A new mathematical model for pattern formation by cranial sutures

Cranial sutures are narrow mesenchymal tissues that connect skull bones to each other. Given that they serve as growth centers in the skull, these undifferentiated tissues play crucial roles in skull development. Cranial sutures are also of clinical importance, because the premature fusion of skull bones results in a pathological condition called craniosynostosis. In newborns, skull sutures are wide and straight; during adolescence, they become thinner and start winding to form an interdigitating pattern. From a functional aspect, as the degree of interdigitation becomes larger, the strength of the connection between bones increases. However, the mechanisms underlying the maintenance of mesenchymal narrow bands or formation of interdigitation remain poorly understood. In the present study, we presented a new mathematical model that can reproduce the suture width maintenance and interdigitation formation. We can predict the width of the mesenchyme bands and wavelengths of suture interdigitations from the model.