Effect of buccolingual root angulation on the mesiodistal angulation shown on panoramic radiographs

ORIGINAL ARTICLE

Effect of buccolingual root angulation on the mesiodistal angulation shown on panoramic radiographs Mariano A. Garcia-Figueroa,a Donald W. Raboud,b Ernest W. Lam,c Giseon Heo,d and Paul W. Majore San Jose, Costa Rica, and Edmonton, Alberta, and Toronto, Ontario, Canada Introduction: The purpose of this study was to evaluate the effect of buccolingual root angulation on the perception of root parallelism in panoramic images. Methods: A skull-typodont device was constructed according to cephalometric norms. The bases of the typodont were partially sectioned so that the buccolingual orientation of 4 adjacent pairs of teeth could be easily modified. Three buccolingual angulations were used for each tooth. Nine image sequences were necessary to analyze all possible buccolingual orientation combinations between adjacent teeth. The true root parallelism angulations relative to an orthodontic archwire were compared with the angulations obtained from scanned panoramic films. Results: The largest root parallelism differences for adjacent teeth occurred between the maxillary canine and the first premolar. The second largest differences occurred in the mandibular canine-premolar area. No significant differences were found in the incisor area. Conclusions: The root parallelism expression in the caninepremolar region can be modified by altering the buccolingual orientation. Buccolingual orientation changes do not seem to affect the incisor area. The clinical usefulness of panoramic radiography to assess root parallelism should be approached with caution, especially in premolar extraction sites. (Am J Orthod Dentofacial Orthop 2008;134:93-9)

D

uring diagnosis, treatment planning, and shortly before the end of orthodontic treatment, the orthodontist takes radiographs to evaluate the overall mesiodistal root angulations of the teeth in the maxilla and the mandible. The literature shows that panoramic radiography is commonly used to assess root inclination and parallelism. In a 2002 survey of orthodontic diagnosis and treatment procedures of American orthodontists, 57.9% and 79.1% of the respondents reported taking progress and posttreatment panoramic radiographs, respectively.1 Panoramic radiography is recommended by the American Board of Orthodontics a

Private practice; clinical instructor, University of Costa Rica, San Jose, Costa Rica. b Associate professor, Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada. c Associate professor, Division of Oral and Maxillofacial Radiology, Faculty of Dentistry, University of Toronto, Toronto, Ontario, Canada. d Assistant professor, Department of Dentistry, Faculty of Medicine and Dentistry, University of Alberta, Edmonton, Alberta, Canada. e Professor and director of Orthodontic Graduate Program, Department of Dentistry, Faculty of Medicine and Dentistry, University of Alberta, Edmonton, Alberta, Canada. Reprint requests to: Paul W. Major, Faculty of Medicine and Dentistry, Room 4051b, Dentistry/Pharmacy Centre, University of Alberta, Edmonton, Alberta, Canada T6G 2N8; e-mail, [email protected]. Submitted, January 2006; revised and accepted, July 2006. 0889-5406/$34.00 Copyright © 2008 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2006.07.034

to assess root inclination and parallelism. This is done to evaluate the adequacy of orthodontic finishing.2 In orthodontics, correct positioning of the teeth in the 3 planes of space is necessary to obtain correct occlusal relationships and a stable result. Root parallelism is an important factor in the distribution of occlusal forces with closed contact points.3 If roots are well positioned, there will be sufficient bone between adjacent teeth. Orthodontically closed extraction sites are more susceptible to open again if adjacent tooth roots are not parallel.4-9 A panoramic image is made by generating an image layer or a focal trough in a standard jaw form and size. Any deviation from this standard jaw form will result in an object that is not centered in the image layer and cause some distortion.10 For this reason, panoramic radiography has shortcomings related to the accuracy of size, location, and form of the image created.11 It has been demonstrated that this radiographic technique also has limitations in assessing angular measurements of tooth inclinations.12-19 Angulation distortion on panoramic radiographs results from the combined distortion in the vertical and horizontal dimensions and at different locations and depths in the focal trough.12 Even though several studies have assessed angular distortion in panoramic radiographs, in most of these studies, no consideration was given to inclinations in 93

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the depth dimension of the body.17,18 It could be hypothesized that changes in tooth orientation in the buccolingual plane might have a bearing on the expression of root parallelism in the image, since distortion can be affected by changes in the object’s depth in the focal trough. The studies in the literature regarding angular distortion and buccolingual orientation changes have the following limitations.13,16,20 1. Some studies were restricted to either the maxilla or the mandible and to specific areas of the jaws such as the anterior segments.16,20 Consequently, the results applied only to the locations where the test films were exposed. 2. The studies were carried out on nonanatomical devices with unrealistic tooth orientations that did not depict true human dentition. Most studies were based on wire meshes and pins representing the dentition and supporting structures.13,16 3. One study used a cylindrical layer and a fixed rotation center of the beam instead of a standard panoramic machine.16 These approximations are valid only in a limited section of the curved layer in panoramic radiography. 4. The authors referred to the angular distortion of individual structures representing teeth and did not quantify the changes in root parallelism between adjacent structures.20 The purpose of this study was to examine whether the expression of root parallelism with adjacent teeth in the image of a typodont-skull device significantly differs when the buccolingual angulations are altered and the mesiodistal angulations are fixed. These results could offer clinical guidelines to the practitioner as to what extent and at what locations buccolingual angulations should be considered when assessing root parallelism on panoramic images. MATERIAL AND METHODS

The anatomic tooth-bearing device described by McKee et al,17,18 with minor modifications, was used to represent realistic buccolingual and mesiodistal tooth angulations based on anatomic and cephalometric principles of the dentition (Fig 1). The natural maxillary and mandibular dentition and supporting bone were removed to allow placement of the maxillary and mandibular typodont. A clear anatomic typodont (Ormco, Orange, Calif) with ideal occlusion from second molar to second molar was used as the toothbearing apparatus. The dental relationship of the typodont teeth was Class I molar and canine with both overjet and overbite of 2 mm.

Fig 1. Anatomic tooth-bearing device used to represent realistic buccolingual and mesiodistal tooth angulations.

Cephalometric measurements from posteroanterior and lateral cephalograms were made to achieve the following positions of the typodont relative to the skull. (1) In the transverse plane, the dental midline of the typodont was coincident with the skull’s skeletal midline. (2) In the anteroposterior plane, a steel ball was placed at a defined A-point. McNamara’s nasion perpendicular to Frankfort horizontal to A-point cephalometric norms were used to idealize the maxillary skeletal anteroposterior position.21 (3) In the vertical plane, the occlusal plane cant to Frankfort horizontal (9°) and the preexisting distance from nasion to maxillary incisor dictated the maxillary vertical position. The mandibular typodont anteroposterior position was determined by its centric occlusion articulation with the maxillary typodont. The typodont was rigidly fixed into the basal bone with pink denture baseplate wax and wires. The bases of the typodont were sectioned in 8 locations corresponding to 8 teeth so that the buccolingual orientation of the teeth could be easily modified. The teeth were chosen to represent tooth pairs of the anterior and intermediate segments of the maxilla and the mandible. The teeth chosen were the maxillary right lateral incisor, the maxillary right central incisor, the maxillary left canine, the maxillary left first premolar, the mandibular left incisors, the mandibular right canine, and the mandibular right first premolar. Two chromium steel balls (Commercial Bearing, Edmonton, Alberta, Canada) measuring 1.58 mm in diameter were glued into position to each tooth. The occlusal-incisal ball was placed in the buccolingual and mesiodistal midpoints of the crown on the incisal-occlusal surface. The apical ball was glued into the center of the root in

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the apical third. An additional chromium steel ball was placed apically to the tooth on the fixed portion of the base as a reference point for the assessment of the buccolingual angulation changes. These steel balls served as landmarks for mesiodistal and buccolingual angulation determinations and radiopaque markers for imaging. The long axis of the tooth was represented by an imaginary line joining the center of the apical and occlusal-incisal markers. The maxillary and mandibular typodont teeth were then bonded with clear orthodontic brackets (Clarity, 3M Unitek, Monrovia, Calif), and a .020-in round stainless steel heat-treated wire (Permachrome resilient, 3M Unitek) was ligated into the bracket slots with elastic modules. The buccolingual orientations were modified by using the archwire as the axis of buccolingual rotation. Each tooth remained attached to the phantom by the archwire, which preserved the original mesiodistal angulation. The buccolingual orientations of the teeth were stabilized with pink denture baseplate wax. Three buccolingual angulations were used for each tooth. The original or neutral buccolingual angulation of each tooth was modified by rotating the root buccally 10° (buccal root torque) and lingually 10° (lingual root torque). Nine buccolingual angulation settings were necessary to analyze all possible buccolingual orientation combinations between adjacent teeth. A coordinate measuring machine (CMM) (model HGC, L. S. Starrett, Athol, Mass) was used with a custom-designed Excel spreadsheet (Microsoft, Redmond, Wash) to determine the true mesiodistal and buccolingual angulations of each typodont tooth relative to the reference archwire. The steel markers and reference archwire were digitized by using varying orientations of external probes with a ruby ball measuring 1 mm in diameter. The measurements consisted of the following digitization points (Fig 2): (1) Tc (tooth crown)— contact of the CMM probe with the most occlusal-incisal surface of the steel ball on the typodont tooth; (2) Tr (tooth root)— contact of the CMM probe with the most apical surface of the steel ball at the apical end of the typodont tooth; (3) Wd (wire distal)— contact of the CMM probe on the apical surface of the reference archwire parallel to the distal contact of the typodont tooth with its neighboring tooth; (4) Wm (wire mesial)— contact of the CMM probe on the apical surface of the reference archwire parallel to the mesial contact of the typodont tooth with its neighboring tooth; (5) A (apical base)— contact of the CMM probe on the labial surface of the steel ball on the apical base; and (6) B (bracket center)— contact of the CMM probe on the anterior and central surface of the bracket, correspond-

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Fig 2. Landmarks used for mesiodistal and buccolingual angle determinations: Tr, tooth root; Tc, tooth crown; Wd, wire distal; Wm, wire mesial; A, apical point; B, bracket point.

ing to the center of rotation of the typodont tooth around the wire (axis). Tc, Tr, Wd, and Wm were used to calculate the mesiodistal angulations of the teeth. Tc, Tr, A, and B were used to compute the buccolingual angulations of the teeth. The mesiodistal angle was the angle between the long axis of the tooth (represented by the steel balls) and the reference archwire. The buccolingual angle was the angle between the long axis and the apical basearchwire reference line. The CMM provided x, y, and z coordinate values (in millimeters) for each digitized point. The coordinate values for each point were entered in the spreadsheet for generation of the “real” mesiodistal and buccolingual angulation of the 9 settings. Each tooth was measured 5 times to calculate the original mesiodistal and buccolingual angulations. Every time the buccolingual angulation was changed, the buccolingual angulation determination for each tooth was repeated 8 times. Mesiodistal angulation greater than 90° represented distal root inclination, and a value less than 90° indicated mesial inclination. The CMM is precise within 0.025 mm according to the manufacturer. The panoramic projections were taken with a PM 2002 EC panoramic unit (Planmeca, Helsinski, Finland). Landmarks were preset on the skull and the panoramic unit to allow for a standardized and reliable positioning technique. The skull was centered in the midsagittal plane with Frankfort horizontal parallel to the floor, and the maxillary and mandibular incisors biting into the bite tab. Preliminary x-rays were taken to

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Table. Mean angular differences (in degrees) between each delta angulation setting and the delta angle for neutral buccolingual orientation Root orientation Buccolingual Neutral-lingual Buccal-neutral Lingual-lingual Lingual-neutral Buccal-buccal Neutral-buccal Lingual-buccal

⌬1

⌬2

⌬3

⌬4

Mean difference

P value

Mean difference

P value

Mean difference

P value

Mean difference

P value

0.88 1.6 ⫺0.45 ⫺0.52 0.45 ⫺0.02 0.6 ⫺0.45

0.120 0.008* 0.445 0.243 0.376 0.965 0.127 0.420

⫺14.23 ⫺7.35 ⫺5.75 ⫺1.35 3.79 6.01 10.18 13.53

0.000* 0.000* 0.000* 0.057 0.000* 0.000* 0.000* 0.000*

⫺0.6 0.3 ⫺0.66 ⫺1.24 ⫺0.94 ⫺0.58 0.27 ⫺1.05

0.193 0.701 0.304 0.399 0.136 0.855 0.595 0.285

⫺9.53 ⫺5.08 ⫺3.78 ⫺3.01 1.64 1.01 3.54 5.2

0.000* 0.000* 0.037* 0.039* 0.000* 0.000* 0.000* 0.000*

Negative values relate to root convergence, and positive values to root divergence. ⌬1, Between the long axes of the maxillary central and lateral incisors; ⌬2, between the long axes of the maxillary canine and first premolar; ⌬3, between the long axes of the mandibular central and lateral incisors; ⌬4, between the long axes of the mandibular canine and first premolar. *The mean difference is significant at the 0.05 level.

determine the exposure setting to achieve the best contrast and least blurring. Two films were used in the cassette on each exposure to compensate for the lack of soft tissue. The panoramic film images were scanned into a computer with a flat bed scanner with resolution of 400 dpi and magnification of 200% (Epson Expression 1680, Epson America, Long Beach, Calif). The measured mesiodistal angulations from the panoramic images were obtained by using custom computer software (panoramic angulator, Crusher Software, Edmonton, Alberta, Canada). The software allowed for digitization of the scanned images with 4 points for the angle determination of each tooth—the same points used during actual mesiodistal angle determination with the CMM. The teeth were digitized on each film randomly to reduce intrarater bias. The digitization process was repeated 16 times. After that, the program created an Excel spreadsheet of the image’s mesiodistal angulations. For evaluating root parallelism expression, the 8 teeth were divided into 4 pairs: maxillary central and lateral incisors, maxillary canine and first premolar, mandibular central and lateral incisors, and mandibular canine and first premolar. To obtain quantification of root parallelism, 2 angles were used. (1) For the tooth closer to the midline, an angle between the long axis of the tooth and the distal segment of the archwire was calculated; the distal angle was the complementary angle of the angle calculated by the software. (2) For the tooth farther from the midline, the angle between the long axis and the mesial segment of the archwire was calculated by the software. The delta angle for each tooth pair was the summation of these angles. The delta angles were used to assess root diver-

gence or convergence between the 4 adjacent tooth pairs. Thus, 4 angles were defined: ⌬1, between the long axes of the maxillary central and lateral incisors; ⌬2, between the long axes of the maxillary canine and first premolar; ⌬3, between the long axes of the mandibular central and lateral incisors; and ⌬4, between the long axes of the mandibular canine and first premolar. Statistical analysis

A pilot study was carried out to determine the sample size. Based on the results, 16 measurements of the mesiodistal angulation of each tooth were necessary to calculate the root parallelism angle for each buccolingual root orientation per tooth pair. The sample size was calculated by using PASS (NCSS, Kaysville, Utah) with a multiple comparison power analysis to obtain a power of 90%. For statistical purposes, the root parallelism angulations (deltas) were divided into 4 independent groups corresponding to the 4 pairs of teeth. It was decided to use the delta angle when both teeth were in their neutral buccolingual orientation because the reference angle to assess root parallelism on the image changes. The mean differences between delta angles when buccolingual orientations were modified and the reference delta angles were calculated by using repeated-measures ANOVA tests and contrast tests. RESULTS

The expression of root parallelism was variably affected by buccolingual root angulations in different regions of the jaws. The Table 1 shows the mean differences between the delta angulations for modified buccolingual angulation settings and the reference delta

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Delta 1 (12/11) Delta 2 (23/24) Delta 3 (31/32) Delta 4 (43/44)

15.00

mean differences (in degrees)

10.00

5.00

0.00

tations were projected more mesially than they were in reality. On the other hand, roots bucally positioned were projected more distally. This phenomenon was seen only in the canine and premolar region, with the maxillary angulations more affected than the mandible. The trends observed in the premolar and canine regions in both arches were not observed on the incisors (Fig 3). DISCUSSION

-5.00

-10.00

-15.00

B/L

N/L

B/N

L/L

N/N

L/N

B/B

N/B

L/B

Buccolingual root orientation

Fig 3. Mean delta angulation differences between different buccolingual angulation settings and the delta angle for neutral buccolingual orientations. Mean angular difference ⫽ (delta angle for each setting per adjacent pair of teeth) ⫺ (delta angle when both teeth were in neutral buccolingual orientations). The letters correspond to the buccolingual orientation of each tooth: B, buccal root torque; L, lingual root torque; N, neutral root torque. The first letter refers to teeth closer to the midline, and the second letter to teeth farther from the midline. Negative values relate to root convergence, and positive values to root divergence.

angle. The mean differences are represented by negative and positive values. Negative values correspond to root convergence, positive values to root divergence. The angular distortion of parallelism was more pronounced in the canine and premolar regions and in the maxilla than the mandible. For ⌬2 (maxillary canine and first premolar), the maximum root convergence was observed when the canine had buccal root angulation and the premolar lingual root angulation. There was a difference of ⫺14° (convergence) between this buccolingual setting and when both teeth were in their original buccolingual angulation. On the other hand, the maximum root divergence was observed when the canine had lingual root orientation and the premolar buccal root orientation. The same distortion pattern, but to a lesser extent, was observed in the mandibular canine and first premolar region (Fig 1). ⌬3 (mandibular central and lateral incisors) was the least affected of all angles with no statistically significant differences. This phenomenon can be explained by the fact that, in the canine and premolar regions of the panoramic image, the roots with lingual root orien-

The results of this study showed that buccolingual tooth-angulation changes can change the perception of root parallelism on panoramic images, but only in the canine-premolar region. If there are significant buccolingual orientation discrepancies between adjacent teeth, treating to the panoramic image expression might lead to root convergence or divergence depending on the orientations of the long axes of the teeth. The root parallelism distortion could be considered clinically insignificant for the anterior regions. ⌬1 (maxillary central and lateral incisors) had some statistically significant differences in the buccolingual settings, but these differences were less than 2.5°, which can be considered clinically insignificant. Variations of as much as 2.5° between a tooth and an established reference point are not a serious problem from a clinical perspective according to previous studies.9,12,17-19 Our results can be explained by the fact that the projection of the jaws is not truly orthogonal, and projection errors are introduced by discrepancies between the angulation of the x-ray beam and the object.22 The central ray of the beam is at all times tangential to the curvature of the dental arches, and angular changes of the beam during the exposure are necessary to fit to the anatomy of the jaws. These angular changes define the projection of each successive part of the jaws. Deviations from true orthogonal projections have been reported to be 15° to 45° in the premolar region; these discrepancies are greater in the maxilla than the mandible.23 In the anterior region, the deviation from a true orthogonal projection is minimal. As a result, any buccolingual orientation changes are less likely to produce an angular image distortion. The projection angle progressively deviates more from the true orthogonal toward the posterior regions, causing any buccolingual root angulation changes to be perceived as mesiodistal angulation changes. The deviations in the canine-premolar region are significant enough to be clinically noticeable. The angular discrepancies on the canine-premolar area were larger for the maxilla than the mandible. The fact that the deviation from the orthogonal projection is less pronounced in the mandi-

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ble than the maxilla might explain why the mesiodistal angular distortion was more marked in the maxilla. As a result, the largest projected angular differences between adjacent teeth occurred between the maxillary canine and premolar. When the canine had buccal root orientation and the premolar lingual root orientation, the root parallelism in the mesiodistal plane was projected on the film as root convergence. Treating to the panoramic radiograph would result in extreme root divergence. The opposite was found when the canine had lingual root orientation and the premolar buccal orientation. Treating to the panoramic radiograph would result in unnecessary root convergence. The most common teeth to be extracted for orthodontic purposes are the mandibular and maxillary premolars.24 This radiographic phenomenon has special importance in extraction sites, since any buccolingual angulation discrepancies between the premolar and the canine, or the premolar and the molar, could be expressed on the image as excessive convergence or divergence of the roots. As stated by previous researchers, the use of panoramic radiographs to assess root angulation and parallelism in the first premolar extraction area might have little clinical value.17 The clinician must be aware of the effect of orthodontic introduction of canine or premolar root torque on perceived root parallelism based on the panoramic radiograph. Axial positioning of teeth in the buccolingual plane is difficult to control orthodontically. Many variables related to the properties of the orthodontic materials might influence the buccolingual orientation of a tooth in the space. These variables include inability to fill the slot, irregularities from the manufacturing of brackets, differences in the stiffness of wire alloys, variations between actual and reported bracket torque values, and ligation modes.25 Moreover, anatomic variables such as facial surface contours and the angle formed by the coronal and radicular long axes are extremely variable in the general population. These variations will result in varying torque expression with direct impact on buccolingual root angulations.26 Different manufacturers use various focal trough dimensions and beam projection angles. The angular distortion of parallelism that we identified might differ with other panoramic units. However, Scarfe et al27 compared optimal beam angulations of 4 panoramic units and found that the Planmeca 2002 CC (used in this study) deviated the least from optimal angulation over most of the dental arch.27 However, those authors compared only a few panoramic units. Perhaps other units, with different focal troughs and rotational patterns, are less susceptible to angular distortion caused

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by buccolingual orientation changes. It can be expected that our findings might be expressed in varying degrees in other panoramic units. Variations in the size and shape of the jaws can also influence the expression of the root angulations and provide different results. If the interproximal surfaces of the teeth are accommodated so that the x-ray beam passes parallel to these surfaces, then little angular distortion can be expected. Root angulation changes of 10° buccally or lingually are, in our opinion, realistic changes that can be achieved with fixed orthodontic appliances. There is still limited information regarding to what extent orthodontic treatment affects buccolingual orientations. Variations of as much of 10° might be anatomically normal in the general population. Since only 2 root orientation changes (1 lingual, 1 buccal) were used in this study, it is impossible to prove that the amount of angular distortion is proportional to the degree of angular changes. Further studies could include more varied lingual and buccal root orientation changes. CONCLUSIONS

The following conclusions can be drawn from this study. 1. When the buccolingual angulation changes, the largest angular differences between adjacent teeth occurred in the canine-premolar area. These discrepancies were larger for the maxillary arch than for the mandibular arch. 2. Buccolingual angulation changes in the incisor area do not seem to affect the expression of root parallelism in panoramic images. 3. The clinical assessment of root parallelism with panoramic x-rays should take into account the buccolingual orientation effects on the angular distortions in the image, especially in premolar extraction sites. REFERENCES 1. Keim RG, Gottlieb EL, Nelson AH, Vogels DS 3rd. 2002 JCO study of orthodontic diagnosis and treatment procedures. Part 3. More breakdowns of selected variables. J Clin Orthod 2002;36: 690-9. 2. American Board of Orthodontics. Grading system for dental casts and panoramic radiographs [CD-ROM]. St Louis; 2002. 3. Dewel BF. Clinical observations on the axial inclination of teeth. Am J Orthod 1949;35:99-115. 4. Mayoral G. Treatment results with light wires studied by panoramic radiography. Am J Orthod 1982;81:489-97. 5. Edwards JG. The prevention of relapse in extraction cases. Am J Orthod 1971;60:128-44. 6. Graber T. Postmortems in posttreatment adjustments. Am J Orthod 1966;52:331-52.

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7. Hatasaka HH. A radiographic study of roots in extraction sites. Angle Orthod 1976;46:64-8. 8. Holdaway R. Bracket angulation as applied to the edgewise appliance. Angle Orthod 1952;22:227-36. 9. Strang R. Factors associated with successful orthodontic treatment. Am J Orthod 1952;38:790-800. 10. Langland OE, Langlais RP, Preece JW. Principles of dental imaging. 2nd ed. Baltimore: Lippincott Williams & Wilkins; 2002. 11. Quintero JC, Trosien A, Hatcher D, Kapila S. Craniofacial imaging in orthodontics: historical perspective, current status, and future developments. Angle Orthod 1999;69:491-506. 12. Wyatt DL, Farman AG, Orbell GM, Silveira AM, Scarfe WC. Accuracy of dimensional and angular measurements from panoramic and lateral oblique radiographs. Dentomaxillofac Radiol 1995;24:225-31. 13. Lucchesi MV, Wood RE, Nortje CJ. Suitability of the panoramic radiograph for assessment of mesiodistal angulation of teeth in the buccal segments of the mandible. Am J Orthod Dentofacial Orthop 1988;94:303-10. 14. Stewart JL, Bieser LF. Panoramic roentgenograms compared with conventional intra-oral roentgenograms. Oral Surg Oral Med Oral Pathol 1968;26:39-42. 15. Philipp RG, Hurst RV. The cant of the occlusal plane and distortion in the panoramic radiograph. Angle Orthod 1978;48: 317-23. 16. Tronje G, Welander U, McDavid WD, Morris CR. Image distortion in rotational panoramic radiography. III. Inclined objects. Acta Radiol Diagn (Stockh) 1981;22:585-92. 17. McKee IW, Williamson PC, Lam EW, Heo G, Glover KE, Major PW. The accuracy of 4 panoramic units in the projection of mesiodistal tooth angulations. Am J Orthod Dentofacial Orthop 2002;121:166-75.

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18. McKee IW, Glover KE, Williamson PC, Lam EW, Heo G, Major PW. The effect of vertical and horizontal head positioning in panoramic radiography on mesiodistal tooth angulations. Angle Orthod 2001;71:442-51. 19. Stramotas S, Geenty JP, Petocz P, Darendeliler MA. Accuracy of linear and angular measurements on panoramic radiographs taken at various positions in vitro. Eur J Orthod 2002;24:43-52. 20. Samfors KA, Welander U. Angle distortion in narrow beam rotation radiography. Acta Radiol Diagn (Stockh) 1974;15: 570-6. 21. McNamara JA Jr. A method of cephalometric evaluation. Am J Orthod 1984;86:449-69. 22. McDavid WD, Tronje G, Welander U. A method to maintain a constant magnification factor throughout the exposure of rotational panoramic radiographs. Dentomaxillofac Radiol 1989;18: 160-8. 23. Welander U, Tronje G, McDavid WD. Layer thickness in rotational panoramic radiography: some specific aspects. Dentomaxillofac Radiol 1989;18:119-24. 24. Graber TM, Vanarsdall RLJr. Orthodontics. Current principles and techniques. 3rd ed. St Louis: Mosby; 2000. 25. Gioka C, Eliades T. Materials-induced variation in the torque expression of preadjusted appliances. Am J Orthod Dentofacial Orthop 2004;125:323-8. 26. Germane N, Bentley BE Jr, Isaacson RJ. Three biologic variables modifying faciolingual tooth angulation by straight-wire appliances. Am J Orthod Dentofacial Orthop 1989;96:312-9. 27. Scarfe WC, Nummikoski P, McDavid WD, Welander U, Tronje G. Radiographic interproximal angulations: implications for rotational panoramic radiography. Oral Surg Oral Med Oral Pathol 1993;76:664-72.