骨表面有效性对骨重建的影响--一个包含骨细胞几何和生物力学耦合规律的数学模型
The influence of bone surface availability in bone remodelling - A mathematical model including coupled geometrical and biomechanical regulations of bone cells
摘要：
骨是一种不断更新的生物材料。更新过程被称为骨重建，由骨吸收细胞（破骨细胞）和骨形成细胞（成骨细胞）操作。在破骨细胞和成骨细胞之间的相互作用中，已经确定了生物化学和生物力学调节机制。在这里，我们专注于一个额外的和了解甚少的骨细胞的潜在的调节机制，涉及骨的微观结构的形态。骨细胞只能在骨表面移除和替换骨。然而，骨表面的微观可用性又取决于不断变化的骨微观结构。这种几何依赖性的重要性是未知的，难以量化的实验。因此，我们开发了一个复杂的骨细胞相互作用的数学模型，考虑到生物化学，生物力学和几何规则。然后，我们研究数值的影响，骨表面的可用性在骨重建内的一个代表性的骨组织样本。骨细胞的活动，这改变了骨的微观结构，并在微观骨表面的可用性，这反过来又影响骨细胞的发育和活动的变化之间的相互依赖性，是使用骨比表面积和骨孔隙率之间的显着的实验关系。我们的模型表明，几何调控激活新的重塑事件可能有显着影响骨孔隙度和骨刚度。另一方面，成骨细胞和破骨细胞分化的晚期阶段的几何调节似乎不太重要。我们的结论是，骨质疏松症的发展可能是加速这种几何规则的皮质骨，但可能减缓骨小梁。
英文摘要：
Bone is a biomaterial undergoing continuous renewal. The renewal process is known as bone remodelling and is operated by bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts). Both biochemical and biomechanical regulatory mechanisms have been identified in the interaction between osteoclasts and osteoblasts. Here we focus on an additional and poorly understood potential regulatory mechanism of bone cells, that involves the morphology of the microstructure of bone. Bone cells can only remove and replace bone at a bone surface. However, the microscopic availability of bone surface depends in turn on the ever-changing bone microstructure. The importance of this geometrical dependence is unknown and difficult to quantify experimentally. Therefore, we develop a sophisticated mathematical model of bone cell interactions that takes into account biochemical, biomechanical and geometrical regulations. We then investigate numerically the influence of bone surface availability in bone remodelling within a representative bone tissue sample. The interdependence between the bone cells' activity, which modifies the bone microstructure, and changes in the microscopic bone surface availability, which in turn influences bone cell development and activity, is implemented using a remarkable experimental relationship between bone specific surface and bone porosity. Our model suggests that geometrical regulation of the activation of new remodelling events could have a significant effect on bone porosity and bone stiffness. On the other hand, geometrical regulation of late stages of osteoblast and osteoclast differentiation seems less significant. We conclude that the development of osteoporosis is probably accelerated by this geometrical regulation in cortical bone, but probably slowed down in trabecular bone.
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