Echeverri L F, Herrero M A, Lopez J M, Oleaga G
Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid (UCM), Plaza de las Ciencias s/n, 28040, Madrid, Spain,
Bull Math Biol. 2015 Jan;77(1):156-83. doi: 10.1007/s11538-014-0055-3. Epub 2014 Dec 24.
This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are proposed to estimate the time required for (1) the formation immediately after fracture of a fibrin clot, described in terms of a phase transition in a polymerization process, and (2) the onset of EFC which is produced when fibroblasts arising from differentiation of chemotactically recruited mesenchymal stem cells remodel a previous fibrin clot by releasing a collagen matrix over it. An attempt has been made to keep models as simple as possible, so that a explicit dependence of the estimates obtained on relevant biochemical parameters involved is obtained.
这项工作关注的是骨折愈合初期发生的一系列事件，从骨断裂到早期纤维性骨痂（EFC）形成。后者提供了一个支架，随后的重塑过程最终将在此支架上实现成功的骨修复。具体而言，提出了一些数学模型来估计以下所需时间：（1）骨折后立即形成纤维蛋白凝块，这可以用聚合过程中的相变来描述；（2）EFC的起始，当趋化募集的间充质干细胞分化产生的成纤维细胞通过在先前的纤维蛋白凝块上释放胶原基质对其进行重塑时产生EFC。已尽力使模型尽可能简单，以便获得所得估计值对所涉及的相关生化参数的明确依赖性。
