This document provides an overview of various methods that have been used for predicting facial growth and development in orthodontics. It discusses early concepts like Hunterian growth theory and Bjork's implant studies showing rotational growth. Methods like Moss' logarithmic spiral concept and Ricketts' arcial growth pattern are explained. Growth prediction grids like Moorrees mesh and Johnston's grid are summarized. The document also mentions Todd's equation for predicting non-linear radial growth and Holdaway's concept of a visualized treatment objective to forecast normal growth and treatment effects.

1. Growth Prediction
Guided by-Dr. Jeevan M. Khatri sir
(Professor & HOD)
Dept. of Orthodontics and Dentofacial Orthopaedics
Presented by-Krutika A. Patankar (3rd YR MDS)
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2. Contents
• Introduction
• Growth assessment Vs Growth prediction
• Need for growth Prediction
• Methods of Prediction in Science (Hirshfield, 1971)
• Growth Prediction in Orthodontics
• Hunterian concept
• Bjork implant study
• Gnomonic Growth and Logarithmic spiral
• Unloaded nerve concept
• Arcial growth of mandible
• Moorrees Mesh
• Johnston’s Grid
• Todd’s equation
• VTO
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3. Introduction
• The understanding of facial growth and occlusal development plays an
important role in orthodontic diagnosis and treatment planning of
problems encountered in dental and skeletal malocclusions.
• What is Growth? An entire series of sequential anatomic and morphologic
changes taking place from the beginning of prenatal life to senility-
Meredith.
• As Proffit says, growth prediction can never be accurate especially when
the child is growing. Growth prediction can be defined as the forecast of
growth related changes with the objective of predicting the direction and
amount of the growth of the maxilla and particularly the mandible as well
as the timing of the adolescent growth period.
• Being able to predict growth will help craniofacial biologists in two
principal ways:
- (i) The science of prediction demands that the knowledge of the
craniofacial biologist be valid and cohesive and that they understand a great
deal about craniofacial growth and
- (ii) Predicting the adult features of a patient will help in the interception
and correction of malocclusion.
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4. Growth assessment Vs Growth prediction
• Growth assessment procedures indicate the growth status of the patient at a
particular time and provide an assessment of the percentage of growth left.
• Growth prediction helps in predicting to a certain extent the response to
treatment and the growth changes.
Growth spurts
Period of sudden acceleration of growth. Due to physiological alteration in hormonal
secretion.
- The timing of growth spurts differs in boys and girls, the following are the timing of
growth spurts-
• A. Just before birth
• B. One year after birth
• C. Mixed dentition growth spurts-Boys:8-11 yrs
Girls:7-9 yrs
• D. Pre-pubertal growth spurt-Boys-14-16 yrs
Girls-11-13 yrs
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5. Need for growth Prediction
• Growth prediction helps the clinician to intercept and correct the
malocclusion.
• Growth prediction can be used as patient education aids.
• Growth prediction (VTO) is helpful in 'visualizing' the treatment
objectives and prioritizes the objectives, keeping in mind the growth
pattern of the patient.
• Growth prediction is a tool for orthodontic treatment planning but
without forcing any particular treatment procedure.
• Response to a particular treatment can be predicted, provided the
patient continues in the same growth direction.
• If the patient continues to be in the growth phase even after
treatment, growth following the conclusion of treatment can be
predicted to plan for retention period, thus ensuring stability of the
results. 5

6. Methods of Prediction in Science (Hirshfield,
1971)
• Theoretical
• Regression
• Experiential
• Time series.
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7. Theoretical method
• Theoretical methods of prediction- Astronomers recently discovered
an earth- sized planet several thousand light years away from us by
collecting a series of inexplicable, apparently random data on the
behavior of celestial bodies until a theoretical model could be
constructed mathematically which might explain all the unusual
activity observed, and a test for a hypothesis was devised.
• Law of Gravitation: F= G m1m2 , G= gravitational constant.
r2
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8. • Regression methods. These methods serve to calculate a value for
one variable, called dependent, on the basis of its initial state and the
degree of its correlations with one or more independent variables.
• Experiential method. Experiential methods are based on the clinical
experience of a single investigator who attempts to quantify his
observations of practice in such a way that they can be codified for
use by others. The best-known example of the experiential method in
craniofacial growth prediction is that of Ricketts, whose estimates of
growth prediction for the individual utilize means derived from a large
sample of treated orthodontic patients. The method is popular and
widely used, but its theoretical base is shaky on two counts. First, the
assumption must be made that the individual being predicted will
behave as the mean of a population of which he is not a member.
Second, the morphology of the mandible and other parts is a clue to
the future growth of the face.
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9. • Time series method. Because of the great interest in prediction of
cranio- facial growth and the limitations of the methods thus far tried,
it seems pertinent to ask whether there might be some other method
of prediction, as yet untried on growth problems, which would
provide the desired accuracy, efficiency, and individuality for clinical
application.
• The methods are of essentially two types:
• (1) time-series analysis which extracts in a mathematical form the
fundamental nature of the process as it relates to time, and
• (2) smoothing methods, either moving averages or exponential, which
operate to give representative or average values to the parameters of
a previously derived time-series equation.
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10. Growth Prediction in Orthodontics
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11. Hunterian concept
The Hunterian concept of mandibular growth was held as a dictum till Bjork
proved that mandible and maxilla underwent rotational growth in his
implant studies.
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12. Bjork implant study
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13. Classification of rotation of mandible(1969)
• Forward rotation of mandible
• Backward rotation of mandible
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14. Gnomonic Growth and Logarithmic spiral
• Following Bjork’s growth rotation concept, Moss and Salentejin
predicted that mandible's rotational growth was along a spiral path.
Moss’ method of predicting the mandibular growth along a
logarithmic spiral derives its inspiration from the concept of “gnomic
growth” by D’Arcy Thompson.
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15. Logarithmic spiral in nature
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16. Archimedean spiral Vs Logarithmic spiral
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17. Gnomonic growth of the human face
• Moss after extensive study indicated that orofacial matrices manifest
gnomonic growth. He sectioned the heads of human fetuses with crown-
rump length ranging from 26 to 163 mm in the midsagittal section. Direct
measurement of the oral, pharyngeal and nasal cavities demonstrated
gnomonic growth of the nasal, oral and pharyngeal spaces
Nasal (left) and Oral (right) functioning spaces of human fetuses
demonstrating gnomonic growth (Adapted from: Moss and Salentijn.
Morphological attributes of logarithmic growth of human face) 17

18. Unloaded nerve concept
• Moss postulated that growth of mandible could be influenced by the
inferior alveolar nerve and its direction depends on the course of the
nerve. He called this 'the unloaded nerve' concept.
• Lead shots were implanted at three foramina along the path of the
nerve, namely the foramen ovale, mandibular foramen, mental
foramen. Lateral cephalograms of all the bones were taken.
• Mandibles at four different stages of development were included in
the study: fetal, deciduous, mixed dentition and adult mandible.
• The X-rays were superimposed and it was found that the path of
inferior alveolar nerve was along a logarithmic curve and that the four
curves of all the mandibles were superimposed
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19. • The equation of the spiral is:
log r = log a + ko
where r = radius of the curve of the spiral
o = angulation of the radial line [in radians] a = value of r when o = 0.
• As the bone increases in size, the spiral itself does not change,
instead, the mandible changes in position and the base appears to
rotate along the spiral, moving to a position where there is less
curvature of a spiral because as the bone lengthens with growth, the
distance between the foramina increases.
• During growth, the gonial angle that was obtuse becomes acute; due
to clockwise rotation, the corpus remains horizontal and the position
of ramus keeps changing and the mandible undergoes a clockwise
rotation along the spiral path.
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20. (A) Location of foramen ovale, mandibular foramen, and mental
foramen in the fetal, deciduous, mixed and adult skulls.
(B) The foramina are aligned perfectly on a logarithmic spiral—a single 20

21. Arcial growth of mandible
• Ricketts described a pattern of arcial growth of mandible.
• The advantage of Ricketts arcial growth pattern was that an arc of
growth can be constructed for every individual depending on the
length of the core of the mandible.
• Improved visualization of the condyle and coronoid by laminography
enabled Ricketts to better observe the bending of the mandible from
infancy to maturity.
• Principle of Arcial Growth
• The normal human mandible grows by supero-anterior (vertical)
apposition at the ramus on a curve or arch which is a segment formed
from a circle. The radius of this circle is determined by using the
distance from mental protuberance (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 (point Eva).
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22. Eva point
Eva point represents the confluence of stress lines on the medial surface
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23. Landmarks used by Ricketts:
Xi point: It represents the geometric center of ramus.
• Xi point is the geometric center of ramus. It is determined by the
intersection of diagonals of a rectangle which has height and width of
ramus as its sides
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24. • R1: Most concave point on the anterior border of ramus.
R3: Deepest point on the sigmoid notch.
R2: Point opposite R1 on the posterior border of ramus. R4: Point opposite
to R3 inferior border.
• DC point: It is the midpoint or the bisecting point of the condylar neck.
• PM point or Suprapogonion: It is the point where the anterior border of
symphysis of mandible turns from convex to concave. It was found to be
the most stable point in mandible and is hence, used as reference.
• MU point (Murray): This point was named after Ricketts’ father. It is a point
on the sigmoid notch where the curve from Eva touches the notch.
• Tr/True radius: It is the center of the arc. It is the intersection of arcs from
Eva and PM drawn with Eva- PM as the radius.
• DC-Xi line constitutes the Condylar axis.
• Xi-PM line constitutes the Corpus axis.
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25. 25

26. Ricketts constructed three arcs:
• Curve A: Curve A was through DC-Xi and PM. If mandibular growth
had been along this curve, then it would open the gonial angle too
wide, which normally does not happen. The resulting mandible will
be too obtuse this way.
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27. • Curve B: This curve was constructed passing from the tip of coronoid
process through the anterior border of ramus, and through Pm. The
mandibular growth along this curve would be bent too much.
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28. • Curve C Arc of Mandible: The final curve was between coronoid and
condylar processes through Eva-PM.
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29. • With the arcial growth of the mandible, it is evident that mandibular
growth is not linear but along an arc.
• Conceptual framework about the direction of mandibular growth has
shifted from being horizontal to vertical with Ricketts’ arcial growth.
• Occlusal plane and mandibular teeth eruption: As mandible grows
along the arc, space is created for the 2nd and 3rd molars. According
to Ricketts, the anterior border does not have to undergo resorption
to accommodate the molars because the molars erupt upward and
forward. With arcial growth and upward and forward eruption of
teeth, the chin is pushed beneath the lower arch.
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30. Serial tracings showing relation of teeth eruption and arc of mandible
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31. Moorrees Mesh
Moorrees constructed a template in the form of a mesh which was
used to superimpose growth changes in serial lateral cephalometric
radiograph.
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32. Johnston Grid
• Johnston designed sex specific templates by utilizing the numerical
standards obtained from the publications of Riolo et al who used the
cephalograms from University of Michigan.
• Method: The Johnston's forecast grid shows the average increments
of growth per year for the points nasion, A, B, nose and posterior
nasal spine. It also gives a method of constructing pogonion, given a B
point. There is no individualization in this method, in that, all the
patients will grow the same amount horizontally and vertically
irrespective of their facial patterns. This method is accurate to about
70 percent
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33. • Forecast grid developed by Johnston. S, sella; N, nasion; P, posterior nasal
spine; Nose, tip of nose; M, any point on the crown of maxillary first
molars; A and B, subspinale and supramentale. The tracing of the
landmarks is superimposed along S-N and registered at S. The points are
then advanced downwards one unit per year 33

34. • (A) Johnston's method of prediction. Each point is extended to predict
the average amount and direction. The basic reference line is sella-
nasion. (B) Comparison of point B growth with pogonion in both
horizontal and vertical directions 34

35. • Regional Superimposition: Regional template is placed over the
cephalogram and measurement is made between 2 points [e.g. PNS-
ANS for maxilla, GO-Pg for mandible] and age noted in years.
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36. Todd’s Equation
The disadvantages of ordinary prediction methods are:
• They are all in the form one of linear coordinate system, either
rectangle or grid system, it cannot predict radial growth, the angular
coordinate of each landmark remains a constant.
• There are many frames of reference used to describe growth. Every
frame of reference can give a description of growth changes, for
example, SN superimposition is markedly different from FH plane
superimposition.
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37. Visualized Treatment Objective (VTO)
• Visualized Treatment Objective was coined by Holdaway.
• A VTO is a cephalometric tracing representing the changes that are
expected during treatment (Proffit).
• Ricketts defines VTO as a visual plan to forecast the normal growth of
the patient and anticipated influences of treatment, to establish
individual objectives that are to be achieved for that patient.
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38. To be continued......
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