Growth prediction/ oral surgery courses

GROWTH
PREDICTION
INDIAN DENTAL ACADEMY
Leader in continuing Dental Education
www.indiandentalacademy.com

CONTENTS
• Growth.
• Growth prediction.
• Gnomonic growth.
• Neurotrophism.
• Logarithmic growth of human mandible.
• Arcial growth of mandible.
• Methods of growth prediction.
• Visual treatment objective.
• Conclusion

GROWTH
TODD: GROWTH IS INCREASING IN SIZE.
PROFITT: GROWTH IS INCREASE IN SIZE OR NUMBER.
Growth is a dynamic process with a stable pattern of changes
resulting in the increase in physical size and mass during it’s course
of development.
Thus, growth is a three-fold process “SELF-
MULTIPLICATION,DIFFERENTIATION,ORGANIZATION”
each according to it’s own kind.A fourth dimension is TIME.

GROWTH
• PATTERN
• VARIABILITY
• TIMING

PATTERN
NORMAL GROWTH PATTERN: Not all tissue systems
of the body grow at the same rate.Muscular and skeletal
elements grow faster than the brain and CNS.
PREDICTABILITY: The proportional relationships can be
specified mathematically and the difference between a
growth pattern is the addition of a time dimension.
VARIABILITY
Variability in growth and development can be expressed
quantitatively to categorize people as normal or abnormal.
It is usually assessed with peer group of children.

TIMING
Variation in timing arises because the same event happens for
different individuals at different times or is viewed differently.
The biologic clocks of different individuals are set differently.
CRITICAL PERIOD
Period of acceleration and cellular replication during which the
organ is most susceptible to damage with permanent impairment
of appearance,growth or function.

GROWTH PREDICTION
GROWTH PREDICTION IS THE FORECASTING OF THE
DIRECTION AND AMOUNT OF GROWTH OF THE
MAXILLA AND MANDIBLE {HORIZONTAL AND
VERTICAL GROWTH TRENDS} AS WELL AS THE TIMING
OF THE ADOLESCENT GROWTH PERIOD.
WHAT IS THE NEED FOR IT????
• HELPS THE CLINICIAN DEALING WITH INTERCEPTION
AND /OR CORRECTION OF DENTOFACIAL
MALOCCLUSIONS.
• DECISIONS CAN BE MADE ABOUT THE NEED FOR
TREATMENT.
• DECISIONS COULD BE MADE ABOUT THE TIMING, TYPE
AND LENGTH OF TREATMENT.www.indiandentalacademy.com

MATHEMATICAL MODELS
 MOSS AND SALENTIJIN proposed A MATHEMATIC
EXPRESSION to describe human mandibular growth.
 RICKETTS created a CEPHALOMETRIC TECHNIQUE
for drawing an arc along which the mandible can be expected to
grow.
The above mathematical models that describe mandibular
growth have evolved from the following FUNDAMENTAL
CONCEPTS:
1. D’ARCY THOMPSON’S STUDY OF SEASHELLS.
2. MOSS’S INTERRELATED THEORIES OF
FUNCTIONAL MATRIX,GNOMONIC FACIAL GROWTH
AND FACIAL NEUROTROPHISM.

GNOMONIC GROWTH
THE CHAMBERED NAUTILUS
THOMPSON ANALYSED THE
GROWTH OF CERTAIN SEA
SHELLS.
THE CHAMBERED NAUTILUS HAS TWO
FUNDAMENTAL CHARACTERISTICS:
The shell grows in size but does not change it’s
shape.Although the shell grows asymmetrically ,the original
shape remains constant.
The process of growth whereupon the addition of
a figure or body leaves the resultant figure or body similar to
the original is called GNOMONIC GROWTH.

The gnomonic growth can be described by a particular kind of
curve called as the LOGARITHMIC or EQUIANGULAR
SPIRAL.
The spiral is characterized by the movement of a point away from
the pole along the radius vector with a velocity increasing as it’s
distance from the pole.The spiral of the Nautilus has been fitted to
a precise formula:
ө =k log r.
Since the future growth of the animal will
continue along that curve ,the spiral can
be generated at any time to reveal the
final shape. www.indiandentalacademy.com

Gnomonic growth of the
human head
Moss indicates that orofacial capsular matrices, particularly the
oro-naso-pharyngeal functioning spaces manifest gnomonic
growth.In one study ,heads of human fetuses with crown-rump
length ranging from 26 to 163 mm were sectioned midsagitally
for direct measurements of the oral ,nasal and the pharyngeal
cavities.
On analysis, the oral and nasal functioning spaces enlarge but do
not change shape.

Moss cited the work of Burdi as the finest example of
gnomonic growth of the nasal functioning space.Using the
cephalometric points sella(S), nasion (N), anterior and
posterior nasal spines(ANS,PNS), and septal point
(SP),Burdi developed the representation of the growth of
the human fetal nasal space during the second trimester.
The space has resituated the surrounding
skeletal units in such a way that the overall
shapes remain similar.
Moss constructed a logarithmic
spiral as suggested by gnomonic
growth.

Ricketts has suggested a number of gnomonic figures that are
correlated to three branches of the trigeminal nerve.The focal
point for the region supplied by one of these branches is the
foramen associated with the nerve.
V1 , V2, V3 = BRANCHES OF THE TRIGEMINAL NERVE
VERTEX OF ORBITAL ANGLE{V1} –SUPERIOR ORBITAL FISSURE.
VERTEX OF NASAL ANGLE {V2} – FORAMEN ROTUNDUM.
VERTEX OF ORAL REGION {V3} –MANDIBULAR FORAMEN.

When lines are extended from the
superior orbital fissure base ,the content
of orbit appears to expand within a
constant angle.
The nasal angle A-pt-ANS describes
growth of nasal capsule.
The oral cavity enlarges within the angle
ANS-Xi-Po.,created by locating the
vertex at Xi,a point that represents the
mandibular foramen .
This property,increase in size without
change in shape satisfies the definition of
gnomonic growth. www.indiandentalacademy.com

NEUROTROPHISM
The functional matrix theory disclaims any intrinsic genetic
determination by bone cells and therefore the information about
the rate and limitation of growth must exist somewhere in the
capsules.Moss contends to a great extent that the message
necessary for controlling growth are derived from the nerves that
innervate these capsules.ultimately the ,DNA , that dominates
craniofacial growth, resides in the chromosomes of brain
cells.RNA or other messages are carried to the end organs by
axoplasmic flow.
The process of neurotrophism or neural nourishment dictates that
at no time are the nerves to be subjected to torsion,compression ,or
tension. This is true with respect to the inferior alveolar nerve
during the development of lower jaw.As a vital constituent of
orofacial capsule ,the Inferior alveolar nerve follows a logarithmic
spiral. www.indiandentalacademy.com

LOGARITHMIC GROWTH OF THE HUMAN
MANDIBLE.
Craniometric studies were performed
by fixing small lead shots affixed to
the Foramen Ovale ,Mandibular
foramen and Mental foramen of
mandibles at various stages of
dentition.The lateral x-rays of these
mandibles effectively outlined the
pathway of the Inferior alveolar
nerve.Consequently ,it is possible to
generate the curve representing
human mandibular growth at any
time.

The logarithmic spiral formulated
by Moss which coincides with the
three foramena of the inferior
alveolar nerve and which
describes the path of mandibular
growth.
As the foramena separate
during growth, the mandible
continually assumes a
position where there is a
less curvature of the
spiral.Because the mandible
does not grow up and out
the rotation of the spiral
must occur.www.indiandentalacademy.com

ARCIAL GROWTH OF MANDIBLE
A normal human mandible grows by superior- anterior 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 the 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}
According to Ricketts ,each individual
generates his own unique arc.3 curves
were ultimately drawn:
CURVE A – Passes through DC -Xi
and Pm .
CURVE B - Passes through tip of the
coronoid process and Pm.
CURVE C – Passes through point Eva
and Pm .
Curve C best fits the Arcial
growth of mandible.www.indiandentalacademy.com

Point Eva ,the confluence of
stress lines on the medial
surface of the ramus.
The curve created through
Eva and Pm with Tr as
centre represents the arc
of mandibular growth.
RICKETTS PREDICTION: The annual increase of
2.5mm when averaged over the years of time.Growth was
found to cease at 14.5 years for females and 19 for
males .This method, now , represents a convenient and
fairly reliable method for mandibular growth prediction.

METHODS OF GROWTH
PREDICTION
 CEPHALOMETRIC METHOD.
• METRIC.
• LONGITUDINAL.
• STRUCTURAL.
 CARTESIAN COORDINATE SYSTEM
MESH DIAGRAM.
 COMPUTERISED METHOD

LONGITUDINAL APPROACH
With this approach, the individual may be
evaluated over a specified period to determine
the pattern of growth.
This concept was clinically applied by Tweed
on his growing patients.
He advocated taking two lateral cephalograms
12 to 18 months apart to evaluate the skeletal
facial changes.
Consequently, the patient was placed into one
of three categories that are used to predict future
growth trends. www.indiandentalacademy.com

LONGITUDINAL APPROACH
TYPE A: The growth of middle and lower face
proceeds in unison with changes in the vertical and
horizontal dimensions being approximately equal.
TYPE B: The middle face grows downward and
forward more rapidly than the lower face.This type of
growth is predominantly in a vertical direction.
TYPE C: The lower face develops at a faster rate
than the middle face.

LIMITATIONS OF THE
LONGITUDINAL APPROACH.
• Tweed’s basic assumption was that the growth pattern would
remain constant. Moore and other investigators and
clinicians concluded that this constancy can only be observed
with population averages but not useful to predict growth
changes in a single individual.
• It is accurate only when it is performed retrospectively but
not prospectively.
• The pattern and rate of growth in one period is not similar to
that occurring in a subsequent period in any given individual.
HENCE ,IT IS CONCLUDED THAT
LONGITUDINAL APPROACH IS NOT AN
ACCURATE METHOD.

METRIC METHOD
This method consists of measuring different structures on a
single x-ray film and then relating these measurements to
future growth changes.
From a clinical perspective, it predicts how strong is the
interrelationship of the changes within a facial structure,
between the various facial structures and between the various
facial structures and other body dimensions.
At this juncture ,it might be helpful to explain the scientific
determination and clinical application of the strength of the
relationships between any two variables.

METRIC METHOD
A correlation coefficient symbolized by a “r” describes the
association or the strength of the relationship between two
variables .
A correlation coefficient also gives the direction,positive or
negative ,of this relationship.It’s use in prediction is derived from
squaring the value of “r”, which is called the coefficient of
determination.
This coefficient describes the amount of variation of the second
variable that can be eliminated if the first variable is known.

METRIC METHOD
According to Horwitz and Hixon, a correlation coefficient may be
statistically significant at the 0.001 level of confidence but is still of
no clinical significance for prediction.
As a rule they suggested an “r” value of 0.8 to be the dividing
line for use in clinical prediction because the coefficient of
determination is 0.64.
That is 64% of the variation can be accounted for in the variable
that is being predicted.
It is with these facts in mind that the available data are interpreted.

LIMITATION OF METRIC
METHOD.
In independent studies by Bjork et al., correlation
coefficiencies for facial dimensions, be it linear or angular,
when related to future growth of that same dimension did not
exceed an “r” of 0.4 or 0.5.
This explains only 16% to 25% of the variation.
THIS IS STILL A FAIRLY LOW CORRELATION FOR
CLINICAL USE.
HENCE THIS METHOD IS OF LESS CLINICAL
APPLICATION.

STRUCTURAL METHOD
The structural method for predicting mandibular
growth direction was developed by Bjork from
superimpositions on metallic implants.
The method consists of reorganizing specific
structural { morphologic} features in the mandible
that indicate future growth trends.
When evaluating mandibular morphology, Bjork
listed seven areas on the cephalogram that should be
evaluated to help predict future mandbular growth
direction.

BJORK’S AREAS
1.The inclination of the condyle as an indication of it’s
growth direction, whether vertically or sagitally.For example,
with vertical condylar growth, the mandible rotates forward.
2.The curvature of the mandibular canal .The more curved the
canal is, the more forward the mandibular rotation will be.
3. Inclination of the symphysis.If it is inclined lingually, the
mandible rotates forward.
4.Shape of the lower border of the mandible.
5.The interincisal angle which is more acute in forward
rotators.
6.The interpremolar or molar angles are also more acute in
forward rotators.
7.Anterior lower face height.www.indiandentalacademy.com

The future direction of mandibular growth is influenced by the
changes in other parts of the craniofacial complex other than
Bjork’s seven landmarks.
These variables are difficult to quantify by any prediction
method because they are essentially unknown to both the
clinician and the patient.
LIMITATION OF THE STRUCTURAL METHOD.
THE LONGITUDINAL,METRIC AND STRUCTURAL
METHODS OF PREDICTION ARE OF A LIMITED
CLINICAL VALUE .RECENT COMPUTER
TECHNOLOGY HAS PROVIDED MORE
SOPHISTICATED APPROACHES TO THIS ONGOING
PROBLEM.

CARTESIAN COORDINATE SYSTEM
MESH DIAGRAM
THE STUDY OF PROPORTIONAL CHANGES IN THE
LOCATION OF LANDMARKS BASED ON UPPER
FACIAL HEIGHT AND FACE DEPTH.
A mesh diagram is used to assess the facial morphology.

A mesh diagram is constructed by first drawing a core
rectangle oriented on the extracranial vertical and scaled on
upper face height {nasion to ANS} and the length of anterior
skull base{Nasion to sella}.By dividing the size of the core
grid rectangle into 2 equal parts, distances for additional
horizontal and vertical grid lines are obtained to complete the
diagram.

The face is thereby inscribed in a rectilinear coordinate system
composed of 24 small rectangles.
The size increases between 8 and 16 years with median
increments of 4.5 mm in boys and 3.5 mm in girls for a height
and smaller increments for length namely 3.2mm and 2.4mm for
boys and girls respectively.

COMPUTERISED
PREDICTION METHODS
Computerization is a tool of analysis rather than a method of
analysis.This is because computers are programmed to use equations
based on either the longitudinal ,metric,structural,or other method of
prediction.
The biggest advantage of computer technology is that it facilitates testing
and applying more complex formulae to growth prediction.www.indiandentalacademy.com

Development of the computerised growth
forecasting.
Brodie described the direction of growth of the various
components of the craniofacial complex thruogh his cephalometric
studies.
Baumrind ,Korn and West conducted a study in attempt to
predict the direction of mandibular growth in 164 class II mixed
dentition subjects and the results clearly show the inability to
differentiate the potential forward rotators from potential
backward rotators and hence concluded this method is unreliable.
Ricketts –Arcial method of growth prediction
Schulhof and Bagha—utilised the science of Biomathematics to
computerize growth and development.

Development of the computerised growth
forecasting
Johnston-use of “printed forecast grid”.
Popovich- craniofacial templates based on individual
age,sex and growth patterns.
Ricketts—the original version of rocky mountain data
systems
Christi: facial print.he compared profile to a fingerprint.
Recent Computer software systems for growth prediction:
 Quick Ceph for Apple Mackintosh
 Rocky mountain data systems for IBM
mainframe systems.
 Facial print- for IBM personal computers.www.indiandentalacademy.com

LIMITATION
“ TO ERR IS HUMAN ; TO REALLY FOUL THINGS UP
REQUIRES A POORLY PROGRAMMED COMPUTER.”
This is not intended to mean that the clinicians should not use the
various computer programs available,but they need to realize that
such programs are useful for general patient education as well as
average growth or treatment simulations and not for individualized
predictions.

VISUAL TREATMENT OBJECTIVE
THE VISUAL TREATMENT OBJECTIVE {VTO}
REPRESENTS A “CEPHALOMETRIC SETUP” WHICH
INCLUDES THE EXPECTED GROWTH AND TREATMENT
CHANGES AS PROJECTED FROM THE ORIGINAL
MALOCCLUSION AND FACIAL MORPHOLOGY.
This treatment forecast was developed by Ricketts
and named by Holdaway.
VTO is a treatment design procedure that
1.Changes the areas due to normal growth,the cranial base ,chin
and maxilla.
2.Changes the areas affected by orthopaedic alteration.
3.Visualises the orthodontic movement of the teeth within the
jaws to a more normal relationship.

CRANIAL BASE PREDICTION
The cranial base is designated by a line joining the most
anterior point of the Foramen Magnum with the Nasion as
seen on the lateral cephalometric radiograph.
PREDICTION: In normal
patient,the cranial base will
grow 2mm per year during the
active growth period.This is
expressed as 1mm of forward
growth of Nasion and 1mm of
backward growth of Basion,both
along the original cranial
baselength.

MANDIBULAR GROWTH PREDICTION
CONDYLAR AXIS:The axis of the condyle is defined as
a line from a point on the Ba-N Line midway between the
anterior and posterior borders at the condylar neck {DC
POINT} to the geometric centre of the mandibular ramus.
CORPUS AXIS: The length of the body of the mandible is
defined by a line from Xi point to the anterior point on the
mandibular symphysis.
PREDICTION:
Condylar axis grows
1mm per year.
Corpus axis grows 2mm
per year.

MANDIBULAR GROWTH PREDICTION
MANDIBULAR ARC: The angle formed by the condylar
and corpus axis describes the configuration of the mandible.
PREDICTION: A small
angle is indicative of steep
mandibular plane
associated with a vertically
growing mandible..
A larger than normal angle
is correlated with a square
mandible associated with
more favourable forward
mandibular growth.

MAXILLARY GROWTH PREDICTION
Nasion and point A grow
forward same amount each year.
The angle formed by intersection
of N-A and Frankfurt horizontal
thus remains same during normal
growth.
Skeletal convexity is determined
by relation between A point and
facial plane.If A is in front of
plane ,skeleton is said to be
convex.
The clinician must realize the effects of orthopedic appliances
on the maxilla and more specifically on the A point..www.indiandentalacademy.com

DENTITION
Once the position of the mandible and maxilla is
determined , a line is drawn between A point and
Po .The incisor teeth are then related to the A-Po
line.
LOWER INCISOR
The mandibular incisor usually stays in a constant
relationship to the A-Po line throughout the
growth.
In ideal situation,the incisal edge is 1mm ahead of
the A-Po line.
* SIGNIFICANCE: Any anterior or posterior
movement of the lower incisor has a two-fold
effect on the archlength of the dentition.If the
lower incisor is moved back 1mm, the archlength
is decreased by 2mm. www.indiandentalacademy.com

UPPER INCISOR
The maxillary incisor also
remains constant to the A-Po line.
The incisal edge of the upper
incisor is 3.5 mm to the A-Po line.
INTERINCISAL RELATIONSHIP
This remains the same during
growth.The normal angle is 130º.
The upper incisor should be 28º and
the lower incisor 22º to the A-Po line.
MOLAR RELATIONSHIP
Position of molars is determined by ideal
incisor position and consequent archlength
discrepancy.The upper molar is 3mm
distal to it’s lower counterpart .

TREATMENT ALTERATIONS
Once the clinician understands the changes that occur with
normal growth,it is just as important to be aware of the
alterations that can occur with various treatment systems.
MANDIBULAR CHANGES
The facial axis is the line between the Pt-
point and the cephalometric
Gnathion.This angle remains stable
during growth and any changes would be
due to clinicians mechanotherapy.During
treatment,the changes that can occur are,
Convexity reduction -1˚/ 5mm of change
Molar correction -1˚/ 3mm of change
Overbite correction -1˚/ 4mm of change
Crossbite correction -1˚to –1.5˚www.indiandentalacademy.com

MAXILLARY CHANGES
Nasion and A point on the maxilla grow forward and equal amount per
year.Any angle that relates these 2 points to each other does not
change with normal growth .
A list of mechanics and their effect on the antero-posterior position of
point A of the maxilla as it relates to the vertical facial plane.{N-Pog}:
Cervical headgear -8mm
Class II elastics -3mm
Activator -2mm
Lingual root torque of 1 -2mm
Class III elastics +3mm
Clinically, the palatal plane {ANS –PNS} rotates in a clockwise
direction as the forces produced by the appliance affect the
midface region. A point will not only move distally but also drop
inferiorly half the distance.

GENETIC APPROACH
Another approach to growth prediction has been from a
genetic viewpoint using a comparison of family likeliness
in siblings and other relations together with suitable
formulae to predict the facial type.
This worked well in predicting
the lower jaw size of a member of
THE HAPSBURG ROYAL
FAMILY who were famous for
their characteristically large
lower jaw.

CONCLUSION
Various methods of growth prediction have been suggested
ranging from the crudest form of clear acetate templates to the
more sophisticated computer databasing .Whichever the
approach,the prediction would be reasonable in ‘average
growers’ but not in ‘abnormal growers’, the patients in whom
the orthodontist may be more interested.
Hence, the orthodontist should obtain diagnostically useful
data that permit the interpretation of dental relationships at all
ages in terms of skeletal,soft tissue and prevailing
environmental factors responsible for the existing
occlusion.Only then will we be able to successfully predict the
future changes that nature will produce and make the necessary
adjustments through our intervention by treatment.www.indiandentalacademy.com

REFERENCES
• GROWTH PREDICTION—RANLEY.
• BIOPROGRESSIVE THERAPY– RICKETTS.
• PAEDIATRIC DENTISTRY – STEWART,THOMAS BARBER.
• COMPUTERIZED FORECASTING ---VTO--- SPIRO
J.CHACONAS

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