3. CONTENTS
INTRODUCTION
PARTS OF STUDY MODEL
PREPARATION OF STUDY MODEL
DENTAL ARCH,ALVEOLAR ARCH & BASAL ARCH
ARCH PERIMETER, ARCH LENGTH & ARCH WIDTH.
MIXED DENTITION ANALYSIS:-
1) Moyers analysis
2) Tanaka and Johnston prediction value
3) Hixon and Oldfather analysis
4) Huckaba analysis
5) Radiographic method
6) Ballard and Wylie analysis
7) V. V. Subba Reddy analysis
4. CONTENTS
8) Suraj analysis
9) M.S. Rani analysis
10) S.P. Aggarwal analysis
11) Regression equation of Ono
12) Staley and Hoag multiple regression equation
13) Basic Hossaik Al-Khandra analysis
14) Sharon Le Chan et. al. analysis
15) Inter lateral incisor width analysis
TOTAL SPACE ANALYSIS
1. Conventional method
2. Tweed method
3. Total space analysis of Merrifield
5. ANALYSIS IN PERMANENT DENTITION
a) ANALYSIS TO DETERMINE NEED FOR ARCH EXPANSION
1. Pont’s analysis
2. Linder Harth analysis
3. Korkhaus analysis
4. Ashley Howes analysis
b) TOOTH SIZE ARCH LENGTH DISCREPANCY ANALYSIS
1. Arch perimeter analysis
2. Carey’s analysis
3. Rees analysis
4. Diagnostic setup
5. Irregular index
6. Larry White analysis
7. Sanin & Savara analysis
5
6. C) UPPER & LOWER TOOTH SIZE DISHARMONY
1. Bolton tooth ratio analysis
2. Anterior coefficient & radius analysis
d) TOOTH SHAPE DISHARMONY
1. Peck & Peck index
e) PHOTOGRAPHIC ANALYSIS OF STUDY MODELS
1. Stereophotogrammetry
2. Occlusograms
3. Holographic image analysis
4. Photocopies of study models
f) COMPUTERIZED ANALYSIS
1. OSCOPO
2. Reflex metrography
12. ȿ Basal arch – arch formed by the corpus mandibularis or maxillaris. It is the measurement of
apical base.
ȿ Alveolar arch – arcal measurement of alveolar process.
ȿ Dental arch – measured through the contact points and represents a series of points on the
crowns of the teeth.
12
ARCH
14. Definition – Model analysis involves the study of max. & mand. Arches in all 3 planes of space (sagittal, vertical
and transverse).
It is a valuable tool in diagnosis & treatment planning.
Normally completed in mixed dentition
It is used to predict the amount of space available for the unerupted permanent teeth
It is an important diagnostic aid to determine whether the treatment plan is going to involve serial extraction,
space maintenance, space regaining or simple periodic observation of the patient.
14
MODEL ANALYSIS
15. ȿ Space related malocclusion in mixed dentition
ȿ Casued by tooth space arch length discrepancies [TSALD]
ȿ TSALD = SPACE AVAILABILITY[SA] – SPACE REQUIRED[SR]
15
TSALD
16. TSALD = SPACE AVAILABILITY[SA] – SPACE REQUIRED[SR]
ȿ SPACE AVAILABILITY =
space available between distal point of
Permanent lateral incisor and mesial
contact point of permanent first molars.
16
SPACE AVAILABILITY SPACE REQUIRED
SPACE REQUIRED =
predicted space needed for permanent
canines and premolars to erupt.
OBTAINED BY
MEASUREMENT ON
THE CAST
PREDICTED BY
MODEL ANALYSIS
18. ȿ An 0.12 brass wire is adapted to the dental arch model so that – its one end is engaged at mesiobuccal line anagle
of the permanent first molar near the marginal ridge.
18
ARCH LENGTH DETERMINATION
19. TSALD = SPACE AVAILABILITY[SA] – SPACE REQUIRED[SR]
ȿ If the value is negative
19
SPACE AVAILABILITY SPACE REQUIRED
If value is positive
AVAILABLE SPACE IS
LESS FOR
ALIGNMENT
AVAILABLE
SPACE IS EXCESS
FOR ALIGNMENT
25. ADAVNTAGES:
ȿ Minimal errors
ȿ Allows analysis for both the arches
LIMITATIONS:
ȿ Time consuming
ȿ Full mouth radiographs are needed.
25
NANCE RADIOGRPAHIC METHOD 1947
26. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Periapical radiograph
ȿ PRINCIPLE:
ȿ Size of an unerupted tooth on radiograph – can be used to
measure size of tooth on eruption
ȿ FORMULA:
26
HUCKABA RADIOGRPAHIC METHOD 1947
SPACE AVAILABLE
SPACE REQUIRED
27. 27
SPACE
AVAILABLE
SPACE
REQUIRED
SR = width of four incisors+ 2X
[width of canine +first premolar+second premolar}
SA = measured by dividing arch into
segements
TSALD = SA - SR
28. ADAVNTAGES:
ȿ Both arches
ȿ Has reasonable reliability in determining the width of
unerupted tooth with fair to good accuracy.
LIMITATIONS:
ȿ Time consuming
ȿ Full mouth radiographs are needed.
28
HUCKABA RADIOGRPAHIC METHOD 1964
29. Co relational statistical methods
1.Moyers mixed dentition analysis
2. Tanaka Johnston analysis
29
CO RELATIONAL STATISTICAL METHODS
30. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Probability chart
ȿ Periapical radiograph
30
MOYERS MIXED DENTITION ANALYSIS 1973
SPACE AVAILABLE
SPACE REQUIRED
Moyers considered four mandibular incisors teeth to be the best
predictors of size of upper and lower canines and premolars
34. ADAVNTAGES:
ȿ Less time consuming
ȿ No radiographs required
ȿ Can be done for both arches
LIMITATIONS:
ȿ Does not mention the specific population from which these charts are derived
ȿ It’s a probability analysis
ȿ It has tendency to overestimate the discrepancy
34
MOYERS MIXED DENTITION ANALYSIS 1973
35. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ CHART
35
M.S. RANI ANALYSIS
She applied Moyers chart to south Indian population and found 35% level was more
applicable.
36. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ MOYERS CHART
36
V.V.SUBBA REDDY ANALYSIS
A probability chart similar to Moyers was developed by a study done on population selected from
KERALA, KARNATAKA, A.P, T.N.
42,41, 31, 32 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24
V.V.R 21.4 21.37 21.52 21.93 22.15 22.25 22. 62 23.86 23.16 23.56 23.67
Moyers 20.4 20.6 20.8 21 21.2 21.4 21.6 21.9 22.1 22.3 22.5
37. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
37
TANAKA AND JHONSTON NALYSIS 1974
SPACE AVAILABLE
SPACE REQUIRED
Uses width of the lower incisors to predict the size of unerupted canines and premolars
38. 38
SPACE
AVAILABLE
SPACE
REQUIRED
SR = width of four mandibular incisors+ 2X
[Estimated width of canine +first premolar + second premolar}
SA = Measured on the cast
TSALD = SA - SR
39. ADAVNTAGES:
ȿ Very simple, Less time consuming
ȿ No radiographs required
ȿ Can be done for both arches
ȿ No charts and tables
LIMITATIONS:
ȿ Derived from European population
ȿ It has tendency to overestimate the discrepancy
39
TANAKA AND JHONSTON ANALYSIS 1974
40. Combination of both radiographic and statistical methods
1.Hixon oldfather
2. Stanley and Kerber
40
COMBINATION METHODS
41. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Table
41
HIXON AND OLDFATHER ANALYSIS 1956
SPACE AVAILABLE
SPACE REQUIRED
Uses width of the lower incisors on one side plus width of unerupted premolars on
radiograph from same side for prediction.
43. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
43
STANLEY AND KERBER ANALYSIS 1981
SPACE AVAILABLE
SPACE REQUIRED
REVISED THE EQUATION TO INCLUDE BOTH SIDES TO REDUCE THE ERROR
Uses width of the lower incisors on one side plus width of unerupted premolars on
radiograph from same side for prediction.[HIXON AND OLDFATHER]
45. ANALYSIS USING REGRESSION EQUATIONS
1. Ballard and Wylie analysis
2. V. V. Subba Reddy analysis
3. Suraj analysis
4. M.S. Rani analysis
5. S.P. Aggarwal analysis
6. Regression equation of Ono
7. Staley and Hoag multiple regression equation
8. Basic Hossaik Al-Khandra analysis
9. Sharon Le Chan et. al. analysis
10. Inter lateral incisor width analysis
45
MIXED DENTITION ANALYSIS METHODS
46. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
46
BALLARD AND WYLIE ANALYSIS
Murray L. Ballard & Wendell L. Wylie made use of assumption of presence of harmony
in tooth size in one’s oral cavity
• x = 9.41 + 0.527y
x = sum of 3,4,5
y = sum of mand incisors ( 21mm)
• x = 5.51 + 0.431y + 0.552 z
z = m-d width of ‘6’
47. 47
• x = 9.41 + 0.527y
x = sum of 3,4,5
y = sum of mand incisors ( 21mm)
• x = 5.51 + 0.431y + 0.552 z
z = m-d width of ‘6’
48. 48
SPACE
AVAILABLE
SPACE
REQUIRED
SR = width of four mandibular incisors+ 2X
[Estimated tooth size from formula]
SA = Measured on the cast
TSALD = SA - SR
• x = 9.41 + 0.527y
x = sum of 3,4,5
y = sum of mand incisors
• x = 5.51 + 0.431y + 0.552 z
z = m-d width of ‘6’
49. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
49
SURAJ ANALYSIS
Measure m-d width of max. & mand. 3,4,5 measured using EQUATION.
REGRESSION EQUATION :-
y = a + bx
y = size of 3,4,5 to be predicted
x = width of mand.42,41,31,32.
a,b = constants derived
50. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
50
S.P.AGARWAL ANALYSIS
He derived a regression equation in North Indian population
REGRESSION EQUATION :-
Width of upper 3,4,5=(x-21.92)+20.33
Width of lower 3,4,5=(x-21.92)+19.65
51. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
51
OTHER ANALYSIS WHICH USED REGRESSION EQUATION
- Staley and Hoag multiple regression equation
- Regression equation of Ono
- Basic Hossaic Al-Khandra analysis
- Sharon-Le-Chan et al. analysis
- Inter lateral width analysis (ILIW)
DIFFERENT REGRESSION EQUATIONS FOR EACH ANALYSIS
52. 52
Mixed dentition analysis methods
TOOTH SPACE ANALYSIS IN MIXED DENTITION
1. Conventional method – Similar to huckaba radiographic analysis
2. Tweed method
3. Total space analysis of Merrifield
53. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Lateral ceph
ȿ IOPAR
53
TWEED METHOD
A facial oriented analysis, incorporating the relations of incisor teeth to basal bone.
SPACE AVAILABLE ,SPACE REQUIRED – CALCULATED SIMILAR TO HUCKABA ANALYSIS
54. 54
TWEEDS ANALYSIS
Case : 7.6 yrs:
Space required =71mm
Space available = 65mm
Discrepancy = - 6mm
ceph correction = 2a = -12mm
Total discrepancy = -18mm
55. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Cephlometric tracing
55
TOTAL SPACE ANALYSIS BY MERRIFIELD
-
This method was divided into 3 areas:-
1.Anterior
2.Middle
3.Posterior
Deficit was calculated in three areas
Sum of deficit in all the areas gives final deficit.
56. PROBLEM:
SOLUTION:
56
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
Malocclusion in mixed dentition stage –
1.Skeletal component
2.Muscular component
3.Dental component
MDA ignores skeletal and muscular component of mixed dentition
analysis
1.Skeletal component – Ensure favorable class I relationship
2.Muscular component – Abnormal habit or muscle function should be
ruled out and treated.
57. PROBLEM:
SOLUTION:
57
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
Exclusion of late mesial shift in our treatment planning
Clinician should decide whether to allow or to restrict late mesial shift
Class – 1 molar relation – LMS not required so permanent molars can be held by space
maintainers
CLASS – II molar relation – decide to hold, distalize or mesialize maxillary molars and /or
mandibular molars
58. PROBLEM:
SOLUTION:
58
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
Inability to reflect the position of incisors with respect to skeletal profile
Any MDA should be preceded by cephalometric evaluation and
cephalometric correction
59. PROBLEM:
SOLUTION:
59
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
CEPHALOMETRIC EVALUATION – ideal position of L1 Lower incisor is
- At the A- Pog line
- -2 to +2mm from N –Pog line
CEPHALOMETRIC CORRECTION for A – Pog line:
Space shall be needed to retract lower incisors lingually towards A – Pog line
Space shall be gained to protract lower incisors labially towards A – Pog line
EVERY DEGREE OR MILLIMETER THE INCISAL EDGE IS DISPLACED
LINGUALY IN THE CEPH = THERE IS REDUCTION IN ARCH PERIMETER BY
ONE MM ON EACH SIDE
60. SOLUTION:
60
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
CEPHALOMETRIC CORRECTION for N – Pog line:
Space shall be needed to retract lower incisors lingually towards N – Pog line
Space shall be gained to protract lower incisors labially towards N – Pog line
EVERY DEGREE OR MILLIMETER THE INCISAL EDGE IS DISPLACED LINGUALY IN THE CEPH
= THERE IS REDUCTION IN ARCH PERIMETER BY ONE MM ON EACH SIDE
61. PROBLEM:
SOLUTION:
61
PROBLEMS AND SOLUTIONS - MIXED DENTITION ANALYSIS
the occlusal plane in mixed dentition is flat
But it might not always be flat leading to inaccurate arch perimeter calculations
Measure depth of curve of spee
Change space requirements
CURVE OF SPEE SPACE NEEDED
1. 3 or less 1mm
2. 4 1.5 mm
3. 5 or more 2 mm
63. 63
PERMANENT DENTITION ANALYSIS METHODS
a) To assess need for expansion
1. Pont’s analysis
2. Linder Harth analysis
3. Korkhaus analysis
4. Ashley Howes analysis
b) TOOTH SIZE ARCH LENGTH
ANALYSIS
1. Arch perimeter analysis
2. Carey’s analysis
3. Rees analysis
4. Diagnostic setup
5. Irregular index
6. Larry White analysis
7. Sanin & Savara analysis
c) UPPER & LOWER TOOTH SIZE DISHARMONY
1. Bolton tooth ratio analysis
2. Anterior coefficient & radius analysis
d) TOOTH SHAPE DISHARMONY
1. Peck & Peck index
e) PHOTOGRAPHIC ANALYSIS OF STUDY MODELS
1. Stereophotogrammetry
2. Occlusograms
3. Holographic image analysis
4. Photocopies of study models
f) COMPUTERIZED ANALYSIS
1. OSCOPO
2. Reflex metrography
64. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
ȿ Sum of incisors (S.I)
ȿ Measured premolar value (M.P.V) = A
ȿ Measured molar value (M.M.V) = B
ȿ Calculated premolar value (C.P.V) = S.I X 100/80
ȿ Calculated molar value (C.M.V) = S.I X 100/64
64
PONTS ANALYSIS
Method to predetermine ideal arch width based on m-d widths of max incisors
INFERENCE:-
- If calculated value > measured value ----- arch needs expansion.
- If calculated value < measured value ----- no need of expansion.
65. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
ȿ Sum of incisors (S.I)
ȿ Measured premolar value (M.P.V) = A
ȿ Measured molar value (M.M.V) = B
ȿ Calculated premolar value (C.P.V) = S.I X 100/85
ȿ Calculated molar value (C.M.V) = S.I X 100/65
65
LINDERLATH ANALYSIS
He made a variation in formula to determine the calculated premolar and molar values
INFERENCE:-
- If calculated value > measured value ----- arch needs expansion.
- If calculated value < measured value ----- no need of expansion.
66. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
ȿ Sum of incisors (S.I)
ȿ Measured premolar value (M.P.V) = A
ȿ Measured molar value (M.M.V) = B
ȿ Calculated premolar value (C.P.V) = S.I X 100/85
ȿ Calculated molar value (C.M.V) = S.I X 100/65
66
KORKHUAS ANALYSIS
He added a perpendicular measurement to linder hath analysis from a point between 2
maxillary incisors to the midpoint of the interpremolar line.
INFERENCE:-
- If calculated value > measured value ----- arch needs expansion.
- If calculated value < measured value ----- no need of expansion.
67. ȿ
67
KORKHUAS ANALYSIS
According to korkhua for a given width of upper incisors – a specific value of distance exist
between midpoint of inter premolar line to point between 2 incisors
INFERENCE:-
- an increase in perpendicular measurement – proclined incisors
- a decrease in perpendicular measurement – retroclined incisors
68. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ FORMULA
68
ASHLEY HOWE ANALYSIS
MEAUREMENT OF TOTAL TOOTH
MATERIAL FROM 6 TO 6
MEAUREMENT OF PREMOLAR
BASAL ARCH WIDTH - PMBAW
MEAUREMENT OF PREMOLAR
ARCH DIAMETER - PMD
69. ȿ
69
ASHLEY HOWE ANALYSIS
PMBAW % = PMBAW X 100
TTM
INFERENCE – II :-
PMBAW % INFERENCE
37 or less -------- need for extraction
44 or more------- non extraction
37 – 44 ----------- borderline
INFERENCE – I :-
PMBAW > PMD – arch expansion possible
PMBAW < PMD – arch expansion not possible
70. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
70
SPACE
AVAILABLE
SPACE
REQUIRED
SR = measured mesio distal width of teeth
mesial to first molar
SA = Measured on the cast Using brass
wire
DONE IN MAXILLARY ARCH
ARCH PERIMETER ANALYSIS
71. 71
ARCH PERIMETER ANALYSIS
TSALD = SA - SR
INFERENCE – :-
ARCH LENGTH DISCREPANCY INFERENCE
0 – 2.5mm proximal stripping can be carried
out to reduce the minimal tooth
material excess
2.5- 5 mm extraction of 2nd premolar is
indicated
> 5 mm Extraction of first premolar is
usually required
72. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
72
SPACE
AVAILABLE
SPACE
REQUIRED
SR = measured mesio distal width of teeth
mesial to mandibular first molar
SA = Measured on the mandibular cast
Using brass wire
DONE IN MANDIBULAR
ARCH
CAREYS ANALYSIS
73. 73
CAREYS ANALYSIS
TSALD = SA - SR
INFERENCE – :-
ARCH LENGTH DISCREPANCY INFERENCE
0 – 2.5mm proximal stripping can be carried
out to reduce the minimal tooth
material excess
2.5- 5 mm extraction of 2nd premolar is
indicated
> 5 mm Extraction of first premolar is
usually required
74. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Scotch tape
74
BASAL ARCH
WIDTH
TOTAL TOOTH
MATERIAL
measured mesio distal width of teeth mesial to
first molar
Draw a line mesial to 6 and extend 8-10
mm from gingival margin
REES ANALYSIS
75. 75
INFERENCE:
1 & 2 disparity of 7mm----extraction
3 ---discrepancy requires reduction of teeth or expansion of arch
4 ---reduction of tooth mass in one/ both arches
CALCULATION :-
1. Upper base – upper tooth material ----- 3.5 (1.5 – 5)mm
2. Lower base – Lower tooth material ----- 4.5 (2 – 7)mm
3. Upper base – Lower base ---- 6.5 (3 – 9.5)mm
4. Upper tooth material – Lower tooth material ----- 7.5 (5 -10)mm
76. ARMAMENTERIUM:
ȿ Dental cast
ȿ Wax bite
ȿ Steps:- 1). Wax bite
2). Separation of teeth
3). Align in desired position
Only for permanent dentition
76
Helps to ascertain amount and direction of tooth movement
DIAGNOSTIC SETUP
77. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
ȿ Sanin and savera and collegues at the university of Oregon, devised a simple and ingenious procedure to identify
individual and group tooth size disharmonies.
ȿ It makes use of precise mesiodistal measurements of crown size of each tooth, appropriate tables for tooth size
distribution in the population and a chart for measurements.
78
SANIN AND SAVARA ANALYSIS
78. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
79
Procedure –
1. Sum of mand 12
2. Sum of max 12
3. Sum of mand 6
4. Sum of max 6
According to him a ratio exists between m-d widths of max. & mand.teeth.
BOLTON’S TOOTH RATIO ANALYSIS
79. ȿ
80
INFERENCE – II :-
< 77.2% ----max ant. tooth mat. Excess
> 77.2% ----mand ant.tooth mat. Excess
INFERENCE – I :-
< 91.3 ------ max tooth mat. Excess
> 91.3 ------ mand tooth mat. Excess
CALCULATION– I :-
Determination of overall ratio –
= Sum of mand 12 X 100 = 91.3%
Sum of max 12
CALCULATION– II :-
Determination of anterior tooth ratio:-
= Sum of mand 6 X 100 = 77.2%
Sum of max 6
80. ȿ
81
CALCULATION– III :-
Amount of max excess
= Sum of max 12 – (Sum of mand 12 X 100)
91.3
CALCULATION– IV :-
Amount of mand excess
=Sum of mand 12 – (Sum of max 12 X 91.3
100
81. ARMAMENTERIUM:
ȿ Dental cast
ȿ Divider
82
Peck Index = m-d crown dimension. X 100
f-l crown dimension.
According to him tooth shape is a determining factor for lower incisor crowding
PECK AND PECK RATIO
According to them for well aligned
- 41,31 P & P index = 88.4 ± 4.3
- 42,32 P & P index = 90.4 ± 4.8
< favorably shaped
> un favorably shaped
82. 83
RECENT ADVANCES
PHOTOGRAPHIC ANALYSIS OF STUDY MODELS
1. Stereophotogrammetry - 3D information
2. Occlusograms - 1:1 photograph of occlusal aspect
3. Holographic image analysis - 3D transparent image of casts
4. Photocopies of study models
f) COMPUTERIZED ANALYSIS
1. OSCOPO - oscilloscope simulation for correcting orthodontic problems in occlusion
2. Reflex metrography- – optical system measuring a point of a dental cast in three planes
83. ȿ There exists numerous analysis based on different criteria.
ȿ Its left to the clinician to decide which analysis best suits to that particular diagnosis and treatment planning to get
expected results.
84
CONCLUSION
84. 1. Hand book of orthodontics – Robert E. Moyer 4th ed.
2. Pediatric dentistry – Stewart R.E.
3. Pediatric dentistry – Pinkham J.R. – 3rd ed.
4. Orthodontics – Graber &Vanarsdall – 3rd ed.
5. Contemporary Orthodontics – Proffit W.R – 3rd ed
6. Dental clinics of North America1978; 22; 563p
7. contemporary orthodontics-William R. Proffit
8. orthodontic diagnosis- Rakosi
9. Hand book of orthodontics –Moyers
10. Text book of Orthodontics –Tweed
85
REFERNCES
85. 11. Computerized tooth width analysis Christopher & Freer, JCO-1999.
12. Digital Models, A new Diagnostic tool, Redmond, JCO-2001
13. The clinical use of occlusograms –White, JCO-1982
14. Holograms as substitutes for study casts-Harradive, AJO –DO-1990
15. A revision of Hixon –Oldfather prediction method –Staley & Derber AJO –DO-1980
16. Text book of Orthodontics-Bishara.
86
REFERNCES
Ultimately the efficiency of the treatment and justice to the patient is all it matters.
Ultimately the efficiency of the treatment and justice to the patient is all it matters.