Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding–unbonding rate of RANK/RANKL/OPG receptor–ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.

骨重建是一个基本的生物过程，它在骨组织的整个生命周期中发展。它是指随着新骨形成和旧骨吸收而改变组织内部微观结构和组成的连续骨转化。骨重建的主要目标是：修复内部微裂纹；宏观刚度和强度适应实际变化的机械需求；和控制钙稳态。了解这一过程并预测其演变对于减少在行动不便期间发生的长期废弃的影响至关重要。在骨植入物的设计中避免长期应力屏蔽也很重要。已经提出了许多数学模型，从最早的纯粹现象学到最新的包括生物学知识。然而，机械驱动力与其触发的生化和细胞过程之间仍然缺乏联系。在这里，根据先前独立模拟骨重塑中的力学生物学和生化过程的工作，我们提出了一个更完整的模型，对皮质骨和小梁骨都有用，它使用一种新的机械转导方法，该方法基于应变对结合-解结合的影响比率RANK / RANKL / OPG受体-配体反应。我们将这个模型的结果与之前的模型进行了比较，在类似条件下显示出良好的一致性。我们还将其应用于现实情况，例如植入髋关节假体后的股骨，在最终骨密度分布方面获得与临床结果相似的结果。最后，我们将这种方法扩展到各向异性情况，不仅得到平均密度，而且得到微观结构的方向均匀化。这种生化方法不仅可以预测机械负荷变化下的骨骼进化，还可以考虑使用合成代谢和分解代谢药物来控制骨密度，例如用于骨质疏松症的药物。