**1. Introduction**

Humeral bilateral asymmetry has been extensively studied in orthopedics, forensics, and paleo/archaeological anthropology [1–3]. Handedness can be inferred from the bilateral asymmetry of the upper limb [4–6]. Evidence from living athletes of unilaterally dominated sports (such as tennis and cricket) suggests a close relationship between humeral bilateral asymmetry and behavioral laterality [7–9]. 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 [11–16].

Long bone diaphyses show grea<sup>t</sup> plasticity to remodel in response to mechanical loadings across a lifetime, especially prior to sexual maturity [17–21]. This remodeling

**Citation:** Zhao, Y.; Zhou, M.; Li, H.; He, J.; Wei, P.; Xing, S. Biomechanical Evaluation on the Bilateral Asymmetry of Complete Humeral Diaphysis in Chinese Archaeological Populations. *Symmetry* **2021**, *13*, 1843. https://doi.org/10.3390/sym13101843

Academic Editor: Antoine Balzeau

Received: 28 August 2021 Accepted: 28 September 2021 Published: 2 October 2021

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makes diaphyseal cross-sectional geometry (CSG) a more effective indicator of bilateral upper-limb use and asymmetry compared to other linear measurements, such as articular breath or bone length [13,20,22–24].

Polar moment of area (J) and second moment of area (SMA) are two commonly adopted CSG parameters in humeral biomechanical analysis. J indicates the cross-section's torsional and average bending rigidity, whereas SMA denotes the exact bending rigidity along a certain axis of a cross-section [3,25]. Owing to the difficulties of obtaining sequential histological cross-sections, most earlier studies focused on the CSG properties of cross-sections placed at 35% or 50% of the humeral biomechanical length (see the definition made by Ruff [26]). J at the 35% cross-section (J35) can reasonably estimate the minimum rigidity of humeral diaphysis and avoids the interference of other anatomical features, as it is situated below the distal edge of deltoid tuberosity and above the supracondylar crest [13,14,16,27–29]. J at the 50% cross-section (J50) provides reasonable estimates of midshaft rigidity [9,14,30–34], and is known to be a reliable indicator of hand preference [5]. When evaluating the directional biomechanical performance of a cross-section, most previous studies only calculated the maximum/minimum SMA or SMA along the standard anatomical axis (anteroposterior or mediolateral) to avoid the complexity of acquiring CSG values in multiple directions [35–37].

However, CSG properties of limited cross-sections and directions are insufficient to estimate the overall biomechanical performance of long bone diaphysis, especially in studies about humeral bilateral asymmetry. According to experimental data from professional baseball players, tensile and shear strains vary among different diaphyseal sections during throwing activities [38], and the degree of bilateral asymmetry evaluated by J was variable along the humeral shaft [16,38]. The shape asymmetry of different cross-sections also indicates that the asymmetry patterns vary in different anatomical directions [24,39].

Morphometric mapping is a 2D visualizing method that is commonly used for displaying the distribution patterns of morphometric and biomechanical properties across the entire diaphysis of a long bone [40,41]; for example, the distribution patterns of cortical bone thickness along the femoral diaphysis, visualized by morphometric maps, differentiate in Neanderthals and *Homo erectus* from modern humans [42,43]. Additionally, morphometric maps, quantifying the external radius across the entire femoral diaphysis, reveal the ontogenetic disparities between wild and captive chimpanzees [44]. The cortical structure of hallucal metatarsals, represented by morphometric maps of cortical bone thickness and bending rigidity, reflects locomotor adaptations of humans, chimpanzees, and gorillas [45]. Finally, morphometric mapping has been established to be an effective approach for quantifying the humeral biomechanical asymmetry across the complete diaphysis [16].

Factors such as geographic location, chronological age, subsistence pattern, and sex are known to influence the pattern of humeral asymmetry in human populations. Varying degrees of humeral asymmetry have been detected among Upper Paleolithic populations from Europe, Africa, and Asia [11]. European samples show a general decrease in humeral asymmetry from the early Upper Paleolithic populations through to the 20th century [13,22]. Foragers and farmers from the pre-Hispanic American Southwest present different humeral asymmetry patterns [36]. Due to the existence of the sexual division of labor, modern human populations with various geographic locations, chronological ages, and subsistence patterns tend to exhibit diverse sexual dimorphism patterns in humeral asymmetry [31,36,37,46].

In the present study, we aim to (1) generate a more comprehensive understanding of humeral asymmetry by evaluating the biomechanical performance across complete diaphysis compared to previous studies, which only used individual cross-sections; and (2) check the reliability of using J35 and J50 to represent the overall humeral biomechanical performance in bilateral asymmetry analysis. To fulfil these targets, specimens were scanned using high-resolution micro-computed tomography (micro-CT), and morphometric mapping was applied to quantify the overall biomechanical asymmetry of humeral diaphysis for its effectiveness in visualization and statistical analysis. To cover as wide a variety of specimens as possible, 40 pairs of humeri from three Chinese archaeological populations, which differ in geographic location, chronological age, and subsistence strategy, were selected to represent East Asian modern humans in the present study.

## **2. Materials and Methods**
