M ATERIALS AND METHODS 1 M aterials

The experimental material comprised serial lateral cephalometric radiographs recorded at approximately six month intervals from age 4 to 7 years and annually thereafter to age 14 years for 11 children (7 girls and 4 boys). All radiographs were recorded with the same cephalostat and same source-film distance, providing a constant magnification of 1.07 at the mid-sagittal plane (MSP). All distances were corrected to absolute values at the MSP. The quality of the radiographic images was assessed as

"very good" on the basis of subjective appraisal of the clarity of fine detail.

The subjects were drawn from a sample of 42 children whose dental and facial growth was monitored with serial radiographs during the period 1952 to 1970. Many of these children had brothers or sisters in the same sample. None of the subjects had received orthodontic treatment during the observation period. The subjects were selected only on the number and quality of their radiographic records and they could not be considered a truly random sample. The details of the cases and radiographic records are shown in Tables 11.1 and 11.2. Examples of the serial radiographs used in the study are shown in Figure 11.1.

Table 11.1 Details of the subjects whose radiographs were used in the study.

subject number

sex Skeletal

Pattern

ultim ate incisor classification 1 f II II d iv .l 2 f II II d iv .l 3 f III III 4 m II II d iv .2 5 m II II d iv .2 6 m II II d iv .l 7 f I I 8 m II II d iv .l 9 f I II d iv .2 10 f II II d iv .l 11 f II II d iv .2

5*/2 years 5 years 4 V2 years 4 years Z à

A

Table 11.2 Distribution of radiographs used in the study.

subject N“.

age (years) at which radiograph was recorded

4 4.5 5 5.5 6 6.5 7 8 9 10 11 12 13 14 1 • • • • • • • • • • 2 • • • • e • • • 3 • • • • • e • • 4 - • e • e • • • • • • • 5 - • • - • • • • • • • • • 6 e • • • • • • • • • 7 - # # • • • • • 8 # • • e # • e • • • 9 # • • • • 10 • • • • • • • • • • 11 • # e • • • •

Key: radiograph available; - no radiograph available.

11.2.2 M ethods

The detection system as described in chapter 9 was used to locate: a) stable natural reference sites in the bone;

and b) the crowns of individual incisors.

11.2.2.1 Registration using natural reference markers

The mandibular image from each radiograph was digitised using a pixel size of 0.13 mm using the experimental apparatus described in chapter 7. Prior to image capture, the maxillary plane of each radiograph was orientated parallel to the x-axis of the system to allow the x and y coordinates to correspond to approximate true horizontal and vertical axes respectively.

The detection system was used to locate reference sites from four regions away from the developing teeth (Figure 11.2). For each subject, one radiograph was selected to be the base-line reference image and this radiograph was used to establish the

a n a to m ic a l c o o r d in a te sy ste m fo r all o th er film s . P ilo t in v e s tig a tio n s had r e v e a le d that f e w ( i f a n y ) b o n y r e fe r e n c e site s w o u ld b e a v a ila b le th r o u g h o u t th e e n tir e s e r ie s o f r a d io g r a p h s th er eb y m a k in g it im p o s s ib le to d ir e c tly r eg iste r th e o ld e s t and y o u n g e s t f ilm s . T h e r e fo r e , a m id -r a n g e rad iograp h w a s u sed rather than u sin g th e e a r lie st ra d io g ra p h a s th e b a s e -lin e r e fe r e n c e . T h u s, h a lv in g th e tim e p e rio d o v e r w h ic h r e fe r e n c e s ite s n e e d e d to rem ain d e te c ta b le .

N atu ral b o n y r e fe r e n c e m arkers w e r e lo c a te d b e tw e e n th e r e fe r e n c e rad iograp h and e a c h o f th e o th er ra d io g ra p h s as d e sc r ib e d in c h a p ter 9 , w h ic h w e r e then u sed to r e g is te r th e im a g e s in p airs.

F ig u re 1 1.2 Sites o f the anatomical reference markers. The anterior sites contained the principal reference markers; the posterior sites w ere used as an additional check on the rotational alignment o f the im ages.

1 1 . 2 . 2 . 2 E x tr a c tio n o f th e r e fe r e n c e s ig n a ls f o r in d iv id u a l in c is o r s

In a d d itio n to d e te c tin g r e fe r en c e site s in th e b o n e , th e d e te c tio n sy ste m w a s a lso u se d to lo c a te th e c r o w n s o f in d iv id u a l in c is o r s . T h is w a s d o n e in e x a c tly th e sa m e w a y a s d e te c tin g r e fe r e n c e site s w ith th e e x c e p tio n that ea c h r e fe r e n c e sig n a l w a s th e o u tlin e o f th e e n a m e l c r o w n o f a p articu lar in c iso r .

T o p r o v id e a ccu ra te r e fe r e n c e sig n a ls th e c r o w n s o f in d iv id u a l in c is o r s had to b e s e le c te d and th eir im a g e s sep arated and c le a n e d o f o v e r ly in g , u n related d e ta ils. T h is w a s a c h ie v e d b y a p p ly in g standard e d g e d e te c tio n o p era to rs to the d ig itise d im a g e s to lo c a te

F ig u r e 1 1 .3 T he location o f the grey-level gradient (B) associated with the enamel outlines in the using a standard edge detection operator applied to the digitised im age.

the grey-level gradient associated with the enamel outlines (Figure 11.3). Once the enamel outlines had been detected they were "cleaned" to remove high frequency noise by applying a median filter which replaced each pixel with the median value in the surrounding eight pixels (Gonzales and Wintz, 1987).

The enamel outlines were then located by eye using blue-green pseudo-colour to improve the visibility of the finest detail (Pratt, 1991) and the image of each external enamel outline was then extracted to provide each reference signal. Application of an interactively controlled threshold to the gradient image enabled the production of a binary valued mask of each tooth. The original image was then multiplied with the mask to remove all structure other than the outline of the enamel of the particular tooth. This final image was then used as the reference signal which was extracted and stored as a square template of 20 x 20 pixels.

11.2.2.3 Tracking the eruption o f the incisors

The template containing the reference signal of each incisor was used to locate the position of the tooth in a second film by using the detection system to search for the cross-correlation peak.

Two searches were made, as in the conventional use of the detection system. The initial search was conducted using only the first two stages of the detection processor (that is, without employing the decorrelator). Having detected the presence and approximate location of each incisor crown in the second image the second search was conducted using the third and fourth stages of the detection system.

The impulse response of the decorrelator used in the location of the bony reference sites was unsuited to the high frequency details and strong spatial gradient associated with the outline of the enamel. Consequently, a new impulse response array consisting a first-order gradient operator, V,^y was used instead (Pratt, 1991).

Once the crown of the incisor had been accurately located the x and y coordinates of the incisor tip were transformed to the coordinate system of the reference film and the process repeated for the next pair of images.

W .2.2 A Assessment o f the eruption path.- For each class of incisor (central and lateral) the transformed coordinates of the right and left incisor tips were averaged to provide a mean position from each successive radiograph. This was done to provide a single measurement relative to the MSP for each class of incisor which was unaffected by minor variations in the projection geometry from film to film.

The mean eruptive path for central and lateral incisors was then determined by a curve fitting procedure, thereby providing an estimate of the continuous path of the teeth from the series of sample points obtained from the radiographs.

To provide an accurate fit of the continuous curve (y) to the individual data points, a high-order polynomial was used, given by the following equation,

y = agX^ -\r a I + a^x^ ... (Eq. 11.1)

To provide a more accurate local fit to the oscillating post-emergence movements of the teeth, a second 14th order polynomial was fitted separately to this part of the eruption path.

polynomial function of the ARCUS^’^^ data analysis program. The coefficients of the polynomial were determined by the computer program to provide a least squares approximation between the curve and the data points.

The amplitude of the post-emergence oscillation was estimated from the successive horizontal inflections of the eruption path determined from the fitted curve. The half period of oscillation was determined from the time delay between successive inflections of the eruption path. The curve fitting and estimation procedure are shown diagrammatically in Figure 11.4.

a m p l i t u d e

F ig u re 1 1 .4 D ia g ra m m a tic representation o f the c u rv e fitting and estim ation p ro ced u res.

11.2.3 Statistical methods

The eruption paths were determined individually for each subject and differences in the general form of the paths were not subjected to statistical analysis. The amplitudes and the periods of post-emergence oscillation were examined for normality using Shapiro-Wilk’s test. Comparisons of the period and amplitude of oscillation between central and lateral incisors were conducted using paired t tests and possible associations between these parameters was examined using Pearson’s product moment correlation.