Bone health is determined by factors including bone metabolism or remodeling. Wnt-10b alters osteoblastogenesis through pre-osteoblast proliferation and differentiation and osteoblast apoptosis rate, which collectively lead to the increase of bone density. To model this, we adapted a previously published model of bone remodeling. The resulting model for the bone compartment includes differential equations for active osteoclasts, pre-osteoblasts, osteoblasts, osteocytes, and the amount of bone present at the remodeling site. Our alterations to the original model consist of extending it past a single remodeling cycle and implementing a direct relationship to Wnt-10b. Four new parameters were estimated and validated using normalized data from mice. The model connects Wnt-10b to bone metabolism and predicts the change in trabecular bone volume caused by a change in Wnt-10b input. We find that this model predicts the expected increase in pre-osteoblasts and osteoblasts while also pointing to a decrease in osteoclasts when Wnt-10b is increased.

中文翻译：

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Wnt-10b 对骨代谢影响的数学模型


骨骼健康由骨代谢或重塑等因素决定。 Wnt-10b通过前成骨细胞增殖和分化以及成骨细胞凋亡率改变成骨细胞生成，共同导致骨密度增加。为了对此进行建模，我们采用了之前发布的骨重塑模型。所得的骨室模型包括活性破骨细胞、前成骨细胞、成骨细胞、骨细胞以及重塑部位存在的骨量的微分方程。我们对原始模型的修改包括将其扩展到单个重构周期并实现与 Wnt-10b 的直接关系。使用小鼠的标准化数据估计和验证了四个新参数。该模型将 Wnt-10b 与骨代谢联系起来，并预测 Wnt-10b 输入变化引起的小梁骨体积变化。我们发现该模型预测了前成骨细胞和成骨细胞的预期增加，同时也表明当 Wnt-10b 增加时破骨细胞会减少。