A MATHEMATICAL METHOD FOR THE COMPARISON OF 3-DIMENSIONAL CHANGES IN THE FACIAL SURFACE

Many attempts have been made to measure and compare the changes in the facial surface brought about by facial reconstructive surgery. Three-dimensional (3-D) analyses have largely consisted of qualitative descriptions rather than a quantitative treatment of these changes. Until recently, the lack of availability of 3-D data for the face and head has limited the advancement of these techniques. However, with 3-D information readily available from a laser scanning system which we have constructed, a technique has been applied which describes mathematically the facial shape and changes occurring in the face in terms of fundamental surface types. The method is described and used to compare the faces of two patients (one a cleft palate patient and the other a long-face, Class II malocclusion patient) before and after surgery along with the clinical description of the surgery, the resulting facial changes, the actual surgery performed, and the predicted surgical expectation. A strong relationship is found between the surface type description and the clinical observations. The implications of the method for surgery, facial aesthetics, and other disciplines are discussed.