Flat bones and sutures formation in the human cranial vault during prenatal development and infancy: A computational model

• We developed a mathematical model of flat bones and sutures morphogenesis.
• We employ a system of reaction diffusion equations that controls bone remodeling.
• The model predicts flat bone formation and growth from ossification centers.
• The results show how sutures form and develop interdigitated patterns.

The processes of flat bones growth, sutures formation and interdigitation in the human calvaria are controlled by a complex interaction between genetic, biochemical and environmental factors that regulate bone formation and resorption during prenatal development and infancy. Despite previous experimental evidence accounting for the role of the main biochemical factors acting on these processes, the underlying mechanisms controlling them are still unknown. Therefore, we propose a mathematical model of the processes of flat bone and suture formation, taking into account several biological events. First, we model the growth of the flat bones and the formation of sutures and fontanels as a reaction diffusion system between two proteins: TGF-β2 and TGF-β3. The former is expressed by osteoblasts and allows adjacent mesenchymal cells differentiation on the bone fronts of each flat bone. The latter is expressed by mesenchymal cells at the sutures and inhibits their differentiation into osteoblasts at the bone fronts. Suture interdigitation is modelled using a system of reaction diffusion equations that develops spatio-temporal patterns of bone formation and resorption by means of two molecules (Wnt and Sclerostin) which control mesenchymal cells differentiation into osteoblasts at these sites. The results of the computer simulations predict flat bone growth from ossification centers, sutures and fontanels formation as well as bone formation and resorption events along the sutures, giving rise to interdigitated patterns. These stages were modelled and solved by the finite elements method. The simulation results agree with the morphological characteristics of calvarial bones and sutures throughout human prenatal development and infancy.