[The vector analysis of the anteroposterior relationship among the apical bases and the incisors].

Using the lateral cephalometric radiographs, the points A, B, maxillary incisor tip (U) and mandibular incisor tip (L) were projected onto the Frankfort horizontal plane and the projected points were defined as a, b, u and 1, respectively. According to the principle of the vector analysis, the vector formula ab - ul = au - bl can always stand irrespective of how the locations of the points a, b, u and 1 vary. The vectors ab, ul, au and bl represent the anteroposterior linear relationship between the upper jaw and the lower jaw, the upper incisor and the lower incisor (overjet), the upper jaw and the upper incisor, and the lower jaw and the lower incisor, respectively with reference to the FH plane. The lateral cephalometric radiographs taken from a total of 863 class I subjects, including 422 males and 441 females, were submitted for the study. The four vector values were obtained from the tracing of each radiograph and the mean values were computed according to sex and age. If a positive value was given to the vector ab, it denoted that point "a" was anterior to point "b", while a negative value denoted that "a" was posterior to "b". Both sexes of the subjects were divided according to their ages into junior primary (JP, 6-8 years), senior primary (SP, 9-11 years), junior high (JH, 12-14 years), and senior high (SH, 15-18 years) groups. No substantial or significant mean difference of each vector between the males and the females in each age group was noted. The mean values of the vector ab were 7.4, 6.8, 6.1 and 4.7 mm in JP, SP, JH and SH groups, respectively with the male and the female data pooled together. This indicates that there was a gradual catching up tendency of mandibular versus maxillary growth. The mean values of the vector ul were 1.4, 2.8, 2.9 and 2.8 mm in each successive age group, respectively showing that the overjet was rather constant with age except in the youngest group. The corresponding mean values were -0.4, -3.9, -5.2 and -6.1 mm for the vector au and -6.3, -8.0, -8.4 and -8.0 mm for the vector bl in JP, SP, JH and SH groups, respectively. The data indicate that both upper and lower incisors were relatively more upright in the youngest group when compared with the other age groups. In the remaining groups the upper incisors exhibited a tendency of gradual labial tipping with age, whereas the lower incisors kept stable in the procumbency.(ABSTRACT TRUNCATED AT 400 WORDS)