Biomechanical modeling of maxillary expansion: Toward an evolutionary boundary value problem for the midpalatal suture

Maxillary expansion is an orthopedic technique used to treat a pathological imbalance of dental occlusion caused by a discrepancy of the transverse widths between the upper and lower jaws, increasing the width of the palate. This malocclusion is often treated through a procedure of induced maxillary expansion, which can normalize both the dental and skeletal components of the craniofacial complex. In this paper, we will review the treatment protocols and the appliances used from the point of view of biomechanical modeling. The aim is to understand how the engineering, based on a scientific understanding of the phenomenology involved, of the new protocols and appliances can be improved and optimized. The present review aims to discuss the clinical scenario, provide the information needed to formulate a novel evolutionary boundary value problem mathematically describing the physiological progress of mineralization of the midpalatal suture (MPS) margins and its modifications induced by the use of appliances necessary to widen the palate, and suggest which predictive models are more likely to improve clinical protocols.