Calculating the Midsagittal Plane for Symmetrical Bilateral Shapes: Applications to Clinical Facial Surgical Planning

It is difficult to estimate the midsagittal plane of human subjects with craniomaxillofacial (CMF) deformities. We have developed a LAndmark GEometric Routine (LAGER), which automatically estimates a midsagittal plane for such subjects. The LAGER algorithm was based on the assumption that the optimal midsagittal plane of a patient with a deformity is the premorbid midsagittal plane of the patient (i.e. hypothetically normal without deformity). The LAGER algorithm consists of three steps. The first step quantifies the asymmetry of the landmarks using a Euclidean distance matrix analysis and ranks the landmarks according to their degree of asymmetry. The second step uses a recursive algorithm to drop outlier landmarks. The third step inputs the remaining landmarks into an optimization algorithm to determine an optimal midsaggital plane. We validate LAGER on 20 synthetic models mimicking the skulls of real patients with CMF deformities. The results indicated that all the LAGER algorithm-generated midsagittal planes met clinical criteria. Thus it can be used clinically to determine the midsagittal plane for patients with CMF deformities.