A new method to mesure mesiodistal angulation and faciolingual with cbct
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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. Sameshima e 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 he basic objectives of orthodontic treatment are to obtain proper positions of all teeth by using vari- ous orthodontic appliances, to form a functional and stable occlusion, and to display the teeth in proper relationships to one another and in harmony with the maxillofacial hard and soft tissues after treatment. Six parameters describe each tooth location in 3-dimensional space. Three are positional (mesiodistal, faciolingual, and occlusogingival), and 3 are angular (mesiodistal angulation, faciolingual inclination, and axial rotation). Nearly half a century ago, Andrews 1,2 studied 120 patients with optimal occlusions and obtained the positional and angular norms for all teeth by measuring their crowns on the study models. Various types of preadjusted appliances that are used a Clinical assistant professor, Advanced Orthodontic Program, Herman Ostrow School of Dentistry, University of Southern California, Los Angeles. b Assistant professor, Clinical Dentistry, Division of Endodontics, Oral Surgery and Orthodontics, Herman Ostrow School of Dentistry, University of Southern California, Los Angeles. c Private practice, Calgary, Alberta, Canada. d Professor and chair, Department of Dentistry; head, School of Dentistry, Faculty of Medicine and Dentistry, University of Alberta, Edmonton, Alberta, Canada. e Associate professor and director, Advanced Orthodontic Program, Herman Ostrow School of Dentistry, University of Southern California, Los Angeles. The University of Southern California has filed a provisional patent application on our behalf to protect our potential intellectual right for developing the meth- odology used in this study to measure the mesiodistal angulation and the facio- lingual inclination of each whole tooth. Reprint requests to: Hongsheng Tong, 20360 Via Manresa, Yorba Linda, CA 92887; e-mail, [email protected]. Submitted, June 2011; revised and accepted, December 2011. 0889-5406/$36.00 Copyright Ó 2012 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2011.12.027 133 TECHNO BYTES
A new method to mesure mesiodistal angulation and faciolingual with cbct
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, [email protected]. 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
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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
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outcomes of various treatment 125-43.modalities: eg, surgical
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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,
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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,
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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
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generation of CBCT de- 14. Ursi WJ, Almeida RR, Tavano O, Henriques
JF. Assessment of me-vices has already shown promising improvement
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Clin Orthod 1990;24:166-73.age resolution with reduced radiation.
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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
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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.
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Kubein-Meesenburg D, Gripp- o3. The USC root vector analysis
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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
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