, which continuously extends to the midshaft in the anterolateral posteromedial aspect. Hubei and Xinjiang are more asymmetrical than Henan, according to their overall magnitude of SMA asymmetry values. For the mean morphometric maps that are defined only by sex, females are more anteroposteriorly asymmetrical between the proximal and mid-distal diaphysis, with a reinforcement of asymmetry near the mid-proximal section. The distribution patterns of males resemble that of Xinjiang, but the regions with highest asymmetry at the proximal and mid-proximal diaphysis are not so prominent, and the region with relatively higher asymmetry along the distal half of the diaphysis in the anterolateral posteromedial aspect is more developed. Males are more asymmetrical than females in general. The mean morphometric map for pooled samples shows uniform areas of asymmetry spanning from the proximal diaphysis, anteroposteriorly, to the mid-proximal diaphysis, mediolaterally, and continuing distally in the anterolateral posteromedial aspect.  For the mean morphometric maps that are defined only by population, Hubei is more asymmetrical across the entire proximodistal diaphysis in the near-anterolateral posteromedial aspect, with a reinforcement of anteroposterior asymmetry along the proximal to mid-proximal diaphysis. The region with high asymmetry for Henan is located in the an- According to the results of MANOVA (Table 1), the differences sourced from sex (P = 0.11), population (P = 0.296), and the interaction of sex and population (P = 0.783) are not statistically significant. The R-squared values reveal that sex, population, and the interaction of sex and population accounted for 5.49%, 5.99%, and 2.74% of the total variation, respectively. Residuals accounted for 85.77% of the total variation. The CV morphometric maps show nearly identical distribution patterns across all the sub-groups and pooled samples ( Figure 3). Relatively high CV values are concentrated in the region between the middle and mid-distal diaphysis, and at the distal extreme in the anteromedial posterolateral aspect. Similarly high CV values appear at the proximal section, mediolaterally, but to a smaller extent compared to the distal section. Henan has localized regions of higher CV values at the proximal extreme, mediolaterally, and at the mid-distal diaphysis in the anteromedial posterolateral aspect, but displays no other differences compared to Hebei and Xinjiang. Females present higher overall CV values than males.  Table 2 and Figure 4 show the result of a multivariate regression fitting all the SMA asymmetry values on the J35 or J50 asymmetry value using pooled samples. The results of  Table 2 and Figure 4 show the result of a multivariate regression fitting all the SMA asymmetry values on the J 35 or J 50 asymmetry value using pooled samples. The results of J 35 and J 50 asymmetry are highly significant (P < 0.001), indicating that the multivariate regression model is effective. According to the R-squared values, J 35 asymmetry accounts for 48.66% of the total variation, whereas J 50 asymmetry accounts for 50.93%. The remaining variations are explained by the residuals, which is 51.34% in the J 35 asymmetry model and 49.07% in the J 50 asymmetry model.  The CC morphometric maps of the sub-groups and pooled samples are sh Figure 5. Across all the CC morphometric maps, the SMA asymmetry values an or J50 asymmetry value are positively correlated among the entire humeral diaph cept for some areas of Henan. When specific to the morphometric maps of CC35, hi values are detected primarily among the distal half of the diaphysis, particularly the mid-distal to distal section, while lower CC35 values are more inclined to di anteroposteriorly over the proximal half of the diaphysis. Henan differs from th sub-groups in that its SMA asymmetry values are negatively correlated with the J metry value in the region between the mid-proximal and middle diaphysis, anter riorly. For the morphometric maps of CC50, high CC50 values are found between th The CC morphometric maps of the sub-groups and pooled samples are shown in Figure 5. Across all the CC morphometric maps, the SMA asymmetry values and the J 35 or J 50 asymmetry value are positively correlated among the entire humeral diaphysis, except for some areas of Henan. When specific to the morphometric maps of CC 35 , high CC 35 values are detected primarily among the distal half of the diaphysis, particularly around the mid-distal to distal section, while lower CC 35 values are more inclined to distribute anteroposteriorly over the proximal half of the diaphysis. Henan differs from the other sub-groups in that its SMA asymmetry values are negatively correlated with the J 35 asymmetry value in the region between the mid-proximal and middle diaphysis, anteroposteriorly. For the morphometric maps of CC 50 , high CC 50 values are found between the proximal and middle diaphysis, anteroposteriorly, which gradually shift in the anterolateral posteromedial aspect, from the middle to distal diaphysis. Comparatively, low CC 50 values tend to follow the approximately anterolateral posteromedial aspect between the mid-distal and distal diaphysis. In comparison to other sub-groups, Henan exhibits a distinct distribution pattern of CC 50 values at the distal humeral section, mediolaterally, with the SMA asymmetry values being negatively correlated with the J 50 asymmetry value.

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].

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 (J 35 and J 50 ) 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][58][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][61][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 J 35 and J 50 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.

Conclusions
This study evaluated humeral biomechanical asymmetry across complete humeral diaphysis based on high-resolution micro-CT, and by quantifiable visualization and statistical methods. Using specimens from three Chinese archaeological populations that varied in geographic location, chronological age, and subsistence pattern, the pattern of humeral asymmetry in East Asian modern humans was investigated. Distinct humeral asymmetry patterns are observed on the mean morphometric map, but are not statistically significant. Analogous distributions of highly asymmetrical regions and CV are observed across nearly all the sexes and populations, indicating possible universality of the humeral asymmetry pattern in East Asian modern humans. These highly asymmetrical regions correspond with major muscle attachments. The diaphyseal regions that are highly varied in bilateral asymmetry tend to present a low asymmetrical level. Although J 35 and J 50 asymmetry are related to the overall humeral asymmetry, it can only explain about half of the total variation. These findings suggest that the overall biomechanical asymmetry of humeral diaphysis is more complicated than previously assumed. This study complements previous findings on humeral asymmetry, and accumulate data and knowledge for future works in this area.

Data Availability Statement:
The data supporting this study are available from the corresponding author on reasonable request.

Acknowledgments:
The authors thank Yemao Hou, Pengfei Yin, and Jiawei Ma for their help in scanning and image processing. The authors also thank Xiujie Wu and Mackie O'Hara Ali for optimizing the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.