Tensor analysis of facial growth in males.

This longitudinal study examines in detail the facial development of 18 untreated, male children with acceptable occlusions. The children were examined in the prepubertal period (age range 7-10 years) and again in their late teens (15-19 years of age). A tensor analysis, which permits the computation of differences in form (that is in size and shape) without specifically measuring either, was employed to describe the facial changes which occurred during this time interval. Values for the x and y co-ordinates of 16 hard and four soft tissue landmarks were determined at each stage. Customized software allowed both graphical and numerical examination of the mean changes over time between 28 triads of points, covering skeletal, dental, and soft tissue elements. The analysis confirmed previous work in describing facial change but was more sensitive than conventional cephalometry, especially where landmarks were evaluated outside the traditional sella-nasion framework.