Department of Infrastructure Engineering, The University of Melbourne, 700 Swanston St, Parkville, Victoria 3010, Australia.
Centre for Limb Lengthening and Reconstruction, Epworth Hospital Richmond, Richmond, Victoria, Australia.
Comput Methods Programs Biomed. 2022 Jan;213:106536. doi: 10.1016/j.cmpb.2021.106536. Epub 2021 Nov 15.
Inflammatory response plays a crucial role in the early stage of fracture healing. Immediately after fracture, the debris and immune cells (e.g., macrophages), recruited into the fracture callus, lead to the secretion of inflammatory cytokines, such as tumor necrosis factor-alpha (TNF-α), which governs the mesenchymal stem cells (MSCs) mediated healing processes. However, it is still unclear how chronic inflammatory diseases (e.g., diabetes) affect the level of TNF-α in fracture callus, ultimately the healing outcomes at the early stage of healing. Therefore, the purpose of this study is to develop a numerical model for investigating TNF-α mediated bone fracture healing.
A mathematical model consisting of a system of partial differential equations that represent the reactive transport of cells and cytokines in the fracture callus is developed in this study. The model is first calibrated by using available experimental data and then implemented to study the effect of TNF-α on the early stage of fracture healing under normal and diabetic conditions.
There is a significant elevation of TNF-α level in facture callus during the first 24 h post-fracture in normal condition, and its influence in the concentration of MSCs and cell differentiation becomes significant three days post-fracture (e.g., the absence of TNF-α signaling could reduce the concentration of MSCs more than 20% in cortical callus). In addition, the excessive secretion of TNF-α induced by diabetes could decrease the concentration of MSCs at the initial stage of healing, particularly reduce the concentration of MSCs in cortical callus by around 25%.
The model predictions suggested that there should be an optimal concentration of TNF-α in fracture callus, which enhances the early stage of healing, and excessive or insufficient secretion of TNF-α might significantly hinder the healing process.
炎症反应在骨折愈合的早期阶段起着至关重要的作用。骨折后，碎片和免疫细胞（如巨噬细胞）被招募到骨折痂中，导致炎症细胞因子（如肿瘤坏死因子-α（TNF-α））的分泌，从而控制间充质干细胞（MSCs）介导的愈合过程。然而，目前尚不清楚慢性炎症性疾病（如糖尿病）如何影响骨折痂中 TNF-α 的水平，进而影响愈合早期的愈合结果。因此，本研究旨在建立一个用于研究 TNF-α 介导的骨骨折愈合的数值模型。
本研究开发了一个由代表骨折痂中细胞和细胞因子反应性运输的偏微分方程系统组成的数学模型。该模型首先通过使用现有实验数据进行校准，然后用于研究 TNF-α 在正常和糖尿病条件下对骨折愈合早期阶段的影响。
在正常情况下，骨折后 24 小时内，骨折痂中 TNF-α 水平显著升高，其对 MSCs 浓度和细胞分化的影响在骨折后三天变得显著（例如，缺乏 TNF-α 信号可能会使皮质骨痂中的 MSCs 浓度降低 20%以上）。此外，糖尿病引起的 TNF-α 过度分泌可能会在愈合的初始阶段减少 MSCs 的浓度，特别是使皮质骨痂中的 MSCs 浓度降低约 25%。
模型预测表明，骨折痂中 TNF-α 应有一个最佳浓度，可增强早期愈合，而 TNF-α 的过度或不足分泌可能会显著阻碍愈合过程。
