The length of long bones is determined by column formation of proliferative chondrocytes and subsequent chondrocyte hypertrophy in the growth plate during bone development. Despite the importance of mechanical loading in long bone development, the mechanical conditions of the cells within the growth plate, such as the stress field, remain unclear owing to the difficulty in investigating spatiotemporal changes within dynamically growing tissues. In this study, the mechanisms of longitudinal bone growth were investigated from a mechanical perspective through column formation of proliferative chondrocytes within the growth plate before secondary ossification center formation using continuum-based particle models (CbPMs). A one-factor model, which simply describes essential aspects of a biological signaling cascade regulating cell activities within the growth plate, was developed and incorporated into CbPM. Subsequently, the developmental process and maintenance of the growth plate structure and resulting bone morphogenesis were simulated. Thus, stress anisotropy in the proliferative zone that affects bone elongation through chondrocyte column formation was identified and found to be promoted by chondrocyte hypertrophy. These results provide further insights into the mechanical regulation of multicellular dynamics during bone development.

中文翻译：

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生长板中的软骨细胞肥大促进应力各向异性，通过软骨细胞柱形成影响长骨发育

长骨的长度由骨发育过程中生长板中增殖软骨细胞的柱形成和随后的软骨细胞肥大决定。尽管机械负荷在长骨发育中很重要，但由于难以研究动态生长组织内的时空变化，生长板内细胞的机械条件（例如应力场）仍不清楚。在这项研究中，使用基于连续体的粒子模型（CbPM），在二次骨化中心形成之前，通过生长板内增殖软骨细胞的柱形成，从力学角度研究了纵向骨生长的机制。开发了一种单因素模型并将其纳入 CbPM，该模型简单地描述了调节生长板内细胞活动的生物信号级联的基本方面。随后，模拟了生长板结构的发育过程和维持以及由此产生的骨形态发生。因此，增殖区的应力各向异性通过软骨细胞柱形成影响骨伸长，并发现软骨细胞肥大会促进该应力各向异性。这些结果为骨骼发育过程中多细胞动力学的机械调节提供了进一步的见解。