1. TECHNO BYTES
A new method to measure mesiodistal angulation
and faciolingual inclination of each whole tooth
with volumetric cone-beam computed
tomography images
Hongsheng Tong,a Reyes Enciso,b Dana Van Elslande,c Paul W. Major,d and Glenn T. Sameshimae
Los 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 fixed in position in a dry human skull. Stainless steel balls were fixed 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 define 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 modified to
generate known angulation and inclination values, and 5-time repeated measurements of these teeth were
compared with the known values. Results: Intraclass correlation coefficients 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 machine's true angulation values showed 5 teeth
with statistically significant differences. However, only the maxillary right lateral incisor showed a mean
difference that might exceed 2.5 for clinical significance. Comparisons between the 5-repeated
measurements of 8 teeth with known mesiodistal angulation and faciolingual inclination values showed no
statistically significant differences between the measured and the known values, and no measurement had
a 95% confidence 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 significant level, directly from the cone-beam computed tomography
volumetric images. (Am J Orthod Dentofacial Orthop 2012;142:133-43)
T
a
Clinical assistant professor, Advanced Orthodontic Program, Herman Ostrow he basic objectives of orthodontic treatment are to
School 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 functional
California, Los Angeles. and stable occlusion, and to display the teeth in proper
c
Private practice, Calgary, Alberta, Canada.
d
Professor and chair, Department of Dentistry; head, School of Dentistry, Faculty relationships to one another and in harmony with
of 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 in
Ostrow School of Dentistry, University of Southern California, Los Angeles.
The University of Southern California has filed 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 angular
odology used in this study to measure the mesiodistal angulation and the facio- (mesiodistal angulation, faciolingual inclination, and
lingual inclination of each whole tooth.
Reprint requests to: Hongsheng Tong, 20360 Via Manresa, Yorba Linda, CA axial rotation). Nearly half a century ago, Andrews1,2
92887; e-mail, drhstong@yahoo.com. studied 120 patients with optimal occlusions and
Submitted, June 2011; revised and accepted, December 2011. obtained the positional and angular norms for all teeth
0889-5406/$36.00
Copyright Ó 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 al
by most orthodontists today are, to a certain degree, 3-dimensional coordinate measuring machine's mea-
derived from the original straight-wire appliances he surements for a few teeth. The coordinate measuring
developed based on these crown norms.1-4 However, machine was also used in an earlier study by Garcia-
although 4 of the 6 parameters defining 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 gold
crowns might not provide clear indications for the standard coordinate measuring machine cannot be
angulation and the inclination of the whole teeth, used on patients, since the tip of the machine's probe
including the roots.5-8 Moreover, straight-wire tech- cannot be brought in contact with the patients’ root
niques rely heavily on precise bracket positioning during apices.
initial bonding, and yet orthodontists at various experi- We have collaborated with the Dolphin company
ence levels have found difficulties in accurately placing (Chatsworth, Calif) and developed the University of
brackets directly on patients' teeth or even indirectly Southern California (USC) root vector analysis program
on 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 each
mostly ignored. It is speculated that the roots might whole tooth using CBCT volumetric images. To test the
also need to be assessed to achieve ideal whole tooth validity of our methodology, we also collaborated with
angulation 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 typodont
initial, progress, and finishing stages of orthodontic CBCT images and the coordinate measuring machine's
treatment to diagnose, monitor, and finalize 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 not
reflect the true 3-dimensional teeth angulations because
the x-ray beam is not always orthogonal to the target MATERIAL AND METHODS
teeth.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 (Faro
the maxillary and mandibular central incisors.19,20 A International, Lake Mary, Fla). The typodont was based
posteroanterior cephalogram might capture the on a modification of the model previously reported by
faciolingual inclinations of a few molars, but the image McKee et al16 and Garcia-Figueroa et al.18 It consisted
quality 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) with
issue. Andrews1-3 did not measure the angulation and synthetic teeth in idealized occlusion from the second
the inclination of teeth from 2-dimensional x-rays but molar to the second molar. As shown by Van Elslande
from 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 mm
mography (CBCT) in orthodontics in recent years have in diameter, were placed at the approximate mesiodistal
allowed us see the roots of teeth in 3 dimensions as and faciolingual centers of the occlusal surfaces, and at
well. 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 of
3-dimensional CBCT images to measure the angulation each whole tooth with reference to the archwires that
of the typodont teeth. They compared these measure- were held in place on the plastic molds of the maxilla
ments with those taken directly from a coordinate mea- and the mandible at approximately the middle of the
suring machine, the gold standard 3-dimensional roots. A mesiodistal plane was created for each tooth
measuring device. They suggested that the constructed that was perpendicular to the horizontal (archwire)
images might be better than conventional panoramic ra- plane. This tooth-specific reference plane passed
diographs in assessing root angulations, although the through the mesial and distal interproximal points
measurements were still off significantly from the true marked on the archwires with crimpable stops. The
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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 first 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 tooth's 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 inclination
ments on 5 separate occasions, 5 days apart, and the in- of each whole tooth as shown below.
traclass correlation coefficient 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-
machine's angulation measurements. The coordinate phin 3D, a 3-dimensional global coordinate system was
measuring machine was reported by the manufacturer first generated for the proper orientation of the head and
to 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, and
within 0.031 . The average of the 5-time repeated coor- the axial plane, each perpendicular to the other 2 planes
dinate measuring machine's angulation measurements (Fig 1). The midsagittal plane evenly divided the right
were used as the true values. and the left halves of the skull; the coronal plane passed
The typodont teeth's mesiodistal angulations and fa- through the maxillary first molar buccal grooves on both
ciolingual inclinations were also measured by using the sides, and the axial plane was the archwire plane. Since
custom 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-dimensional
3G volume scanner (AFP, Elmsford, NY) was used ac- global coordinates: 1 saved for the maxilla, and 1 saved
cording to the manufacturer’s instructions as shown for the mandible.
also by Van Elslande et al.21 Twenty-five independent The digitization of each tooth's long axis was done in
images were obtained from separate CBCT scans for all 3 plane views, each perpendicular to the other 2
the previous study, and 5 of them were randomly views. Parallel movements of the sagittal, coronal, and
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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 tooth's crown point.
axial planes were made so that each would pass through archwire was digitized in the same way after the global
the 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-specific coordinate system for the
(Figs 2 and 3). A red dot was digitized at the intersection mesiodistal angulation and the faciolingual inclination
of the 3 perpendicular planes in 1 of the 3 plane views; it measurements was set up. Once the arch form was
would also appear automatically in the other 2 views. digitized, the custom USC root vector analysis program
The 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, each
from the mandibular left second molar to the mandibu- specific for only 1 tooth for its mesiodistal angulation
lar right second molar. Figure 4 shows all the white and faciolingual inclination measurements (Fig 5): the
stainless steel markers replaced by the red digitization transverse plane was the same axial plane at either the
points. The green lines represented the long axes of maxillary or the mandibular archwire level as in the
the 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 perpendicular
arch, the global coordinate saved for the maxillary teeth to the archwire; the short light blue line represented the
was restored first, and the maxillary archwire was digi- mesiodistal plane that also passed through each tooth
tized 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 faciolingual
the 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-specific coordinate.
ror image of the right side half arch to the left side, con- As shown in Figure 6, A, the mesiodistal angulation
structing a symmetrical arch form. The mandibular was measured from the projection of the tooth's long
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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 tooth's root point, and it was digitized (red dots).
axis on the mesiodistal plane to the vertical line formed
by the intersection of the mesiodistal and faciolingual
planes. If the root center was distal to the crown center,
the measurement would be positive; otherwise, it would
be negative. The faciolingual inclination was measured
from the projection of the tooth's long axis on the facio-
lingual plane to the vertical line formed by the same
intersection 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, it
would be negative.
At this point, the custom USC root vector analysis
program would use algorithms to measure the mesiodis-
tal angulation and the faciolingual inclination values for
all 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 by
podont images above were used again, except that the red digitization dots, and the teeth's long axes are shown
root points of the maxillary right first molar and first 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 defined
the mandibular left lateral incisor and first molar were through the following three steps (Fig 7): (1) in the axial
not digitized at the stainless steel balls representing slice view (Fig 7, A) at the crown point level, the image
American 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 coefficients for the mesiodistal an-
gulation and faciolingual inclination measurements
were calculated.
One-sample t tests were used to check for statistically
significant differences between our 5-time repeated me-
siodistal angulation measurements and the coordinate
measuring machine's 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 and
based on 4 points along the archwire relative to the follow- faciolingual inclination measurements with the given
ing tooth positions: midincisor, right canine, right second mesiodistal angulation and faciolingual inclination
premolar, and right second molar (yellow dots). The left values for each of the 8 selected teeth. The a level was
side half arch was the mirror image of the right side half. adjusted to 0.05/8 5 0.00625.
The tooth-specific coordinate system was based on the
arch form and the crown point of each tooth: the trans-
verse plane was the maxillary archwire plane; the faciolin- RESULTS
gual plane (long straight green line) passed each tooth The intraclass correlation coefficients for the 5-time
crown 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 analysis
blue line) was perpendicular to the faciolingual plane at
the crown point (dark blue dot) of each tooth.
in Dolphin 3D were 0.998 and 1.000, respectively, with
95% confidence intervals of 0.996 to 0.999 for the an-
gulations, and 0.999 to 1.000 for the inclinations. The
intraclass correlation coefficient for the 5 repeated an-
was rotated so that for the tooth to be digitized, the fa- gulation measurements with the coordinate measuring
ciolingual 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 measurements
mesiodistal (Fig 7, B) or faciolingual (Fig 7, C) slice and the coordinate measuring machine's 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% confidence 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 for
C), the mesiodistal plane was moved 10 mm lingually. each tooth. Five teeth (maxillary right lateral incisor
After these parallel movements of the reference planes, and canine, maxillary left first premolar, and mandibular
the 3-plane intersection would be at a point that was left canine and first premolar) of the 28 teeth showed
20 mm apical, 10 mm lingual, and 5 mm distal from statistically significant differences between our angula-
the crown point. The root point was digitized at this in- tion measurements and the coordinate measuring
tersection. Trigonometric calculation should give the machine's true values. The mean differences of our
tooth 14.04 of mesiodistal angulation and 26.57 of fa- 5-time measurements from the coordinate measuring
ciolingual inclination. For the maxillary right first molar machine's true values and the 95% confidence intervals
and the mandibular left lateral incisor, the root points for these teeth were the following: maxillary right lateral
were placed mesially instead of distally to reflect their incisor, 2.15 (95% CI, 1.439 -2.861 ); maxillary right
distal angulation; for the 2 mandibular molars, the canine, 0.876 (95% CI, 0.585 -1.168 ); maxillary left
root points were placed buccally instead of lingually to first premolar, 1.098 (95% CI, 0.914 -1.282 ); mandib-
reflect their lingual crown inclinations. ular left canine, 1.97 (95% CI, 1.486 -2.454 ); and
mandibular left first 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 signifi-
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.
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7. Tong et al 139
Fig 6. A, Mesiodistal angulation was measured in the mesiodistal plane and defined as the angle formed
by the projection of the tooth's 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 defined as the angle formed by the projection of the tooth's 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 finishing.22-25 Even a naturally
faciolingual inclination values, measurements were also occurring normal occlusion might not be maintained
done 5 times, and the intraclass correclation coefficient for life.26 However, orthodontists still strive to obtain
was 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 final panoramic radiographs to check for
fidence 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 have
of the 8 teeth for both angulation and inclination evaded visual inspection can be magnified in the mis-
showed any statistically significant difference between alignment of the roots and become easily detectable.13,14
the measured and the known values. None of the teeth Until just recently, there have been only a few radio-
had a 95% confidence 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 at
DISCUSSION the target tooth orthogonally. Periapical radiographs can-
High-quality orthodontic treatment requires that all not be taken with an orthogonal view of multiple teeth on
teeth 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 dental
treatment. The focus of the specialty of orthodontics has arch, might show orthogonal images of only a few teeth.27
been mostly on the positions of the crowns of teeth, and Various studies have indicated its limitations, especially in
little attention has been given to the roots.5-8 This is the canine and first premolar areas.16-18 However, the
because the positions of the roots rarely pose esthetic or American Board of Orthodontics still recommends the
functional problems, since they are mostly invisible and use of panoramic x-rays in assessing the angulation of
away from the occlusal contacts. Although the correct the roots.28 General root parallelism is required, and
positioning of the roots in the basal bone might reduce points are deducted if the roots of adjacent teeth are
the 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 recently
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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 first 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 display
Orthodontics 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 insignificant.29-31 Van Elslande
The assessments of the root or the whole tooth angu- et al21 measured the angulation of the typodont teeth
lation and inclination really require that we see the from the panoramic-like images constructed from
whole tooth in 3 dimensions. A coordinate measuring CBCT scans and compared them with the coordinate
machine has been used to measure the angulation16,21 measuring machine's measurements. It was concluded
and the inclination18 of typodont teeth directly. Al- that the constructed panoramic-like images were more
though considered a gold standard 3-dimensional mea- accurate than the conventional panoramic radiographs
suring 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 the
root apices of the patients’ teeth by the machine's probe conventional panoramic radiograph, other problems
is 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 center
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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
machine's 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 À0.548 1.167 0.373 Mesiodistal angulation
UR 2 À2.150 0.573 À2.861 À1.439 0.001* UR 4 À0.16 0.335 À0.576 0.256 0.345
UR 3 À0.876 0.235 À1.168 À0.585 0.001* UR 6 0.40 0.344 À0.027 0.827 0.060
UR 4 0.339 0.300 À0.034 0.711 0.065 UL 1 À0.46 0.370 À0.920 0.000 0.050
UR 5 0.677 0.647 À0.126 1.480 0.079 UL 5 À0.32 0.396 À0.812 0.172 0.145
UR 6 0.455 0.295 0.088 0.821 0.026 LR 3 0.04 0.356 À0.403 0.483 0.814
UR 7 À0.667 0.336 À1.084 À0.249 0.011 LR 7 0.32 0.270 À0.016 0.656 0.057
UL 1 0.733 0.618 À0.035 1.500 0.057 LL 2 À0.08 0.217 À0.349 0.189 0.456
UL 2 0.365 0.730 À0.541 1.272 0.326 LL 6 À0.08 0.270 À0.416 0.256 0.544
UL 3 À0.572 0.377 À1.040 À0.104 0.027 Faciolingual inclination
UL 4 1.098 0.148 0.914 1.282 0.001y UR 4 À0.19 0.563 À0.889 0.509 0.492
UL 5 0.112 0.321 À0.287 0.510 0.479 UR 6 À0.35 0.179 À0.572 À0.128 0.012
UL 6 0.571 0.397 0.078 1.065 0.032 UL 1 À0.19 0.438 À0.734 0.354 0.387
UL 7 À0.457 0.313 À0.846 À0.069 0.031 UL 5 À0.13 0.305 À0.509 0.249 0.394
LR 1 À0.295 0.415 À0.810 0.220 0.187 LR 3 0.07 0.472 À0.516 0.656 0.757
LR 2 À1.300 0.650 À2.107 À0.494 0.011 LR 7 0.05 0.593 À0.687 0.787 0.860
LR 3 À1.356 0.432 À1.893 À0.819 0.002 LL 2 0.13 0.283 À0.221 0.481 0.362
LR 4 1.018 0.390 0.534 1.502 0.004 LL 6 0.17 0.324 À0.232 0.572 0.306
LR 5 À0.045 0.311 À0.431 0.342 0.764
U, Upper (maxillary); L, lower (mandibular); R, right; L, left; 1, cen-
LR 6 À0.484 0.329 À0.892 À0.076 0.030
tral incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second
LR 7 À0.247 0.540 À0.918 0.424 0.365
premolar; 6, first molar; 7, second molar.
LL 1 0.216 0.374 À0.249 0.681 0.266
*One-sample t test: level of a 5 0.05/8 5 0.00625 (Bonferroni ad-
LL 2 À0.819 0.901 À1.938 0.300 0.112
justment for multiple comparisons).
LL 3 À1.970 0.390 À2.454 À1.486 0.001y
LL 4 À1.286 0.255 À1.603 À0.970 0.001y
even though minor but statistically significant differ-
LL 5 0.023 0.500 À0.598 0.644 0.924
LL 6 À0.407 0.396 À0.899 0.085 0.083 ences existed for some teeth between our measurements
LL 7 0.144 0.606 À0.608 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, first premolar; 5, second and never happened in the same teeth on the contralat-
premolar; 6, first 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 significant 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 digitization
trough are stretched, and structures facial to the center of the crown and root points at the intersection of 3
trough are shrunk. The amount of distortion is also re- perpendicular planes simultaneously helped to ensure
lated to the amount of faciolingual inclination, since precision; the special algorithms used to set up the
a tooth with a large inclination would have its root far- tooth-specific coordinate system for automatic mea-
ther from the center trough. As for measuring the facio- surements was another way to reduce human errors to
lingual inclination of each tooth in 3 dimensions, no a minimum. Our study showed that the reliability and
clinical tools have been available. With the help from the accuracy of our program were comparable to those
Dolphin, we have developed the USC root vector analysis of the coordinate measuring machine's gold standard.
program to measure each whole tooth's mesiodistal an- This new tool can be used to measure the mesiodistal
gulation and faciolingual inclination directly from the angulation and the faciolingual inclination of each whole
CBCT 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 could
teeth showed that our angulation and inclination mea- provide guidance for orthodontic finishing. 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 coefficients. pliances that will no longer ignore the roots. Some new
Our angulation measurements also compared well with treatment systems such as Invisalign (Align Technology,
the coordinate measuring machine's 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 al
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CONCLUSIONS 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. The
program to measure the mesiodistal angulation and
accuracy of 4 panoramic units in the projection of mesiodistal tooth
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We thank Swann Liao for writing the custom USC
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