Measurements of facial points during growth utilizing centroids

Interest in methods for predicting facial growth has contributed a great deal to orthodontic diagnosis and treatment planning during the last few decades. One early attempt was that of Broadbent¹ who used a longitudinal cephalometric survey to assess the downward and forward path of facial growth. He concluded that the facial pattern became established at the completion of the deciduous dentition. Brodie²,³ used Broadbent's material to investi­gate growth at various points in the skull. He concluded that the morphogenetic pattern of a human individual is established at three months and that once attained, it does not change. He stated "the whole face is stable and that the only area of adjustment available is to be found in the teeth and alveolar process." ⁴ Meanwhile, other studies have shown that the "pattern stability" concept does not apply to all individual cases. Goldstein⁵ showed that the height of the face grew most and at the highest rate, then its depth and finally its width. Bjork⁶ studied facial prognathism and found that it increases during growth, which may be due to the alteration in relationship between the cranial base and jaw length. There was a slightly greater increase in mandibular progna­thism as compared with maxillary prognathism. This was further associated with the increase in ramus height. Later, this study was confirmed by Lande.⁷ Brodie⁸ discussed facial growth and found that the nasal floor tends to remain stable. In contrast, the portion was found to vary in both horizontal and vertical directions.
In an extensive study, Enlow⁹-¹⁰ believed that the continued growth of the facial skeleton involved "all parts in each individual bone undergoing an extreme, complex series of successive remodelling changes." Kerr¹¹ investigated those dento-facial changes which resulted from growth on longitudinal material of 85 lateral skull cephalostats at 5,10 and 15 years. He superimposed the film on de Coster's and the sella-nasion line. In this study, considerable individual variation was recorded.

From the above studies, it is clear that research workers superimpose cephalograms (or tracings) routinely to visualize growth increments although there are inherent errors in such a method. Meanwhile, Bjork¹²-¹³-¹⁴ introduced a measure of consistency by inserting metal (vitallium) implants under local anesthesia into the facial bones of children to facilitate growth studies. He differentiated between movements or displacements of each bone and growth at the bony surface due to remodelling. This technique was also used by Robertson¹⁵ on neonate cleft palate patients. However, its infallibility was questioned by Julius¹⁶ who found that migration and dislodg-ment of the implants caused significant error in implant superimposition. So far, two main types of facial growth predictions have been used. The first type uses statistical information on average growth incre­ments according to the age and the sex of the subject.¹⁷-¹⁸ Because of the properties of statis­tical rules, such predictions will be reasonably correct in a majority of cases, but unfortunately they are less likely to be correct in subjects whose facial growth deviates markedly from the norm and where prediction, from a clinical point of view, is most needed.
The second type uses selected features of the facial structure of the patient to predict future development trends. Among such methods are the presence or absence of a series of structural traits in the lower face,-¹⁹-²⁰ the classification of facial structure into facial types, each with their own growth potential.²¹-²² Solow and Nielsen²³ found a relationship between cranio cervical posture in pre-pubertal children and the direction of facial development during the subsequent period of growth.
Johnson²⁴ criticized the conventional tracings which used anatomical points as references and for measuring changes during growth and orthodontic treatment. He introduced points and baselines related to centres of area (centroids) within the projected skull outline. He later asserted that by an accumulation of logical, circumstantial and statistical evidence, the centre of area of the tracing of a lateral skull cephalogram appeared to be its least variable point, while the least variable line was that connecting the centres of the cranium, skull and face.²⁵
From the review of literature, it seems that methods employed to study the nature of facial growth are numerous and lack consistency and popularity. The reason may be that there is no stable reference line or plane to relate moving skeletal structures to it. Alternatively, a mathe­matical solution may be of significance to accurately assess facial growth. Therefore, measurements of movements for facial cepha-lometric points in this study will be assessed using the centroid based analysis.

Materials

Thirty-six lateral skull radiographs of eighteen subjects were used in this study, 11 boys and 7 girls. Half of the radiographs were taken at the age of 9 years and the other 18 radiographs were taken at the age of 16 years. The radio- graphs were selected so that they depict the presence of a complete outer cranium outline for centroid measurements. The radiographs were selected from a bigger sample collected by Professor B.C. Leighton of the King's College Dental Hospital, England.

Methods

i) The lateral radiographs were traced in a routine manner and cephalometric points were located.

ii)   Cephalometric points (Fig.  1) used in this study were:

iii) Centroid measurements: After the lateral radiographs were traced, the sample was digitized using an Apple ME enhanced personal computer to locate the centroids. The craniofacial centroid line (CFC) was located by joining the centres of cranium and face to the centre of the skull. (Fig. 2)

iv) Locating  the vertical and horizontal lines for measurements:

From the centre of cranium "C" and along the craniofacial centroid a line at 45° degree angle was drawn clockwise and vertically (Fig. 3) and at 45° degree anti-clockwise line was drawn horizontally (Fig. 4).

Cephalometric points were measured linearly to the nearest half-millimeter from the vertical and the horizontal lines by dropping perpen- diculars to them. To eliminate linear distortions between subjects, ratios between points were calculated.

Statistical Analysis

The data were subjected to descriptive statistics and student t-test. Ratios of move- ments in horizontal and vertical directions were calculated as the ratio of parameter 1 (P,) where:

In the vertical dimension, all points measured showed a consistently downward shift except for points Sella and Nasion which moved upwards with Nasion moving more upwards than Sella. The standard deviation for points Nasion, apices of upper incisor and lower incisor were the highest among other measured points. In the horizontal dimension, all points moved forwards at different rates. Points Gonion, Menton and Condylion had the greatest standard deviations, respectively, (Tables 1, 2 and 3).

A new mathematical method was introduced in this study to estimate craniofacial growth changes in anatomic points. Vertical and horizontal growth changes were calculated in millimeters and percentages for a sample of eleven boys and seven girls at ages 9 and 16 years. The greatest percentage change for the pooled sample was 11.75% upward movement for Nasion (S.D   ±17.90) and 11.46% downward movement for Gonion (S.D. ± 3.25). Significant differences between girls and boys in the vertical direction were observed for point B, Pogonion, Gnathion and Mention. While in the horizontal direction, significant differences were found for ANS, point A, Apex and tip of upper incisor and tip of upper incisor and tip of lower incisor, point B, Pogonion, Gnathion, Menton and Condylion.