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GROWTH ROTATION
Contents
Introduction
Concepts related to rotation
Enlow’s counterpart principle
Rotational terminology
- Matrix rotation
- Intramatrix rotation
- Total rotation
Types of rotation
Rotation of maxilla
Methods of prediction of growth rotation
Structural sign as prediction of growth rotation
Implication of mandibular rotation in orthodontic treatment
Association between facial height development and mandibular growth rotation
Variations in treatment plan
Conclusion
INTRODUCTION
ROTATION
The angular movement of one rigid body relative to the other
Ex; a wheel may rotate with reference to its supporting structures and frame work.
Odegard (1970) described the rotation as a change in the orientation that can occur between the implant line and the lower border of the mandible
This concept was elaborated by Lavergne & Gasson in 1970 as ‘positional rotation’ changes in the orientation of the mandible relative to the cranial base and ‘morphologic rotation’ changes in the shape of the mandible.
Later BJORK (1950) has shown that the direction of facial growth is curved, giving a rotational effect.
GROWTH ROTATION is most obvious in MANDIBLE
IN MAXILLA -- small and completely masked by surface remodeling.
Why RAMUS-CORPUS rotation occurs?
1.To compensate the normal growth process of other structures like middle cranial fossa, spheno-occipital synchondrosis, midface region. MANDIBLE has to grow, as well rotate according to the structures.
2. To prevent the change in occlusal relationship or to maintain the occlusal relationship.
HOW THIS HAPPENS?
DUE TO REMODELLING AND DISPLACEMENT
Changes in midface region or nasomaxillary complex (forward and downward) vertical length of ramus increases antero-posterior length of ramus also increases, helps in 3rd molar eruption.
Corpus is COUNTERPART of maxillary arch. Mandibular corpus gets adjusted to maxillary arch. Same time mandibular condyle is pushed by middle cranial fossa.
Rotation in corpus.
Gonial angle must change in order to prevent in occlusal relationship.
ENLOW’S COUNTERPART PRINCIPLE
GROWTH OF ANY GIVEN FACIAL OR
CRANIAL PART RELATES SPECIFICALLY TO OTHER STRUCTURAL AND GEOMETRIC COUNTERPARTS IN THE FACE AND CRANIUM.
DIFFERENT PARTS &THEIR COUNTERPARTS ARE:-
1.Nasomaxillary complex relates to the anterior cranial fossa.
2.Horizontal dimension of the pharyngeal space relates to the middle cranial fossa.
3.Middle cranial fossa and ramus are counterpart.
4.Maxillary and mandibular arches are mutual counterparts.
5.Bony maxilla and corpus of mandible are counterparts.
6.Maxilary tuberosity and lingual tuberosity are counterparts.
These structures develop MORPHOLOGIC COMPENSATION].
Facial development is a basic and important biologic concept.
Functional and structural balance
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Growth rotations in relation to Orthodontics.
Determining rotational growth changes
Mandibular rotations
Clinical significance of Rotation :
Relationship between Condylar growth and Rotations
Relationship between Dentition and Rotations
Relationship between Chin position and Rotations
Prediction of Rotation
Prediction by the structural method
Reliability of prediction
Maxillary rotations
Maxillary Rotational Patterns:
Cranial base rotations
Interrelationship between rotation of skeletal components
Orthodontics and Rotation
Treatment protocol
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2. INDIAN DENTAL ACADEMY
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3. CONTENTS
•
•
•
•
•
•
•
•
•
•
INTRODUCTION
REVIEW OF LITERATURE
FACIAL ROTATIONS
MANDIBULAR ROTATIONS
ROTATION OF MANDIBLE DURING GROWTH
PREDICTION OF MANDIBULAR GROWTH ROTATION
PRINCIPLE OF ARCIAL GROWTH OF MANDIBLE
MAXILLARY ROTATIONS
MUTUAL ROTATION OF BOTH JAWS
COMPARISON OF SHORTFACE AND LONGFACE
CLINICAL IMPLICATIONS OF JAW ROTATIONS
CONCLUSION
BIBILOGRAPHY
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4. INTRODUCTION
An intensive study of the growth of the human head will
inevitably lead to the realization that it involves the most
complicated anatomical complex in all creation.The inter
relationships are infinite and the cause and effect of these
relationship almost cannot be estimated.
The phrase growth rotation was introduced in 1955 by
Bjork. In reporting a case states the lowering of the
mandible during growth was “considerably greater
posteriorly than anteriorly, Bjork drew attention to what he
called the mandibular rotation”.
This was based on the fact that Bjork metallic implants,
had given him precise markers from which he could infer
the sites and amount of growth and resorption in a given
mandible.
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5. INTRODUCTION
By superimposing two consecutive tracings of the childs
mandible registered on the implants, the image of the older
mandible appeared to have rotated during the intervening
period relative to its original shape.
Orthodontic and orthopedic treatment can change the
facial growth direction, various terms have been used to
describe how orthodontic and orthopedic treatment affects
the growth.
These include stimulation, inhibition, retardation,
redirection, correction and guidance. The use of such
terminology indicates that growth manipulation is possible.
Hence a thorough knowledge regarding the craniofacial
morphogenesis and mutual jaw relationship and rotational
patterns is essential for diagnosis, treatment planning and
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correction of the malocclusion.
6. REVIEW OF LITERATURE
• Lande in 1952 - Pointed that lower border of mandible on average becomes
less steeply inclined with growth.
• Bjork in 1955 –Drew attention to mandibular growth rotation as a feature of
normal facial growth,& he done metallic implant study & demonstrated the much
greater underlying mandibular rotation that was masked by periosteal
remodelling at the lower border.
• F. F. Schudy in 1965 – studied growth changes which produce rotation of the
mandible and depending on the vertical growth and horizontal growth (condylar
growth) he classified rotation in to clockwise rotation and counterclockwise
rotation.
•Bjork in 1969- Discussed different direction of rotation of the mandibular
implant line & the relation of these to mandibular form.
•Odegard in 1970 –Discribed as a rotation, the change in orientation that occur
b/w the implant line & the lower border of the mandible.
•Bjork & Skieller in 1972 –Demonstrated that dentoalveolar adaptation in
response to mandibular growth rotation could result in occlusal change such as
late lower incisor crowding.
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7. REVIEW OF LITERATURE
• Lavergne & Gasson in 1977 - Discribed “positional rotation” change in the
orientation of the mandible relative to the cranial base, & “morphogenetic
rotations” change in the shape of the mandible.
• Bjork & Skieller in 1983 – Rotation of invarient structure in the mandible
( implant /natural reference structure) relative to the cranial base was termed
“total rotation”.
Rotation of the lower border of the mandible relative to the cranial base
was “matrix rotation” and change in the orientation of implant line in the
mandible relative to the lower border was “intramatrix rotation”.
• Dibbets in 1985 – Introdused the term “ counter balancing rotation ‘ for
what is essentially “intramatrix rotation” with the implication that the
changes discribed by this term represent adjustments of the contribution of
condylar growth to overall growth in the length of the mandible.
• Rune et al in 1987 – reviewed the terms introdused by Bjork & Skeiller in
1983 & remarked that in the context of intramatrix rotation Bjork & Skeiller’s
interpritation of the findings seems to have no relation to the general
concepts of craniofacial bone growth.
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8. FACIAL ROTATIONS
• The expansion of the frontal and particularly, the
temporal lobes of the cerebrum relates to a rotation of
the orbits towards the midline. The eyes come closer
together.
• Two separate axes of orbital rotation are thus
associated with the massive expansion of the
cerebrum. One displaces the orbits vertically, and the
other carries them horizontally in medial directions into
a binocular position.
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9. • The enlarged human cerebrum also causes a
downward rotational displacement of the olfactory
bulbs. In all other mammals, they are nearly upright or
obliquely aligned, depending on the size and
configaration of the frontal lobes.
• In man , the bulbs have been rotated into horizontal
positions by the cerebrum. This is a significant factor in
the basic design of the human face.
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10. •
The plane of the nasomaxillary region is thereby approximately
perpendicular to the plane of the olfactory bulbs. This is a major
anatomic and functional relationship involved in the basic plan of the
face in any mammal.
•
As the bulbs become rotated progressively from a vertical
position to a horizontal one because of increase in brain size or
because of its shape (1,2,3), the whole face is similarly rotated from
a horizontal to a vertical plane(1a,2a,3a). Or stated another way,the
face is rotated down by the expanded anterior cranial floor as it
rotates downward as result of the enlargement of the frontal lobes.
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11. • The maxilla of most mammals has a triangular
configuration. In man, it is uniquely rectangular. This is
caused by a rotation of the occlusion into a horizontal
plane to adapt to the vertical rotation of the whole
midface.
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12. • The occlusal plane in most mammals, including man, is
approximately parallel to the Frankfort plane ( a plane from the top
of the auditory meatus to the inferior rim of the orbit).This aligns
the jaws in a functional position relative to the visual, olfactory, and
hearing senses.
• In the human maxilla, the design change that allows for this
resulted in the creation of a new arch positioning facial region, the
suborbital compartment. Most of this expanded area is occupied
by the maxillary sinus.
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14. THE ROTATION OF MANDIBLE DURING GROWTH
• In 1951 Bjork conducted a mixed longitudinal study by the
use of metallic implants of about 100 children of each sex
covering the age period from 4 to 24 years by means of the
implant method, he located sites of growth and resorption in
the individual jaws and examined individual variations in
direction and intensity.
• By super imposing consecutive tracings, he concluded
that, rotation involved marked resorption in the lower border
of the mandible in the gonial region which masked the
underlying mandibular rotation.
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15. Until longitudinal studies of growth using metalic implants
were carried out in 1960, by Bjork and coworkers in
Copenhagen, the extent to which both maxilla and mandible
rotate during growth was not appreciated.
•
• The reason is that the rotation that occurs in the core of
each jaw called internal rotation ,tend to be masked by
surface changes and alteration in the rate of tooth eruption.
The surface changes produce external rotation .
It is easier to visualize the internal and external rotation of the
jaws by considering the mandible first. The core of the mandible
is the bone that surrounds the inferior alveolar nerve the rest of
the mandible consist of its several functional processes.
•
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17. Bjork and Skieller distinguished two contribution to internal rotation
(which they called total rotation) of the mandible:
1) matrix rotation or rotation around the condyle. fig(A)
2) intramatrix rotation, or rotation centered within the body of the mandible.
fig(B)
• When the implant line or reference line rotates forward relative to the S-N
line during growth the rotation is designated as and negative (more growth
posteriorly) and positive (more growth anteriorly) if it is rotated backward.
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18. Internal rotation of mandible ranging up to 10-15
degrees.
•
• For an average individual with normal vertical facial
proportion, there is about a -15 degree (forward)
internal rotation from age 4 to adult life.
• Of this, about
25% results from
matrix rotation (A)
and 75% results
from intramatrix
rotation(B).
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19. During the time that the core of the mandible rotates
forward an average of 15 degrees, the mandibular plane
angle, representing the orientation of the jaw to an outside
observer, decrease only 2- 4 degrees on an average.
•
• The reason that the internal rotation is not expressed in
jaw orientation because suraface changes (external
rotation) tend to compensate.
• This means that the posterior part of the lower border of
the mandible must be an area of resorption ,while anterior
aspect of lower border is unchanged or undergoes slight
apposition.
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20. • On an average, there is about 15 degrees of
internal rotation, forward rotation.
• 11 to 12 degrees of external , backward rotation
producing the 3- 4 degree decrease in mandibular
plane angle observed in the average individual
during childhood and adolescence .
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21. According to Bjork (1969) – Based on the center of rotation he
classified rotation as forward rotation and backward rotation.
FORWARD ROTATION: When posterior growth is greater than anterior.
This may occur in the following 3 Types.
TYPE I (Forward Rotation):
• There is a forward rotation about
centers in the joints. The lower
dental arch is pressed into the
upper, resulting in deep bite as well
as under development of the
anterior face height.
• The cause may be occlusal
imbalance due to loss of teeth or
powerful muscular pressure.
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22. TYPE II: Forward rotation of the mandible about a center
located at the incise edges of the lower anterior teeth.
• This is due to the combination of marked development of
the posterior face height and normal increase in anterior face
height.
• The posterior part of the mandible then rotated away from
the maxilla.
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23. The increase in posterior face height has 2 components:
(1)
One is lowering of the middle cranial fossa in relation to
the anterior one as the cranial base bends, the condylar
fossa then being lowered.
(2)
Second is the increase in the height of the ramus due to
vertical direction growth at the condyles, the mandible is
lowered more than it is carried forward.
•
Because of the muscular and ligamentous attachments
carry it forward in relation to the maxilla with the center at
the incisal edges of the lower incisors.
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24. TYPE III FORWARD ROTATION : This occurs in
anomalous occlusion of the anterior teeth where there is a
large overjet.
• The center of rotation no longer lies at the incisors but is
displaced backward to the level of the premolars.
• In this case, the dental arches are pressed into each
other and a basal deep bite develops and the anterior face
height becomes underdeveloped.
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25. BACKWARD ROTATION:- Less frequent than forward.
TYPE I BACKWARD ROTATION: - Centre of rotation lies in the
TMJ This occurs when :
(a) The bite is raised by orthodontic means.
(b) In the case of flattening of the cranial base. Where the middle
cranial fossa is raised in relation to the anterior, which also
raises the mandible .
c) In case where there is incomplete
development in height of the middle
cranial fossa.
• This underdevalopment of the
posterior face height leads to a
backward rotation of mandible, with
over devalopment of the anterior
face height and this results in
increase in anterior face height and
possibly open bite. The mandible is
normal.
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26. TYPE II BACKWARD ROTATION:
• Centre of rotation is situated at the most distal occluding molars,
This occurs in connection with growth in the saggital direction at the
condyles.
• As the mandible grows in the direction of its length it is carried
forward more than it is lowered in the face and because of its
attachment to muscles and ligaments it is rotated backward.
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27. Shudy described rotation as:
1) Clockwise rotation: ( as viewed from the patients right side) This is
a result of excessive vertical growth as it relates to horizontal growth, and
tends to cause a reduction in the vertical overbite. The point of rotation is at
the condyles.
fig showes :Growth study from 6 to10
years the chin grew downward and
forward and the mandibular plane
moved downward in parallel manner.
At age 10 the condyles almost
completely ceased growing. Then chin
movied downward and backward,
mandibular plane became 7degree
steeper. The post. Growth analysis
showed that the condyles grew 4mm
while vertical growth in the molar area
was 10.5mm . The mandibular 1st
molars moved backward about 3mm;
thus it would have been impossible to
have corrected a class II condition
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under these circumstances.
28.
2) Counter Clockwise rotation -Is result of a
deficiency in vertical growth as related to horizontal
growth and tends to cause an increase of the vertical
overbites.
Fig .Showing the growth of
female, age 11 to 14 years ,
here condyles grew out of
proportion to vertical molar
growth. This resulted in a 4
degree rotation and marked
forward swing of the
mandible ,a 2mm increase
in vertical overbite.
Extremes of this condition
cause closed bites.
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29. • Growth at the mandibular condyle only produces a
forward component of the chin, not a downward, nor
a downward and forward component. It is only when
vertical increments of facial growth begin assert
their influence on condylar growth through occlusal
contact that a downward and forward direction of the
chin is produced.
Thus the final
vector of growth of the chin is a resultant of the
struggle between the horizontal growth and vertical
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growth, in other words, b/w condylar growth and
30. Then what are these vertical “elements” of growth which
produce an increase in facial height???
1. Anterior-posterior growth at nasion.
2. growth in the corpus of the maxilla which produces as
increase in the distance from nasion to the anterior nasal
spine and causes the maxillary molars and posterior
nasal spine to move away from the sella -nasion plane.
3. Growth at the maxillar posterior alveolar processes
causing the molar teeth to move away from the palatal
plane.
4. Growth at the mandiular posterior alveolar processes
causing the molar teeth to move occlusally.
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31. •When Pog-nasion grow forward at an equal
rate, increment A =sum of increments
I,II,III& IV, In other words the condyles
must equal the antero-posterior growth at
nasion,plus the vertcal growth of the corpus
of the maxilla,plus the vertical growth of
the maxillary alveolar process,plus the
vertical growth of the mandibular alveolar
process.
• When growth at A exceeds I,II,III,&IV,
the mandibular plane becomes flatter & Pog
moves forward more than nasion.
• When growth of the sum of I,II,III,&IV
exceeds A, Pog will move backward with
relation to nasion & mandibular plane will
become steeper.
• When growth at A equals the sum of
I,II,III, & IV, the mandibular plane moves
down in a parallel manner.
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32. Three cephalogrms were taken 1) in
centric occlusion with denture in
place.2)in a position of overclosure with
denture removed and 3)with a block of
wax b/w dentures.
• As the molar height increases the
chin swings downward &backward, the
mandibular plane becomes steeper,the
gonial angle moves posteriorly and the
facial angle decreases.
• Thus,by varying the molar height we
were able to change the facial angle, i.e
molar height not only controls the
vertical position of the chin, but also
anteroposterior position.
• These principles have a very definite application to
the treatment of class II malocclusion. Too much
vertical growth of the molar teeth would prevent the
forward positioning of the chin and thereby render class
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II correction very difficult.
33. • What is the clinical application?
All investigation are agreed that orthodontic
treatment does not stimulate growth at the
mandibular condyles.If this is true we have only
the vertical increments that we may possibly
change to serve our purposes. i.e. if we can inhibit
vertical growth it will have the same effect as
stimulating growth at the condyles.
If vertical growth
is deficient we try to stimulate it, & if vertical
growth is excessive we try to inhibite it.
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34. THE BEHAVIOUR OF THE OCCLUSAL PLANE DURING MANDIBULAR ROTATION
The inclination of occlusal plane seemes to reflect natures
attempt to compensate for inharmonies of growth. The vertical
growth of the anterior alveolar processes seems to try to
compensate for the inharmonies b/w posterior alveolar growth
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and ramus growth.
•
35. • In a study of 62 untreated & 50 treated cases by Creekmore –
Compared forward movement of the chin.
• The untreated group had an average SN-MP angle of 34
degrees and treated 31.5 degrees.
• The untreted group Pog moved forward an average of
3.48mm, while in treated group this reding was 2.49mm.
• This showes that treatment retards the forward positioning of
the chin. The cause of this difference was a difference in the
amount of vertical devalopment of the molar area.
• A number of investigators have found that there is little or no
difference b/w mandibular length in class I & class II
malocclusions.
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36. • In a comparison of retrognthia and prognathia Bjork
states that, “ a comparison b/w the two extreme
percentiles indicate that mean length of the lower jaw is
practically the same in both”.
• Maj & Luzi in discussing class II, div I malocclusion states
“in most instances, the component parts (maxilla &
mandible) are normal by themselves but their association
results in a disharmony”.
• Thus, it can be said that most class II cases have had
average horizontal growth. Their principal shortcoming is
that they have had too much vertical growth.
•The vertical component of growth limits the horizontal
component. This in turn prevents the forward movement
of the chin.
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37. Dr.Tom Creekmore & Schudy designed a high pull face bow
for extraoral anchorage. Elastic traction is then applied in an
upward & back ward direction for inhibiting the downward
growth of the maxillary alveolar process & possibly the body of
the maxiila. This type of traction is used primarily on open bite
cases & individules with high SN-MP angles.
• When vertical growth is deficient, resulting in a deep
overbite, we try to stimulate the vertical growth of the alveolar
processes with class II elastics and / or the conventional face
bow headgear with cervical traction.
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38. Subsequently Bjork and skieller showed that different patterns
emerged when different registration for super imposition were used i.e.,
a striking contrast in the mandibular position was seen when
superimposed on the cranial base and superimposed on metallic
implants.
They classified rotation in to 1) Total rotation 2) matrix rotation
3) intramatrix rotation
1.
1) TOTAL ROTATION:
The rotation of the
mndibular corpus measured
as a change in inclination of
an implant line in the
mandibular corpus relative to
the anterior cranial base
(Bjork and skieller)
2.
Solow and Huston called
this the “True rotation” and
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39. 2) MATRIX ROTATION:
Bjork and skieller - Defined it “as a rotation of the soft
tissue matrix of the mandible relative to the cranial base”. The soft
tissue matrix is the tangential mandibular line. It has its center at
the condyles.
•Solow and Houston called this “apparent rotation” and
•Proffit called this “total rotation”.
• Lavergne & Gasson called it as Positional rotation.
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40. 3) INTRAMATRIX ROTATION:According to Bjork and skieller- It is the change in inclination of a reference
line/ implant line in the mandibular corpus relative to the tangential
mandibular line. The center of rotation lies in the corpus. (Fig B)
•
•
•
•
Solow and Houstion called this Angular remodeling of the lower border.
Proffit called it External rotation.
Lavergne & Gasson called it as Morphogenetic rotation.
Dibbets called it as Counterbalancing rotation
Fig (A):matrix rotation
Fig (B):intramatrix rotation
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41. THREE DIFFERENT INTERPRETATION
OF INTRAMATRIX ROTATION
1)
1) According to Bjork and skieller:- They speculated
that the intramatrix rotation reflected in the rotation of the mandibular
corpus relative to the lower border is a result of genetically
determined condylar growth and that the center of rotation lies in the
corpus and not in the condyles.
According to them mandibular growth rotation may be found to be
closely associated with both the direction and the amount of growth
at the condyles
First , mandible “wiggles” or move from side to side with in its
matrix.
Second, this “wiggling” is associated predominantly with the corpus
but it is caused by the growing condyle.
Third, rotation results from,or compensates for, a genetically
determined program. This last conclusion, in particular, makes
rotation an attractive item in growth prediction.
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42. 2) Lavergne and Gasson defined rotation as:
a) Morphogenetic- Concerning the shape of the mandible.
Similar to intramatrix rotation.
b) Positional- Dealing with the position of the mandible with in
the head. Similar to matrix rotation
They used a line joining condylon and pogonion to
superimpose cephalogram and the angle between the 2
implant lines is determined & this corresponds to the degree
of “ morphogenetic rotation”.
The fact that fixed points, represented by the implants, are
measured in relation to a line that represents the contours of
the mandible brings Lavergen & Gasson’s scheme of
“morphogenetic rotation” into focus with Bjork’s definition of
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43. • Lavergne & gasson concluded that:
• “ Anterior rotation of the mandible is associated with a
vertical or even anterior condylar growth direction and a
marked closure of the gonial angle and these minimize
the effects of mandibular growth.
• They postulated that intramatrix rotation is essentially
a compensating mechanism which is capable of reducing
or enlarging the mandibular length by opening or closing
the gonial angle.
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44. • The Size of the gonial angle has an important
influence upon the degree of anterior rotation.
The smaller the gonial angle, the greater
rotation is produced for each mm of forward
movement of the pogonion.
• An obtuse gonial angle compensate for a
short ramus and corpus i.e. the gonial angle
helps to compensate for length.
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45. 3) Dibbets: (AJO-DO,1985-Jun)
Gave a third interpretation which is based on
two hypothetical divergent patterns of growth.
a) One pattern postulates condylar growth as a
segment of a circle with its centre at the chin. The
whole mandible would then rotate around itself
within its periosteal contours,resulting in
“intramtrix rotation” with out enlargment of the
mandible.
b) The other pattern is a linear growth curve of the
condyle, without any “intramatrix rotation”and
maximum enlargement of the mandible.
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46. Two methods of superimposing
the mandible:
Fig (A) :tracing, at different ages,
of the same mandible registered
upon natural reference structures
“Bjork approach”. (inner cortical
structure of the symphysis, tip of
the chin, & mandibular canal) .
Note the curved condylar growth
direction and extensive
resorption of the inferior border
Fig (B): same mandible as in (A),
superimposed upon the
traditional Hunterian conception
of posterior ramal deposition
&anterior ramal resorption
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47. Schematic illustration of intramatrx rotation :
fig (A), two mandibles superimposed on their external contours. Note
divergence of the implant lines indicative of “intramatrix rotation” not
reflected in dimensional change or alteration of mandibular contours.
fig (B), the same two mandibles superimposed on the implant markers.
There is lack of concordance of mandibular contours, indicating extensive
remodeling during development.
• The figure is constructed in a
such a manner that the center
of rotation is on the chin,this
indicates condyle growes on a
circular arc (C-C’) with the
radius of fixed length, running
from the center at the chin to
the condyle. It is noted that the
form of the mandible has not
changed in fig (A).
• He showed that external configuration of the mandible need not change
its form or position within the head to allow intra matrix rotation and any
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resorption or deposition only serves to maintain the original contours.
48. According Dibbets growth of the condyle has at least 2
effects:
1) Intramatrix rotation
2) Enlargement
So linear growth pattern due to growth of the condyle,
It follows that every millimeter of condylar growth along the
pogonion- condylon diagonal would enlarge the mandible by
1 mm. in the event that the direction of the condylar growth
follows a pattern that enlarge the mandible maximally, then it
would follow that the hardly any “itramatrix rotation” will
occur. All growth increments will be expressed in
dimensional gain.
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49. •
This is compensated by remodeling at the lower
border. This mechanism is termed as the
“counterbalancing rotation”. (Dibbet’s)
•
Thus counterbalancing rotation is mechanisum
“relates to circular condylar growth,accompained by
selective co-ordinated remodeling, which does not
contribute to the incremental growth of the
mandible”
i)
It neutralizes effect of growth of the condylar
cartilage.
ii) Result in selective enlargement of the mandible.
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50. Enlow categorised rotations as:
a) Displacement type
b) Remodeling type
a) Displacement type - Involves the rotational
positioning of the entire mandible. This is caused by
changes in the placement of junctional contacts with
cranial floor and the maxilla i.e., the dimensions and
angular positions of these separate parts directly affect
the rotational position of the mandible.
b) Remodeling
type : This utilizes depository and
resorptive growth processes and produces angular
and dimensional changes in the ramus and corpus
of an individual mandible i.e., rotations in these
parts occur in relation to one another.
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51. a) Displacement rotation: (for exp)
i) If the cranial base angle is open, the effect can be a
downward
and backward displacement rotation of the
mandible.
• If the cranial base angle is closed converse effect is seen.
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52. ii) If the nasomaxillary complex is vertically long, a down
word and backward displacement rotations of the whole
mandible results.
A vertically-short nasomaxillary complex has a
converse effect.
Vertically long nasomaxillary complex
Vertically short nasomaxillary complex
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53. b) Remodeling rotation- there are 2 reasons why a
mandible undergoes the remodeling type of rotation.
1. The first is to prodce a more upright ramus alignment
relative to the corpus. This is necessary to accomodate the
continued vertical growth of the naso-maxillary region and the
eruption of the permanent dentition.
2. The seconds reason is to provide ramus corpus angular
adjustments to accomodate the effects of the whole
mandibular displacement rotation i.e., if the whole mandible
is aligned in an upward and forward manner, an upward
inclined mandibular corpus and occlusal plane would result.
This can be offset by an opening of ramus-corpus angular
relationship and similarly a downward inclined mandibular
corpus can be offset by a closing of ramus- corpus angle.
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54. • Most
of the remodeling changes in the ramus corpus
angular relationship are carried out by the ramus. However
bone deposition on the inferior bordor may occur which
rotates the mandibular plane inferiorly .
• A mandible characterically has a more prominent
antegonial notch, if the gonial angle opened. Fig (a)
• A mandible has a less prominent antegonial notch (fig
(b) if the gonial angle becomes closed.
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55. • Effect of whole mandible rotations and ramus-to-corpus
rotations are opposite. when the entire mandible is aligned
downward, a mandibular retrusive effect is prodused, but
when just the corpus is aligned downward, a mandibular
protrusive effect results. An upward whole mandible
alignment is mandibular protrusive, and an upward
alignment of the corpus only is mandibular retrusive.
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56. TERMINOLOGIES & SUMMARY OF GROWTH ROTATION
CONDITION
BJORK
SCHUDY
ANTERIOR GROWTH
GREATER THAN
POSTERIOR GROWTH
BACK WARD
ROTATION
CLOCKWISE
ROTATION
POSTERIOR GROWTH
GREATER THAN
ANTERIOR GROWTH
FORWARD
ROTATION
COUNTER
CLOCKWISE
ROTATION
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57. Bjork &
Condition Skieller
Rotation of
mandibular
core
relative to
cranial
base
Total
rotation
Rotation
of
mandibular
Plane
relative to
cranial base
Matrix
rotation
Rotation of
Mandibular
plane
relative to
core of
mandible
Intra
matrix
rotation
Solow,
Houston
True
rotation
Apparent
rotation
Proffit
Lavergne,
Gasson
Enlow
Dibbets
Internal
rotation
Total
rotation
Positional
rotation
Angular
External MorphogRemodrotation enetic
eling
Rotation
Of lower
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border
Displacement
rotation
Remodelling
Rotation
Counter
Balancing
rotation
58. PREDICTION OF MANDIBULAR
GROWTH ROTATION
If an attempt is made to assess the growth trend at
an early age , this information can be used in
designing the treatment or evaluating the problems
that may arise before growth is completed.
In spite of several attempts in recent years,
there is still doubt as to the extent to which growth
of the face as a whole can be predicted from a single
profile rediograph.
In an attempt to analyse the possibility of predicting
growth of single facial dimension, Bjork and Palling
correlated liner and angular measurements at
pubertal age with residual growth of these dimension
up to adulthood. These correlations were however
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found to be low.
59. • Hixson suggested that the best estimate of an adult facial
dimension for a given child is to use the dimension presented
by the child and add to that the remaining average growth for
the group. Several authors adopted this method. However,
this estimate would fit an average but not an extreme growth
pattern, where prediction from a clinical point is more
important.
• Levergne tried to individualize the prediction by a
subdivision according to morphogenetic types.
•Ricketts arcial method of long range growth prediction uses
geometric procedures to gain information about the growth
pattern of the mandible.
• A computerized system for short range facial growth
prediction and treatment simulation, based on longitudinal
observations of individual growth rate and direction has been
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developed by Bjorn-Jorgensen.
60. A growth analysis consists of essentially 3 items:
1) Assessment of the development in shape of
the face which ,in the first place, implies
changes in the intermaxillary relationship.
2) Assessment of whether the intensity of the
facial growth is high or low.
3) Evaluation of the individual rate of maturation.
This is important in establishing whether
puberty has been reached and when the
growth may be expected to be completed.
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61. According to Bjork
In the assessment of shape there are three methods.
1) Longitudinal method
2) Metric method
3) Structural method
I) longitudinal method: which is commonly used,
consists of following the course of development in annual
celphalometric films.
It is for the subjects displaying the most pronounced
changes is facial forms that the diagnoisis of growth pattern
is important.
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62. Limitation of longitiudinal method are:
1. Pattern of growth is not constant and the pattern
recorded at a juvenile age may be changed
by
adolescence.
2. It permits the observation of changes in the sagittal jaw
relation with growth, and those changes occurring in the
vertical jaw relation are masked due to remodeling of lower
border of the mandible.
Changes in the vertical positions of the jaws in the form of
rotation appear to be smaller when assessed with
conventional longitudinal x-ray films by using the base of
the mandible as the reference than when assessed with the
help of implants.
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63. • For clinical purposes, the analysis of vertical development
of the face may done using natural reference structures in
the mandible. By superimposing two radiographs taken at
different ages and orienting them with reference to these
structures, one may estimate the growth pattern of the
mandible by reading the angle between the nasion sells lines
for the two ages.
•
Longitudunal method of analysis of
mandibular growth rotation from the
angle b/w the N-S lines,at two stages
(A&B) after superimposition of the
mandibles on natural reference
structures.
(1)Tip of the chin
(2) Inner cortical structure at the inferior
border of the symphysis.
(3) lower contour of a molar germ.
(4) from the time mineralization of the
crown is visible untile the roots
begin to form.
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64. II) METRIC METHOD:
• Aims at a prediction of facial development on the basis
of facial morphology, determined metrically from a single
x- ray film. However, prediction of development from size
and shape at childhood is not very accurate.
•
The growth in length of the mandible during
adolescence, could not be judged from its size before
puberty.
• The changes in shape of the face during adolescence,
expressed in terms of anglular measurements, were also
weakly correlated with the shape of the face at 12 years,
which is the age at which treatment is instituted or
planned.
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65. III) STRUCTURAL METHOD:
•
Is based on information concerning the
remodelling process of the mandible during
growth, gained from the implant studies.
•
The principle is to recognize specific structural
features that develop as a result of remodeling in
particular type of mandibular rotation.
•
A prediction of the subsequent course is then
made on the assumption that the trend will
continue.
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66. STRUCTURAL SIGNS OF GROWTH ROTATION:
• There are seven signs and not all of them will be
found in a particular individual, but the greater the
number, the more reliable the prediction will be.
They are
1.
2.
3.
4.
5.
6.
7.
Inclination of the condylar head
Curvature of the mandibular canal
Shape of lower border of mandible
Inciination of the symphsis
Inter molar angle
Inter incisal angle
Anterior lower face height.
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67. 1) A
forward or backward inclination of the condylar head is a
characteristic sign of forward or backward rotation
FORWARD ROTATION
BACKWARD ROTATION
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68.
2) Curvature of the mandibular canal:
In the vertical of condylar growth, the curvature of the
canal tends to be greater than that of the mandibular
contour (b) whereas in the sagittal type curvature of
the canal is smaller than the mandibular counter (a).
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a) Horizontal growth
b) Vertical growth
69.
3) Shape of the lower border of the mandible-
In forward growth rotation there is apposition below the
symphysis and anterior part of the mandible producing
anterior rounding , while resorption at the angle produces a
concavity. (a)
In back ward growth rotation the anterior rounding is
absent resulting in a linear shape of anterior lower border and
the contour at the jaw angle is convex. (b)
a) Forward
rotation
b) Backward
rotation
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70. a. 4) Inclination of the symphysis-
• This is measured as the angle between the tangent to
the anterior surface of the mandible and the anterior
cranial base.
This is an important feature in mandibular growth
prediction because this surface is free from
remodeling.
In forward growth rotation
( fig. a & b)
characterized by
retroclination of the syphysis,
irrespective of small (a) or
great(b) mandibular
inclination.
In backward growth
rotation (c) characterized by
proclination of the symphysis
& great inclination of the
mandible, (d) pathologic
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form.
71. 5) Inter molar angle
• The inter molar angle tends to increase in forward
rotation of the mandible and decrease when the rotation
is directed backward.
Change in molar inclination
a)Forward rotation
b)Backward rotation
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72. 6) Inter incisal angle:
In backward rotation the inter incisal angle is
redused (b), where as in forward rotation it is
increased (a).
•
b) Backward rotation
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a) Forward rotation
73. 7) Anterior lower face height:
• In forward growth rotation there is deep overbite
and reduced lower face height.
• In backward rotation there is increased lower face
height and open bite.
a) Forward growth
rotation of the
mandible with normal
incisal occlusion
b) Forward rotation
with deep over bite &
redused LAFH
c) Backward rotation
with increased LAFH
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75. PRINCIPLE OF ARCIAL GROWTH OF THE
MANDIBLE
(Robert M. Ricketts 1972)
•The essence of this principle is as follows, a
normal human mandible grows by superior-anterior
(vertical) apposition at the ramus on a curve or arc,
which is a segment formed from a circle.
• The radius of this circle is determined by using
the distance from supra pogonial ( Pm) to a point at
the forking of the stress lines at the terminus of the
oblique ridge on the medial side of the ramus.
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76. • Intially
to locate the arc of the mandibular
growth a stable landmark is selected in the center
of the mandibular ramus and this is obtained by
bisecting the height of the ramus and the mid
point termed xi point.
• This mid point is
selected because as
Bjork reported earlier
there is remodeling
changes observed on
the surface of the
mandible and he also
reported that supra
pogonial area (Pm)
was stable.
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77. • By selecting these landmarks first curve tested was one from
Pm, xi, and Dc point (bisecting the condyle) by extending this arc
the size increase was produced but not enough bending is
resulted.
• He was satisfied with the landmark Pm as it is reliable reference and
retained it for further study.
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78. • The second arc was explored by using the tip of
the coronoid process (CR), the anterior border of
the ramus at its deepest curve (R1) and the same
Pm point.
• The extension of this
curve exhibited the
segment of a circle too
small in radius and
resulted in excessive
bending of the mandible
when the same gradient
of growth was employed
for a projection.
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79. It was obvious that the characteristics of typical growth
had been bracketed by the two arcs produced. One
straightening the mandible too much and the other
bending. A true arc of growth therefore must be some
where in the mandible between the condyloid and the
coronoid process and between the ramal center and
anterior border of ramus.
•
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80. • They construoted an experimental arc bisecting
the two previously arcs. By establishing a halfway
point between xi and R1 points and using the
distance from this point to Pm as a radius of a circle
an arc could be produced.
• The use of this arc still bent the mandible a
fraction too much. In addition, a radius selected
from this point would increase with size of the
mandible and a progressive increase or a changing
arc or ultimate spiral shape would result.
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81. • On examining the weathered mandible state
of disintegration of 850 years old mandible
they traced the interprismatic substance of
the external cortical bone. And therefore
clearly showed stress lines in the outer and
inner plate.
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82. • Close examination confirmed the covergence of stress lines
at the protuberance menti. The stress lines seemed to swing
downward and then upward and backward and outward
through the external obligue ridge.
• From this ridge on the exernal table at the base of cornoid
process the stress lines are divided at the base of the coronoid
process.
• An irregular gnarled area was located at this area on the
lateral surface as the strees seemed to divide forward or
backward in respect to coronoid and condyloid demands.
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83. • Even in the medial aspect greater bifurcating of stress
lines observed followed the mylohyoid ridge upward into a
thick mass to terminate at a ‘y’ shaped bony prominence.
• This was almost the center of anterior superior quadrant
of the ramus they even observed a small apparently
nutritive foramena immediately superior to this area on the
medial aspect. It was hypothesized that these might be
trophic for a possibly an important growth area.
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84. • Experimentally, two new points (Eva and true radius (TR)) were
located geometrically, point Eva is also a biologic point as it is
located over the point of forking of the stress lines in the ramus.
• When the size increase of the mandible as determined in the
computer study was incrementally added to the arc at the sigmoid
notch, It was found that the predicted mandible was almost
absolutely correct in size and form when compared with final
composite.
• The method as devised proved extremely accurate in fifty treated
cases which were predicted and compared for period of as long as
fourteen years.
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87. • Having
the arc as a tool for prediction is satisfactory, the
next problem lay in the amount of growth to forecast on the
arc. The yearly increase from the combined studies was found
to be almost precisely 2.5 mm. Cutoffs for growth were
determined to the 14.5 years for females and age 19 years for
males.
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89. •Further
studies
consistent with the
gonion behaviour and
found that the gonial
angle
drifted
posteriorly on the arch
almost exactly one
half or 50% of the total
increase in mandibular
growth on the arc.
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90. • The final consideration is need to complete forecasting of the mandibular
form this is a critical point because it helps to determine the space available
for the developing mandibular third molar at the anterior border of the
ramus.
• For this determination the ramus reference (RR) point was reemployed.
As the time 1 tracing is compared with forecast being constructed. It is
assumed that stable bone is located in this area.
• Thus with normal anatomical contouring the coronoid process is
connected to RR point. Which tends to determine ramal width, Slightly
below this point, The external oblique ridge will show apposition of almost
0.4. mm per year.
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92. Maxillary rotation
• It is less easy to divide the maxilla into a core of bone and a
series of functional processes.
• The alveolar process is certainly a functional process in the
classic sense. If implants are placed above the maxillary alveolar
process, core of the maxilla undergoes a small and variable
degree of rotation, forward or backward .
• This internal rotation is analogous to the intramatrix rotation of
the mandible. Matrix rotation is not possible for maxilla.
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93. At the same time that the internal rotation of maxilla
is occurring, there are also varying degrees of
resorption on the nasal side and apposition of bone on
the palatal side in the anterior and posterior parts of
the palate.
•
• Similar variations in the amount of eruption of the
incisors and molars occur.These changes amount, to
an external rotation.
• External rotations opposite in direction and equal
in magnitude to the internal rotation, so that the two
rotations cancel and the net change in jaw orientation
is zero.
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94. • Until longitudinal studies of growth using mettalic
implants in the jaws were carried out in the 1960 by
Bjork and co-workers in Copenhagen the extent to
which the maxilla and mandible rotate during growth
was not appreciated. In fact rotation of maxilla
during normal growth had not been suspected.
• However now we are aware that the maxilla does
Indeed show rotations during growth and this
rotation may be divided.
1. Vertical rotation of the Maxilla
2. Transverse mutual rotation of the two maxilla
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95. Vertical rotation of the Maxilla
1. Super imposition of the longitudinal profile radiographs on
the sella- nasion line show generally an almost parallel
lowering of the nasal floor as described the Brodie in 1941.
which led to the view that during growth the maxilla is lowered
without rotation in the vertical plane.
2. However implants Studies by Bjork and skieller (1972) have
shown that the downward and forward displacement of the
maxilla during growth is associated with a varying degree of
vertical rotation which is most cases is directed forward.
Despite the vertical rotation of the maxilla, the inclination of the
nasal floor, the palate as well as well as the orbital floor to the
anterior cranial base is maintained by differential resorption
and deposition.
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97. • Generally inclination of the maxillary base stable and no
growth dependent changes are seen, environmental
influences such as neuromuscular dysfunction, occlusal
forces, gravity and nasorespiratory malfunction can modify
this inclination as upward & forward tipping of the anterior
part of the maxilla seen in confined mouth breathes.
• A downward and backward tipping of the anterior part of
the maxillary base is seen as a natural compensation in
patients with vertically growing faces.
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98. Transverse mutual rotation of the two maxilla:• The right and left maxilla are 2 separate bones joined
along the medial suture and Bjork in his experiment
placed an anterior & lateral implant in each maxilla so
that the distance between each implant is constant
throughout growth.
• He found that the increase in width from the age of 1011 years in the nine case measured between the lateral
implants was an average 3 1/2 times as great as that
between the anterior implants.(3.0mm against 0.9mm).
That the lateral implants separated more than the anterior
during growth indicate that the two maxilla rotate in
relation to each other in the transverse plane.
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99. As a result of the mutual transverse rotation :
• The lateral segments of the dental arch separate
more posteriorly.
• The distance between the first molars increases more
than the distance between the canines
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101. MUTUAL ROTATION OF U/L JAW BASES:
• Rotations of the mandible can be decisive in establishing
the vertical proportions of the face. In a horizontal rotation
the anterior face profile is short whereas in a vertically
rotating mandibular pattern it is long. A horizontal rotation
means that there is a predisposition towards a deep overbite.
•An excessively vertical rotation means a tendency toward an
open bite the inclination of the maxillary base is also
important to the occlusal relationship. The resultant
dentoalveolar malocclusion depends on the combination of
these rotations we can differentiate the following type of
rotations as shown by Lavergne and Gasson.
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102. 1) Convergent rotation of jaw bases: This creates a
severely deep overbite.
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103. 2) Divergent rotation of the jaw bases: This can
cause marked open bite problems. In severe cases
orthognathic surgery is required for the correction.
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104. 3) Cranial rotation of both jaw bases:
In this there is horizontal growth pattern & there is a
relatively harmonious rotation of both jaws in an
upward and forward direction. The upward and
forward rotation of the maxilla compensates for the
upward and forward mandibular rotation, offsetting
what could be a deep bite.
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105. 4) Caudal or downward and backward rotation of
the both bases: In relatively harmonious manner the
downward and backward maxillary rotation offsets what
could be an open bite created by the downward and
backward mandibular rotation.
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107. 1) Short face syndrome
• They are characterized by short anterior lower face height with
excessive forward rotation of the mandible during growth resulting
from both an increases in the normal internal rotation and decrease
in external compensation.
This results in:
Nearly horizontal palatal plane
Mandibular morphology of the “ square jaw” type
Low mandiular plane angle
Square gonial angle
Deep bite
Crowded incisors
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108. Long face syndrome
This is characterized by increased anterior and total face
height and results primarily from a lack of the normal forward
internal rotation or even a backward internal rotation. The
internal rotation in turn is primarily matrix rotation not
intramatrix rotation.
2)
This results in:
• Palatal plane rotates
down posteriorly.
• Mandible shows an
opposite backward
rotation.
• Increase in mandibular
plane angle.
• Associated with open
bites .
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109. CLASSIFICATION OF
SHORT FACE SYNDROME & LONG FACE SYNDROME
• Based on the parameters like ramus length, the SN to MP
angle, and posterior vertical maxillary dentoalveolar height
the short face syndrome group is divided into two sub types.
SUBTYPE I:
It is characterised by a long ramus and extremely low
SN-MP angle and slightly redused posterior maxillary
dentoalveolar height.
SUBTYPE II:
A short ramus and a vertical maxillary deficiency were the
dominant findings, while the SN-MP angle was only slightly
redused. These persons manifest extreme reduction of lower
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110. The long face syndrome group can be sub divided in to
Two sub types:
SUBTYPE I: Is characterised by a long ramus, increased
occlusal plane to palatal plane angle, an increased SN to MP
angle, and excessive lower anterior facial height. These
persons manifest the most typical clinical characteristics of
the the long face syndrome and have excessively long face.
SUBTYPE II: However, extreme backward and downward
rotation of the mandible combined with a short or extremely
short ramus, is associated with an increase in LAFH. The
increase in posterior maxillary height was not striking in this
subtype.
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112. CLINICAL IMPLICATIONS OF GROWTH ROTATIONS
• Vertical malocclusion often receives less consideration
than sagittal. No doubt, this is due in some measure to
difficulty in detecting their relation to facial growth types.
• More extreme the rotation of the mandible during growth ,
the greater the clinical problems that it presents. It is
important to predict such rotations at an early stage,
regardless of whether or not malocclusions have developed.
• Extreme rotation, whether forward or backward greatly
influences the paths of eruption of the teeth. This has a bearing
on the orthodontic tooth movement and account must be taken
in planning treatment.
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113. • The path of eruption of the mandibular teeth is upward and some what
forward. The normal internal rotation of the mandible carries the jaw
upward in front.
• This rotation alters the eruption path of incisors, tending to direct
them more posteriorly, Because the internal jaw rotation tends to
upright the incisors, the molars migrate further mesially during growth
than do the incisors and this is reflected in the decrease in arch length
that normally occurs.
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114. • Since the forward internal rotation of the mandible
is greater than that of the maxilla, normal decrease
in mandibular arch length is somewhat greater than
the decrease in maxillary arch length.
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115. • Individuals of short face type have excessive forward
rotation of the mandible during growth, resulting from both
an increase in normal internal rotation and a decrease in
external compensation. The result is a horizontal palatal
plane and a low mandibular plane angle. A deep bite
malocclusion and crowded incisors are also often seen.
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116. • In long face individuals, the palatal plane rotates down
posteriorly. The mandible shows a backward rotation
with an increase in mandibular plane angle. This type of
rotation is associated with anterior open bite
malocclusion and anterior face height increases.
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117. •Posterior rotations are induced by orthodontic
treatment and this is usually associated with the use
of class II clastics, anchore bends and bite plane.
However these are transient.
•In the child growth in lower anterior face height is
accelerated during treatment of this type but will
subsequently lag while posterior face height catches
up thus there may be no long term effects on the
position of the mandible relative to the cranial base.
In adults or in children where the treatment induced
increase in anterior face height exceeds that which
would normally have occurred with growth, there will
often be a gradual anterior rotation associated with
intrusion of the teeth under the influence of occlusal
forces.
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•
118. However in some cases, where anterior face height is
increased by treatment the position of the mandible relative
to the cranial base will change permanently because of
adaptation in the cranio cervical musculature and fascia and
probably head posture. This occurs more commonly in
cases that already have a tendency to posterior mandibular
growth rotation.
•
• When facial morphology indicates that vertical growth
has been excessive or that condylar growth has been
deficient we try to inhibit the downward growth of the
maxillary molars we could use a face bow with a high pull
head gear.
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119. •
When it has been determined that vertical growth is
deficient, resulting in deep overbite, we try to stimulate the
vertical growth of the alveolar process with class II elastics
and/or the conventional face bow with cervical traction.
• Clockwise rotations of the mandible would not help
reduce the ANB angle and would not aid in correction class
II molar relation.
•
However it would tent to help correct the vertical
overbite, while on the other hand counter clockwise
rotations is nearly always accompanied by forward
movement of the pogonion, a flattending of the mandibular
plane which tends to increase the vertical overbite and
renders vertical overbite correction and retention more
difficult.
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120. CONCLUSION
• We orthodontist are interested in facial growth and
development basically because growth can be altered for
the need of application of therapy. Therefore we should
predict future growth changes that occur. There by avoid
making undesirable changes and can alter undesireble
growth pattern.
• The rotation of the mandible during growth appears to be
a complex phenomenon showing annual variataions in
direction & intensity. Such rotation is not only dependent on
mandibular factors, but also is strongly related to the
intensity of growth of both jaws.
• Clinician should confine his effort to correct the abnormal
growth pattern during the process of correcting the
malocclusion for better prognosis.
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121. BIBILOGRAPHY
1) F.F. Schudy: The rotation of the mandible resulting from growth: its
implications in orthodontic treatment. Angle orthodontics,1965- vol.35,
No.1, 36-50.
2) Bjork. A : Prediction of mandibular growth rotation Am.Journ of
orthodontics 1969-55: 585-599.
3) Robert M.Ricketts: A Principle of Arcial Growth of
mandible;1972;42;4;368-386
4) Jean Lavergne, Nicole Gasson: A metal implant study of mandibular
rotation: Angle Ortho-1976-46;146-150
5) Bjork.A.,Skieller: Prediction of mandibular growth rotation evaluated from
a longitiudinal implant sample:AJO-DO;1984-Nov-359-370
6) Sheldon Baumrind: prediction of mandibular rotation:an empirical test of
clinician performance: AJO-DO ,1984-NOV-371-385.
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122. BIBILOGRAPHY
7) J.M.H.Dibbets : The puzzle of growth rotation – AJO-DO1985JUN-473-480
8) Beni Solow & william j. Houston :Mandibular rotations:
concept and terminology- EJO-1988 (10) 177-179.
9) Surender K. Nanda : growth patterns in subjects with long
and
short faces, AJO-DO-1990;98;247-58
10) W.J.B. Houston et al – A Textbook of Orthodontics, 2nd edn
11) Donald.H.Enlow:Facial growth. 3rd Edn., W.B. Saunders Co.,
12) Willliam R.Proffit; contemporary orthodontics; 3rd edn
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123. BIBILOGRPHY
13) Thomas. Rakosi et al:Orthodontic diagnosis: colour
atlas and manual
14) T.M. Grebar & Swain : text book of Orthodontics current
principals and tecq ,1st edn.
15) Thomas. Rakosi : text book of cephalometric radiography
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