TECHNO BYTES

Predicting tooth-size discrepancy: A new formulautilizing revised landmarks and 3-dimensionallaser scanning technology

Emil Bailey,a Gerald Nelson,b Arthur J. Miller,c Larry Andrews,d and Earl Johnsonb

New York, NY, and San Francisco and San Diego, Calif

aPrivabInterOrthoof CacProfeDentidPrivaThe aucts oReprinOrofaSan FSubm0889-Copyrhttp:/

574

Introduction: The goal of this study was to develop a more accurate formula to forecast tooth-sizediscrepancies in patients based on not only the size of the whole teeth but also functional archcomponents derived from normal cusp-fossa interdigitation that should be obtained as the final treatmentgoal. Methods: A total of 141 dental casts from Dr Larry Andrews' collection of “normal occlusions” that neverreceived orthodontic treatment were scanned with an Ortho Insight 3D Laser Scanner (Motion View Software,Chattanooga, Tenn). Individual tooth sizes and portions of tooth sizes were measured with the Motion ViewSoftware. For each set of models, potential tooth-size discrepancies were calculated by using both theoriginal Bolton analysis and the new Johnson/Bailey analysis developed by this team at the University ofCalifornia at San Francisco (UCSF). Six tooth-size discrepancy ratios were computed and included theBolton (2) and the new (4) Johnson/Bailey analysis ratios for the anterior arch component, posterior archcomponent, and overall ratio of the maxillary and mandibular arches. The Johnson/Bailey analysis utilizeddifferent landmarks and groups of teeth. It consequently divided the maxillary segment by the mandibularsegment, in contrast to the Bolton ratios, which divided the mandibular sums by the maxillary totals.Results: The Bolton anterior segment ratio ranged from 70.68 to 84.81, with a mean of 77.91 (SD, 2.43)(3.1%). The Bolton overall ratio ranged from 86.19 to 96.62, with a mean of 91.64 (SD, 61.74) (1.8%). TheJohnson/Bailey posterior discrepancy ratio ranged from 0.98 to 1.23, with a mean of 1.10 (SD, 60.04)(3.6%). Its anterior discrepancy ratio ranged from 0.91 to 1.14, with a mean of 1.03 (SD, 60.04) (3.9%).The Johnson/Bailey overall discrepancy ratio ranged from 0.98 to 1.15, with a mean of 1.06 (SD, 60.03)(2.8%). Conclusions: Two methods were used to forecast tooth-size discrepancies between opposingarches in a sample with clinically acceptable occlusions. The new approach provided more specific ratiosutilizing more clinically relevant functional arch components derived from dental cusp-fossa interdigitation.(Am J Orthod Dentofacial Orthop 2013;143:574-85)

Atooth-size discrepancy is defined as a lack ofharmony between the mesiodistal widths of in-dividual teeth or groups of teeth when related to

their functional counterparts of the opposing arch. Any

te practice, New York, NY.im chair and health science professor of clinical orthodontics, Division ofdontics, Department of Orofacial Sciences, School of Dentistry, Universitylifornia at San Francisco, San Francisco, Calif.ssor, Division of Orthodontics, Department of Orofacial Sciences, School ofstry, University of California at San Francisco, San Francisco, Calif.te practice, San Diego, Calif.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.t requests to: Earl Johnson, DDS, Division of Orthodontics, Department ofcial Sciences, School of Dentistry, University of California at San Francisco,rancisco, CA 94143-0438; e-mail, earl.johnson@ucsf.edu.itted, October 2011; revised and accepted, September 2012.5406/$36.00ight � 2013 by the American Association of Orthodontists./dx.doi.org/10.1016/j.ajodo.2012.09.022

discrepancy will result in either spacing in 1 arch ora compromise in functional relationships. To achievegood occlusion with the correct overbite and overjet,the maxillary and mandibular teeth must be propor-tional in size to each other. The mesiodistal widths ofteeth were first formally investigated by Black in1902.1 He measured large numbers of teeth and pro-duced tables of mean dimensions that are still used asreferences today.

Many authors have studied tooth widths in relationto occlusion after Black's investigation.2-15 Bolton16-21

to date has provided the best-known studies of tooth-size discrepancies in relation to orthodontic treatmentgoals. He evaluated tooth-size relationships of 55 sub-jects with excellent occlusions and developed 2 ratiosfor estimating tooth-size discrepancy.

The Bolton anterior ratio is the sum of all 6 anteriormandibular teeth (canines and incisors) divided by the

Fig 1. Ortho Insight 3D from Motion View Software showing the maxilla and the mandible after thelaser scan.

Table I. Definitions of the sites used in the Johnson/Bailey analysis

Site DefinitionCusp tip Apex (most incisal/occlusal point) of the crown as it lies on the axis of the toothVirtual occlusal plane Flat occlusal plane computed from all maxillary and mandibular cuspsMaxillary left posteriorsegment

Total distance between the maxillary left canine tip and the mesiobuccal cusp tip of the maxillary left first molar

Maxillary right posteriorsegment

Total distance between the maxillary right canine tip and the mesiobuccal cusp tip of the maxillary right first molar

Maxillary anterior segment Distance between the maxillary canine cusp tips including all incisorsMandibular left posteriorsegment

Distance between the mesial contact point of the mandibular left first premolar to the mesiobuccal groove betweenthe mesial and middle cusps of the mandibular left first molar

Mandibular right posteriorsegment

Distance between the mesial contact point of the mandibular right first premolar to the mesiobuccal groovebetween the mesial and middle cusps of the mandibular right first molar

Mandibular anteriorsegment

Distal contact point of the mandibular canine to the distal contact point of the contralateral canine

Bailey et al 575

sum of all 6 anterior maxillary teeth (canines and inci-sors), multiplied by 100.

The Bolton overall ratio is the sum of all 12 man-dibular teeth (first molars, premolars, canines, and in-cisors) divided by the sum of all 12 maxillary teeth(first molars, premolars, canines, and incisors), multi-plied by 100.

American Journal of Orthodontics and Dentofacial Orthoped

Currently, a tooth-size discrepancy is commonly as-sessed via the Bolton analysis. It allows the clinician togain foresight into the final fit of the maxillary and man-dibular arches before actually treating a patient, withoutresorting to a physical diagnostic setup (teeth set in waxto an ideal occlusion). A patient who did not match thesuggested Bolton ideal ratios was, most probably,

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Fig 2. The Bolton analysis is based on mesiodistal widths of teeth at contact points. The anteriorportion ismeasured from the distal surfaces of the canines; the posterior portion ismeasured from distalsurfaces of the first molars. The vertical maxillary landmark boundary lines (PMx, P

1Mx, AMx, and A1

Mx)are not in the same locations as the mandibular landmark boundary lines (PMn, P

1Mn, AMn, A

1Mn).

Mx, Maxillary;Mn, mandibular; P, distal borders of posterior segments; A, distal borders of the anteriorsegment; Ant, anterior; Post, posterior.

Fig 3. The Johnson/Bailey analysis is based on measurements of cusps, tips, and grooves as they re-late to the functional components of an ideal occlusion. Themaxillary anterior section is measured fromcanine tip to canine tip. The mandibular anterior segment is measured from the distal surface of thecanine to the distal surface of the opposing canine. Vertical lines A and A1 form the distal boundariesof the anterior section and the mesial boundaries of the posterior section. The maxillary posteriorboundaries are themesial cuspal tips of themaxillary first molars. Themandibular posterior boundariesare the mesiobuccal grooves of the mandibular first molars. Vertical lines P and P1 form the distalboundaries of the posterior section. Mx, Maxillary; Mn, mandibular; L, left; R, right; Ant, anterior;Post, posterior.

576 Bailey et al

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Fig 4. Measurements utilizing Ortho Insight 3D softwarein a 3D environment. A, Maxillary canine divided into 2portions. The mesial half is represented by the red lineas seen on the average occlusal plane, while the distalhalf is represented by the yellow line. B, Mandibular firstmolar divided into 2 portions. The red line representsthe mesial portion of the tooth bound by the mesiobuccalgroove and the contact point asmeasured on the averageocclusal plane. Perpendicular lines from the average oc-clusal plane used in producing measurements betweenlandmarks on teeth are represented by the blue and pur-ple arrows.

Table II. Definitions of the ratios used in the Johnson/Bailey analysis

Ratio DefinitionPosteriordiscrepancyratio

Dividing the maxillary posterior left and rightsegments by both mandibular posterior right andleft segments

Anteriordiscrepancyratio

Dividing the maxillary anterior segment by themandibular anterior segment

Overalldiscrepancyratio

Dividing the maxillary anterior segment and themaxillary posterior left and right segments by themandibular anterior segment and the mandibularposterior left and right segments

Fig 5. Ranking from least to most inA, the Bolton anteriorratio and B, the Bolton overall ratio for the 141 subjectsfrom the Andrews' collection.

Bailey et al 577

expected to have either a tooth-size excess or deficiencyin 1 dental arch. The amount of ratio deviation indicatesthe size of the future difference between the teeth in the2 arches.

It can be argued, however, that a flaw of the Boltonanalysis is that it does not take the functional relation-ships of individual teeth in centric occlusion into ac-count when selecting how to segment an arch intomeasurement components. Angle,22 in his classification

American Journal of Orthodontics and Dentofacial Orthoped

system (Class I, Class II, and Class III), relied on the de-scription of the relationships of cusps, fossae, contacts,and grooves in a normal occlusion. Andrews23 alsostressed these relationships in his “6 keys of occlusion.”The Bolton analysis does not take into account the

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Table III. Linear measurements of teeth and ratios ac-cording to the Bolton analysis on the first 25 of 141subjects

Subject

Maxilla3-3(mm)

Mandible3-3(mm)

Boltonanteriorratio

Maxilla6-6(mm)

Mandible6-6(mm)

Boltonoverallratio

1 45.55 35.94 78.90 91.27 82.42 90.302 48.34 36.80 76.13 96.55 87.60 90.733 49.89 38.43 77.03 100.88 90.42 89.634 45.54 36.74 80.68 93.94 85.44 90.955 46.71 36.93 79.06 96.49 88.89 92.126 48.86 40.00 81.87 99.76 92.36 92.587 49.72 38.17 76.77 99.87 90.37 90.498 46.60 34.71 74.48 93.50 86.06 92.049 46.86 36.50 77.89 93.62 86.43 92.32

10 45.93 35.65 77.62 95.79 85.20 88.9411 50.78 40.43 79.62 99.51 92.39 92.8412 49.08 37.98 77.38 99.15 89.70 90.4713 47.10 35.48 75.33 93.53 84.73 90.5914 46.40 36.06 77.72 93.09 86.70 93.1415 48.15 37.31 77.49 95.23 88.83 93.2816 52.39 40.34 77.00 102.07 95.81 93.8717 47.48 37.87 79.76 98.22 91.54 93.2018 48.42 39.32 81.21 99.12 93.12 93.9519 44.25 34.89 78.85 89.85 82.25 91.5420 46.85 36.83 78.61 96.61 88.37 91.4721 49.99 38.30 76.62 98.96 88.98 89.9222 52.47 39.41 75.11 102.92 94.47 91.7923 44.63 34.51 77.32 89.57 81.45 90.9324 47.24 38.24 80.95 97.80 91.04 93.0925 51.44 40.97 79.65 104.26 94.43 90.57

3-3, Intercanine width; 6-6, interfirst molar width.

578 Bailey et al

cusp/groove/fossa relationships. The Bolton anterioranalysis compares the total widths of all 6 anteriormaxillary teeth with the total widths of all 6 anteriormandibular teeth. This approach ignores how the teethfit and function. From the functional point of view,only the sum of the mesial half of both maxillary ca-nines and the widths of the 4 maxillary incisors shouldbe compared with their lower functional counterparts,which is the sum of the mandibular canines and inci-sors. The distal half of the maxillary canine functionswith the mandibular posterior teeth, not with the ante-rior teeth. From a functional view, the sum of the distalhalf of the maxillary canine, and the widths of bothmaxillary premolars and the mesial half of the mesio-buccal cusp of the maxillary first molars should becompared with the sum of the widths of the 2 mandib-ular premolars and the mesial portion of the mandibu-lar first molar (from its mesiobuccal groove forward).The fundamental difference between the landmarksof the Bolton analysis and the landmarks orthodontistsuse to assess and relate the functional fit of the max-illary and mandibular teeth creates a potential problem.This was pointed out in several other studies.9

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Furthermore, the Bolton analysis was derived froma small sample of 55 subjects with “excellent occlu-sions.”20 Numerous studies have outlined the inherentvariations in natural occlusion in populations. Smithet al13 stated that the parameters considered normalfor the Bolton index can only be applied to white femalesubjects, and that significant differences exist in theoverall, anterior, and posterior interarch ratios betweenwhite, black, and Hispanics. Some people suggest thatpopulation-specific standards are necessary for clinicalassessments. Other authors found that discrepancies,when using the Bolton index, are seen more frequentlyin patients with Class III malocclusions; this alluded tothe inherent tooth-size discrepancies between differentmalocclusion groups.2,24,25 A literature review byOthman and Harradine9 stated that the Bolton standarddeviation is probably not a good guide to the prevalenceof a clinically significant tooth-size discrepancy in thegeneral population.

MATERIAL AND METHODS

This was a retrospective study of a group of untreatedsubjects who had been evaluated and selected by DrLarry Andrews23 of San Diego, Calif, to represent an or-thodontically untreated population with “ideal occlu-sions.” Each subject was represented by unmountedstudy casts. No x-ray records were available.

The inclusion criteria required each subject to havecomplete dentition with or without third molars, no re-maining deciduous teeth, and a symmetric mandible.Excluded were subjects with any missing teeth, mandib-ular pathology, syndrome or disease that could affectmuscular skeletal function or development (eg, tempo-romandibular disorder or rheumatoid arthritis), obviousperiodontal disease, or previous orthodontic treatment.Subjects were not excluded based on molar relationshipor sagittal skeletal relationship, unless the deviationsfrom normal were due to mandibular problems. Onehundred forty-one subjects from more than 500 metthe inclusion criteria for this retrospective study. Allwere included in this study. Institutional review boardapproval from the University of California's Committeeon Human Research was not required, since the dentalmodels had no patient identifiers.

All 141 study models were scanned with a 3D laserscanner (Ortho Insight 3D Laser Scanner; Motion ViewSoftware, Chattanooga, Tenn). Each maxillary and man-dibular cast was scanned individually. In addition, 7two-dimensional photographs of each set of casts weretaken. The scanner scanned at a resolution of 35 to 40mm. The robotic table and scanning arms offered 3axes of motion and 6 degrees of freedom. There were3 line-generation lasers and 1 industrial-level camera

Journal of Orthodontics and Dentofacial Orthopedics

Fig 6. Differences between the calculated Bolton anterior ratio of each of the 141 subjects from theideal Bolton ratio, which is 91.30.

Bailey et al 579

to capture the laser data. The scanner had a maximumscan volume of 43 43 2 in. Scan time was 2.5 minutesfor each cast, although 1.5 minutes is now possible byusing the updated Ortho Insight 3D software.

The Ortho Insight 3D software was used to recon-struct the casts and measure tooth sizes and distanceson each virtual cast. The software was used to occludethe models, digitize the teeth, separate the teeth, detectlandmarks, establish facial axis, and measure the mesio-distal widths of each tooth (Fig 1; Table I). A custom al-gorithm to measure tooth widths by using specifiedlandmarks for both the Bolton index and the Johnson/Bailey index was designed by the investigator and codedby the lead engineer at Motion View Software. This algo-rithm was then debugged and verified by an investigator(E.B.). The measurement algorithm is described ingreater detail below.

Because of the lack of wax bites for the models in theAndrews' collection, an alternative method for occludingmodels was accomplished with the Ortho Insight 3Dsoftware. The steps for modeling articulation wereused as outlined by the Ortho Insight 3D Manual. Twoadditional steps were added by an investigator (E.B.).The “snap to fit” function was used to occlude themodels farther into maximum intercuspation. The finalsoftware-generated occlusion was verified and adjustedby comparing it with the 2-dimensional photographs ofthe articulated casts.

A tooth's mesiodistal width was defined as the maxi-mum side-distal distance between the anatomic contact

American Journal of Orthodontics and Dentofacial Orthoped

points when the teeth are aligned. These measurementswere made parallel to the virtual occlusal plane.21 Thecusp tip of the maxillary canine is usually considered theapex (most incisal point) of the crown. Since the datawere collected from cast models and roots were not avail-able as measurement landmarks, the cusp tip was definedaccording to the Andrews' guidelines.23 The mesiobuccalcusp tip of the maxillary molar was defined as the apex(most occlusal point) of the mesiobuccal cusp. The differ-ent segments were then defined for both the Bolton andJohnson/Bailey analyses (Figs 2 and 3). The mesiobuccalgroove of the mandibular first molar was the linguallyinclined vertical groove on the labial side, which dividesthe mesial cusp from the distal cusp.

A virtual occlusal plane was established as the “bestfit” by using all the cusp tips of the occluded models.It was refined and adjusted by optimizing its positionso that the sum of the squares of the distance thateach cusp deviated from the occlusal plane was mini-mized, much like an optimized average line on a scatter-gram. The resulting virtual occlusal plane was thesurface on which all distance measurements were made.

Every measurement landmark of interest had a lineprojected from it perpendicular to the virtual occlusalplane. All distance measurements were made from theseprojected intersection points on the virtual occlusalplane surface. Mesiodistal tooth width measurementswere made between intersection points of perpendicularprojections from the mesial and distal contact points tothe virtual occlusal plane.

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Fig 8. Box plot displays of the Bolton anterior ratio andthe Bolton overall ratio indicating the medians, ranges,and 25% and 75% quartiles.

Fig 7. Histogram distributions ofA, the Bolton anterior ra-tio and B, the Bolton overall ratio.

580 Bailey et al

Measurement of just a portion of the total mesiodis-tal tooth widths had to be handled differently. First,a line was constructed on the virtual occlusal planefrom the mesial contact point projection to the distalcontact point projection as described above. For themaxillary canines and molars, a second line was con-structed on the virtual occlusal plane, from the cusptip projection intersection point perpendicular to themesiodistal contact line (Fig 4, dotted red line). For themaxillary canines, this line served to separate the totalcanine width into anterior and posterior segments thatbelonged to the 2 separate functional segments. Forthe maxillary molars, this line divides the total con-structed mesiodistal distance into mesial and distal seg-ments. The mesial segment was added to the maxillarypremolar widths and the distal portion of the maxillarycanine creating the entire posterior segment.

For the mandibular first molars, a line was first con-structed on the virtual occlusal plane from the mesialcontact point projection to the distal contact point

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projection. A second line was projected from the buccalgroove perpendicular to and intersecting the virtual oc-clusal plane surface. Then, a third line was constructedfrom the buccal groove intersection point (on thevirtual occlusal plane) perpendicular to the molar'smesiodistal line on the virtual occlusal plane. This linesplits the molar's mesiodistal width into 2 distinct sec-tions. The mesial section is the portion of the mandibularmolar width to be included with the mandibular premo-lars in the calculation of the lower posterior segment.

The Johnson/Bailey formula divides the arches intofunctional segments, which are more closely related tothe static and functional occlusal goals that should beachieved after orthodontic treatment. We separatelymeasured and compared the functional components ofthe maxillary and mandibular arches via the anterior dis-crepancy ratio and the posterior discrepancy ratio. Theoverall discrepancy ratio is derived by dividing the sumof the 3 maxillary segments by the sum of the 3 mandib-ular segments (Table II).

The posterior discrepancy ratio-left is determined asfollows: maxillary posterior segment-left divided bymandibular posterior segment-left.

The posterior discrepancy ratio-right is determined asfollows: maxillary posterior segment-right divided bymandibular posterior segment-right.

The anterior discrepancy ratio is the maxillary ante-rior segment divided by mandibular anterior segment.

The overall discrepancy ratio is determined as fol-lows: maxillary posterior segment-left plus posteriorsegment-right plus anterior segment divided by man-dibular posterior segment-left plus posterior segment-right plus anterior segment.

Note that the Johnson/Bailey maxillary arch sums aredivided by the mandibular arch sums. The Bolton

Journal of Orthodontics and Dentofacial Orthopedics

Fig 9. Ranking from the least to the most in the Johnson/Bailey analysis posterior discrepancy ratioson A, the left side; B, the right side; C, the Johnson/Bailey analysis anterior discrepancy ratio; and D,the Johnson/Bailey analysis overall discrepancy ratio.

Bailey et al 581

analysis does the opposite. The ratio 1.00 equals parity.Ratios higher than 1.00 usually indicate a maxillary seg-ment excess or a mandibular segment deficiency.

Before manual verification in single-tooth mode, theteeth were digitized and virtually separated, and land-marks were identified according to the steps describedin the Ortho Insight 3D manual. Landmarks were thenmanually verified twice, in single-tooth mode, on everytooth on everymodel. Distanceswere calculated automat-ically by using our modified Ortho Insight 3D software.The individual toothmeasurementsweremeasuredwithin0.01 mm by using the digitized models and Ortho Insight3D software. To test reliability, measurements were re-peated 3 times on 5 casts by 5 investigators, and the co-efficient of variation (standard deviation/mean) wasa mean of 0.02, indicating that having an investigatoruse the Ortho Insight 3D system with the same dentalmodels produces highly reproducible numbers related to

American Journal of Orthodontics and Dentofacial Orthoped

the width of the dentition and with a coefficient of varia-tionmuch smaller than that demonstrated with the actualanalysis of the sample.

Statistical analysis

The individual tooth measurements were used in theBolton anterior and overall ratios as well as the Johnson/Bailey posterior discrepancy ratio, anterior discrepancyratio, and the overall discrepancy ratio. The means, me-dians, standard deviations, ranges, and 25 and 75 per-centiles were determined for the 6 ratios. Thehistogram distribution and ranking of the measurementsin each ratio were also calculated for this sample.

RESULTS

The range of the Bolton analysis for the anterior ratiowas 70.90 to 84.82, with a mean of 77.91 (SD, 62.43).

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Table IV. Segment measurements with posterior, anterior, and overall discrepancy ratios for the first 25 subjects

Subject

Lt MxPS

(mm)

Rt MxPS

(mm)

MxAS(mm)

Lt MnPS

(mm)

Rt MnPS

(mm)

MnAS(mm)

Lt posteriordiscrepancy

ratio

Rt posteriordiscrepancy

ratio

Anteriordiscrepancy

ratio

MaxillaPS 1 AS(mm)

MandiblePS 1 AS(mm)

Overalldiscrepancy

ratio1 19.72 18.75 37.53 17.46 17.17 35.85 1.13 1.09 1.05 76.00 70.48 1.082 20.48 20.91 39.64 18.99 18.40 36.86 1.08 1.14 1.08 81.03 74.25 1.093 22.39 22.83 40.57 19.38 19.70 38.14 1.16 1.16 1.06 85.79 77.22 1.114 21.32 21.71 35.89 19.06 19.14 36.87 1.12 1.13 0.97 78.92 75.07 1.055 22.35 20.42 37.55 19.04 19.19 36.60 1.17 1.06 1.03 80.32 74.83 1.076 22.51 22.17 38.80 20.09 20.77 39.88 1.12 1.07 0.97 83.48 80.74 1.037 22.43 22.43 36.86 19.16 19.65 38.17 1.17 1.14 0.97 81.72 76.98 1.068 20.32 21.69 36.38 19.02 18.52 34.70 1.07 1.17 1.05 78.39 72.24 1.099 20.17 20.58 38.13 18.70 18.35 36.32 1.08 1.12 1.05 78.88 73.37 1.08

10 21.24 21.13 35.88 18.78 18.99 35.74 1.13 1.11 1.00 78.25 73.51 1.0611 21.12 20.78 41.79 19.30 18.79 40.16 1.09 1.11 1.04 83.69 78.25 1.0712 21.76 22.29 37.67 18.90 18.32 37.93 1.15 1.22 0.99 81.72 75.15 1.0913 20.00 20.70 37.80 18.67 18.34 35.53 1.07 1.13 1.06 78.50 72.54 1.0814 20.32 21.11 37.09 18.86 18.20 36.25 1.08 1.16 1.02 78.52 73.31 1.0715 19.98 20.59 39.09 19.03 18.71 37.32 1.05 1.10 1.05 79.66 75.06 1.0616 21.34 22.06 43.06 20.53 20.74 40.27 1.04 1.06 1.07 86.46 81.54 1.0617 22.39 21.88 37.46 19.74 19.30 38.01 1.13 1.13 0.99 81.73 77.05 1.0618 20.77 22.23 38.24 19.67 19.44 39.36 1.06 1.14 0.97 81.24 78.47 1.0419 18.75 19.35 36.65 17.88 17.24 34.78 1.05 1.12 1.05 74.75 69.90 1.0720 20.84 21.65 36.63 20.32 19.67 36.89 1.03 1.10 0.99 79.12 76.88 1.0321 21.85 20.61 40.42 19.48 19.44 38.11 1.12 1.06 1.06 82.88 77.03 1.0822 22.26 22.65 42.24 19.97 20.37 39.38 1.11 1.11 1.07 87.15 79.72 1.0923 20.11 20.05 34.86 17.11 17.61 34.51 1.18 1.14 1.01 75.02 69.23 1.0824 22.75 21.88 37.48 19.74 19.33 38.14 1.15 1.13 0.98 82.11 77.21 1.0625 21.32 23.57 42.59 20.80 20.54 40.97 1.03 1.15 1.04 87.48 82.31 1.06

Lt, Left; Rt, right; Mx, maxillary; Mn, mandibular; PS, posterior segment; AS, anterior segment.

582 Bailey et al

The overall ratio varied from 86.19 to 96.62 with a meanof 91.64 (SD,61.74) (Fig 5; Table III). The difference ofthe overall ratio for each subject varied positively andnegatively with as much as a 5-mm difference betweenindividual patients and the ideal Bolton ratio (Fig 6).The Bolton anterior and overall ratio distributions arerepresented in Figure 7, and the central tendency isshown in the box plot (Fig 8).

The Johnson/Bailey analysis posterior segment discrep-ancy ratio ranged from 0.98 to 1.23 with a mean of 1.10(SD, 60.04) for the entire population of 141 subjectsfrom Andrews' study23 (Fig 9; Table IV). The anterior seg-ment discrepancy ratio ranged from 0.91 to 1.14 witha mean of 1.03 (SD, 60.04). The overall ratio varied from0.98 to 1.15 with a mean of 1.06 (SD, 60.03). The histo-gram distributions are shown in Figure 10. The anteriorand overall discrepancy ratios could exceed 1.00. Thebox-plot analysis indicated the central tendency and rangeof the data (Fig 11; Table V).

DISCUSSION

Andrews' sample has been accepted worldwide as anexample of subjects with untreated ideal occlusions.26,27

The 6 keys of occlusion that he derived from this sampleare now the gold standard of orthodontic treatment

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outcomes. His sample evaluated in our project, bydefinition, should not have a Bolton discrepancy. Ourdata show that the Bolton analysis produces a widerange of numbers when applied to these modelsdefined originally as ideal. Our goal was to use morefunctionally related landmarks for the Johnson/Baileyratios. Orthodontic clinicians want to know what thetooth sizes should be to achieve an ideal occlusionwith Class I molar and canine relationshipsdemonstrating normal overbite and overjet. Anaccurate ratio system should forecast whether therewill be a discrepancy and help to determine whethercompensating interproximal reduction or dentalmesiodistal buildup is indicated.

The proposed Johnson/Bailey analysis creates the an-terior and posterior segment ratios based on cusp-fossarelationships that orthodontists seek for an ideal treat-ment result. The goal is to be able to detect an abnormalrelationship between the teeth of the 2 arches early in or-thodontic treatment or to decide early in treatment onthe size of any replacement teeth. If the maxillary poste-rior segment to the mandibular posterior segment ex-ceeds 1.00, then the maxillary canine might be fartherforward than is normally accepted. This approach pro-vides a more realistic way to relate the maxillary and

Journal of Orthodontics and Dentofacial Orthopedics

Fig 10. Histogram distributions of the Johnson/Bailey posterior discrepancy ratios on A, the left side;B, the right side; C, the anterior discrepancy ratio; and D, the overall discrepancy ratio.

Bailey et al 583

mandibular teeth and forecast tooth-size discrepanciesafter treatment with an ideal Class I occlusion. Our pro-posed method of evaluating discrepancies between pre-treatment tooth sizes and the tooth sizes required forideal occlusion is more clinically appropriate than theBolton analysis.

The original appeal of the Bolton analysis was thatan orthodontist could save time by applying its math-ematical formula and avoid a conventional mechanicaldiagnostic setup. Many clinicians have used this ap-proach for the past 50 years. Presently, we can access3-dimensional virtual environment tools, which, as wehave shown, can quickly and more accurately deter-mine a tooth-size discrepancy.28-40 One canimmediately apply this information to assess possibleavenues of orthodontic treatment as they pertain tothe final treatment outcome. Using an algorithmdeveloped in the Motion View Software, which usesthe ideal ratios derived from Andrews' models,

American Journal of Orthodontics and Dentofacial Orthoped

a clinician can assess tooth-size discrepancies ina matter of seconds on 3-dimensional models in a vir-tual computer-aided design and manufacturing envi-ronment. Future work is also needed to testa sample of known tooth-size discrepancies. Thiscan be done retrospectively using finished patientswith clinically determined discrepancies. Such workshould also be expanded to include a broader rangeof subjects from the general population, representingdifferent molar classifications, sexes, and culturalgroups.

CONCLUSIONS

When we applied the Bolton analysis to 141 dentalcasts representing ideal untreated occlusions, wefound a wide range in the Bolton ratios. A new for-mula, the Johnson/Bailey analysis, was developedfrom the same database, based on cusp/fossa/grooverelationships to predict the expected future interarch

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Table V. Means, standard deviations, and minimumand maximum values of the 5 ratios used in the 2 ap-proaches of the Bolton and Johnson/Bailey analyses

Mean SD

Coefficientof

variation Minimum MaximumBolton anteriorsegment ratio

77.91 2.43 3.1% 70.68 84.81

Bolton overall ratio 91.64 1.74 1.8% 86.19 96.62Johnson/Baileyposteriordiscrepancy ratio

1.10 0.04 3.6% 0.98 1.23

Johnson/Baileyanteriordiscrepancy ratio

1.03 0.04 3.9% 0.91 1.14

Johnson/Baileyoveralldiscrepancy ratio

1.06 0.03 2.8% 0.98 1.15

Fig 11. Box plot displays of the left and right Johnson/Bailey posterior discrepancy ratios, the anterior discrep-ancy ratio, and the overall discrepancy ratio, indicatingthe medians, ranges, and 25% and 75% quartiles.MxPS, Maxillary posterior segment; MnPS, mandibularposterior segment; MxAs, maxillary anterior segment;ManAS, mandibular anterior segment.

584 Bailey et al

tooth-size discrepancies as they relate to an ideal ClassI occlusion postorthodontic treatment. A method ofdetecting a posterior tooth-size discrepancy was in-troduced with the use of the Johnson/Bailey posteriorratio. The new analysis was developed by using3-dimensional laser scanning equipment and soft-ware, which allowed rapid evaluation of the dentalcasts in 3-dimensional virtual space and provideda method to apply the new formula.

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