ANTIFUNGALEFFICACYOFSALIVARYHRPS
19. Spiechowicz E, Bak 2, Bielunska S. Clinical evaluation of natamycjn 2.5 % suspension in the treatment of a denture stomatitis infected with Condida albicans. Castellania 1970;5:175-80. 20. Brant EC, Santarpia III RP, Brasseur M, Hong A, Pollock JJ. HRP inhibition of germ tube formation and pH [Abstract]. J Dent Res 1989;266:682.
Contributing
author
Ling Xu, Graduate (PhD) student, Department of Oral Biology and Pathology, State University of New York at Stony Brook, School of Dental Medicine, Stony Brook,
Reprint requests to: DR. ROBERT P. RENNER SCHOLL OF DENTAL MEDICINE STATE UNIVERSITY OF NEW YORK AT STONY BROOK STONY BROOK, NY 11794-8706
ematical Thomas
R. Katona,
model PBD,
of mandibular
protrusion
DMDa
Indiana University, Schoolof Dentistry, and Purdue University School of Engineering Technology, Indianapolis,
and
Ind.
Mathematical expressions were derived to describe the sagittal plane movements of the mandible. It was shown that mandibular rotation during protrusion was a function of incisor and condylar guidances, initial mandibular angulation, mandibular size, and the extent of the excursion. Cusp tip displacement and center of rotation calculation algorithms were also developed for the protrusive path. (J PROSTWET DENT 1991;66:699-705.)
M
ucb of dentistry focuses around the kinematics of the mandible as it is displaced under various constraints. This focus includes Posselt’sl diagram of motion, retruded contact-maximum intercuspation (RC-IC) discrepancies, occlusal interferences and adjustment, cusp morphology, temporomandibular joint (TMJ) dysfunction, and the design and use of pantographs, facebows, and articulators. The vast literature pertaining to these phenomena represents diverse philosophies. Recent examples include studies on occlusal equilibration2-5 and the influence of anterior guidance,6 measurement of incisor and/or condylar guidances7-g and RC-IC discrepancies,1° articulator evaluation,‘l and mathematical analyses.12-l4 The shared engineering problem in these diverse studies is the movement of a rigid body (the mandible or articulator member), parts of which are guided along specific directions. This study derived mathematical expressions to describe these constrained movements of the mandible. The results represent a mathematical analog to the graphical description of Posselt’s diagram.
AL AND
METHODS
In Posselt’s diagram (Fig. 1) displacement 1-2 represents mandibular central incisor border movement from intercuspal (IC) to edge-to-edge relationship. As the mandibu-
%ssistant Professor, Department of Orthodontics, School of Dentistry, and Department of Mechanical Engineering, of Engineering and Technology. 10/1./25939 THE JOURNAL
OF PROSTHETIC
DENTISTRY
School
lar incisor edge moves from position 1 to 2 along the maxillary incisor, the condyle displaces from position 4 to 6 along the articular eminence (Fig. 2). Since this protrusion of the mandible is constrained by condylar and incisor guidances, the schematic in Fig. 3 was used to derive the equations that govern the movement. The nomenclature and initial values are listed in Table I. The geometric analysis yielded equations la and lb: aCOS(A)
+
lCOS(T’)
= lCOS(T) + bCOS(B)
@a)
and aSIN
+ lSIN(T’)
= lSIN(T)
+
These equations were solved simultaneo the governing equations: T’ = B - ARCSINE[SIN(B-T)
1
(lb:
T’ to give
+ (a/I)SIN(A-B)]
@a),
or in terms of b instead of a, T’ = A - ARCSINE[SIN(A-T) -t (b/l)SIN(AThese equations state that T’, the displaced angulation of the mandible, is a function of guidances (A and B), initial mandibular angulation (T), and mandibular size (1). Depending on the form of the equation, the rotation also depends on the distance traveled by the condyle (a in equation Za) or by the mandibular incisor (b in equation 2b). The relationship between a and b was also determined by solving equation la for a: a = [ICOS(T) + bCOS(B) - lCOS(T’)]/COS(A)
(3)
Note that equation lb could also be solved for a, but t,he denominator in the resultant expression would be SIN(A) instead of COS(A). But the value of A, the condylar guidance, can be zero degrees, and in that case, using equation lb would require division by zero because SIN(o) = 0. 699
Tab&e I. parentheses)
Nomenclature
and
initial
values
(in
A-Xondylar guidance (0, 20, 40, 60, and 80 degrees) B-Incisor guidance (0, 20, 40, and SO degrees) ?--Length of line segment joining condyle and mandibular incisor tip (= L-4 = 2-51, (iQ0 9mnj T--initiai angulation of r,he mandible (25 degrees) T’-hgulation of the mandible in the displaced position b-Distarxe moved by the mandibuiar incisor along the maxiilary incisor (= I-2) ad a-Corresponding distance moved by the condyle (= 4-5) d: e--Distances from eondyle, along and ~er~e~~~c~~a~ to 1 -used to define location of any point, P, fixed relative to rmadibie (cl = 60 and e = -20 Ear molar cusp tip; d = 80 and e = -10 for premolar cusp tip) Rx, Fy-Horizon*eal and vertical dispiacement components of point P, located by d and e
~nforrnati~~
fmm
Chilean (=
100
mm)
Fig.
the
articles illad
and and
T (= 25 degrees)
4: A. illustrates
situation
by Kohno were used
the
(case
0. 8).
of the
a.nd the
cmdyTe,
results
fm
e. Fig.
5 shows
~K~t~~s~o~
changes
Fig.
6 is a graph
qequation
3).
the
tip,
the
for
A f
rna~~~b~~ar
by the
con
yEe (a).
11 Lists
the
~~~r~i~ate$
dur-
between
a
to
that (b)
incisor
~~~~~~ti~~
r~~at~onsb~~
tip
12)
displace-
B cases.
= 1 Gorresponds
incisor
No.
a
of the
> I indicates
mandibular
traveled
of
b/a b/a
2b)
A
B cam
~§~~a~erne~t
an
all cme8.
are the
a molar
prescribed
fm-
A typica!
is shown in Fig. 4, B. Depicted meats
and Nakand ts approximate
the
c%
is greater
b/a
than
C I is the
the
distance
opposite
condi-
tion. Table
0 the the
first
0~10
8. if the mandible i~%tanta~eQ~% COR
13, and
“69. Fig.
manaible
paotrud
a~~FQ~irnate duced
the
by pure
rotrusion
teeth
rotation the
early
extended
tooth tuaH
that
changes
full
5 mm.
when
the
about
the
the
maximum
is also
Table
No.
then I, 7,
the
dis-
PI
occurred
in
mweme CO discrepancy
edge-to-edge
identified
~~~t~~ta~e~~~
in the
rn~~~rn~~t
greatest
(correspoa
b)
transkion, as in cases
initial
the maximum the
pure
that
critical
experienced
calculations
the
to the
b = 5 mm column),
initial in
underwent was undehed,
errors
represents
dsxing
of the
imxement
mm
of the
columrl
curred
7
maximum
placements mm
mm
errors
from
QC-
As the
~e~ati~~§b~~
(the
increased.
deviation in the
that K.
frrom table.
T t
MODEL
OF MANDIBULAR
PROTRUSION
2
Fig. 2. Intercuspation mandibular position, 4-l. Mandibular position during incisor edge-to-edge relationship, 5-2. (Note that 1-2 corresponds to l-2 on Posselt’s diagram, Fig. 1.) Location of point fixed relative to mandible is given by d and e.
ig. 3. Schematic of Fig. 2 used to derive governing equations.
A = B, the~ (A-B) - 0 and therefore (a/l)SIN(A-B) = 0, because SIN(O) = 0, Thus SIN@-T’) = SIN(B-T), or B-T’ = B-‘r and tnerafore T’ = T. 2. Con&_ar guidance is less than incisor guidance: If A < B, her (A-Pa < 0 and tlmerefcre (a/l)SIN(A-B) < 0, T&EJ@agyI; Of ;P&.Ofg;,“:ETIC J-~;haT:s’=p:
because SIN(negative angle) < 0. Thus from equation 2c, SIN(B-T’) < SIN(B-T), or B-T’ < B-T, and therefore T’ >T. 3. Similarly, it can be shown that if condylar guidance is greater that incisor guidance, A > B, then T’ < T. 701
ficatim of the resdts of ohno and Nakano’s study is impossible. As they nt out, the amount of rotatian depends om the gzlidances. tation
is also
in the
incisor
a function
aad
of the
condyiar
distance
moved
by
the
mam-
guidances.
Nakano8 also state t~~t~~a~~~~~ng~~t~~~ owever, the graph f equation 3 (Fig. 6) and the calculated ratios /a fm thefisst increment in all four c~~h~mati~ms of the ~~e~~a~~t~es le BHB).Fig. 6 also reveals that the b/a raextent of ~rQtFnsiQm. 22, 13, 14, 17, 18, and 19 are prsbably Fe~resemtatj~e sf cst ~~~~~~~~a~s in the range of imisor ad c~rn~y~a~guidances. hem using t pIkate man0.9 mm) as a pure himge Iocatfon to ~~~~~t~~rn
for
these
cases, 0th
the
largest
during
the
0~s generally initial
edge-to-edge e No. initial
and
final
errors
at 0,7%
1'7 exhibited and
~rotF~si~m
in&m
contact the
7T?G1-,resgectively.
greatest The
MODEL
OF MANDIBULAR
PROTRUSION
CASE
#
8
Fig. 4. Displacement calculations for representative B > A (A) and A > B (B) cases.1 is prescribed movement of mandibular incisor edge (along l-2 in Figs. 1, 2, and 3); C is calculated concomitant displacement of condyle (along 4-5 in Figs. 2 and 3) with prescribed condylar angulation, A; M and PM are calculated corresponding displacements of molar cusp tip (d = 60 mm and e = -20 mm in equation 4) and a premolar cusp tip (d = 80 mm and e = -10 mm), respectively. Each marker on incisor (1) line represents a 1 mm increment in b, distance moved by mandibular incisor along maxillary incisor. Same markers are used on other lines to identify corresponding locations of premolar and molar cusp tips and condyle.
other combinations were reproduced to within 0.3% at the initial movement, and to 3% at b = 5 mm. These results suggest that a simple hinge articulator with an adjustable hinge point may be a useful (but cumbersome) clinical instrument to reproduce sagittal plane movements. The axis must be locatable anterior (x > 0), posterior (x < 0), superior (y > 0), and inferior (y < 0) to
THE
JOURNAL
OF PROSTHETIC
DENTISTRY
the condyle. Limitations, however, include the fact that the closer the values of the guidances are to each other, the farther away the COR moves. That is, as A and B approach the same value, the COR moves to infinity. The greater the difference between A and B, the closer the COR, but the errors in the reproduction of the movements increase. Although the clinical significance is not immediately
103
--------------_._-.____. .- .--.“.-”-.._-. - - -... -___---------.--- ..----. ~-.- _______
._ __ ._--
-.--
-.---
_I
I!? 5 28
MODEL
OF MANDIBULAR
PROTRUSION
dY
(mm)
-6.0 Fig. 7. Changes in location of instantaneous CORs from their initial positions as mandible moves from IC to edge-to-edge relationship. Initial locations are listed for each case in Table II.
ante; (2) the prominence of the compensating curve; (3) the inclination of the plane of orientation; (4) the inclination of the incisal guidance; and (5) the heights of the cusps.15 The guidances (1 and 4) appear explicitly in the formulation presented in this article. The compensating curve (2) and the plane of orientation (3) appear implicitly in the specification of the location of the cusp tip with respect to the frame of reference used. Cusp tip heights (5), however, must be interpreted in terms of cusp slopes. The slopes are such that no interference is created as the mandible moves from IC. Height is a secondary parameter that can be defined in terms of the calculated slope and the mesiodistal width of the cusp. The approach presented in this article will be applied to the mathematical modeling of occlusal adjustment. Further work will also be undertaken to include the effects of nonlinear guidances. REFERENCES 1. Posselt U. Physiology of occlusion and rehabilitation. Philadelphia: FA Davis Co, 1962:44. 2. Wenneberg B, Nystrom T, Carlsson GE. Occlusal equilibration and other stomatographic treatment in patients with mandibular dysfunction and headache. J PROSTHET DENT 1988;59:478-83. 3. Forssell H, Kirveskari P, Kangasniemi P. Effect of occlusal adjustment on mandibular dysfunction. Acta Odontol Stand 1986;44:63-9. 4. Magnusson T, Carlsson GE. Occlusal adjustment in patients with residual or recurrent signs of mandibular dysfunction. J PROSTHET DENT 1983;49:706-10.
THE
JOURNAL
0F
PROSTHETIC
DENTISTRY
5. Riise C. Rational performance of occlusal adjustment. J PHO~THZT DENT 1982;48:319-27. 6. Brose MO, Tanquist RA. The influence of anterior coupling on mandibular movement. J PROSTHET DENT 1987;57:345-53. 7. Hobo S, Takayama H. A new system for measuring condylar path and computing anterior guidance. Part I. measuring principle. Int ,J Prosthodont 1988;1:99-106. 8. Kohno S, Nakano M. The measurement and development of anterior guidance. J PROSTHET DENT 1987;57:620-5. 9. El-Gheriani AS, Winstanley RB. Graphic tracings of condylar paths and measurements of condylar angles. J PROSTHET DENT 1989;61:77-87. 10. Rosner D, Goldberg GF. Condylar retruded contact position and intercuspal position correlation in dentulous patients. Part I: three-dimensional analysis of condylar registrations. J PROSTHET DENT 1986;56: 230-g. 11. McMillan DR, McMillan AS. A comparison of habitual jaw movements and articulator function. Acta Odontol Stand 1986;44:291-9. 12. Eichhold WA, Chen M, Welker WA. A formula to determine the lateral condylar guidance from intraoral needlepoint tracings. J PROSTHET DENT 1986;56:698-701. 13. Rosner D. A mathematical approximation of the angle of closure from retruded contact. J Periodontol 1973;44:228-35. 14. Rosner D. A chairside analysis of the feasibility of selective grinding. J PROSTHET DENT 1981;45:30-6. 15. Hanau RL. Full denture prosthesis-intraoral technique for Hanau articulator model H. 4th ed. Buffalo, NY: University of Btiffalo. 1930:28.
Reprint
requests
to:
DR. THOMAS R. KATONA SCHOOL OF DENTISTRY INDIANA UNIVERSITY 1121 W. MICHIGAN ST. INDIANAPOLIS, IN 46202
19. Spiechowicz E, Bak 2, Bielunska S. Clinical evaluation of natamycjn 2.5 % suspension in the treatment of a denture stomatitis infected with Condida albicans. Castellania 1970;5:175-80. 20. Brant EC, Santarpia III RP, Brasseur M, Hong A, Pollock JJ. HRP inhibition of germ tube formation and pH [Abstract]. J Dent Res 1989;266:682.
Contributing
author
Ling Xu, Graduate (PhD) student, Department of Oral Biology and Pathology, State University of New York at Stony Brook, School of Dental Medicine, Stony Brook,
Reprint requests to: DR. ROBERT P. RENNER SCHOLL OF DENTAL MEDICINE STATE UNIVERSITY OF NEW YORK AT STONY BROOK STONY BROOK, NY 11794-8706
ematical Thomas
R. Katona,
model PBD,
of mandibular
protrusion
DMDa
Indiana University, Schoolof Dentistry, and Purdue University School of Engineering Technology, Indianapolis,
and
Ind.
Mathematical expressions were derived to describe the sagittal plane movements of the mandible. It was shown that mandibular rotation during protrusion was a function of incisor and condylar guidances, initial mandibular angulation, mandibular size, and the extent of the excursion. Cusp tip displacement and center of rotation calculation algorithms were also developed for the protrusive path. (J PROSTWET DENT 1991;66:699-705.)
M
ucb of dentistry focuses around the kinematics of the mandible as it is displaced under various constraints. This focus includes Posselt’sl diagram of motion, retruded contact-maximum intercuspation (RC-IC) discrepancies, occlusal interferences and adjustment, cusp morphology, temporomandibular joint (TMJ) dysfunction, and the design and use of pantographs, facebows, and articulators. The vast literature pertaining to these phenomena represents diverse philosophies. Recent examples include studies on occlusal equilibration2-5 and the influence of anterior guidance,6 measurement of incisor and/or condylar guidances7-g and RC-IC discrepancies,1° articulator evaluation,‘l and mathematical analyses.12-l4 The shared engineering problem in these diverse studies is the movement of a rigid body (the mandible or articulator member), parts of which are guided along specific directions. This study derived mathematical expressions to describe these constrained movements of the mandible. The results represent a mathematical analog to the graphical description of Posselt’s diagram.
AL AND
METHODS
In Posselt’s diagram (Fig. 1) displacement 1-2 represents mandibular central incisor border movement from intercuspal (IC) to edge-to-edge relationship. As the mandibu-
%ssistant Professor, Department of Orthodontics, School of Dentistry, and Department of Mechanical Engineering, of Engineering and Technology. 10/1./25939 THE JOURNAL
OF PROSTHETIC
DENTISTRY
School
lar incisor edge moves from position 1 to 2 along the maxillary incisor, the condyle displaces from position 4 to 6 along the articular eminence (Fig. 2). Since this protrusion of the mandible is constrained by condylar and incisor guidances, the schematic in Fig. 3 was used to derive the equations that govern the movement. The nomenclature and initial values are listed in Table I. The geometric analysis yielded equations la and lb: aCOS(A)
+
lCOS(T’)
= lCOS(T) + bCOS(B)
@a)
and aSIN
+ lSIN(T’)
= lSIN(T)
+
These equations were solved simultaneo the governing equations: T’ = B - ARCSINE[SIN(B-T)
1
(lb:
T’ to give
+ (a/I)SIN(A-B)]
@a),
or in terms of b instead of a, T’ = A - ARCSINE[SIN(A-T) -t (b/l)SIN(AThese equations state that T’, the displaced angulation of the mandible, is a function of guidances (A and B), initial mandibular angulation (T), and mandibular size (1). Depending on the form of the equation, the rotation also depends on the distance traveled by the condyle (a in equation Za) or by the mandibular incisor (b in equation 2b). The relationship between a and b was also determined by solving equation la for a: a = [ICOS(T) + bCOS(B) - lCOS(T’)]/COS(A)
(3)
Note that equation lb could also be solved for a, but t,he denominator in the resultant expression would be SIN(A) instead of COS(A). But the value of A, the condylar guidance, can be zero degrees, and in that case, using equation lb would require division by zero because SIN(o) = 0. 699
Tab&e I. parentheses)
Nomenclature
and
initial
values
(in
A-Xondylar guidance (0, 20, 40, 60, and 80 degrees) B-Incisor guidance (0, 20, 40, and SO degrees) ?--Length of line segment joining condyle and mandibular incisor tip (= L-4 = 2-51, (iQ0 9mnj T--initiai angulation of r,he mandible (25 degrees) T’-hgulation of the mandible in the displaced position b-Distarxe moved by the mandibuiar incisor along the maxiilary incisor (= I-2) ad a-Corresponding distance moved by the condyle (= 4-5) d: e--Distances from eondyle, along and ~er~e~~~c~~a~ to 1 -used to define location of any point, P, fixed relative to rmadibie (cl = 60 and e = -20 Ear molar cusp tip; d = 80 and e = -10 for premolar cusp tip) Rx, Fy-Horizon*eal and vertical dispiacement components of point P, located by d and e
~nforrnati~~
fmm
Chilean (=
100
mm)
Fig.
the
articles illad
and and
T (= 25 degrees)
4: A. illustrates
situation
by Kohno were used
the
(case
0. 8).
of the
a.nd the
cmdyTe,
results
fm
e. Fig.
5 shows
~K~t~~s~o~
changes
Fig.
6 is a graph
qequation
3).
the
tip,
the
for
A f
rna~~~b~~ar
by the
con
yEe (a).
11 Lists
the
~~~r~i~ate$
dur-
between
a
to
that (b)
incisor
~~~~~~ti~~
r~~at~onsb~~
tip
12)
displace-
B cases.
= 1 Gorresponds
incisor
No.
a
of the
> I indicates
mandibular
traveled
of
b/a b/a
2b)
A
B cam
~§~~a~erne~t
an
all cme8.
are the
a molar
prescribed
fm-
A typica!
is shown in Fig. 4, B. Depicted meats
and Nakand ts approximate
the
c%
is greater
b/a
than
C I is the
the
distance
opposite
condi-
tion. Table
0 the the
first
0~10
8. if the mandible i~%tanta~eQ~% COR
13, and
“69. Fig.
manaible
paotrud
a~~FQ~irnate duced
the
by pure
rotrusion
teeth
rotation the
early
extended
tooth tuaH
that
changes
full
5 mm.
when
the
about
the
the
maximum
is also
Table
No.
then I, 7,
the
dis-
PI
occurred
in
mweme CO discrepancy
edge-to-edge
identified
~~~t~~ta~e~~~
in the
rn~~~rn~~t
greatest
(correspoa
b)
transkion, as in cases
initial
the maximum the
pure
that
critical
experienced
calculations
the
to the
b = 5 mm column),
initial in
underwent was undehed,
errors
represents
dsxing
of the
imxement
mm
of the
columrl
curred
7
maximum
placements mm
mm
errors
from
QC-
As the
~e~ati~~§b~~
(the
increased.
deviation in the
that K.
frrom table.
T t
MODEL
OF MANDIBULAR
PROTRUSION
2
Fig. 2. Intercuspation mandibular position, 4-l. Mandibular position during incisor edge-to-edge relationship, 5-2. (Note that 1-2 corresponds to l-2 on Posselt’s diagram, Fig. 1.) Location of point fixed relative to mandible is given by d and e.
ig. 3. Schematic of Fig. 2 used to derive governing equations.
A = B, the~ (A-B) - 0 and therefore (a/l)SIN(A-B) = 0, because SIN(O) = 0, Thus SIN@-T’) = SIN(B-T), or B-T’ = B-‘r and tnerafore T’ = T. 2. Con&_ar guidance is less than incisor guidance: If A < B, her (A-Pa < 0 and tlmerefcre (a/l)SIN(A-B) < 0, T&EJ@agyI; Of ;P&.Ofg;,“:ETIC J-~;haT:s’=p:
because SIN(negative angle) < 0. Thus from equation 2c, SIN(B-T’) < SIN(B-T), or B-T’ < B-T, and therefore T’ >T. 3. Similarly, it can be shown that if condylar guidance is greater that incisor guidance, A > B, then T’ < T. 701
ficatim of the resdts of ohno and Nakano’s study is impossible. As they nt out, the amount of rotatian depends om the gzlidances. tation
is also
in the
incisor
a function
aad
of the
condyiar
distance
moved
by
the
mam-
guidances.
Nakano8 also state t~~t~~a~~~~~ng~~t~~~ owever, the graph f equation 3 (Fig. 6) and the calculated ratios /a fm thefisst increment in all four c~~h~mati~ms of the ~~e~~a~~t~es le BHB).Fig. 6 also reveals that the b/a raextent of ~rQtFnsiQm. 22, 13, 14, 17, 18, and 19 are prsbably Fe~resemtatj~e sf cst ~~~~~~~~a~s in the range of imisor ad c~rn~y~a~guidances. hem using t pIkate man0.9 mm) as a pure himge Iocatfon to ~~~~~t~~rn
for
these
cases, 0th
the
largest
during
the
0~s generally initial
edge-to-edge e No. initial
and
final
errors
at 0,7%
1'7 exhibited and
~rotF~si~m
in&m
contact the
7T?G1-,resgectively.
greatest The
MODEL
OF MANDIBULAR
PROTRUSION
CASE
#
8
Fig. 4. Displacement calculations for representative B > A (A) and A > B (B) cases.1 is prescribed movement of mandibular incisor edge (along l-2 in Figs. 1, 2, and 3); C is calculated concomitant displacement of condyle (along 4-5 in Figs. 2 and 3) with prescribed condylar angulation, A; M and PM are calculated corresponding displacements of molar cusp tip (d = 60 mm and e = -20 mm in equation 4) and a premolar cusp tip (d = 80 mm and e = -10 mm), respectively. Each marker on incisor (1) line represents a 1 mm increment in b, distance moved by mandibular incisor along maxillary incisor. Same markers are used on other lines to identify corresponding locations of premolar and molar cusp tips and condyle.
other combinations were reproduced to within 0.3% at the initial movement, and to 3% at b = 5 mm. These results suggest that a simple hinge articulator with an adjustable hinge point may be a useful (but cumbersome) clinical instrument to reproduce sagittal plane movements. The axis must be locatable anterior (x > 0), posterior (x < 0), superior (y > 0), and inferior (y < 0) to
THE
JOURNAL
OF PROSTHETIC
DENTISTRY
the condyle. Limitations, however, include the fact that the closer the values of the guidances are to each other, the farther away the COR moves. That is, as A and B approach the same value, the COR moves to infinity. The greater the difference between A and B, the closer the COR, but the errors in the reproduction of the movements increase. Although the clinical significance is not immediately
103
--------------_._-.____. .- .--.“.-”-.._-. - - -... -___---------.--- ..----. ~-.- _______
._ __ ._--
-.--
-.---
_I
I!? 5 28
MODEL
OF MANDIBULAR
PROTRUSION
dY
(mm)
-6.0 Fig. 7. Changes in location of instantaneous CORs from their initial positions as mandible moves from IC to edge-to-edge relationship. Initial locations are listed for each case in Table II.
ante; (2) the prominence of the compensating curve; (3) the inclination of the plane of orientation; (4) the inclination of the incisal guidance; and (5) the heights of the cusps.15 The guidances (1 and 4) appear explicitly in the formulation presented in this article. The compensating curve (2) and the plane of orientation (3) appear implicitly in the specification of the location of the cusp tip with respect to the frame of reference used. Cusp tip heights (5), however, must be interpreted in terms of cusp slopes. The slopes are such that no interference is created as the mandible moves from IC. Height is a secondary parameter that can be defined in terms of the calculated slope and the mesiodistal width of the cusp. The approach presented in this article will be applied to the mathematical modeling of occlusal adjustment. Further work will also be undertaken to include the effects of nonlinear guidances. REFERENCES 1. Posselt U. Physiology of occlusion and rehabilitation. Philadelphia: FA Davis Co, 1962:44. 2. Wenneberg B, Nystrom T, Carlsson GE. Occlusal equilibration and other stomatographic treatment in patients with mandibular dysfunction and headache. J PROSTHET DENT 1988;59:478-83. 3. Forssell H, Kirveskari P, Kangasniemi P. Effect of occlusal adjustment on mandibular dysfunction. Acta Odontol Stand 1986;44:63-9. 4. Magnusson T, Carlsson GE. Occlusal adjustment in patients with residual or recurrent signs of mandibular dysfunction. J PROSTHET DENT 1983;49:706-10.
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5. Riise C. Rational performance of occlusal adjustment. J PHO~THZT DENT 1982;48:319-27. 6. Brose MO, Tanquist RA. The influence of anterior coupling on mandibular movement. J PROSTHET DENT 1987;57:345-53. 7. Hobo S, Takayama H. A new system for measuring condylar path and computing anterior guidance. Part I. measuring principle. Int ,J Prosthodont 1988;1:99-106. 8. Kohno S, Nakano M. The measurement and development of anterior guidance. J PROSTHET DENT 1987;57:620-5. 9. El-Gheriani AS, Winstanley RB. Graphic tracings of condylar paths and measurements of condylar angles. J PROSTHET DENT 1989;61:77-87. 10. Rosner D, Goldberg GF. Condylar retruded contact position and intercuspal position correlation in dentulous patients. Part I: three-dimensional analysis of condylar registrations. J PROSTHET DENT 1986;56: 230-g. 11. McMillan DR, McMillan AS. A comparison of habitual jaw movements and articulator function. Acta Odontol Stand 1986;44:291-9. 12. Eichhold WA, Chen M, Welker WA. A formula to determine the lateral condylar guidance from intraoral needlepoint tracings. J PROSTHET DENT 1986;56:698-701. 13. Rosner D. A mathematical approximation of the angle of closure from retruded contact. J Periodontol 1973;44:228-35. 14. Rosner D. A chairside analysis of the feasibility of selective grinding. J PROSTHET DENT 1981;45:30-6. 15. Hanau RL. Full denture prosthesis-intraoral technique for Hanau articulator model H. 4th ed. Buffalo, NY: University of Btiffalo. 1930:28.
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