This document discusses various methods for predicting facial growth, including cephalometric methods like Moorrees mesh, Johnston's transformation grid, and Rickett's arcial growth prediction of the mandible. Non-cephalometric methods discussed include logarithmic spiral, Hirschfield and Moyers, and Todd's equation. The need for growth prediction in orthodontic treatment planning and challenges with accuracy are also addressed. The conclusion is that while various methods have been proposed, growth prediction is most reasonable for "average growers" but not "abnormal growers," and an orthodontist's experience is an important additional factor.

1. N.MOTHI KRISHNA
I YEAR MDS
DEPARTMENT OF OTHODONTICS
AND DENTOFACIAL OTHOPEDICS
ORTHODONTICS

2. GROWTH PREDICTION

3. DEFINITION
• Growth prediction can never be accurate especially
when the child is growing (Proffit).
• Growth prediction can be defined as the forecast of
growth related changes with the objective of
predicting the direction and the amount of growth of
maxilla and particularly mandible as well as timing of
adolescent growth period.

4. Need for growth prediction
1. To intercept and correct malocclusion.
2. As patients educational aid.
3. VTO.
4. Tool for orthodontic treatment planning.
5. Response to particular treatment can be predicted.
6. To plan for retention period.

5. Methods of prediction
(Hirschfield 1971)
1. Theoretical
2. Regression
3. Experimental
4. Time series

6. 1.Theoretical

7. 2.Regression

8. 3.Experiential

9. 4.Time series
1. Time series analysis:which extracts in a
mathematical form the fundamental nature of the
process as it relates to time.
2. Smoothing method : either moving averages or
exponential which operate to give representative or
average values to the parameters of a previously
derived time-series equation.

10. Growth prediction in
orthodontics
 Growth prediction is usually not done for all cases
but mainly for perverted cases.
 Every child has a genetically determined pattern
which is acted upon by environmental influences.
 Growth prediction often does not satisfy the purpose
it was originally invented for.
 Development of satisfactory treatment plan is
seldom important.

11. Classification
Cephalometric methods
 Moorree’s mesh
 Johnston’s transformation grid
 rickett’s arcial growth of
mandible .
 Bjork’s implant growth rotational
studies
 VTO
Non cephalometric methods
 Logarithmic spiral
 Hirschfield and moyers.
 Todd’s equation
 FEM

12. HUNTERIAN CONCEPT
• Given by john hunter.
• He noticed linear growth of mandible(lengthening).
• Resorption in anterior border and deposition in
posterior border.

14. Gnomonic growth and
logarithmic spiral
Bjork
• He proved that maxilla and mandible underwent rotational
growth.
Moss and Salentejin
 They predicted that mandibular rotation grows in spiral path.
 Moss predicted that mandibular growth is along a logarithmic
spiral.
 He actually inspired from gnomonic growth concept of D’arcy
Thompson.

15. What is gnomonic growth ?
• The portion of increment which when added doesnot alter shape but only
produces an increase in size is called gnomon in Greek by Aristotle.
• D ‘arcy Thompson has explained from chambered nautilus .
1.shell grows in size with no change in shape .
2.can be described by a curve which is called logarithmic spiral or
equiangular spiral.

16. • O= k log r

17. Gnomonic growth of
rectilinear figures
1:1.618

18. Gnomonic growth
of human face
• Lead shots are implanted at three foramina along the
path of the nerve namely foramen ovale,mandibular
foramen,mental foramen.
• As the bone increases in size the spiral itself doesnot
change ,instead, the mandible itself changes in position
and the base appears to rotate along the spiral .
• As the bone lengthens in growth the distance between
the foramina increases.

20. Arcial growth of
mandible
• Given by rickets
• An arc of growth can be constructed for every
individual depending on the length of the core of the
mandible.
• He used points which are immune to surface
deposition and resorption.

21. • Xi point is at the level of occlusal plane.
• In some cases at the level of mandibular foramen.

22. 1.curve A – gonial angle will be too wide.
2.curve B - mandible will be bent too much.
3.curve C – mandible follows this curve.

23. Occlusal plane and mandibular
teeth eruption
• With upward and forward eruption of teeth the chin
is pushed beneath lower arch.

24. Drawbacks of arcial
growth prediction
•1. It relies heavily on the operators skill in tracing the
cephalogram.
•2. Mitchell & Jordan (1975) concluded Ricketts uses
chronological age rather than the skeletal age. If the
patient is in a growth spurt or lag phase it will alter the
result.
•3. The growth increments constants are for a fixed
population.

25. Moorrees mesh
• Moorres constructed a template in the form of mesh
which was used to superimpose growth changes in
serial lateral cephalometric radiograph.
• Moorrees mesh consists of equal sized rectangles
which are 24 in number.

27. • Mesh diagram analysis
of mesognathic face.
• Transformations of
horizontal grid lines
indicates a slightly long
anterior face height and
short posterior face
height.

28. • Retrusive mandible
• Class 2 division 1 case
• Pouting lip
• Stub nose

29. • Class 3 malocclusion.
• The transformation of
horizontal grid lines
indicate the cephalad
position of sella
turcica,articulare and
basion as well as to
lesser degree gonion.

30. Advantages-
• graphically display pt’s
deviation
• Normal mesh diag is
readily understood by
patient
Disadvantage
• complex and laborious
method

31. Johnston’s grid
• He designed age and sex specific templates.
• The grid shows the average increments of growth per
year for the points nasion,A,B,nose and posterior nasal
spine.

32. • This method do not fit a random series of patients
• It is not easy to evaluate the significance of the forecasting error.
• A patient who is 11years old can have an overall skeletal age of 9
years which is normal but if the cranial base and maxilla are
uniformly 11years and mandible alone is 8years this condition is
abnormal.
• Malocclusion is the integration of small deviations of all parts of the
face.Deviations from normal of every part can be individually
assessed i.e to say that dental or skeletal cause of malocclusion is
differentiated for example skeletal is normal but maxillary dentition
has moved forward.

33. Todd’s
• Todd said external environment and genetic influence
Cannot be ignored.
• Global influence on biomechanics of growth is force of gravity.
• Human skull is considered as a spherical tank filled with fluid.
• If all bone elements are displaced or placed in the direction of
gravitational pressure as suggested by wolff’s law then they
will all move outward long radial lines emanating from the
center of sphere.
• P= a R(1-cos 0)

34. The bone elements place themselves in the direction of functional
pressure and increase or decrease their mass to reflect the amount of
functional pressure.” The overall pattern of craniofacial growth is
primarily controlled by biomechanical influences.”

35. LIMITATIONS:
• Heads are not perfectly spherical
• There are other sources of stress operating on
craniofacial complex besides the force gravity
• The orientation of the head with respect to the gravity
does not remain fixed.

36. VTO
• Coined by holdaway.
• Relatively simple and accurate method of predicting
molar and incisor relationship on the basis of growth
and treatment alterations.
• Acts as a blueprint.
• VTO is a cephalometric tracing representing the
changes that are expected during treatment.

38. Rickketts vto
1. The cranial base prediction
2. The mandibular growth prediction
3. The maxillary growth prediction
4. The occlusal plane position
5. The location of the dentition
6. The soft tissue of the face

39. 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.

40. 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 center 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.

41. • 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
favorable forward mandibular growth.

42. 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..

43. 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 arch length of the
dentition.If the lower incisor is moved back 1mm, the arch
length is decreased by 2mm.

44. UPPER INCISOR
• 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

45. FEM
Mathematical modeling of craniofacial skeletal
growth.
Technically two ideas are present :
1. use of growth strain tensor
2. use of a finite element method.

46. Growth tensors
• Tensor in general- fundamental description of
growth.
• Concept of gen. tensor- involves a set of numbers
that describe a 3-dimensional field.
• The numbers that specify a tensor are called the
components.

47. • Finite element : fundamental attribute of the finite element is its
ability to dicretize or subdivide structures or bodies into 2-3
dimensional elements each of which is called as finite element.
• Each line is connected at one end to at least one other line. The
point of connection is termed as nodes.
• The lines and planes conceptually subdivide the body into a series
of contiguous finite elements , a process called Discretization.
• Ex- triangle – 3noded 2dimensional finite element

48. Inference
• The elongation takes place in the direction of the
long axis of the principal direction of the growth or in
the other words the finite element is strained.
• This resulted in maximal elongation of the continuum
of the points in one direction and minimal elongation
of continuum of points in perpendicular direction.

49. C -axis
M point- by Nanda & Meritt (AJO 1994)
• It is a constructed point representing the center of
the largest circle that is tangent to the superior,
anterior & palatal surfaces of maxilla as seen in the
saggital plane.

50. • C-Axis: The line from the sella (S) to M- point is
defined as C- axis.

51. • It permits the quantification of a complex maxillary growth
process
• Age group -7.4-18.75yrs
• The regression formula is independent of gender within the
chronological age studied.
• Upto age 14, both male and females show- growth increment
of 1.41mm &1.31mm/yr.
• The mean growth axis angle (C-axis- SN) increased for both
males and females.
• Males = 3.98
• Females = 2.25

52. G Axis
• G –Axis : A growth vector for mandible.
Length of sella to g- point.
• G point : it is a point representing the center of largest circle
that is tangent to the internal inferior, anterior, and post
surfaces of the mandibular symphyseal region as seen on
lateral cephalograms.
• 1.6mm per year(females)
• 2.3mm per year(males)
• Mandible grows downwards and backwards

54. AN INSTRUMENT FOR ANALYSIS OF
FACIAL GROWTH (AJO 1969 )

55. A SIMPLIFIED APPROACH TO PREDICTION
( AJO 1975 )

56. FRONTAL SINUS & MANDIBULAR GROWTH
PREDICTION(AJO DO 1991 DEC)
• Brown,Molleson & Chinn – study on lateral ceph
• The surface area(sq.mm) of frontal sinus –assessed by
summagraphic decoder linked to a microcomputer
• Negative ANB angle – small maxilla & large
mandible coincided with large frontal sinus
• Larger frontal sinus has larger mandible.

57. ANTEGONIAL NOTCH FOR GROWTH
PREDICTION(AJO DO 1992 )
• Singer , Mamandras &
Hunter
• Presence of prominent
antegonial notch-arrested
growth of mandibular
condyles
• So deep antegonial notch –
Backward rotating mandible

58. Growth prediction from posture - Solow and
Siersbæk-Nielson AJO-DO 1992 May
• Children with a large craniocervical angle and an
upright position of the upper cervical column
displayed a more vertical subsequent facial growth
pattern , than children with a small craniocervical
angulation and a backward inclination of the upper
cervical column.
• Small cervical angle – horizontal growth

59. FORECASTING AND MONITORING FACIAL
GROWTH - MEW (AJO-DO AUG 1993 )

60. • Attractive eyes are associate with full cheek bones
and that flat cheeks provide less appeal .
• The development of maxilla may well play a role in
these variations.
• Chubby cheeks have special appeal.
• If the maxilla is small it leads to undesirable face, eye
looking exophthalmic with flat face.

61. AN ACCURATE METHOD OF PREDICTING MANDIBULAR GROWTH
POTENTIAL BASED ON BONE MATURITY (AJO DO 2001 )
Mandibular total length at the final stage can be accurately
predicted by
• Ossification events of third middle phalanx and radius
• Growth prediction method
• Growth percentage method
• Multiple regression method
• growth chart method
- Bone age as a parameter was calculated by both Tanner –
Whitehouse2 method and CASMAS

62. Objective of the study was
 To present a prediction formula using skeletal maturity
indicator
 To clarify which method is most accurate
- Growth potential and growth prediction method – most useful
predictors of mandibular growth potentials

63. 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 in order to predict in abnormal growers the additional factor that
an orthodontist should add is experience and sound knowledge on
growth.

64. References
• Growth Prediction—Ranley.
• Bioprogressive therapy– Ricketts.
• Computerized forecasting ---VTO--- Spiro j.Chaconas
• An instrument for analysis of facial growth – AO 1969
• Prediction of craniofacial growth:the state of the art – AJO Nov 1971
• A simplified approach to prediction – AJO 1975
• The prediction of facial growth – AO April 1980
• Growth prediction from posture - Solow and Siersbæk-Nielson AJO-DO May
1992
• Frontal sinus & mandibular growth prediction-AJO DO 1991 Dec
• Antegonial notch for growth prediction-AJO DO 1992
• Forecasting and monitoring facial growth - AJO-DO Aug 1993
• Prediction of mandibular growth rotation- AJO DO Dec 1998
• An accurate method of predicting s growth potential based on bone maturity -AJO DO 2001