Undegradable scaffolds, as a key element in bone tissue engineering, prevail in the present clinical applications, and the bone in-growth into such scaffolds under mechanical stimulus is an important issue to evaluate the bone-repair effect. This work aims to develop a mathematical framework to investigate the effect of mechanical stimulus on the bone in-growth into undegradable scaffolds. First, the osteoclast and osteoblast activities were coupled by their autocrine and paracrine effects. Second, the mechanical stimulus was empirically incorporated into the coupling cell activities on the basis of experimental observations. Third, the effect of mechanical stimulus including intensity and duration on the bone in-growth process was numerically studied; moreover, the homeostasis of scaffold-bone system under the mechanical stimulus was also treated. The results showed that the numbers of osteoblasts and osteoclasts in the scaffold-bone system tended to constants representing the system homeostasis. Both the mechanical intensity and duration optimized the final bone formation. The numerical results of the bone formation were comparable to the experimental results in rats. The findings from this modeling study could be used to explain many physiological phenomena and clinical observations. The developed model integrates both cell and tissue scales, which can be used as a platform to investigate bone remodeling under mechanical stimulus.

中文翻译：

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在机械刺激下骨向不降解的多孔周期性支架内生长的数学模型。

在当前的临床应用中，不可降解的支架是骨组织工程中的关键要素，在机械刺激下骨骼向内生长到这种支架中是评估骨修复效果的重要问题。这项工作旨在建立一个数学框架，以研究机械刺激对骨骼生长为不可降解支架的影响。首先，破骨细胞和成骨细胞的活动通过它们的自分泌和旁分泌作用相结合。第二，在实验观察的基础上，将机械刺激经验性地结合到偶联细胞的活动中。第三，对强度和持续时间等机械刺激对骨骼生长过程的影响进行了数值研究。此外，还研究了机械刺激下支架-骨系统的稳态。结果表明，支架-骨系统中成骨细胞和破骨细胞的数量趋于代表系统稳态的常数。机械强度和持续时间都优化了最终的骨形成。骨形成的数值结果与大鼠的实验结果相当。该建模研究的结果可用于解释许多生理现象和临床观察。所开发的模型整合了细胞和组织尺度，可以用作研究机械刺激下骨骼重塑的平台。骨形成的数值结果与大鼠的实验结果相当。该建模研究的结果可用于解释许多生理现象和临床观察。所开发的模型整合了细胞和组织尺度，可以用作研究机械刺激下骨骼重塑的平台。骨形成的数值结果与大鼠的实验结果相当。该建模研究的结果可用于解释许多生理现象和临床观察。所开发的模型整合了细胞和组织尺度，可以用作研究机械刺激下骨骼重塑的平台。