Issues related to the prediction of craniofacial growth

The prediction of craniofacial growth involves four central issues: (1) What frame of reference should be adopted for measuring change? (2) What type of coordinate system should be used? (3) How should the change be described? (4) How can the change be explained biologically? In an effort to address these issues within a common framework, we are presenting a mathematical model for predicting the course of craniofacial growth in any given individual. The model is derived from a few basic assumptions about the long-range effects gravitational pressure on the remodeling of bone and is expressed formally as a single geometric transformation. The validity of the model is examined empirically, using data for twenty individuals from the Denver Child Research Council's longitudinal growth study. The predictions of the model are found to be in close correspondence with the actual morphologic changes in each individual over periods ranging from 8 to 17 years. These findings suggest that a transformational approach to the study of human growth may provide clinicians with a valuable tool for long-range treatment planning.