Visual Cephalometric Analysis Using Tetragon and Trigon

Tetragon: A VisualTetragon: A Visual
Cephalometric AnalysisCephalometric Analysis
www.indiandentalacademy.comwww.indiandentalacademy.com

ORTHODONTICS IS A TRENDY SCIENCE

This is mainly dueThis is mainly due
 : Better understanding of the subject: Better understanding of the subject
 Better research infrastructure and methodologyBetter research infrastructure and methodology
available now.available now.
 Urge to learn newUrge to learn new
 Urge to have quick and easy option.Urge to have quick and easy option.

What has sustained in orthodontics areWhat has sustained in orthodontics are
methods :methods :
1.} which are easy to perform1.} which are easy to perform
2.} less time consuming2.} less time consuming
3.} uncomplicated3.} uncomplicated
4.} and methods that really work4.} and methods that really work

The shift of focus from molars toThe shift of focus from molars to
incisors in treatment planningincisors in treatment planning

 ANGLE 1920: Orthodontics mainly focused onANGLE 1920: Orthodontics mainly focused on
the molar relationship as Class I , Class II, Classthe molar relationship as Class I , Class II, Class
III. Non extraction and expansionIII. Non extraction and expansion
 TWEED 1940: Emphasis on the lower incisors ,TWEED 1940: Emphasis on the lower incisors ,
extraction.extraction.
 Poor emphasis on the upper incisor position wasPoor emphasis on the upper incisor position was
mainly due to the lack of surgical option and lackmainly due to the lack of surgical option and lack
of functional therapy.of functional therapy.

 With the advent of the improved orthodontic andWith the advent of the improved orthodontic and
surgical techniques, the emphasis has shiftedsurgical techniques, the emphasis has shifted
more toward the upper incisormore toward the upper incisor
 The main aim of treatment planning is mainly toThe main aim of treatment planning is mainly to
envision the ideal position for the upper incisors.envision the ideal position for the upper incisors.
The other part of the treatment plan is thenThe other part of the treatment plan is then
decides how to to fit all other teeth subsequentlydecides how to to fit all other teeth subsequently
in relation to the ideal upper incisor position.in relation to the ideal upper incisor position.

In the present state the treament planning isIn the present state the treament planning is
divided in following four stagesdivided in following four stages
Stage I :Setting a Planned incisor positionStage I :Setting a Planned incisor position
for the upper incisors.for the upper incisors.
Stage II: lower incisors.Stage II: lower incisors.
Stage III: remaining lower teeth.Stage III: remaining lower teeth.
Stage iv : remaining upper teeth.Stage iv : remaining upper teeth.

 This has increased the importance ofThis has increased the importance of
evaluation of the inclination of the upperevaluation of the inclination of the upper
incisors and the lower incisorsincisors and the lower incisors
before treatmentbefore treatment
mid treatmentmid treatment
post treatmentpost treatment

Tetragon: A Visual Cephalometric AnalysisTetragon: A Visual Cephalometric Analysis
1.} Easy and quick away of assessing the1.} Easy and quick away of assessing the
malocculsion.malocculsion.
2.} Give a comprehensive picture in a short2.} Give a comprehensive picture in a short
time.time.
3.} Easy superimposition can help in3.} Easy superimposition can help in
assessing the inclination change ofassessing the inclination change of
anteriors.anteriors.

The analysis is based on twoThe analysis is based on two
geometric constructs:geometric constructs:
 THE TETRAGON :THE TETRAGON :a polygon thata polygon that
represents the maxillo-dento-mandibularrepresents the maxillo-dento-mandibular
complex.complex.
 THE TRIGONTHE TRIGON: a complementary triangle: a complementary triangle
situated above the Tetragonsituated above the Tetragon

THE TETRAGONTHE TETRAGON
 Is made up of the palatal plane, theIs made up of the palatal plane, the
mandibular plane, and the axes of themandibular plane, and the axes of the
maxillary and mandibular central incisors .maxillary and mandibular central incisors .

THE TRIGONTHE TRIGON
It is a complementary triangle situatedIt is a complementary triangle situated
above the Tetragon . It is formed betweenabove the Tetragon . It is formed between
thethe
a. the palatal plane (PNS-ANS)-a. the palatal plane (PNS-ANS)-
b. the pterygoorbital plane (Pt -Or)b. the pterygoorbital plane (Pt -Or)
c. pterygopalatal plane (Pt-PNS).c. pterygopalatal plane (Pt-PNS).

Construction of the TetragonConstruction of the Tetragon
The four angles of the tretragon that alwaysThe four angles of the tretragon that always
add up to 360°. In an "ideal" skeletal andadd up to 360°. In an "ideal" skeletal and
dental Class I patient, the four angles are asdental Class I patient, the four angles are as
follows:follows:
1. Intersection of the palatal plane and the1. Intersection of the palatal plane and the
axis of the maxillary central incisor (110°).axis of the maxillary central incisor (110°).
2. Intersection of the maxillary and mandibular2. Intersection of the maxillary and mandibular
central incisor planes (130°).central incisor planes (130°).

3. Intersection of the mandibular incisor axis3. Intersection of the mandibular incisor axis
and the mandibular plane (90°).and the mandibular plane (90°).
4. Intersection of the mandibular plane and4. Intersection of the mandibular plane and
the palatal plane (30°).the palatal plane (30°).

110 degree
130 degree
90 degree
30 degree

This Tetragoniometer, constructed from four protractors and fourThis Tetragoniometer, constructed from four protractors and four
sliding rulers, can be used to measure the Tetragon and to show howsliding rulers, can be used to measure the Tetragon and to show how
the various planes and angles will change when any one is modifiedthe various planes and angles will change when any one is modified

If any angle is modified, either by growth orIf any angle is modified, either by growth or
by orthodontic treatment, the angles of theby orthodontic treatment, the angles of the
Tetragon will change, but their sum will stillTetragon will change, but their sum will still
be 360°.be 360°.
If that is not the case, it means either thatIf that is not the case, it means either that
the tracing is inaccurate or that one or morethe tracing is inaccurate or that one or more
angles have been calculated incorrectlyangles have been calculated incorrectly

Construction of the TrigonConstruction of the Trigon
 In an ideal skeletal and dental Class IIn an ideal skeletal and dental Class I
occlusion , the angles of the Trigon are asocclusion , the angles of the Trigon are as
follows:follows:
1. Intersection of the Pt-Or plane and the Pt-PNS1. Intersection of the Pt-Or plane and the Pt-PNS
plane, called "Upper Pt" (85°).plane, called "Upper Pt" (85°).
2. Intersection of the Pt-PNS plane and the palatal2. Intersection of the Pt-PNS plane and the palatal
plane, called "Lower Pt" (87°).plane, called "Lower Pt" (87°).
3. Intersection of the Pt-Or plane and the palatal3. Intersection of the Pt-Or plane and the palatal
plane (8°).plane (8°).

Upper pt , 85 degree.
Lower pt , 87 degree
Angle between the palatal
plane and the pterygoid
plane- 8 degrees
In any patient, the three angles should always total 180°.In any patient, the three angles should always total 180°.

Together, the Tetragon and the TrigonTogether, the Tetragon and the Trigon
provide a clear picture of the position of theprovide a clear picture of the position of the
maxillo-dentomandibular structures withinmaxillo-dentomandibular structures within
the craniofacial complex.the craniofacial complex.

The inclination of the maxillary base toThe inclination of the maxillary base to
cranial base is a very important value .cranial base is a very important value .
It is traditionally measured in the RakosiIt is traditionally measured in the Rakosi
funtional analysis by measuring the anglefuntional analysis by measuring the angle
between the palatal plane and thebetween the palatal plane and the
perpedicular to the Frankfort’s horizontalperpedicular to the Frankfort’s horizontal
at the soft tissue nsionat the soft tissue nsion

The Tetragon along with the TrigonThe Tetragon along with the Trigon
togethertogether
provides an visual aid in the assessment ofprovides an visual aid in the assessment of
the inclination of the maxillary plane.the inclination of the maxillary plane.

 The inclination of the palatal plane isThe inclination of the palatal plane is
especially important in proper diagnosis ofespecially important in proper diagnosis of
cases of :cases of :
 open bite,open bite,
 deep overbite,deep overbite,
 increased lower facial heightincreased lower facial height
 reduced lower facial heightreduced lower facial height
 long faced patient etc.long faced patient etc.

The angle formed by theThe angle formed by the
intersection of the Pt-Orintersection of the Pt-Or
plane, which representsplane, which represents
the cranial base, and thethe cranial base, and the
palatal plane, whichpalatal plane, which
represents the base ofrepresents the base of
the maxilla, indicates thethe maxilla, indicates the
overall inclination of theoverall inclination of the
Tetragon.Tetragon.

• If the Trigon points anteriorly (toward
the face), it is positive, indicating that
the Tetragon is inclined upward or
counterclockwise .
• If it points posteriorly, it is negative,If it points posteriorly, it is negative,
indicating that the Tetragon is inclinedindicating that the Tetragon is inclined
anteriorly, away from the palatal plane,anteriorly, away from the palatal plane,
in a clockwise directionin a clockwise direction
•If the palatal plane and the Pt-Or planeIf the palatal plane and the Pt-Or plane
are parallel, their angulation will beare parallel, their angulation will be
neutral or 0°, but the sum of the twoneutral or 0°, but the sum of the two
remaining angles will still be 180remaining angles will still be 180

This visual cephalometric analysis can be aThis visual cephalometric analysis can be a
useful diagnostic tool foruseful diagnostic tool for
a.} treatment planning,a.} treatment planning,
b.} surgical preparation, andb.} surgical preparation, and
c.} evaluation of growth,c.} evaluation of growth,
d.} treatment progress, and post -treatmentd.} treatment progress, and post -treatment
results.results.

 The relationship of theThe relationship of the
palatal plane to the longpalatal plane to the long
axis of the maxillaryaxis of the maxillary
central incisors verycentral incisors very
important --the upperimportant --the upper
incisor palatal plane angleincisor palatal plane angle
(UIPPA).(UIPPA).
 This angle is just asThis angle is just as
important as the lowerimportant as the lower
incisor mandibular planeincisor mandibular plane
angle (LIMPA).angle (LIMPA).
UIPPA ANGLE

When the maxilla, represented by theWhen the maxilla, represented by the
palatal plane (ANS-PNS), is relocated, thepalatal plane (ANS-PNS), is relocated, the
angulation of the maxillary incisor shouldangulation of the maxillary incisor should
be in harmony with the palatal plane, justbe in harmony with the palatal plane, just
as the mandibular incisor is placed inas the mandibular incisor is placed in
relation to the mandibular plane.relation to the mandibular plane.

 Because the anterior planes of theBecause the anterior planes of the
Tetragon represent the axial inclinations ofTetragon represent the axial inclinations of
the maxillary and mandibular centralthe maxillary and mandibular central
incisors and their positions in space, theincisors and their positions in space, the
analysis will indicate whether they need toanalysis will indicate whether they need to
be intruded, extruded, or retracted.be intruded, extruded, or retracted.

According to the shape of the Tetragon , theAccording to the shape of the Tetragon , the
author has divided the malocculsion in 10 differentauthor has divided the malocculsion in 10 different
categories which are:categories which are:
 Class I malocclusionClass I malocclusion
 Class I malocclusion withClass I malocclusion with
bimaxillary protrusionbimaxillary protrusion
 Class II div 1 malocculsionClass II div 1 malocculsion
 Class II div 2 malocculsion.Class II div 2 malocculsion.
 Class III malocculsion due toClass III malocculsion due to
large mandible and retrusivelarge mandible and retrusive
maxillary incisors.maxillary incisors.
 Class III malocculsion withClass III malocculsion with
slightly retrusive maxilla , largeslightly retrusive maxilla , large
mandible and lingually inclinedmandible and lingually inclined
mandibular inciorsmandibular inciors
 Class II bases with parallelClass II bases with parallel
incisor inclinationsincisor inclinations
 Class I bases with parallelClass I bases with parallel
incisor inclinationsincisor inclinations
 Class III bases with parallelClass III bases with parallel
incisor inclinationincisor inclination
 Lingually inclined maxillary andLingually inclined maxillary and
mandibular incisorsmandibular incisors

Class I malocclusionClass I malocclusion
110 dgrees
130 degrees
90 degrees
30 degrees

130 degres
Class I malocculsion due to bimaxillary
protrusion
104 degrees
98 degrees

3. Class II, division 1 malocclusion
120 degrees
138 degrees
80 degrees

Class II, division 2 malocclusion.
90 degrees
165 degees
90 degrees
25 degrees

Class III malocclusion with
retrusive maxillary incisors and
large mandible
100 degrees
160 dgrees
70 degrees
30 degrees

Class III malocclusion with slightly retrusive
maxilla, large mandible, and lingually
inclined mandibular incisors.
.
110 degrees
155 degrees
60 degrees
35 degrees

With parallel incisor planes
90 degrees
180 degrees
60 degrees
30 degrees

with parallel incisor planes
90 degrees
180 degrees
60 degrees
30 degrees

Case with lingually inclined
maxillary and mandibular incisors.
80 degrees
190 degrees
60 degrees
30 degrees

The most important use of this analysis is thatThe most important use of this analysis is that
is a very quick and a visual aid in theis a very quick and a visual aid in the
comprehension of the treatment progression.comprehension of the treatment progression.
Especially the inclination change of the upperEspecially the inclination change of the upper
and lower incisors is very immediately notedand lower incisors is very immediately noted
by the superimpositions of the pre andby the superimpositions of the pre and
posttreament tetragon tracings.posttreament tetragon tracings.

For superimpositions the tretragon is oriented onFor superimpositions the tretragon is oriented on
the Pt-Or plane and registered on Ptthe Pt-Or plane and registered on Pt
The Pt-Or plane is a useful reference because ofThe Pt-Or plane is a useful reference because of
its stability and its proximity to the structuresits stability and its proximity to the structures
involved in orthodontic treatment.involved in orthodontic treatment.
The pterygomaxillary fossa, is formed byThe pterygomaxillary fossa, is formed by
osseous structures that house many importantosseous structures that house many important
nerves and blood vessels. It seems to remainnerves and blood vessels. It seems to remain
stable throughout the life of the individualstable throughout the life of the individual

A 13-year-old female
Class II, division 1
malocclusion .
The initial visual cephalometric
analysis indicated
1.} maxillary incisors were
protrusive relative to the palatal
plane (123°),
2.} the mandibular incisors
were retrusive relative to the
mandibular plane (80°).
The severe overjet was
confirmed by the tracing

 Because of the patient's age and tooth-Because of the patient's age and tooth-
size discrepancy, two maxillary firstsize discrepancy, two maxillary first
bicuspids and thebicuspids and the
 Mandibular right central incisor wereMandibular right central incisor were
extracted to achieve a functional Class IIextracted to achieve a functional Class II
molar and Class Imolar and Class I
 Canine relationship, and to eliminate theCanine relationship, and to eliminate the
overjet and crowding.overjet and crowding.

 Final cephalometricFinal cephalometric
analysis showed thatanalysis showed that
UI- PP was reducedUI- PP was reduced
considerably, toconsiderably, to
 103°, with an103°, with an
intrusion of 1mm.intrusion of 1mm.
The interincisalThe interincisal
angle was increasedangle was increased
by 4° due to theby 4° due to the
retraction ofretraction of
 the maxillary incisorsthe maxillary incisors
and the uprightingand the uprighting
and proclination ofand proclination of
the mandibularthe mandibular
incisors.incisors.

The tetragon superimpositions are very effective visual aids in the assessment
of the torque change brought out during the treatment
Even the amount the intrusion produced can be easily visualized by
superimposotions.

Modifications proposed by MBTModifications proposed by MBT

They recommend dividing the teragon againThey recommend dividing the teragon again
into two triangle.into two triangle.
The upper triangle and the lower trianlgeThe upper triangle and the lower trianlge

The upper triangle as the angles as followsThe upper triangle as the angles as follows
 Palatal plane to occlusal plane.Palatal plane to occlusal plane.
 Upper incisors to the palatal plane.Upper incisors to the palatal plane.
 Upper incisors to the occlusal plane.Upper incisors to the occlusal plane.
117 degrees
60 degrees
57/58 degree

The lower triangle has the following anglesThe lower triangle has the following angles
 Mandibular plane to the occlusal planeMandibular plane to the occlusal plane
 Lower incisors to the occusal plane.Lower incisors to the occusal plane.
 Lower incisors to the mandibular plane.Lower incisors to the mandibular plane.
64 degrees
18 degree
98 degrees

Steiner was the first to propose the different inclination of the incisors , depending
upon the amount of skeletal discrepancy.

Similarly in the MBT have described different inclination ofSimilarly in the MBT have described different inclination of
the upper and lower anteriors depending upon the skeletalthe upper and lower anteriors depending upon the skeletal
disprecancy as followsdisprecancy as follows
1.} Class I { arnett values}1.} Class I { arnett values}
2.} Class I{ Michigan normal}2.} Class I{ Michigan normal}
3.} Class I { low angle}3.} Class I { low angle}
4.} Class high angle4.} Class high angle
5.} Class II5.} Class II
6.} Class III6.} Class III

Visual Cephalometric Analysis Using Tetragon and Trigon

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