Prediction of craniofacial growth: the state of the art.

M ost predictions of growth are based on some mathematical model of the growth process, two kinds of which can be distinguished: (1) the transformed coordinate method of D’Arcy Thompson,Z5 applied to human growth by MedawaPg and to craniofacial growth by Moorrees and Lebret,2z and (2) equations producing curves descriptive of processes--some intended to be of general application (for example, Gompertz’ equation, Weiss and Kavanaugh’P model, and the compound Gompertz-linear equation of LairdIE). Others were intended only for specific kinds of growth, such as Huxley’sle allometric equation and Tanner’sz4 equation. Useful though these equations may be for the analysis and description of growth, they have in common one unavoidable shortcoming so far as prediction is concerned: They do not adequately describe any single growth series. The orthodontist wishes to predict the future sizes and relationships of parts of a single person whose growth is usually abnormal and who may not be represented in any populations thus far studied. This article considers the state of the art in quantitative prediction of craniofacial measures of particular interest to orthodontists.