These mathematical models were solved using the finite volume method. 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. 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. 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). Signaling pathways causative for cell differentiation include the actions of extracellular proteins driven by information from genes. 2Department of Anthropology, Pennsylvania State University, University Park, PA, USAīones 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.1The Penn State Computational Biomechanics Group, Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA, USA.
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