Displacements prediction from 3D finite element model of maxillary protraction with and without rapid maxillary expansion in a patient with unilateral cleft palate and alveolus

BACKGROUND: Both maxillary protraction and rapid expansion are recommended for patients with cleft palate and alveolus. The aim of the study is to establish a three-dimensional finite element model of the craniomaxillary complex with unilateral cleft palate and alveolus to simulate maxillary protraction with and without rapid maxillary expansion. The study also investigates the deformation of the craniomaxillary complex after applied orthopaedic forces in different directions. METHODS: A three dimensional finite element model of 1,277,568 hexahedral elements (C3D8) and 1,801,945 nodes was established based upon CT scan of a patient with unilateral cleft palate and alveolus on the right side in this study. A force of 4.9 N per side was directed on the anatomic height of contour on the buccal side of the first molar. The angles between the force vector and occlusal plane were −30°, −20°, −10°, 0°, 10°, 20°, and 30°. A force of 2.45 N on each loading point was directed on the anatomic height of contour on the lingual side of the first premolar and the first molar to simulate the expansion of the palate. RESULTS: The craniomaxillary complex displaced forward under any of the loading conditions. The sagittal and vertical displacement of the craniomaxillary complex reached their peak at the protraction degree of −10° forward and downward to the occlusal plane. There were larger sagittal displacements when the maxilla was protracted forward with maxillary expansion. The palatal plane rotated counterclockwise under any of the loading conditions. Being protracted without expansion, the dental arch was constricted. When supplemented with maxillary expansion, the width of the dental arch increased. Transverse deformation of the dental arch on affected side was different from that on unaffected side. CONCLUSIONS: Protraction force alone led the craniomaxillary complex moved forward and counterclockwise, accompanied with lateral constrain on the dental arch. Additional rapid maxillary expansion resulted in a more positive reaction including both larger sagittal displacement and the width of the dental arch increase.