Maxillary distraction osteogenesis: a two-dimensional mathematical model.

Patients with cleft lip and palate with severe maxillary retrusion usually have a mandible with anterior-superior autorotation and subsequent overclosure and loss of the vertical facial dimension. Maxillary distraction osteogenesis can correct the sagittal maxillomandibular relationship and should simultaneously reestablish vertical dimension through maxillary vertical height increase and clockwise rotation of the mandible to restore facial balance. We present a two-dimensional mathematical model in the sagittal plane, which reestablishes sagittal and vertical skeletal deficiencies and proper occlusal alignment for planning maxillary advancement with distraction osteogenesis in patients with cleft lip and palate. The model is illustrated in a case of a 13-year-old boy with a complete bilateral cleft lip and palate and severe maxillary retrusion. The two-dimensional mathematical model described in this article allows the surgeon and orthodontist to calculate in a simple and accurate way the ideal distraction vector to advance the maxilla to its desired position.