Cone-beam computed tomography for assessment of palatal displaced canine position: a methodological study

Abstract

Objective: To assess the inter- and intraexaminer reliability of a measurement method for evaluation of eruption angles and position of palatal displaced canines (PDCs) with cone-beam computed tomography (CBCT) images and to test the validity of the measured angles on a dry skull.

Materials and methods: Twenty patients (eight boys, 12 girls; age 11.4±1.2 years) were randomly chosen among 67 patients from a study evaluating the interceptive effect of extracting the deciduous canine in children with PDCs. In total, 60 images were analyzed, because each patient had three CBCT examinations (baseline, 6-month control, and endpoint). Two observers assessed the following measurements twice: mesioangular and sagittal angle, vertical position, canine cusp tip, and canine apex to dental arch. The validity of the angular measurements was tested against angular measurements on a dry skull using mathematical formulations.

Results: The inter- and intraexaminer mean differences for angular and linear measurements were all low and statistically insignificant (P>.05). The mean differences between the physical and 3D measurements were 0.5±0.39 mm for the sagittal angle and 0.22±0.19 mm for the mesioangular angle.

Conclusions: Linear and angular measurements on CBCT images are accurate and precise and can be used to assess the precise position of a PDC.

Figures

Figure 1.

Mesioangular angle of PDC measured on a coronal view.

Figure 2.

Sagittal angle and vertical position measured on a sagittal view.

Figure 3.

Distance from the canine cusp tip measured to the dental arch on an axial image.

Figure 4.

Root apex of the canine measured to the dental arch on an axial image.

Figure 5a,b.

3D images of the dry skull with the direct measurements. Definitions are explained in detail in Table 1.

Figure 6.

Illustration of how the sagittal angle (V1), corresponding to the sagittal angle in Figure 2, was determined by projecting the canine (dotted drawing) on the reference line in a 2D plane. Thus, the measurements A2 (Iic-sp), A3 (Iic-pm), B2 (Iac-sp), and B3 (Iac-pm) (Table 1) were projected onto the reference plane. The reference plane is an imaginary plane constructed using the reference line, which is a horizontal line between the spina nasalis (sp) and pterygomaxillare (pm) and a vertical line. Using this projection, a line passing through Iic(p) and Iac(p) was created. Lines were then drawn from Iic(p) and Iac(p) to sp and pm. The next step was to determine the projection of the line a2 (Iic(p)-sp) (Figure 8). All the distances, a3 (Iic(p)-pm), b2 (Iac(P)-sp), and b3 (Iac(p)-pm), were obtained in a similar way. To find the sagittal angle, the angles p1, p2, p3, and f and the distance x (Iic(p)-Iac(p)) had to first be determined. As the distances a2 (Iic(p)-sp), a3 (Iic(p)-pm), and D (sp-pm) have been previously obtained, the angle p1 was calculated using the Law of Cosines: cos(p1)  =  (D2 + a22 − a32)/(2 × D × a2). The distances b2, b3, and D were used for calculation of the angle p2 using the Law of Cosines. The angle p3 was obtained by subtracting p2 from p1. The Law of Cosines was also used in the determination of the distance x: x2  =  a22 + b22 − [2 × a2 × b2 × Cos (p3)]. Angle f was then calculated using the following formula: cos(f)  =  (a22 + x2 − b22)/(2 × a2 × x). The sagittal angle was obtained by summing up the angles p1 and f. Abbreviations and definitions are shown on the right side.

Figure 7.

The triangle illustrates how the projection of line a2 (Iic(p)-sp) on the reference plane was determined. As the distances A1 (Iic-reference plane) and A2 (Iic-sp) were already known by the direct measurements made on the dry skull, the α angle was calculated using the trigonometric equation cos(α)  =  (A1/A2). The α angle was then used in the equation tan(α)  =  (a2/A1) to calculate distance a2. Abbreviations and definitions are shown on the right side.

Figure 8.

Illustration of how the mesioangular angle (V2) corresponding to the mesioangular angle in Figure 1 was obtained. The dotted drawing indicates the canine. The distances hi (Iic(p)-(sp-pm)) and ha (Iac(p)-(sp-pm)) and the angle p4 were needed for the calculation of V2. As the distances A1 (Iic-RP) and B1 (Iac-RP) would have already been measured from the dry skull, the following equations were used to calculate the distances hi and ha: hi  =  sin(p1) × a2, and ha  =  sin(p2) × b2. To calculate the angle p4, the tangent equation was used: tan(p4)  =  (A1 − B1)/(hi − ha). The mesioangular angle was obtained by summing up the angle p4 with 90 degrees. Abbreviations and definitions are shown on the right side.

Figure 9.

Mean values and standard deviations of sagittal and mesioangular angles on different occasions obtained by physical and 3D measurements. n.s indicates nonsignificant difference.