颅骨的骨是由间充质细胞在围绕大脑的表面分化成成骨细胞而形成的,最终形成矿化骨。引起细胞分化的信号传导途径包括由基因信息驱动的细胞外蛋白的作用。我们假设细胞和细胞外分子的相互作用,与细胞分化有关,可以使用图灵的反应扩散模型建模,由两个相互作用的分子(活化剂和抑制剂)控制的图案形成的数学模型。在这项研究中,我们假设高浓度的激活剂区域发展成主要的骨化中心,颅骨的最早部位。除了图灵模型,我们使用另一个扩散方程来模拟与骨生长相关的形态发生素(可能与骨化中心形成相关的形态发生素相同)。这些数学模型使用有限体积法求解。计算域和模型参数是使用大量实验数据确定的,这些实验数据显示了携带致病突变的小鼠及其未受影响的同窝动物在不同胚胎天的小鼠颅骨形成。结果表明,在我们的模型中形成的五个骨化中心的相对位置与实验数据中确定的位置相同。随着骨骼从这些骨化中心生长,骨头之间形成缝线。
Bones of the cranial vault are formed by the differentiation of mesenchymal cells into osteoblasts on a surface that surrounds the brain, eventually forming mineralized bone. Signaling pathways causative for cell differentiation include the actions of extracellular proteins driven by information from genes. We assume that the interaction of cells and extracellular molecules, which are associated with cell differentiation, can be modeled using Turing\'s reaction-diffusion model, a mathematical model for pattern formation controlled by two interacting molecules (activator and inhibitor). In this study, we hypothesize that regions of high concentration of an activator develop into primary centers of ossification, the earliest sites of cranial vault bone. In addition to the Turing model, we use another diffusion equation to model a morphogen (potentially the same as the morphogen associated with formation of ossification centers) associated with bone growth. These mathematical models were solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data showing skull bone formation in mouse at different embryonic days in mice carrying disease causing mutations and their unaffected littermates. The results show that the relative locations of the five ossification centers that form in our model occur at the same position as those identified in experimental data. As bone grows from these ossification centers, sutures form between the bones.