1. TECHNO BYTESA new method to measure mesiodistal angulationand faciolingual inclination of each whole toothwith volumetric cone-beam computedtomography imagesHongsheng Tong,a Reyes Enciso,b Dana Van Elslande,c Paul W. Major,d and Glenn T. SameshimaeLos Angeles, Calif, and Calgary and Edmonton, Alberta, Canada Introduction: The purpose of this study was to develop a methodology to measure the mesiodistal angulation and the faciolingual inclination of each whole tooth (including the root) by using 3-dimensional volumetric images generated from cone-beam computed tomography scans. Methods: A plastic typodont with 28 teeth in ideal oc- clusion was xed in position in a dry human skull. Stainless steel balls were xed to the occlusal centers of the crowns and to the apices or bifurcation or trifurcation centers of the roots. Cone-beam computed tomography images were taken and rendered in Dolphin 3D (Dolphin, Chatsworth, Calif). The University of Southern California root vector analysis program was developed and customized to digitize the crown and root centers that dene the long axis of each whole tooth. Special algorithms were used to automatically calculate the mesiodistal angulation and the faciolingual inclination of each whole tooth. Angulation measurements repeated 5 times by using this new method were compared with the true values from the coordinate measuring machine measurements. Next, the root points of 8 selected typodont teeth were modied to generate known angulation and inclination values, and 5-time repeated measurements of these teeth were compared with the known values. Results: Intraclass correlation coefcients for the repeated mesiodistal angu- lation and faciolingual inclination measurements were close to 1. Comparisons between our 5-time repeated angulation measurements and the coordinate measuring machines true angulation values showed 5 teeth with statistically signicant differences. However, only the maxillary right lateral incisor showed a mean difference that might exceed 2.5 for clinical signicance. Comparisons between the 5-repeated measurements of 8 teeth with known mesiodistal angulation and faciolingual inclination values showed no statistically signicant differences between the measured and the known values, and no measurement had a 95% condence interval beyond 1 . Conclusions: We have developed the novel University of Southern California root vector analysis program to accurately measure each whole tooth mesiodistal angulation and faciolingual inclination, in a clinically signicant level, directly from the cone-beam computed tomography volumetric images. (Am J Orthod Dentofacial Orthop 2012;142:133-43) Ta Clinical assistant professor, Advanced Orthodontic Program, Herman Ostrow he basic objectives of orthodontic treatment are toSchool of Dentistry, University of Southern California, Los Angeles.b Assistant professor, Clinical Dentistry, Division of Endodontics, Oral Surgery and obtain proper positions of all teeth by using vari-Orthodontics, Herman Ostrow School of Dentistry, University of Southern ous orthodontic appliances, to form a functionalCalifornia, Los Angeles. and stable occlusion, and to display the teeth in properc Private practice, Calgary, Alberta, Canada.d Professor and chair, Department of Dentistry; head, School of Dentistry, Faculty relationships to one another and in harmony withof Medicine and Dentistry, University of Alberta, Edmonton, Alberta, Canada. the maxillofacial hard and soft tissues after treatment.e Associate professor and director, Advanced Orthodontic Program, Herman Six parameters describe each tooth location inOstrow School of Dentistry, University of Southern California, Los Angeles.The University of Southern California has led a provisional patent application 3-dimensional space. Three are positional (mesiodistal,on our behalf to protect our potential intellectual right for developing the meth- faciolingual, and occlusogingival), and 3 are angularodology used in this study to measure the mesiodistal angulation and the facio- (mesiodistal angulation, faciolingual inclination, andlingual inclination of each whole tooth.Reprint requests to: Hongsheng Tong, 20360 Via Manresa, Yorba Linda, CA axial rotation). Nearly half a century ago, Andrews1,292887; e-mail, drhstong@yahoo.com. studied 120 patients with optimal occlusions andSubmitted, June 2011; revised and accepted, December 2011. obtained the positional and angular norms for all teeth0889-5406/$36.00Copyright 2012 by the American Association of Orthodontists. by measuring their crowns on the study models.doi:10.1016/j.ajodo.2011.12.027 Various types of preadjusted appliances that are used 133

2. 134 Tong et alby most orthodontists today are, to a certain degree, 3-dimensional coordinate measuring machines mea-derived from the original straight-wire appliances he surements for a few teeth. The coordinate measuringdeveloped based on these crown norms.1-4 However, machine was also used in an earlier study by Garcia-although 4 of the 6 parameters dening tooth Figueroa et al18 to show the effect of changing the facio-positions are dictated by the crowns and are easy to lingual inclination of a few selected teeth on their mesio-monitor clinically, later research has shown that distal angulation measurements. However, the goldcrowns might not provide clear indications for the standard coordinate measuring machine cannot beangulation and the inclination of the whole teeth, used on patients, since the tip of the machines probeincluding the roots.5-8 Moreover, straight-wire tech- cannot be brought in contact with the patients rootniques rely heavily on precise bracket positioning during apices.initial bonding, and yet orthodontists at various experi- We have collaborated with the Dolphin companyence levels have found difculties in accurately placing (Chatsworth, Calif) and developed the University ofbrackets directly on patients teeth or even indirectly Southern California (USC) root vector analysis programon the teeth of stone models.9-12 So far, the roots that in the Dolphin 3D module to directly measure the mesio-constitute about half of the whole tooth have been distal angulation and the faciolingual inclination of eachmostly ignored. It is speculated that the roots might whole tooth using CBCT volumetric images. To test thealso need to be assessed to achieve ideal whole tooth validity of our methodology, we also collaborated withangulation and inclination. the research group from the University of Alberta, Ed- Traditionally, panoramic x-rays have been used at the monton, Alberta, Canada, who provided the typodontinitial, progress, and nishing stages of orthodontic CBCT images and the coordinate measuring machinestreatment to diagnose, monitor, and nalize the angula- mesiodistal angulation measurement data for the typo-tions of the teeth.13,14 However, studies have indicated dont teeth to compare with our results.that panoramic x-rays have distortions and do notreect the true 3-dimensional teeth angulations becausethe x-ray beam is not always orthogonal to the target MATERIAL AND METHODSteeth.15-18 For faciolingual inclinations, the only We measured the mesiodistal angulation of the typo-assessment tool available is the lateral cephalogram for dont teeth with the coordinate measuring machine (Farothe maxillary and mandibular central incisors.19,20 A International, Lake Mary, Fla). The typodont was basedposteroanterior cephalogram might capture the on a modication of the model previously reported byfaciolingual inclinations of a few molars, but the image McKee et al16 and Garcia-Figueroa et al.18 It consistedquality is usually poor and rarely used. of transparent plastic anatomic typodont maxilla and As we know, the position of teeth is a 3-dimensional mandible (Kilgore International, Coldwater, Mich) withissue. Andrews1-3 did not measure the angulation and synthetic teeth in idealized occlusion from the secondthe inclination of teeth from 2-dimensional x-rays but molar to the second molar. As shown by Van Elslandefrom study models that are 3-dimensional. Fortunately, et al,21 the typodont was mounted on a dry human skull.the development and use of cone-beam computed to- Stainless steel balls (Small Parts, Miramar, Fla), 1.58 mmmography (CBCT) in orthodontics in recent years have in diameter, were placed at the approximate mesiodistalallowed us see the roots of teeth in 3 dimensions as and faciolingual centers of the occlusal surfaces, and atwell. This lets us accurately evaluate the mesiodistal an- the approximate centers of the root apices for single-gulation and the faciolingual inclination of each whole rooted teeth or the centers of the bifurcation or trifurca-tooth (crown and root) rather than just the crown. How- tion at the level of the root apices for multi-rooted teeth.ever, there is no clinically useful tool currently available A line connecting the 2 centers on each tooth repre-to systemically measure whole tooth angulation and in- sented its long axis.clination in 3 dimensions. Van Elslande et al21 had to The coordinate measuring machine was used to de-construct 2-dimensional panoramic-like images from termine the actual mesiodistal angular measurement of3-dimensional CBCT images to measure the angulation each whole tooth with reference to the archwires thatof the typodont teeth. They compared these measure- were held in place on the plastic molds of the maxillaments with those taken directly from a coordinate mea- and the mandible at approximately the middle of thesuring machine, the gold standard 3-dimensional roots. A mesiodistal plane was created for each toothmeasuring device. They suggested that the constructed that was perpendicular to the horizontal (archwire)images might be better than conventional panoramic ra- plane. This tooth-specic reference plane passeddiographs in assessing root angulations, although the through the mesial and distal interproximal pointsmeasurements were still off signicantly from the true marked on the archwires with crimpable stops. TheJuly 2012 Vol 142 Issue 1 American Journal of Orthodontics and Dentofacial Orthopedics

3. Tong et al 135 Fig 1. Setting up the global coordination system for the maxillary arch: the midsagittal plane (red) evenly dividing the right and left sides, the coronal plane (green) at the buccal groves of the maxillary right and left rst molars, and the axial plane (blue) at the maxillary archwire level.mesiodistal angulation of a tooth was the measurement selected and imported into the Dolphin Imaging 3D pro-of the angulation between the projection of the tooths gram. The USC root vector analysis program was devel-long axis on the mesiodistal plane and the vertical line. oped in the Dolphin 3D module to measure both the One investigator (D.V.E.) made repeated measure- mesiodistal angulation and the faciolingual inclinationments on 5 separate occasions, 5 days apart, and the in- of each whole tooth as shown below.traclass correlation coefcient values were calculated to Once the typodont digital imaging and communica-determine the reliability of the coordinate measuring tions in medicine (DICOM) data were imported into Dol-machines angulation measurements. The coordinate phin 3D, a 3-dimensional global coordinate system wasmeasuring machine was reported by the manufacturer rst generated for the proper orientation of the head andto be accurate to within 0.013 mm. For angular mea- the maxillofacial structures. This coordinate system in-surements, the machine was found to be accurate to cluded the midsagittal plane, the coronal plane, andwithin 0.031 . The average of the 5-time repeated coor- the axial plane, each perpendicular to the other 2 planesdinate measuring machines angulation measurements (Fig 1). The midsagittal plane evenly divided the rightwere used as the true values. and the left halves of the skull; the coronal plane passed The typodont teeths mesiodistal angulations and fa- through the maxillary rst molar buccal grooves on bothciolingual inclinations were also measured by using the sides, and the axial plane was the archwire plane. Sincecustom USC root vector analysis program. For the the maxillary and mandibular teeth had separate arch-CBCT scan of the same typodont used above, a NewTom wire planes, there were also 2 separate 3-dimensional3G volume scanner (AFP, Elmsford, NY) was used ac- global coordinates: 1 saved for the maxilla, and 1 savedcording to the manufacturers instructions as shown for the mandible.also by Van Elslande et al.21 Twenty-ve independent The digitization of each tooths long axis was done inimages were obtained from separate CBCT scans for all 3 plane views, each perpendicular to the other 2the previous study, and 5 of them were randomly views. Parallel movements of the sagittal, coronal, andAmerican Journal of Orthodontics and Dentofacial Orthopedics July 2012 Vol 142 Issue 1

4. 136 Tong et al Fig 2. Locating the maxillary right central incisor crown point before digitization: parallel movements of the sagittal (red), coronal (green), and axial (blue) planes were made to intersect at the center of the stainless steel ball representing the tooths crown point.axial planes were made so that each would pass through archwire was digitized in the same way after the globalthe center of the white stainless steel marker represent- coordinate saved for the mandibular arch was restored.ing either the crown or the root point of each tooth Then the tooth-specic coordinate system for the(Figs 2 and 3). A red dot was digitized at the intersection mesiodistal angulation and the faciolingual inclinationof the 3 perpendicular planes in 1 of the 3 plane views; it measurements was set up. Once the arch form waswould also appear automatically in the other 2 views. digitized, the custom USC root vector analysis programThe order of digitization was from the maxillary right would automatically construct another 3-plane coordi-second molar to the maxillary left second molar, and nate system consisting of multiple coordinates, eachfrom the mandibular left second molar to the mandibu- specic for only 1 tooth for its mesiodistal angulationlar right second molar. Figure 4 shows all the white and faciolingual inclination measurements (Fig 5): thestainless steel markers replaced by the red digitization transverse plane was the same axial plane at either thepoints. The green lines represented the long axes of maxillary or the mandibular archwire level as in thethe teeth after the digitization was completed in both global coordinate system; the straight green line repre-arches. sented the faciolingual plane that passed through each Next we digitized the archwires. For the maxillary tooth crown point (dark blue dot) and was perpendiculararch, the global coordinate saved for the maxillary teeth to the archwire; the short light blue line represented thewas restored rst, and the maxillary archwire was digi- mesiodistal plane that also passed through each toothtized in the axial plane view set at the archwire level crown point, but was perpendicular to the faciolingual(Fig 5). Four teeth on the right side were digitized along plane. The mesiodistal angulation and the faciolingualthe archwire: midincisor, canine, second premolar, and inclination were measured for each tooth in its corre-second molar. The software program would add the mir- sponding tooth-specic coordinate.ror image of the right side half arch to the left side, con- As shown in Figure 6, A, the mesiodistal angulationstructing a symmetrical arch form. The mandibular was measured from the projection of the tooths longJuly 2012 Vol 142 Issue 1 American Journal of Orthodontics and Dentofacial Orthopedics

5. Tong et al 137 Fig 3. Digitization of the maxillary right central incisor root point: parallel movements of the sagittal (red), coronal (green), and axial (blue) planes were made to intersect at the center of the stainless steel ball representing the tooths root point, and it was digitized (red dots).axis on the mesiodistal plane to the vertical line formedby the intersection of the mesiodistal and faciolingualplanes. If the root center was distal to the crown center,the measurement would be positive; otherwise, it wouldbe negative. The faciolingual inclination was measuredfrom the projection of the tooths long axis on the facio-lingual plane to the vertical line formed by the sameintersection of the mesiodistal and faciolingual planes(Fig 6, B). If the root center was lingual to the crown cen-ter, the measurement would be positive; otherwise, itwould be negative. At this point, the custom USC root vector analysisprogram would use algorithms to measure the mesiodis-tal angulation and the faciolingual inclination values forall teeth automatically. Teeth with known mesiodistal angulation and facio-lingual inclination values were measured. The same 5 ty- Fig 4. All crown and root points have been replaced bypodont images above were used again, except that the red digitization dots, and the teeths long axes are shownroot points of the maxillary right rst molar and rst pre- in green.molar, the maxillary left central incisor and second mo-lar, the mandibular right second molar and canine, and the apices of these teeth but at locations denedthe mandibular left lateral incisor and rst molar were through the following three steps (Fig 7): (1) in the axialnot digitized at the stainless steel balls representing slice view (Fig 7, A) at the crown point level, the imageAmerican Journal of Orthodontics and Dentofacial Orthopedics July 2012 Vol 142 Issue 1

6. 138 Tong et al scans of the same typodont obtained from the University of Alberta. Digitizations were done a week apart, and intraclass correlation coefcients for the mesiodistal an- gulation and faciolingual inclination measurements were calculated. One-sample t tests were used to check for statistically signicant differences between our 5-time repeated me- siodistal angulation measurements and the coordinate measuring machines true mesiodistal angulation values for each tooth. The a level was adjusted to 0.05/28 5 0.001786 for the multiple t tests based on the Bonferroni adjustment. One-sample t tests were also used to com-Fig 5. The maxillary arch on the right side was digitized pare the 5-time repeated mesiodistal angulation andbased on 4 points along the archwire relative to the follow- faciolingual inclination measurements with the givening tooth positions: midincisor, right canine, right second mesiodistal angulation and faciolingual inclinationpremolar, and right second molar (yellow dots). The left values for each of the 8 selected teeth. The a level wasside half arch was the mirror image of the right side half. adjusted to 0.05/8 5 0.00625.The tooth-specic coordinate system was based on thearch form and the crown point of each tooth: the trans-verse plane was the maxillary archwire plane; the faciolin- RESULTSgual plane (long straight green line) passed each tooth The intraclass correlation coefcients for the 5-timecrown point (dark blue dot) and was perpendicular to repeated mesiodistal angulation and faciolingual incli-the maxillary arch; the mesiodistal plane (short light nation measurements with our USC root vector analysisblue line) was perpendicular to the faciolingual plane atthe crown point (dark blue dot) of each tooth. in Dolphin 3D were 0.998 and 1.000, respectively, with 95% condence intervals of 0.996 to 0.999 for the an- gulations, and 0.999 to 1.000 for the inclinations. The intraclass correlation coefcient for the 5 repeated an-was rotated so that for the tooth to be digitized, the fa- gulation measurements with the coordinate measuringciolingual direction was shown vertically and the mesio- machine was 0.995 with a 95% CI of 0.991 to 0.997.distal direction was shown horizontally; (2) in the Differences between our angulation measurementsmesiodistal (Fig 7, B) or faciolingual (Fig 7, C) slice and the coordinate measuring machines true angula-view, the transverse plane at the crown point level was tion values were calculated, and the 5-time mean differ-moved 20 mm apically; and (3) in the mesiodistal slice ences, the standard deviations of the mean differences,view (Fig 7, B), the faciolingual plane was moved 5 and the 95% condence intervals are shown in Table I,mm distally, and in the faciolingual slice view (Fig 7, along with the P values from the 1-sample t test forC), the mesiodistal plane was moved 10 mm lingually. each tooth. Five teeth (maxillary right lateral incisorAfter these parallel movements of the reference planes, and canine, maxillary left rst premolar, and mandibularthe 3-plane intersection would be at a point that was left canine and rst premolar) of the 28 teeth showed20 mm apical, 10 mm lingual, and 5 mm distal from statistically signicant differences between our angula-the crown point. The root point was digitized at this in- tion measurements and the coordinate measuringtersection. Trigonometric calculation should give the machines true values. The mean differences of ourtooth 14.04 of mesiodistal angulation and 26.57 of fa- 5-time measurements from the coordinate measuringciolingual inclination. For the maxillary right rst molar machines true values and the 95% condence intervalsand the mandibular left lateral incisor, the root points for these teeth were the following: maxillary right lateralwere placed mesially instead of distally to reect their incisor, 2.15 (95% CI, 1.439 -2.861 ); maxillary rightdistal angulation; for the 2 mandibular molars, the canine, 0.876 (95% CI, 0.585 -1.168 ); maxillary leftroot points were placed buccally instead of lingually to rst premolar, 1.098 (95% CI, 0.914 -1.282 ); mandib-reect their lingual crown inclinations. ular left canine, 1.97 (95% CI, 1.486 -2.454 ); and mandibular left rst premolar, 1.286 (95% CI, 0.97 -Statistical analysis 1.603 ). However, only the maxillary right lateral incisor To ensure that the measurement methodology de- measurement might be close to 2.5 for clinical signi-scribed above was reliable, the principal investigator cance. Faciolingual inclination measurements were not(H.T.) randomly chose 5 images from the 25 independent made with the coordinate measuring machine.July 2012 Vol 142 Issue 1 American Journal of Orthodontics and Dentofacial Orthopedics

7. Tong et al 139 Fig 6. A, Mesiodistal angulation was measured in the mesiodistal plane and dened as the angle formed by the projection of the tooths long axis (green line) and the red line that represented the faciolingual plane and the mesiodistal plane intersection; B, faciolingual inclination was measured in the faciolingual plane and dened as the angle formed by the projection of the tooths long axis (short green line) and the long green line that represented the mesiodistal plane and the faciolingual plane intersection. The blue line in A and B represented transverse planes that were parallel to the occlusal plane. For the teeth with known mesiodistal angulation and high-quality orthodontic nishing.22-25 Even a naturallyfaciolingual inclination values, measurements were also occurring normal occlusion might not be maintaineddone 5 times, and the intraclass correclation coefcient for life.26 However, orthodontists still strive to obtainwas 1 for both the angulation and the inclination. Dif- proper root positions for the best treatment outcome.ferences between measured values and the known values Since the use of preadjusted appliances does not guaran-were calculated, and the 5-time mean differences, stan- tee ideal root positions, most orthodontists take initial,dard deviations of the mean differences, and 95% con- progress, and nal panoramic radiographs to check fordence intervals are shown in Table II, along with the root alignment in addition to checking for pathology.P values from the 1-sample t test for each tooth. None This is because minor crown tipping that might haveof the 8 teeth for both angulation and inclination evaded visual inspection can be magnied in the mis-showed any statistically signicant difference between alignment of the roots and become easily detectable.13,14the measured and the known values. None of the teeth Until just recently, there have been only a few radio-had a 95% condence interval above 1 . graphic methods to check root position, each with some problems. To measure the mesiodistal angulation of each tooth accurately, the x-ray beam must be aimed atDISCUSSION the target tooth orthogonally. Periapical radiographs can- High-quality orthodontic treatment requires that all not be taken with an orthogonal view of multiple teeth onteeth are placed in their proper positions for a stable a curved dental arch at the same time. Panoramic x-rays,and functional occlusion and an esthetic appearance after although designed to follow the curvature of the dentaltreatment. The focus of the specialty of orthodontics has arch, might show orthogonal images of only a few teeth.27been mostly on the positions of the crowns of teeth, and Various studies have indicated its limitations, especially inlittle attention has been given to the roots.5-8 This is the canine and rst premolar areas.16-18 However, thebecause the positions of the roots rarely pose esthetic or American Board of Orthodontics still recommends thefunctional problems, since they are mostly invisible and use of panoramic x-rays in assessing the angulation ofaway from the occlusal contacts. Although the correct the roots.28 General root parallelism is required, andpositioning of the roots in the basal bone might reduce points are deducted if the roots of adjacent teeth arethe amount of relapse, however, research has indicated not parallel or come in contact with one another.that long-term stability cannot be expected even with Exceptions have been made for the canine areas recentlyAmerican Journal of Orthodontics and Dentofacial Orthopedics July 2012 Vol 142 Issue 1

8. 140 Tong et al Fig 7. Digitization of the root point for the known mesiodistal angulation and faciolingual inclination. A, Set the axial view at the maxillary archwire level, then move the transverse plane to the crown point level for the maxillary right rst premolar to be digitized, rotate the image in the axial view so that the faciolingual direction of the tooth was shown vertically and the mesiodistal direction was shown hori- zontally. B, The mesiodistal plane view showing that the transverse plane (blue) was moved 20 mm apically, and the faciolingual plane (red) was moved 5 mm distally from the crown point. C, The facio- lingual plane view showing that the mesiodistal plane (green) was moved 10 mm lingually. The inter- section of the transverse plane (blue), the mesiodistal plane (green), and the faciolingual plane (red) was where the root point was digitized. D, Diagram showing the 3-dimensional relationship: a, b, c, d, and g each at a corner of a cubic with each side 20 mm long. The center of the crown is placed at point c. cd points mesiodistally; cg points faciolingually, and cb points occlusogingivally; cb, 20 mm api- cal; be, 5 mm distal; bf, 10 mm lingual; r, designated root point; and yellow arrow, presumed long axis of the tooth. The mesiodistal angulation a and the faciolingual inclination b for the tooth were calculated to be 14.04 and the 26.57 , respectively.(www.americanboardortho.com). The American Board of obtained from CBCT scans have been shown to displayOrthodontics does not have special requirements for the dentofacial structures in a 1:1 ratio, and distortions,faciolingual inclination of the roots. if any, are clinically insignicant.29-31 Van Elslande The assessments of the root or the whole tooth angu- et al21 measured the angulation of the typodont teethlation and inclination really require that we see the from the panoramic-like images constructed fromwhole tooth in 3 dimensions. A coordinate measuring CBCT scans and compared them with the coordinatemachine has been used to measure the angulation16,21 measuring machines measurements. It was concludedand the inclination18 of typodont teeth directly. Al- that the constructed panoramic-like images were morethough considered a gold standard 3-dimensional mea- accurate than the conventional panoramic radiographssuring device, the coordinate measuring machine cannot in assessing tooth angulation. Although this new tech-be used on patients clinically, since direct contact of the nique takes care of the nonorthogonal problem of theroot apices of the patients teeth by the machines probe conventional panoramic radiograph, other problemsis not possible. In recent years, CBCT technology has arise: image formation is 1:1 only at the center of the se-been used in orthodontics, and the volumetric images lected arch trough, structures lingual to the centerJuly 2012 Vol 142 Issue 1 American Journal of Orthodontics and Dentofacial Orthopedics

9. Tong et al 141 Table I. Comparison between the USC mesiodistal an- Table II. Comparison between the USC mesiodistal gulation measurements and the coordinate measuring angulation and faciolingual inclination measurements machines true values of the typodont teeth and the known values of the typodont teeth Mean 95% CI 95% CI Tooth difference ( ) SD (upper and lower) P value* Mean difference ( ) SD (upper and lower) P value* UR 1 0.309 0.691 0.548 1.167 0.373 Mesiodistal angulation UR 2 2.150 0.573 2.861 1.439 0.001* UR 4 0.16 0.335 0.576 0.256 0.345 UR 3 0.876 0.235 1.168 0.585 0.001* UR 6 0.40 0.344 0.027 0.827 0.060 UR 4 0.339 0.300 0.034 0.711 0.065 UL 1 0.46 0.370 0.920 0.000 0.050 UR 5 0.677 0.647 0.126 1.480 0.079 UL 5 0.32 0.396 0.812 0.172 0.145 UR 6 0.455 0.295 0.088 0.821 0.026 LR 3 0.04 0.356 0.403 0.483 0.814 UR 7 0.667 0.336 1.084 0.249 0.011 LR 7 0.32 0.270 0.016 0.656 0.057 UL 1 0.733 0.618 0.035 1.500 0.057 LL 2 0.08 0.217 0.349 0.189 0.456 UL 2 0.365 0.730 0.541 1.272 0.326 LL 6 0.08 0.270 0.416 0.256 0.544 UL 3 0.572 0.377 1.040 0.104 0.027 Faciolingual inclination UL 4 1.098 0.148 0.914 1.282 0.001y UR 4 0.19 0.563 0.889 0.509 0.492 UL 5 0.112 0.321 0.287 0.510 0.479 UR 6 0.35 0.179 0.572 0.128 0.012 UL 6 0.571 0.397 0.078 1.065 0.032 UL 1 0.19 0.438 0.734 0.354 0.387 UL 7 0.457 0.313 0.846 0.069 0.031 UL 5 0.13 0.305 0.509 0.249 0.394 LR 1 0.295 0.415 0.810 0.220 0.187 LR 3 0.07 0.472 0.516 0.656 0.757 LR 2 1.300 0.650 2.107 0.494 0.011 LR 7 0.05 0.593 0.687 0.787 0.860 LR 3 1.356 0.432 1.893 0.819 0.002 LL 2 0.13 0.283 0.221 0.481 0.362 LR 4 1.018 0.390 0.534 1.502 0.004 LL 6 0.17 0.324 0.232 0.572 0.306 LR 5 0.045 0.311 0.431 0.342 0.764 U, Upper (maxillary); L, lower (mandibular); R, right; L, left; 1, cen- LR 6 0.484 0.329 0.892 0.076 0.030 tral incisor; 2, lateral incisor; 3, canine; 4, rst premolar; 5, second LR 7 0.247 0.540 0.918 0.424 0.365 premolar; 6, rst molar; 7, second molar. LL 1 0.216 0.374 0.249 0.681 0.266 *One-sample t test: level of a 5 0.05/8 5 0.00625 (Bonferroni ad- LL 2 0.819 0.901 1.938 0.300 0.112 justment for multiple comparisons). LL 3 1.970 0.390 2.454 1.486 0.001y LL 4 1.286 0.255 1.603 0.970 0.001y even though minor but statistically signicant differ- LL 5 0.023 0.500 0.598 0.644 0.924 LL 6 0.407 0.396 0.899 0.085 0.083 ences existed for some teeth between our measurements LL 7 0.144 0.606 0.608 0.896 0.623 and those of the machine. We were unable to explain U, Upper (maxillary); L, lower (mandibular); R, right; L, left; 1, cen- these differences, which appeared almost randomly tral incisor; 2, lateral incisor; 3, canine; 4, rst premolar; 5, second and never happened in the same teeth on the contralat- premolar; 6, rst molar; 7, second molar. eral side. Our measurements of selected typodont teeth *One-sample t test: level of a 5 0.05/28 5 0.001786 (Bonferroni with known angulation and inclination values were adjustment for multiple comparisons); yStatistically signicant dif- also highly accurate. A number of factors might have ference. contributed to this high precision in our methodology. Taking orthogonal views of the teeth and digitizationtrough are stretched, and structures facial to the center of the crown and root points at the intersection of 3trough are shrunk. The amount of distortion is also re- perpendicular planes simultaneously helped to ensurelated to the amount of faciolingual inclination, since precision; the special algorithms used to set up thea tooth with a large inclination would have its root far- tooth-specic coordinate system for automatic mea-ther from the center trough. As for measuring the facio- surements was another way to reduce human errors tolingual inclination of each tooth in 3 dimensions, no a minimum. Our study showed that the reliability andclinical tools have been available. With the help from the accuracy of our program were comparable to thoseDolphin, we have developed the USC root vector analysis of the coordinate measuring machines gold standard.program to measure each whole tooths mesiodistal an- This new tool can be used to measure the mesiodistalgulation and faciolingual inclination directly from the angulation and the faciolingual inclination of each wholeCBCT volumetric images. tooth in patients with normal occlusion, an important The test of our custom program with the typodont step toward establishing a clinical standard that couldteeth showed that our angulation and inclination mea- provide guidance for orthodontic nishing. Such stan-surements in Dolphin 3D were highly reproducible as in- dards might be helpful in designing new orthodontic ap-dicated by the high intraclass correlation coefcients. pliances that will no longer ignore the roots. Some newOur angulation measurements also compared well with treatment systems such as Invisalign (Align Technology,the coordinate measuring machines measurements, San Jose, Calif), SureSmile (Orametrix, Richardson, Tex),American Journal of Orthodontics and Dentofacial Orthopedics July 2012 Vol 142 Issue 1

10. 142 Tong et alIncognito (3M-Unitek, Monrovia, Calif), and Insignia 2. Andrews LF. Straight wire: the concept and appliance. San Diego,(Ormco, Orange, Calif) might benet from this as well Calif: K-W Publications; 1989. 3. Andrews LF. The diagnostic system: occlusal analysis. Dent Clinby being root conscious while setting up the teeth virtu- North Am 1976;20:671-90.ally before treatment. In addition, this new tool can also 4. Andrews LF. The straight-wire appliance. Br J Orthod 1979;6:be used to compare the outcomes of various treatment 125-43.modalities: eg, surgical treatment vs camouage, and ex- 5. Dewel BF. Clinical observations on axial inclination of teeth. Am Jtraction vs nonextraction. We can also compare the Orthod 1949;35:98-115. 6. Carlsson R, Ronnerrman A. Crown-root angles of upper central in-norms of different ethnic groups to set ethnic-specic cisors. Am J Orthod 1973;64:147-54.goals for patients with different backgrounds. 7. Bryant RM, Sadowsky PL, Hazelrig JB. Variability in three morpho- Our custom program has certain limitations. It can- logic features of the permanent maxillary central incisors. Am J Or-not be used for patients with malocclusions, since set- thod 1984;86:25-32.ting up the global coordinate system and digitization 8. Germane N, Bentley BE Jr, Isaacson RJ. Three biologic variables modifying faciolingual tooth angulation by straight-wire appli-of the maxillary and mandibular dental arches require ances. Am J Orthod Dentofacial Orthop 1989;96:312-9.the subjects to have normal or near normal occlusions. 9. Taylor NG, Cook PA. The reliability of positioning pre-adjustedModications to the program might need to be made brackets: an in vitro study. Br J Orthod 1991;19:25-34.if malocclusions, especially asymmetries, are present. 10. Balut N, Klapper L, Sandrik J, Bowman D. Variations in bracketAnother potential limitation might be that the placement in the preadjusted orthodontic appliance. Am J Orthod Dentofacial Orthop 1992;102:62-7.3-dimensional image quality of the patients teeth is 11. Armstrong D, Shen G, Petocz P, Darendeliler MA. A comparison ofnot as good as those of the stainless steel balls used accuracy in bracket positioning between two techniqueslocal-in this typodont study because of more complicated izing the centre of the clinical crown and measuring the distanceoverlapping of structures, restorations, patient move- from the incisal edge. Eur J Orthod 2007;29:430-6.ment, and so on. Radiation safety should always be 12. Suarez C, Vilar T. The effect of constant height bracket placement on marginal ridge leveling using digitized models. Eur J Orthoda concern. Exposing patients even to a slightly ele- 2009;32:100-5.vated amount of radiation might be justied only if 13. Mayoral G. Treatment results with light wires studied by pano-its use leads to better treatment; this still remains to ramic radiography. Am J Orthod 1982;81:489-97.be seen. However, the newer generation of CBCT de- 14. Ursi WJ, Almeida RR, Tavano O, Henriques JF. Assessment of me-vices has already shown promising improvement in im- siodistal axial inclination through panoramic radiography. J Clin Orthod 1990;24:166-73.age resolution with reduced radiation. 15. Lucchesi MV, Wood RE, Nortje CJ. Suitability of the panoramic ra- diograph for assessment of mesiodistal angulation of teeth in theCONCLUSIONS buccal segments of the mandible. Am J Orthod Dentofacial Orthop We developed the custom USC root vector analysis 1988;94:303-10. 16. McKee IW, Williamson PC, Lam EW, Heo G, Glover KE, Major PW. Theprogram to measure the mesiodistal angulation and accuracy of 4 panoramic units in the projection of mesiodistal tooththe faciolingual inclination of each whole tooth from angulations. Am J Orthod Dentofacial Orthop 2002;121:166-75.a typodont. 17. Owens AM, Johal A. Near-end of treatment panoramic radiograph in the assessment of mesiodistal root angulation. Angle Orthod1. Measurements made with the USC root vector anal- 2008;78:475-81. ysis program compared well with the gold standard 18. Garcia-Figueroa MA, Raboud DW, Lam EW, Heo G, Major PW. Ef- of the coordinate measuring machines measure- fect of buccolingual root angulation on the mesiodistal angulation ments. shown on panoramic radiographs. Am J Orthod Dentofacial Or- thop 2008;134:93-9.2. The USC root vector analysis program could also 19. Steiner CC. Cephalometrics in clinical practice. Angle Orthod 1959; measure accurately the teeth with known values of 29:8-29. angulation and inclination. 20. Knsel M, Jung K, Attin T, Attin R, Kubein-Meesenburg D, Gripp- o3. The USC root vector analysis program is valid and Rudolph L. Systematic evaluation of the features inuencing the ac- can be applied to patients clinically. curacy of third order measurements. Eur J Orthod 2009;31:547-55. 21. Van Elslande D, Heo G, Flores-Mir C, Carey J, Major PW. Accuracy of mesiodistal root angulation projected by cone-beam computed We thank Swann Liao for writing the custom USC tomographic panoramic-like images. Am J Orthod Dentofacial Or-root vector analysis program, Carlos Flores-Mir for a crit- thop 2010;137(4 Suppl):S94-9.ical review of this article, and Victoria Rodriguez for 22. Huggins D. The retention phase of treatment; the importance ofassistance with CBCT. root positioning as an aid to stability of the occlusion. Aust Orthod J 1994;13:100-5.REFERENCES 23. Ormiston JP, Huang GJ, Little RM, Decker JD, Seuk GD. Retrospec- tive analysis of long-term stable and unstable orthodontic treat- 1. Andrews LF. The six keys to normal occlusion. Am J Orthod 1972; ment outcomes. Am J Orthod Dentofacial Orthop 2005;128: 62:296-309. 568-74.July 2012 Vol 142 Issue 1 American Journal of Orthodontics and Dentofacial Orthopedics

11. Tong et al 14324. Nett BC, Huang GJ. Long-term posttreatment changes measured and panoramic radiographs. American Board of Orthodontics. by the American Board of Orthodontics objective grading system. Am J Orthod Dentofacial Orthop 1998;114:589-99. Am J Orthod Dentofacial Orthop 2005;127:444-50. 29. Lascala CA. Analysis of the accuracy of linear measurements ob-25. Driscoll-Gilliland J, Buschang PH, Behrents RG. An evaluation of tained by cone beam computed tomography (CBCT-NewTom). growth and stability in untreated and treated subjects. Am J Or- Dentomaxillofac Radiol 2004;33:291-4. thod Dentofacial Orthop 2001;120:588-97. 30. Hutchinson SY. Cone beam computed tomography panoramic im-26. Little RM. Stability and relapse of dental arch alignment. Br J Or- ages vs. traditional panoramic radiographs [thesis abstract]. Am J thod 1990;17:235-41. Orthod Dentofacial Orthop 2005;128:550.27. Goaz PW, White SC. Oral radiology: principles and interpretations. 31. Lagravre MO, Roger JC, Major PW. Three-dimensional accuracy e 2nd ed. St Louis: Mosby; 1987. 314-338. of measurements made with software on cone-beam computed28. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, tomography images. Am J Orthod Dentofacial Orthop 2008;134: Cangialosi TJ, et al. Objective grading system for dental casts 112-6.American Journal of Orthodontics and Dentofacial Orthopedics July 2012 Vol 142 Issue 1