The quadrilateral analysis is a method for assessing the skeletal configuration of the dentofacial complex. It was developed in 1983 and examines both horizontal and vertical dimensions. Key components include maxillary and mandibular base lengths, anterior and posterior facial heights, sagittal ratios, and angles. Facial types include normodivergent, hypodivergent, and hyperdivergent. The analysis helps locate skeletal discrepancies and determine if orthodontic or surgical treatment is needed. A sample patient analysis shows proclined incisors, a retruded chin, increased anterior upper facial height, and mild skeletal disturbances.

1. QUADRILATERAL ANALYSIS
by Tony Pious

2. History
∗ The quadrilateral analysis was
developed by Rocco J.Di.Paolo
in 1983
∗ Initially a clinical verification of
lower facial proportion was
accomplished
using
32
untreated orthodontic cases
later along with Chinnapi, Di
paolo and Langley expanded it
to include 180 untreated cases.

3. ∗ The quadrilateral analysis concerns primarily with the
skeletal configurations of the individual dentofacial
complex in both the horizontal and the vertical
dimensions regardless of dentoalveolar relationships.

4. Comparison with standard methods of measurement
∗ The standard method of anteroposterior jaw measurement was the
ANB angle. But this proved to be varied as the positions of the
anatomical landmarks greatly influenced the readings. eg-The
horizontal and vertical shift of the nasion affected the readings and
also the rotation of the jaws.
∗ The WITS appraisal was a more effective means to measure this
relationship as it was un affected by the shift in the position of the
nasion or the rotation of the jaws.
∗ But the problem with the wits appraisal was that it was unable to
determine which jaw was affected or the extent of the variation

5. Skeletal Assesment :
∗ The concept of lower facial proportionality states that in a
balanced facial pattern there is a 1:1 proportionality that exists
between the maxillary base length and the mandibular base
length, also the average of the anterior lower facial height and
posterior lower facial height equals these denture base lengths.
∗ Therefore max length =mandibular length=ALFH+PLFH
2
∗ The standard deviation between the measurement is + or -1.5
mm

6. ∗ The two horizontal facial planes used in the construction of the
quadrilateral are the palatal plane(ANS-PNS) and the mandibular
plane(GoGN) A measure of anterior upper facial height is
established and related to the cranial base(S-N)
∗ Maxillary base length :
The maxillary base length is determined horizontally
between two points projected on the palatal plane. The
anterior
limit of Maxillary base length is determined by
projecting a
perpendicular from point A upward to the
palatal plane
while posterior limit is determined by
projecting a
perpendicular from the most inferior portion of
the
pterygomaxillary fissure down to the palatal plane.

8. ∗ Mandibular base length:
The mandibular base length is measured horizontally
between
two points projected on the mandibular plane. The
anterior
limit of the mandibular base length is determined
by
projecting a perpendicular from point B downward to
the
mandibular plane while posterior limit is determined by projecting
a perpendicular from pont j downward to the mandibular plane.
∗ Point J is located at the deepest point of the curvature formed at a
junction of the anterior portion of the ramus and corpus of the
mandible. This point can also be located by drawing a tangent
through the most posterior point of the arc on the anterior border
of the ramus. A second line is drawn parallel to the mandibular
plane along the alveolar crest of the molar teeth, Angle formed by
two lines is bisected. The intersection of this bisector to the inner
curvature of the mandible is point J

10. ∗ Anterior lower facial height is measured from the projection
of point A onto the palatal plane to the projection of point B onto
the mandibular plane. Posterior lower facial height is measured
from the projection of PTM onto the palatal plane to the projection
of point J onto the mandibular plane.
∗ Anterior upper facial height is measured from the projection of
point A onto the palatal plane to the nasion on the cranial base
plane a proportional relationship exists between the anterior upper
facial height and anterior lower facial height 45:55
∗ Anterior lower facial height and anterior upper facial height
intersect at a point A on the palatal plane. The intersection forms an
angle of facial convexity(165-178) This angle relates the quadrilateral
to the cranial base and upper face and is a means of establishing a
skeletal profile assessment .

12. Dental Assessment:
∗ Pt.A line: maxillary incisor position is determined by
drawing a line through Point A parallel to the anterior
lower facial height. A measurement is then made by
drawing a perpendicular from this line to the most
anterior point on the maxillary central incisor.The
average measurement is 5 mm. Plus or minus 1 mm.
∗ Pt B line: mandibular incisor position is determined by
drawing a line through point B .This line is parallel to the
anterior lower facial height.From this line measurement
is made by drawing a perpendicular from this line to the
most anterior point on the mandible central incisor.The
average measurement is 2 mm (+ or -) 1 mm

14. ∗ Pogonion Line: It is constructed by joining a line tangent
to pogonion and parallel to anterior facial height.The
most anterior point of mandibular central incisor is then
related perpendicular to the pogonion line.This
measurement will indicate whether the chin is excessive
or deficient in size.The average is 2 mm anterior or
posterior to the pogonion.

15. Sagittal Ratio:
∗ The sagittal ratio is important in assesing the relative
anteroposterior position of the maxillary and the
mandibular bony bases. Skeletal malformations of the
jaws may be either in the bony bases or located
posteriorly. Therefore pinpointing the area of the
deformity will have a significant impact on whether or
not a certain surgical procedures are indicated. for eg-In
a case of mandibular prognathism it would be necessary
to determine whether the reduction of the bony base
length is required or the mandibular surgery posterior to
the bony base area.

16. Method:
The lines that are used to measure the bony base lengths in
the quadrilateral pattern are extended posteriorly to a point X. This
forms the sagittal angle.
When the anterior and posterior lower facial heights are
parallel and the maxillary and mandibular bony bases are equal a
proportional relation exists with the sides A B C D of the similar
isoceles triangle. The ratio of A to B and C to D is called the sagittal
ratio.
Any forward or retroposition of the bony base will cause
unequal lengths of the posterior legs(linesA and C).In balanced
skeletal patterns the sagittal ratio in adoloscents is 1.0:1.50 + or –
0.05
In adults it is 1.0:1.45 + or – 0.05

18. ∗ Angle of facial convexity is measurement of the
skeletal profile: This angle is formed by the
intersection of anterior lower facial height with
anterior upper facial height and relates the quad
to the upper face. The degree of convexity will
vary depending upon the skeletal type and the
position of the quad pattern as it relates to the
upper face.It shows possible areas of cranial
facial deflections and bony base discrepancies.
∗ The sagittal angle is 23 + or - 1

20. Facial types:
∗ Type 1 :This face has a normodivergent pattern
showing a favorable vertical growth.
∗ In majority of the cases Type 1 cases the
maxillary and mandibular basal arch lengths are
equal and the average vertical height is equal to
the arch length.
∗ Malocclusion in this group are dentoalveolar in
origin

22. ∗ Type 2:This
face is hypodivergent showing a
predominant horizontal growth pattern. There is a
reduction in lower facial height with an undesirable
growth pattern resulting in a skeletal deep bite. The
average vertical height is deficient compared to the
denture base length.

23. A deficient average vertical height is associated with any of the
followin
1)maxillary and mandibular base lengths are comparable in size.
2)maxillary base length is longer than the mandibular base length.
3) mandibular base length longer than the maxillary base length.

25. ∗
Type 3 :
∗ This face is hyper divergent showing a predominantly vertical
growth pattern.Increase in lower facial height with an undesirable
vertical growth pattern , resulting in an skeletal open bite.Average
vertical height is excessive when compared to the denture base
lengths . Posterior alveolar compensation may prevent a dental
open bite in some cases. These cases usually present with a deep
curve of spee and lack of posterior alveolar development.

27. CONCLUSION
Hence the quadrilateral analysis helps not only in
determining the skeletal discrepancy but it also helps in
locating the defect and determining the extent of the
defect. Therefore helps in determining weather the
particular case requires orthodontic treatment or a
surgical treatment or a combination of both.

30.
NORMAL
PATIENT VALUE
INFERENCE
DENTAL
Point A line
5 mm + 1 mm
13 mm
Proclined upper incisor
Point B line
2mm + 1mm
5 mm
Proclined lower incisor
Pogline
2 mm
8mm
Retruded chin
SKELETAL
Max base length
-
56
-
Mandibular base length
-
56
-
Anterior lower facial height
-
66
-
Posterior lower facial height
-
38
-
RATIO
1:1:1
1:1:0.9
Near balanced ratio
Anterior upper facial height
-
62
-
AUFH:ALFH
45:55
Angle of convexity
165° - 175°
169°
Normal
Sagittal angle
23° + 1°
29°
Convex angle
A:B:C:D
1.0:1.45
1:1.02
Unequal proportion
62:66
Increased AUFH
(mild skeletal
disturbances)

31. THANK YOU