Compensating Curves in Prosthodontics

COMPENSATING CURVE
PRESENTED BY-
DR. PARTHA SARATHI ADHYA
(1st year PGT, Dept. of Prosthodontics and Crown &
Bridge)
Under the guidance of :-
Prof.(Dr.) Jayanta Bhattacharyya.(H.O.D)
Prof.(Dr.) Samiran Das.
Dr. Sayan Majumdar.
Dr. Saumitra Ghosh.
Dr. Preeti Goel.

CONTENTS
 Introduction
 Compensating Curve.
 Curve of Monson .
 Curve of Wilson
 Curve of Spee
 Curve of Pleasure .
 Compensating curve formula.
 Hanau’s Quint.
 Role of Compensating Curve in Fixed Denture Prosthesis.
 Review of literature

The determination of the occlusal plane is one of the most important
steps in prosthodontic rehabilitation of edentulous patients. The position of the
occlusal plane forms the basis for ideal tooth arrangement.
The three dimensional arrangements of dental cusps and incisal edges in
the natural human dentition are classically described as spherical, with the
occlusal surfaces of all teeth touching a segment of the surface of a sphere, called
the curve of Monson. It is divided into an anteroposterior curve called the curve
of Spee and a mediolateral curve called the curve of Wilson.
Reestablishment of these curves of natural dentition is essential during
rehabilitation of a patient in prosthodontics. Replacement of natural occlusal
curves with artificial teeth are collectively known as compensating curves.
Introduction

COMPENSATING CURVE
 The anteroposterior curving (in the median plane) and the
mediolateral curving (in the frontal plane) within the alignment
of the occluding surfaces and incisal edges of artificial teeth
that is used to develop balanced occlusion.-GPT-9
 The arc introduced in the construction of complete removable
dental prostheses to compensate for the opening influences
produced by the condylar and incisal guidance’s during lateral
and protrusive mandibular.-GPT-9

CURVE OF MONSON [GEORGE S. MONSON, U.S.
DENTIST, 1869-1933]
 curve of occlusion in which each cusp and incisal edge
touches or conforms to a segment of the surface of a sphere 8
inches in diameter with its center in the region of the glabella.-
GPT-9
 if jaw development was ideal, an equilateral triangle would be
formed by straight lines drawn connecting the centers of both
condyles and connecting these centers and a point at the
mesioincisal angle of the lower central incisors. – Bonwill.
 the points on the lower jaw teeth which move in contact with
those in the skull lie on the surface of a sphere.- Von Spee.

 Bonwill triangle was equilateral, ideal conditions seldom prevailed
and that usually an isosceles triangle resulted, with the short side
between the condyle centers.
 the center of a sphere with a radius of approximately 4 inches is
equidistant from the occlusal surfaces of the teeth and the center of
the condyles and that lines drawn from the center of this sphere must
pass through the long axis of each tooth.
 This “spherical theory” has been modified and further interpreted by
Morton, Maxwell.

 Validity of Curve of Monson
 Although Monson’s principles apply in ideal conditions, the latter,
again, are seldom found in the adult dentitions.
 Growth and development and environmental factors (i.e., the
physiologic condition of the dental structure) have caused a deviation
from the “ideal” because of loss of teeth, malposed and malaligned
teeth, periodontal disease, altered muscular function, habit patterns.

CURVE OF WILSON [GEORGE H. WILSON, U.S.1855-
1922]
 In the theory that occlusion should be spherical, the curvature
of the cusps as projected on the frontal plane expressed in
both arches; the curve in the mandibular arch being concave
and the one in the maxillary arch being convex.- GPT-9
 the curve of Wilson also permits lateral mandibular excursions
free from posterior interferences

 The curve of Wilson results from lingual inclination of the mandibular
posterior teeth, making the lingual cusps lower than buccal cusps on
the mandibular arch; the buccal cusps are higher than palatal cusps
on the maxillary arch because of the buccal inclination of maxillary
posterior teeth.

 Role of Curve of Wilson in occlusion
 The curve of Wilson also permits lateral mandibular excursions free
from posterior interferences.
 Aligning both maxillary and mandibular posterior teeth with the
principal direction of muscle contraction produces the greatest
resistance to masticatory forces and creates the inclinations that
form the curve of Wilson.
 the curve of Wilson was positively correlated to intercanine,
interpremolar, and intermolar distances . This means that as the
curve of Wilson became steeper, these distances became smaller.

 Role of Curve of Wilson in mastication
 When the curve of Wilson gets altered, masticatory function may be
impaired because increased activity is required to get the food onto
the occlusal table.

CURVE OF SPEE [FERDINAND GRAF SPEE, PROSECTOR
OF ANATOMY, GERMANY, 1855-1937]:
 The anatomical curve established by the occlusal alignment
of the teeth, as projected onto the median plane, beginning
with the cusp tip of the mandibular canine and following the
buccal cusp tips of the premolar and molar teeth, continuing
through the anterior border of the mandibular ramus and
ending at the anterior aspect of the mandibular condyle.-
GPT-8
 The arc of a curved plane that is tangent to the incisal edges
and the buccal cusp tips of the mandibular dentition viewed in
the sagittal plane.

o Proposition one: Spee indicated that from a profile view, the molar
surfaces lie on the arc of a circle which, continued posteriorly,
touches the anterior border of the condyle.
o Proposition two: It is easy to demonstrate the curve in cases with
marked attrition than in cases with well-preserved cusps.
o Proposition three: When other points besides molars were included
in measurements from the line of occlusion, they, along with the
condyle, could be on a common arc.
 Spee suggested that this geometric arrangement defined the most
efficient pattern for maintaining maximum tooth contacts during
chewing and considered it an important tenet in denture construction.

 Role of Curve of Spee in mastication
 Osborn reported that the curve of Spee had a positive correlation
with the inclination of masseter muscle. This forward tilt of the
mandibular posterior teeth arrangement maximizes the muscular
efficiency during chewing.
 The axis of each lower tooth on the curve of Spee is aligned nearly
parallel to its individual arc of closure around the condylar axis to
align each tooth for maximum resistance to functional loading

 Role of Curve of Spee in occlusion
 The curve of Spee permits total posterior disclusion on mandibular
protrusion, given proper anterior tooth guidance.
 The curve of Spee may be pathologically altered due to rotation,
tipping, or extrusion of teeth.
 Mew quotes that whenever the curve of Spee is increased, the
margins of the tongue will be seen to overlay the lingual cusps of the
mandibular premolar, and the greater the curve, the more likely it is
to overlay both the lingual and buccal cusps, often with scalloping.

 ANALYSIS OF THE CURVE OF SPEE AND THE CURVE OF WILSON IN
ADULT INDIAN POPULATION: A THREE-DIMENSIONAL MEASUREMENT
STUDY
o Sowmya Velekkatt Surendran, Sharmila Hussain1, S.
Bhoominthan, Sanjna Nayar, Ragavendra Jayesh.
o The Journal of Indian Prosthodontic Society | Oct-Dec 2016 |
Vol 16 | Issue 4.
 Hydrocollied impression of 60 subjects (30 male, 30 female )
taken and master casts are obtained.
 The cusp tips of canines, buccal cusp tips of premolars and
molars, and palatal/lingual cusp tips of second molars of 60
maxillary and 60 mandibular casts obtained were marked with
an indelible marker

 Three dimensional (x, y, z) coordinates of the cusp tips of the
molars, premolars, and canines of the right and left sides of
the maxilla and mandible were obtained with three
dimensional coordinate measuring machine.
 In Indian population, males have a greater radius of the curve
of Spee and curve of Wilson compared to females.
 For males and females, the mean radius of curve of Spee and
curve of Wilson are greater in maxillary arch than mandibular
arch.

 Deepest cusp tip was the distobuccal cusp of the first molar in
the maxillary arch and the mesiobuccal cusp of the first molar
in the mandibular arch in both males and females.
 In maxillary and mandibular arches, the mean radius of the
right and left curve of Spee was similar. This was observed in
both the genders.
 In the selected subjects, the radius of the curve of Spee and
curve of Wilson are greater than the 4 inch (100 mm) radius
proposed by Monson.

CURVE OF PLEASURE [MAX A. PLEASURE,
U.S. DENTIST, 1903-1965]
 A helicoid curve of occlusion that, when viewed in the frontal
plane, conforms to a mediolaterally convex curve in which the
lingual surfaces of the teeth are more coronal to the buccal
surfaces, except for the last molars, which reverse that
pattern.- GPT-9
 in excessive wear of the teeth, the obliteration of the cusps
and formation of either flat or cuppedout occlusal surfaces,
associated with reversal of the occlusal plane of the premolar,
first and second molar teeth (the third molars being generally
unaffected), whereby the occlusal surfaces of the mandibular
teeth slope facially instead of lingually and those of the
maxillary teeth incline lingually.- GPT-9

o 1st proposed by the Avery brothers in 1929.
o It increases total efficiency. The stability of the upper denture
during speech, laughter, coughing, sneezing, etc..
o Enhanced stability of the lower denture during closure against
a morsel of food.
o Unimpaired balancing contacts.
o Increased cutting efficiency because of the longitudinal sliding
movement of the lower cutting ridges.
o Reduced occlusal pressure and tissue trauma.

COMPENSATING CURVE FORMULA
o When the two buccal cusp tips and the highest-situated
lingual cusp tip are connected with straight lines, these lines
circumscribe a small plane which is called the “cusp plane.”
o The inclination of the cusp plane to the plane of occlusion is
called the “cusp plane angle.”

 The tips of the incisors, the cuspid, and the cusp plane of the
bicuspids are on the line PP’,. The cusp plane of the molars is
on the line MM’,. These lines each form an angle with the
plane of occlusion. This angle (ω) is identical with the cusp
plane angle.

o of the protrusive facets with various condylar guidance
inclinations is calculated in relation to the plane of occlusion.
On varying the cusp plane angle, the cusp angulation of the
protrusive facets has to be altered accordingly to retain the
Same incline of the facets to the plane of occlusion.
o The action of the compensating curve is as follows. The cusp
angulation of the protrusive facets of the molars (calculated in
accordance with the cusp incline table) must be reduced with
an angle equal to the cusp plane angle (w) . This relation can
be expressed by means of the formula :
C= Ԑ- ώ
o where C is the cusp angulation, Ԑ= the cusp angulation
according the table and, ώ = the cusp plane angle. This
formula is called the “formula for the compensating curve

 BICUSPID ARRANGEMENT
o The angul.ation of the bicuspid plane to the condylar guidance
is: ß’=β+ω
o which is greater than the inclination of the condylar guidance
(β). Therefore, the cusp angulation may be steeper to attain
antagonistic contact for protrusive movement. Consequently,
the curve of occlusion decreases the cusp angulation for the
molars and increases the cusp angulation of the bicuspids.

 we do not use high cusps for the bicuspids. In the region of
these teeth, therefore, the antagonists lose their contact
during protrusive gliding movements. This is also true on the
balancing side during lateral movements. The advantages of
this arrangement are the possibility of chewing hard food in
the bicuspid region and the coincidentally obtained
antagonistic contact in the front and in the molar region.

HANAU’S QUINT
 Rules for balanced denture articulation including incisal
guidance, condylar guidance, cusp length, the plane of
occlusion, and the compensating curve.-GPT-9
 [K × I]/[OP × C × OK].
o K = the inclination of condylar guidance,
o I = the inclination of the incisal guidance,
o C = the height of the cusps,
o OP = the inclination of the plane of orientation,
o OK = the prominence of the compensating curve.

 In order to obtain a smooth, balanced occlusion, the compensating
curve must be in harmony with the other factors of occlusion. This
relationship is expressed in Hanau’s Quint.

 TRAPOZZANO CONCEPT
 His Triad of Occlusion, which is simpler than Hanau's Quint but
eliminates the important compensating curve. the plane of orientation
since its location is highly variable within the available inner ridge
space.
 Incisal guidance
 Condylar guidance
 Cusp angle.

 BOUCHER CONCEPT
 Trapozzano's concept that the occlusal plane could be located at
various heights to favor a weaker ridge, and he recommended that
the occlusal plane "be oriented exactly as it was when the natural
teeth are present. '' He believed that this must be done to conform to
anatomic and functional needs.
 There are three fixed factors: The orientation of the occlusal plane,
the incisal guidance, and the condylar guidance.
 "The value of the compensating curve is that it permits an alteration
of cusp height without changing the form of the manufactured teeth .
. . . If the teeth themselves do not have cusps, the equivalence of
cusps can be produced by using a compensating curve. '‘
 The compensating curve enables one to increase the effective height
of the cusps without changing the form of the teeth.
 The angulation of the cusp is more important than the height of the
cusp.

 Lott concept
 Lott studied Hanau's work and clarified the laws of occlusion by
relating them to the posterior separation that is the resultant of the
guiding factors.
 The greater the angle of the condyle path, the greater is the posterior
separation.
 The greater the angle of the overbite (vertical overlap), the greater is
the separation in the anterior region and the posterior region
regardless of the angle of the condylar path
 The greater the separation of the posterior teeth, the greater, or
higher, must be the compensation curve

 Posterior separation compensation curve to balance the occlusion
requires the introduction of the plane of orientation
 The greater the separation of the teeth, the greater must be the
posterior teeth.
 Levin concept
 The condylar guidance is fixed and is recorded from the patient.
 The incisal guidance is usually obtained from the patient’s esthetic
and phonetic requirements. However, it can be modified for special
requirements.
 The compensating curve is the most important factor for obtaining
balance. Monoplane or low cusp teeth must employ the use of a
compensating curve.
 Cusp teeth have the inclines necessary for obtaining balanced
occlusion but nearly always are used with a compensating curve.

 My concept of the laws of articulation is quite similar to Lott's, but I
would eliminate the plane of orientation. I am in agreement with
Boucher 3 as to the need for the compensating curve and that the
occlusal plane should be included only in its correct anatomic
position, i.e., in the position that conforms to the patient's anatomy,
esthetics, and function.

ROLE OF COMPENSATING CURVE IN FIXED
DENTURE PROSTHESIS
 Cones should follow an anteroposterior curve (of Spee) and a
lateral curve (of Wilson).

ROLE OF COMPENSATING CURVE IN FIXED
DENTURE PROSTHESIS
 Pankey-Mann-Schuyler (PMS) philosophy
o The incisal guidance was the developed intraorally with acrylic
resin to satisfy esthetic and functional requirements.
o Optimal occlusal plane is selected as dictated by the curve of
Monson and mandibular posterior teeth are restored in
harmony with the anterior guidance such that they will not
interfere with the condylar guidance.
o Group function occlusion on the working side during lateral
excursions.
o Maximum number of contacts on posterior teeth in centric
relation.

o Maxillary posterior occlusal surfaces are developed after the
completion of mandibular restorations by the functionally
generated path technique (FGP).
o Use of FGP records allows eliminating all occlusal
interferences and establishing functional form of the occlusal
surfaces of the restoration.

 Hobo concept
o Hobo and Takayama in their study revealed that anterior
guidance influenced the working condylar path and concluded
that they were dependent factors.
o cusp angle be considered as the most reliable determinant of
occlusion as cusp angle does not deviate and is 4 times more
reliable than the condylar and incisal path which show
deviation.

 Boardrick’s Occlusal Plane Analyser (BOPA)
 BOPA is used to determine and achieve an occlusal plane that
fulfills both the functional, occlusal as well as the aesthetics
requirement in cases that require full mouth rehabilitation.
 It was based on an anthropological study in 1919, that
Monsoon proposed the anteroposterior curve of the teeth
forms a sphere, with the center of rotation located in the
region of the glabella.
 The Broadrick Flag allows the construction of the Curve of
Spee in perfect harmony with the anterior condylar guidance
allowing total posterior tooth disclusion on mandibular
protrusion

o Anterior survey point (ASP) was selected on midpoint of disto-
incisal edge of mandibular canine, from which long arc of 4-
inch radius was drawn on flag with use of compass.
o Posterior survey point (PSP) was located on disto-buccal cusp
of distal mandibular molar. If position of this tooth were
deemed unacceptable, anterior border of condylar element on
articulator could be selected as PSP.

o Short arc of 4-inch radius was drawn from PSP on flag to
intersect long arc at center of curve of Spee.
o Point of compass was placed at center of flag, and 4-inch
radius was drawn through buccal surfaces of mandibular
teeth.
o The angle of the condylar guidance is not less than the curve
of Spee, as this would introduce posterior protrusive
interferences
o The center should always lie along the long arc drawn from
the anterior survey point, but it may be moved in an anterior or
posterior direction from the intersection of this arc with that
drawn from the posterior survey point.

 Significance of BOPA
o Preliminary determination of an acceptable plane of occlusion
on the study models as an aid in treatment planning.
o Preliminary determination of the amount of reduction that will
be required when each tooth is prepared.
o In the laboratory wax-up and final metal ceramic restoration,
determination of the height of each cusp tip, which helped in
establishing the curve of Spee and the curve of Wilson.

 Simplified Occlusal Plane Analyser (SOPA)
o Composed of a compass of 4 inch radius.
o Touch the compass lead (C) to the tip of the lower cuspid.
Position the compass point (D) on the center line (for the 4”
radius) of the SOPA flag.
o Arc the compass lead to the back molar . This establishes the
optimum occlusal plane height for the posterior teeth.

THE ROLE OF OCCLUSAL CURVATURES AND MAXILLARY ARCH
DIMENSIONS IN PATIENTS WITH SIGNS AND SYMPTOMS OF
TEMPOROMANDIBULAR DISORDERS
 Georgios Kanavakisa; Noshir Mehtab.
 Angle Orthodontist, Vol 84, No 1, 2014.
o 100 subjects were taken randomly and impression were taken
of both arches.
o For the investigation of TMJ disorders RDC-TMD criteria was
used along with various joint sounds were also investigated.
o Measurements on plastermodels were performed with the use
of a digital caliper.
o The depth of the curve of Spee was measured at the most
distal premolar and at the molar level. The highest value on
each side was recorded.

o The curve of Wilson (COW) on each side was measured as
the angle between the frontal projected buccal-lingual plane of
the cusp tips on the first mandibular molars, according to Ali et
al.
 Results-
o This finding was consistent on both sides, so it can be
concluded that people with a flatter curve of Spee present a
higher incidence of joint sounds during lateral excursions.
o The curve of Wilson was positively correlated to intercanine,
interpremolar, and intermolar distances.
o subjects with a steeper COW presented narrower maxillary
arches.
 Conclusion
o Subjects with TMJ sounds present a flatter COS.
o Deep occlusal curvatures are not associated with TMJ pain or
pain of muscular origin.

ASSOCIATION BETWEEN OCCLUSAL CURVATURE AND MASTICATORY
MOVEMENTS WITH DIFFERENT TEST FOODS IN HUMAN YOUNG ADULTS
WITH PERMANENT DENTITIONS
 Kenji Fueki , Eiko Yoshida, Kota Okano, Yoshimasa Igarashi.
 Archives of Oral Biology (2013).
o Forty-six subjects (21 females, 25 males, mean age 25.0
years, range 20–32 years), with completely natural dentition
and Angle Class I molar relationship were taken.
o Upper and lower dental casts of each subject were mounted
on a semi-adjustable articulator. The mandibular cast mounted
on the lower member of the articulator was fixed to a
threedimensional measuring gauge (QM-measure 353,
Mitsutoyo Mfg., Tokyo, Japan). The coordinates of the mid-
points of the canine cusps, and the buccal and lingual cusps
of the premolars, first and second molars were measured and
digitized.

o The approximate spheres were calculated from the
measurements according to the Broadrick Occlusal Plane
Analyzer using a custom made software.
o Mandibular movements during unilateral chewing of six test
food items (chewing gum, cheese, kamaboko, boiled beef,
gummy jelly and raw carrot) until the subjects felt ready to
swallow were recorded using a six-degrees-of-freedom
mandibular movement recording system.

o Conclusion-
o subjects with larger SR tended to show masticatory cycles
with greater vertical and lateral amplitude, faster
opening/closing velocity, shorter opening/closing/oc-
cluding/cycle duration, and they tended to chew the test foods
until ready to swallow with less number of chewing strokes
and chewing time compared to those with smaller SR.
o The mean value of curve of spee is 112mm which is greater
than 4 inch as described by Mansoon.

Conclusion
Difference of opinions exist regarding importance of
compensating curves during fabrication both removable denture
prosthesis and (tooth supported or implant supported) fixed denture
prosthesis.
From experts’ opinion, literature reviews and case reports, it is
evident that prosthodontist should have a sound knowledge about the
occlusal curves of natural dentition and compensating curves.
To achieve success in clinical practice, establishment of
compensating curves in dental prosthesis is one of the important key
factors which increases patients’ compliance as well as longevity of the
restoration.

References
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