Growth prediction1

• Growth and Development is a remarkable
tale of an orderly sequence by which each
human being blossoms out from a minute
cell to an adult man
www.indiandentalacademy.com

• Growth is defined as :
· Multiplication of living substance (J.S.
Huxley)
· increase n size, proportion and progressive
complexity (Krogman)
· an increase in size (Todd)

• Growth has some characteristics like :
• Pattern
• Variability
• Timing

• Why is understanding growth so important?
• Growing
• Non-Growing
• Brodie in 1938 said “There seems to be a
definite correlation between success of
treatment and growth. Apparently growth
and development accounts for a
considerable part of change which takes
place during orthodontic treatment”

• Correction of dentofacial malocclusions
would be helped immeasurably if he could
predict with a degree of certainty the adult
features of his patient
• If the dentist could forecast the child’s adult
appearance with or without therapeutic
intervention, decisions could be made about
the timing, type, and length of treatment
• In borderline cases, decisions on whether to
treat at all could be better weighed

• For growth prediction to be feasible at all,
craniofacial growth must be orderly

Fibonacci series and divine
proportion
• What is Fibonacci series ?
0 1 1 2 3 5 8 13 21++ =+ ==+ =

• It would appear that the principle of the
golden section and Fibonacci numbers are
basic to this orderly arrangement and
growth of the human face
• Mandible grows on the logarithmic spiral
which has a basis the golden triangle, in
turn, related to the golden section which is
related to the Fibonacci series

What is Prediction?
• According to Kendall and Buckland “ The
process of forecasting the magnitude of
statistical variations, at some future point of
time”
• “Specifying the amount and direction of
future growth in the context of a base line
or reference point”

Need for Growth Prediction
• Is a change in the vertical or horizontal
relationship of the upper to the lower jaw
indicated?
• Should the lower incisor be repositioned both
horizontally and vertically?
• What movement of the upper incisor is required?
• Should anchorage be prepared or preserved in the
lower arch?
• Is movement or stabilization required for the
upper molars?

• Will the tooth movement bring about a
desired esthetic result which will still be
acceptable at maturity?
• Will post-treatment growth affect retention?
• Will there be space for the third molars
given a specific treatment?

• The principal proponents of growth
prediction Ricketts and Holdaway have
suggested that the major value of the
technique is the compilation of all the
treatment factors (mechanics, growth,
skeletal and soft tissue) together on paper to
see how they inter-relate

What are we interested in predicting in
the craniofacial complex?
• According to Hirschfield and Moyers :
• Future size of a part
• Relationship of parts
• Timing of growth events
• Vectors of growth
• Velocity of growth
• The effects of orthodontic therapy on any of
the above predicted parameterswww.indiandentalacademy.com

• Future size of a part
The prediction of future size, as Burstone has
pointed out, is primarily a problem of predicting
future increments which are to be added to a size
that is already known
• Relationship of parts
perhaps the most important prediction for the
clinician is the future relationship of parts, i.e. the
future facial pattern. Johnson found measures of
relationship and proportion to be of greater
predictive significance than the linear size of
anatomic parts.

• Timing of growth events
Growth spurts
• Vectors of growth
Most predictive methods thus far presume a
continuation of the pattern first seen
Therefore, the presumption is made that the
vectors of growth present at the time of prediction
will remain

• Velocity of growth
It would be of use to know the future
expected rate of growth
Prediction of velocity is most important
during the pubescent spurt

• The effects of orthodontic therapy on any of
the above predicted parameters
Our knowledge of prediction might best
proceed by learning to predict untreated
growing faces
The clinician must always wonder what
effects his therapy have on the predicted
and actual growth of one specific face

Methods of Prediction
• Theoretical
• Regression
• Experiential
• Time series

Theoretical method
• Collection of series of relevant, random data
• Mathematical construction of a theoretical model
• Theoretical development of a hypothesis from the
model
• Proving the hypothesis practically
• The model began theoretically and was proved
practically
• Implication in orthodontics :
• Theoretical models of craniofacial growth have
not yet been defined mathematically in terms
precise enough to permit the application of the
method to predictionwww.indiandentalacademy.com

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. E.g. Johnston grid

• Ultimate accuracy of cephalometric
prediction may be limited to some extent by
intrinsic errors within the cephalometric
method itself
• Contemporary methods seem inadequate to
provide an efficient estimate of individual
changes attributable only to growth

Drawbacks
• The assumption within the method that the
coefficients remain constant over thw whole
time period.
• An individual whose growth is to be
predicted in clinical practice may not even
be a member of the population upon which
the regression equation was based

Experiential method
• They 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 used by others. E.g.
Ricketts

Drawbacks
• Theoretical basis is shaky on two counts:
– The assumption must be made that the
individual being predicted will behave as the
mean of a population of which he is a not a
member
– The morphology of the mandible and other
parts is a clue to the future growth of the face

Time-series methods
• Accuracy, efficiency and individuality for
clinical application
• “Random walk” type or process
• These methods consists of two types:
time-series analysis
smoothing methods

• Time-series is considered to be composed
of four parts :
1. Trend or long-term movement
2. Oscillations about a trend
3. Cyclic or periodic events
4. Random (unsystematic) components

• Exponential smoothing is a way of
estimating the current value of a parameter
by means of some sort of average of past
values of that parameter
• Prediction is then based on coefficients
derived from the smoothed parameters.
• Since the coefficients will change in accord
with changes in parameter, the predicted
coefficients will change in accord with
changes in the parameter

Classification of Growth
Prediction
• Based on average values
• individualized prediction
• manual
• computerized
• short range
• long range

Most predictions of growth are based on some
mathematical model of the growth process,
two kinds of which can be distinguished:
(1) the transformed coordinate method of
D’Arcy Thompson
(2) Equations producing curves descriptive of
processes

Growth studies
• The numeric standards from which the
present specific templates were drafted are
derived from 3 major studies reports. They
are:
• Michigan Growth study
• Bolton-Brush Growth study
• Burlington Growth study

Short comings of Growth Studies
• Existing data sets are too small to allow
subdivision in different categories :
– Bolton’s data is age specific only
– michigan has subdivision on the basis of sex
– Burlington has subdivision on the basis of
facial types

• All data sets are derived from whites of
Northern European descent
• sample mostly consists of normal children.
• The patient to be predicted for growth may
not have the average amount or direction of
growth

• Johnston forecast Grid
• template methods
• schematic template
• anatomically complete template
• Ricketts prediction
• short range
• long range
• Holdaway soft tissue VTO
Growth prediction methods

Johnston’s forecast grid
• Based on the addition of mean increments of
growth by direct superimposition on a printed grid
• The land marks used are :
Sella
Nasion
Tip of nose
Point M
Point A
Point B
Posterior Nasal Spinewww.indiandentalacademy.com

• Tracing of landmarks is superimposed along S-N
and registered at S
• The points are then advanced downward and
forward one unit per year
• Vectors for A, B and M were inferred from
descriptive templates prepared by Hries and
associates and the behavior of N and P was
patterned after reports by Ricketts

Template Method
• When an average cephalometric tracing is
made of a group by connecting the average
values of each landmark, the composite
tracing thus prepared is called a Template
• There are 2 types of templates :
– Schematic template
– Anatomically complete template

Schematic template
• The schematic templates show the changing
position of selected landmarks with age on a
single template
• Michigan and Burlington growth studies have
developed this type of templates
• Michigan templates have sub-divisions on the
basis of sex
• Burlington templates have subdivision on the
basis of facial pattern

anatomically complete template
• Based on Bolton growth study data.
• Age-specific
• A reference template is selected so that the
lengths of anterior cranial base are same
• The growth is predicted by advancing the
template ages from the reference templates

V.T.O.
• The term VTO is used in two different
contexts :
• VTO as a diagnostic test for functional
appliances
• Growth prediction VTO
– Holdaway’s VTO
– Ricketts’ VTO

Various soft and hard tissue land
marks used in various growth
prediction methods

• Soft-tissue facial angle

• Nose prominence

• Superior sulcus depth measured to a
perpendicular to Frankfort and tangent to
the vermilion border to the upper lip

• Soft-tissue sub-nasale
to H line

• Skeletal profile convexity

• Basic upper-lip
thickness

• Upper lip strain measurement

• H angle

• Lower lip to H line, Inferior sulcus to H
line, soft tissue chin thickness

Tracing of Holdaway measurements
on an ideal profile

VTO by Myerson and Katona
• In the case of Steiner Analysis, it can be
demonstrated with geometric principles that
the sum of the following 4 angles is equal to
180 degrees
– ANB
– Mandibular incisor to the NB plane
– Maxillary incisor to the NA plane
– Interincisal angle

• The first treatment in obtaining the visual
treatment objective involves a clinical
judgment - determination of the desired
angulation of the mandibular incisor to the
NB plane
• In actual planning of treatment, the desired
angulation of the lower incisor to the NB
plane must be left to the judgment of the
individual clinician

• Downs - Interincisal angle 131 degrees
• Reidel - suggested that the relationship
between maxillary and mandibular incisors
is best determined by functional and
esthetic considerations

• From a functional standpoint the
relationship of maxillary lingual crown
contour to mandibular incisal edge position
is more important than the interincisal angle
• Considering esthetics, he suggested that the
upper and lower incisor facial crown angle
should approach 0 degrees or a straight line

• Because of variations in crown axis/root
axis angulation ass seen in dilaceration, an
optimal facial crown angle of 0 degrees
does not always correlate to any single
“ideal” interincisal angle
• The interincisal angle most appropriate to a
particular case must be determined by
drawing a cephalometric incisor “setup”
with a facial crown angle of 0 degrees

• Determine the angulation of lower incisor to
NB plane
• Set upper and lower incisors at a facial
crown angle of 0 degrees
• Measure the resulting interincisal angle
• Estimate the expected ANB angle following
treatment
• Calculate the required upper incisor to NA
angulation

Ricketts Growth Prediction
• Growth Estimation - 1957
• Cephalometric Analysis and Synthesis-1961
• Short-range VTO -
• Long-range VTO - 1972

CEPHALOMETRIC ANALYSIS
AND SYNTHESIS
• The Static Synthesis
– Estimation is made almost entirely for the
movement of the teeth and changes in lips
– the lower incisor is positioned with one SD of
the normal to the APo
– the upper incisor is then adjusted to it with
normal overbite and overjet
– the necessary anchorage can be envisioned by
movement of the posterior teeth

• The Dynamic Synthesis
– Growth of the chin - foremost consideration
– Cranial areas are employed for basal refernces

• Cranial Behavior
– Maxilla seemed to grow forward at almost an
identical rate with nasion
– SNA angle changed very little
– 1 mm per year of growth on the SN plane can
be expected and Sella-Basion is usually about
two-thirds of that amount

• Mandibular Behavior
– estimating the change in the chin by the
direction of the Y axis or growth axis of the
face
– in the ave. Class II case the Y axis tended to
open about one degree during a two year period
during treatment
– In Class III cases, the Y axis closed one degree
or more during orthodontic treatment

• So the final consideration for estimation of
change in the direction of the Y axis
revolves around the original facial pattern
• the amount of growth of the mandible
– knowledge of average case is the starting point
– average yearly expectancy is about 2.5 to 3 mm
of growth on the Y axis

• Change the Y axis and lengthen it for
estimated growth, draw the symphysis and
establish the mandibular plane backward
from the symphysis consistent with the tilt
of the mandible

• Maxilla Behavior
– Behavior of Point A from a vertical and
horizontal standpoint is estimated
– Point A and the anterior nasal spine usually
drop vertically about one-third the total facial
height increase during treatment
– about two-thirds height increase is measured in
the denture area or lower face

• Cephalometric Tooth Set Up
– Lower incisor is related to the A-Pog line
depending on the environmental forces
operating on the denture and the age of the
patient

• Analysis - “where he was”
• Synthesis - “where to go”

Arcial growth of mandible – Long
Range VTO
• “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)”

• By plotting a line through the long axis of
the condyle and neck and extending it to the
lower mandible, the bending of the
mandibular form during growth had been
studied

• Bjork’s implant studies had revealed that the
lower border of the mandible was resorbing and
that the mandibular plane was not acceptable as a
reference base for growth analysis
• The next move toward improving the method was
to identify a “central core” cephalometrically
• External form of mandible

• First, a point (Xi) in
the center of the ramus
was located

• Occlusal plane holds a strong tendency to
pass through Xi point
• Xi also represents the entrance of the
neurotrophic bundle into the mandible

• Second, a point at the superior aspect of the
symphysis was selected as suprapogonion
(Pm)
– Stress-center acc. to Ricketts
– Site of a reversal line acc. to Enlow

• Third, point Dc as
located
• Corpus axis
• Condyle axis

Bending occurred in an orderly manner and therefore the
greater the magnitude of growth, the greater the bending
Mandible was found to bend about half degree each yearwww.indiandentalacademy.com

• Constructed an experimental arc bisecting
the two previous arcs
• The use of this arc still bent the mandible a
fraction too much
• Stress lines

Apposition of the lower
border of the symphysis
for males occurs at about
1 mm each 8 years
From the point Mu the
mandible is grown on the
arc at the sigmoid notch
about 2.5 mm each year

K factor
Coronoid is extended
upward and outward at a
rate of 0.8 mm per year
Condyle in this average
individual is extended
upward and backward
0.2 mm per year

Drift of the mandible
occurs almost precisely
at a pace of 50% of the
total mandibular growth

• Oblique ridge of the
mandible shows
apposition of about 0.4
mm each year
• This is a critical point
because it helps to
determine the space
available for the
developing mandibular
third molar

Growth prediction1

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