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Pitchfork Analysis
1. SEMINAR PRESENTATION
Pitchfork Analysis
DEPARTMENT OF ORTHODONTICS AND
DENTOFACIAL ORTHOPAEDICS.
Presented by: Guided by:
Dr. Deeksha Bhanotia Dr. Mridula Trehan.
M.D.S. Second year. Professor & Head.
Department of Orthodontics
and Dentofacial Orthopaedics
1
2. CONTENTS:
1.Introducion
2.Superimposition Landmarks
3.Superimposition methods of
a. Cranial base
b. Maxilla
c. Mandible
4.Pitch fork analysis
a. Cranial Base Superimposition
b. Maxilla
c. Mandible
5.Pattern of Craniofacial Growth
6.Measurement of Changes:
a. Jaw growth/displacement relative to cranial base
b. Tooth Movement relative to basal bone
c. Molar relationship and overjet change
7.Reliability
8.Conclusion 2
3. INTRODUCTION:
A cephalometric superimposition is an analysis of lateral
cephalograms of the same patient taken at different times.
It is used to evaluate a patient's growth pattern between different
ages and to evaluate changes in the dentoalveolar and basal
relationships after a course of orthodontic or surgical treatment.
Cephalometric procedures and evaluations are considered in the
light of; pretreatment objectives, orthodontic treatment modalities
used, long-term follow-up of the treatment results and during the
retention and post-retention periods.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
3
4. The comparison of cephalometric head films taken at intervals
is a method used by researchers and clinician to obtain a
general view of growth changes and/or to determine the effect
of orthodontic treatment on the jaws and teeth.
In growing skulls the various bones move apart from each other
at different rates.
The anatomic landmarks adjacent to growth locations will move
apart more than those further from the growth sites.
To determine the effect of growth of treatment, tracings of the
head films, are superimposed on those landmarks least affected
by growth.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
4
6. Superimposition Landmarks:
Soon after the discovery of Broadbent’s
cephalometer, cephalometrics has been
extensively used by anatomists and
orthodontists to find out variations in
craniofacial morphology and growth of the
human face.
Traditionally cranial base structures were used
to superimpose the lateral cephalogram taken at
an interval (or at intervals) to either study the
growth of the face and dental arches or evaluate
changes due to treatment.
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and
Dentofacial Deformities,3rd edition, Elseiver; 2020 6
7. The cranial base was considered stable since
majority of the growth of the middle cranial
base (90–95%) was thought to be completed at
7 years of age.
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and
Dentofacial Deformities,3rd edition, Elseiver; 2020
7
8. The anatomical anterior cranial base (ACB)
extends from foramen caecum to nasion,
the middle cranial base from foramen
caecum to hypophyseal fossa
the posterior cranial base from hypophyseal
fossa to foramen magnum.
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and Dentofacial
Deformities,3rd edition, Elseiver; 2020
8
anterior
middle
posterior
9. The anterior segment of the cranial base,
which extends to a relatively short distance
from foramen caecum to nasion, continues to
grow into adulthood as a result of growth at
bony and frontal sinuses.
The posterior segment of the cranial base
that extends from hypophyseal fossa to the
foramen magnum continues growth into
early adulthood as a result of the activity of
the spheno-occipital synchondrosis (SOS).
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and Dentofacial
Deformities,3rd edition, Elseiver; 2020
9
10. It is the middle segment of the cranial base,
which extends from the anterior boundary of
the hypophyseal fossa to the foramen caecum
anteriorly, and completes its growth earliest in
life, reaching 62% of the adult size at birth,
94% between 4 and 7 years of age and 98% of
the adult size between 8 and 13 years of age.
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and
Dentofacial Deformities,3rd edition, Elseiver; 2020
10
11. These structures are internally stable after the
fusion of the spheno ethmoid, fronto ethmoid,
and inter-sphenoid synchondroses by about 8
years of age.
Therefore, these structures were considered as
a stable reference for cephalometric
superimposition. The points easily identifiable
on radiographs and reproducible with
accuracy were chosen for superimposition.
Kharbanda OP. Orthodontics Diagnosis and Management of Malocclusion and
Dentofacial Deformities,3rd edition, Elseiver; 2020 11
12. Cranial Base:
Many attempts have been made to overcome the problem of
analyzing the growing face in the absence of stable non growing
reference lines or anatomic landmarks.
Broadbent used the Bolton plane (Bolton point to nasion) to
demonstrate downward and forward growth of the face beneath the
cranium.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
12
13. Ricketts elected to use Frankfort plane and pterygoid vertical to
create the zero point of a coordinate system.
The basic cranial axis (Ba-nasion) is used as a baseline for growth
analysis.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
13
14. The most widely accepted and most conventional method of
assessing overall dento facial change is to superimpose two serial
tracings with point registration at sella and the S-Na lines
superimposed one over the other.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
14
15. The displacement of nasion up or down during growth at the
frontonasal suture cannot be disregarded.
Bjork studies however showed that in 90% of cases only a very
small changes can be detected, while in the remaining cases,
growth changes amounted to +-1mm with only two exceptions
where the difference was 2mm.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955 15
16. Positional changes resulting from growth or treatment can also be
evaluated using a grid system.
The system entails superimposing headfilm tracings along the
anterior cranial base with sella as a point of registration.
The Grid is formed by a line dropped from sella perpendicular to
the occlusal plane.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955 16
17. Changes in the position of the maxilla and mandible can then be
measured in reference to the grid.
To evaluate growth/Displacement of the maxilla and mandible and to
register movements of upper and lower molars and incisors, Johnson
developed Pitchfork analysis.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
17
18. MAXILLA
Among the most popular superimposing method of maxilla is
that of superimposing serial headfilms along the palatal plane
from ANS to PNS with the films registered at ANS
(McNamara).
To more accurately assess maxillary dental changes, Downs
recommended that the nasal floor in the headfilms be made to
coincide and the tracings registered on the anterior surface of
maxilla, thereby eliminating the problem of change in the
region of ANS.
Jacobson A. Radiographic
Cephalometry, Quintessence
Publishing Co ; 1955
18
19. To eliminate the possible appositional changes at
ANS, the Research Workshop on Cephalometrics
in 1960 advocated superimposition of the superior
and inferior surfaces of Hard palate.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955 19
20. Using implants, Doppel et al compared various maxillary
superimposition methods and concluded that for clinical
purposes the method of maxillary superimposition that most
closely approximates implant superimposition is as follows:
the anterior and posterior contours of the zygomatic
arches are superimposed allowing for the floor of the orbit to
be raised more than the palatal plane is lowered in a ratio of
1.5:1
Jacobson A. Radiographic
Cephalometry, Quintessence
Publishing Co ; 1955
20
21. Mandible
To evaluate intramandibular change, the method agreed on
by a workshop on cephalometry conducted in 1960 was that
of superimposing radiographs along the lower border of the
mandible and on the inner table of the symphysis.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955 21
22. Various accepted mandibular planes are:
1. Tangent to the lower border of the mandible.
2. A line extending from gonion to gnathion, both points
which are variable.
3. A plane joining gonion to menton , likewise with variable
points.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955 22
23. Other superimposition method is by Bjork,
who uses natural reference structures in the
growth analysis of the mandible.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
23
24. By superimposing two radiographic tracings taken at
different ages and orienting them with reference to those
structures, growth pattern of mandible can be estimated
with fairly high degree of accuracy.
Jacobson A. Radiographic Cephalometry, Quintessence Publishing Co ; 1955
24
25. Pitch fork Analysis
Given by Dr. Lysle E.Johnston and presented in
the British Journal of Orthodontics 1996.
The purpose of this analysis is to describe a
method of cephalometric analysis design, that has
evolved over the past two decades and which is
designed specifically to measure the dental and
skeletal effects that combines to produce the
occlusal changes that are the goals of treatment.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 25
26. The change in the molar and incisor relationship can
be expressed as an exact algebraic sum:
Positive= If it reduces overjet/ Corrects a class II.
Negative= If it increases the overjet.
Accordingly, this accounting can support comparisons
of change between treatments and between treatment
phases, not only with respect to magnitude, but also
source( ie skeletal or dental).
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 26
27. The Pitchfork analysis uses Apical base changes
(ABCH) ie the sum of maxillary and mandibular
translatory growth relative to cranial base.
It represents the net effect of skeletal growth ,
usually the amount that the mandible has
outgrown the maxilla.
Lysle E.,
Johnston Jr.
Balancing the
Books on
Orthodontic
Treatment: An
Integrated
Analysis of
Change . British
Journal Of
Orthodontics.199
6;23:2:93-102 27
28. Thus Apical base Changes (ABCH) plus upper
and lower molar movement equals the change in
molar relationship.
Apical base Changes (ABCH) plus upper and
lower incisor movement equals change in overjet.
Lysle E.,
Johnston Jr.
Balancing the
Books on
Orthodontic
Treatment:
An Integrated
Analysis of
Change .
British
Journal Of
Orthodontics.
1996;23:2:93-
28
29. The pitch fork analysis thus requires that the
skeletal change is measured as actual physical
displacement, rather than apparent change in the
position of a landmark due to surface remodeling.
Thus measurements must be executed with
respect to landmarks that have a good chance of
being physically the same at both time points.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 29
30. The present analysis of occlusal change employs
three general superimpositions----
a. Cranial base
b. Maxilla
c. Mandible
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102
30
31. Cranial Base Superimposition
Sella (S) and Nasion (Na) undergo change by local
remodeling during the growth period.
However , the literature argues that the bony
anatomy from the anterior half of sella turcica to the
region of foramen caecum and the internal outline
of the frontal bone is suffiently stable to support
meaningful anterior cranial base superimposition.
Lysle E., Johnston Jr.
Balancing the Books
on Orthodontic
Treatment: An
Integrated Analysis of
Change . British
Journal Of
Orthodontics.1996;23:
2:93-102
31
32. Specifically, Bjork and Skieller(1983) suggest that the
following “natural reference structures” be employed:
a. the anterior wall of sella turcica (and its point of
intersection with the lower contours of the anterior clinods)
b. the greater wings of the sphenoid
c. the cribriform plate
d. the orbital roofs
e. the inner surface of the frontal bone.
Lysle E.,
Johnston Jr.
Balancing the
Books on
Orthodontic
Treatment: An
Integrated
Analysis of
Change . British
Journal Of
Orthodontics.199
6;23:2:93-102 32
33. Maxilla
Best -fit registration for the
maxilla is both the:
a. zygomatic process of
the maxilla(right and left side
averaged).
b. on the bony
anatomical details superior to
the incisors.
Lysle E., Johnston Jr. Balancing the Books on
Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of
Orthodontics.1996;23:2:93-102 33
34. The superior and inferior
surfaces of the posterior
hard palate assist in
orientation and to minimize
the probability of gross
errors in antero-posterior
registration.
Lysle E., Johnston Jr. Balancing the Books on
Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of
Orthodontics.1996;23:2:93-102 34
35. Mandible
For the purpose of measuring tooth
movement relative to basal bone,
mandibular regional superimposition
commonly is effected via a mandibular and a
lingual-symphysis registration.
Lysle E., Johnston
Jr. Balancing the
Books on
Orthodontic
Treatment: An
Integrated Analysis
of Change . British
Journal Of
Orthodontics.1996;
23:2:93-102
35
36. Implant studies, however,
suggest that greater
validity can he achieved by
using the mandibular
canal, tooth germs (prior
to the initiation of root
formation), and the
individual bony
architecture in the labial
aspect of the symphysis
(Bjork and Skicller, 1983:
Dibbets, 1990; Fig. 5).
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
36
37. Unfortunately, many of these bony details
are often absent, difficult to see, or distorted
by among-series variation in head placement.
When, as is sometimes the case, nothing
seems to match (except, perhaps, bony
details within the symphysis), the mandibular
plane can be used as a substitute orientation
line, especially if there has been minimal
growth between cephalograms.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 37
38. Indeed, if there has been little change in
overall size, any superimposition that seems
to show marked growth rotation probably is
wrong.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
38
39. The pattern of craniofacial growth
Before the measurement of skeletal and
dental change is examined, it should be noted
that the three superimpositions described
here can also be useful in illustrating the
overall pattern of growth.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 39
40. When each tracing has been
executed in appropriate detail,
'fiducial lines' (arbitrary straight
lines several inches long marked
on either end with registration
crosses) are drawn adjacent to
cranial base, maxilla, and
mandible of one tracing.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis of
Change . British Journal Of Orthodontics.1996;23:2:93-102 40
41. Once the fiducial lines have been transferred
through out the series, they serve not only to
record the superimpositions to facilitate the
process of measurement (and re-
measurement), but also to provide a greatly
simplified picture of change seen from the
vantage point of any of the three facial areas.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 41
42. When the cranial base fiducial
lines are superimposed, the
seperation of the mandibular
and maxillary fiducial lines
represents the translatory
growth ---
both in amount and
angulation ---
of the jaws relative to
cranial base.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102 42
Fiducial lines
43. Measurement of change:
Although the face undergoes widespread
change during orthodontic treatment, only
effects that are felt at the level of the
occlusion can have a direct impact on the
molar and incisor relationships.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 43
44. The occlusion, therefore, represents the
'bottom line', the site at which change in the
upper and lower jaws comes together and is
integrated.
For this reason, the pitchfork analysis
measures change projected onto the plane of
occlusion.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
44
45. Accordingly, the pitchfork analysis uses a
functional' occlusal plane ( FOP) similar to
that suggested by Jenkins ( 1955) and
defined as “the average occlusal plane of the
buccal teeth, including canine and first
permanent molar·”
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 45
Functional
occlusal
plane
46. As used here, Functional Occlusal Plane is 'a
best-lit line passing through the occlusal
overlap in the region of the first molars,
premolars and canines (especially when
premolars have been extracted).”
46
47. Thus it is insensitive to incisor movement, it is
representative of the bulk of the buccal occlusion,
and it is relatively stable over time, although its
angulation with respect to cranial base tends to
decrease slightly and progressively as the
mandible outgrows the maxilla.
Unfortunately, the functional occlusal plane also
tends to he technically challenging. It can serve as
the basis of an analysis of change only if great
care is exercised during the execution of the
tracings.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102 47
48. Firstly, it is important to remember that
Functional Occlusal Plane is defined mostly
by the premolars and first permanent molars,
the second and third molars, and incisors
must he ignored.
Secondly, the line is placed by inspection.
either with respect to the radio-opacities
created by cuspal overlap or to the
radiolucencies scattered among cusps along
the line of the occlusion.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 48
49. When a two-film series is to be analysed the
maxilla are superimposed, and the two
Functional Occlusal Plane then they are
averaged by inspection to yield a Mean
Functional occlusal plane (MFOP) which is
passed through to each tracing.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 49
50. This averaging is aided, once again, by the use of a lined
acetate strip.
When change is to be measured in a series of more than
two films, the Mean Functional Occlusal Plane is obtained
by averaging the initial and final functional occlusal
planes.
Lysle E., Johnston Jr.
Balancing the Books on
Orthodontic Treatment:
An Integrated Analysis
of Change . British
Journal Of
Orthodontics.1996;23:2:
93-102 50
51. Once the Mean Functional Occlusal Plane
has been established and transferred to all
tracings in the series, regional
superimposition within cranial base, maxilla,
and mandible is used to measure the various
components of antero-posterior change that
make up the tines of the pitchfork.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
51
52. Jaw growth/displacement relative to cranial
base
In the anterior cranial base, 'wing point' (W, the
point at which the greater wings of the sphenoid
crosses jugum sphenoidale ) commonly serves as a
registration point and is used here as the cranial-
base reference point from which maxillary and
mandibular displacement are measured .
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
52
53. To maximize both its validity and reliability,
the anterior-cranial-base fiducial line is used
to passW from one tracing through to the
others in the series.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
53
54. To measure displacement of the maxilla
relative to cranial base (MAX), the maxillary
fiducial lines are superimposed and the
separation of theW points measured parallel
to Mean Functional Occlusal Plane (MFOP)
(Figs 3 and 4)
Lysle E., Johnston Jr. Balancing the Books on
Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of
Orthodontics.1996;23:2:93-102
54
55. Mandible:
The separation of D-points is measured
parallel to Mean Functional Occlusal Plane
(MFOP) (Fig. 4).
This measurement represents Apical Base
Change (ABCH), the growth/displacement of the
mandible relative to maxillary basal bone.
Lysle E., Johnston Jr.
Balancing the Books on
Orthodontic Treatment: An
Integrated Analysis of
Change . British Journal Of
Orthodontics.1996;23:2:93
-102
55
56. Since the mandible outgrows the maxilla, ABCH
commonly is positive.
Whatever its sign (and cause), mandibular
displacement relative to cranial base (MAND)
then can be estimated by subtraction:
MAND = ABCH- MAX.
For example, if the maxilla underwent 3
mm of forward translatory growth, and the
mandible out-grew it by 4 mm,
MAND = 4 - (-3) = 7 mm.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102
56
57. These three measurements abstract the
sagittal growth of the jaws and, together with
tooth movement, account for change in
molar relationship and overjet.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated
Analysis of Change . British Journal Of Orthodontics.1996;23:2:93-102 57
58. Tooth movement relative to basal bone
Tooth movement is measured parallel to
Mean Functional Occlusal Plane from the
vantage point of a superimposition within
either the maxilla (Fig. 7) or mandible (Fig. 8)
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
58
59. Molar crown movement is measured at the
mesial contact point,
root movement from the point at which the
long axis is crossed by a line drawn between
the apices of the buccal roots.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102 59
60. Crown movement is the algebraic sum of root
movement and a component due to tipping.
Thus, the tipping component can be estimated
by subtracting root movement from crown
movement.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102
60
61. The same procedure can be applied to the
incisors; however, it may be less important to
resolve separate tipping and bodily effects here
than in the molar region.
Lysle E., Johnston Jr. Balancing the Books on Orthodontic Treatment: An Integrated Analysis
of Change . British Journal Of Orthodontics.1996;23:2:93-102 61
62. Molar relationship and overjet change'
The change in molar relationship is measured
by registering on the mesial contact point of
one molar (upper or lower) and then
measuring the separation of the contact point
of the other.
Lysle E., Johnston Jr.
Balancing the Books on
Orthodontic Treatment: An
Integrated Analysis of
Change . British Journal Of
Orthodontics.1996;23:2:93
-102 62
63. the change in overjet, by registering on the
averaged incisal edge of the upper or lower
incisors and then measuring the displacement
of the averaged incisal edge in the other arch
(Fig. 9).
Lysle E., Johnston Jr.
Balancing the Books on
Orthodontic Treatment:
An Integrated Analysis of
Change . British Journal
Of
Orthodontics.1996;23:2:9
3-102
63
64. Reliability:
The reliability of this technique as a whole
can he estimated from double-
determinations.
In past studies of Class II treatment, 5-10
percent of the subjects were selected at
random, and their cephalograms retraced
and re-measured.
Based on Dahlberg's formula Based on
Dahlberg's formula may he seen, most
standard deviations lie in the regi0n of 0·5-0·7
mm.
64
65. In any event, power calculations based on the
present data imply that samples of about 30
have a reasonable probability (say, 80-90 per
cent) of resolving treatment effects in the
range of 0.5 -1·0 mm.
65
66. Conclusion:
This method of Cephalometric analysis is
designed to provide an integrated accounting
of the source-skeletal growth or tooth
movement.
Each of the components is measured
separately , however as a group they sum to
provide a “complete” explanation of changes
in overjet and molar relationship.
66
67. References
1. Jacobson A. Radiographic Cephalometry, Quintessence
Publishing Co ; 1955
2. Kharbanda OP. Orthodontics Diagnosis and Management
of Malocclusion and Dentofacial Deformities,3rd edition,
Elseiver; 2020
3. Lysle E., Johnston Jr. Balancing the Books on Orthodontic
Treatment: An Integrated Analysis of Change . British
Journal Of Orthodontics.1996;23:2:93-102
67