a proposed format for mandibular displacement analysis in fixed prosthodontics

A proposed format for mandibular displacement analysis in fixed prosthodontics

Timothy 0. Hart, D.D.S.,’ William F. P. Malone, D.D.S., Ph.D.,** James Sandrick, Ph.D.,*** Douglas Bowman, Ph.D.,*+** and Yvonne M. Balthazar, D.D.S., M.S.***** Marquette University, School of Dentistry, Milwaukee, Wis.; Northwdstern University, Dental School, Chicago, Ill.; and Loyola University, School of Dentistry, Chicago, Ill.

I- d rote ures and materials involved in the articulation of the maxillomandibular relationship are subject to numerous sources of error. The importance of analyz- ing this relationship is reflected by the literature devoted to mandibular positional analysis.

Various formats of three-dimensional mandibular descriptions have been used in static and dynamic studies. Several investigations have studied single-point displacements and their envelopes of motion.le5 Other studies have relied on mechanical recording and play- back mechanisms for describing mandibular displacement and have used three-dimensional traces engraved in plastic blocks to record mandibular position.‘,‘j*’ However, there is no consistent format in the literature for a comprehensive description of mandibular displacement. Lack of data compatibility prevents the comparison of results among different studies analyz- ing interocclusal regis.ration materials and hinge axis location.

The major purpose of this investigation was to establish a method of evaluating materials, techniques, and procedures that relate the mandibular to the maxillary arch.

Prior to mounting casts, the two halves of an articulator are mechanically related to one another by means of the two simulated condylar areas and the incisal pin and table assembly. The clinical recording of maxillomandibular relationships is desired without the influence of the dentition. In these instances the maxillary and mandibular members of the articulator are related by means of the two condylar mechanisms

Recipient of Staniey D. Tylman Award, 1981. *Adjunct Instructor, Fixed Prosthodontics, Marquette University. **Professor of Fixed Prosthodontics, Northwestern University. ***Professor of Dental Materials, Loyola University. ****Professor of Physiology, Loyola University. *****Assistant Professor of Fixed Prosthodontics, Marquette

University.

54

alone. An articulator transverse axis of orientation is therefore described by its condylar analogues. Proce- dures and materials involving the intercast relationship have a direct effect on the position of this axis. Any evaluation of interocclusal registration materials and techniques involves description of displacements of the articulator transverse axis brought about by such procedures. This study seeks to define displacements in terms of a mathematical format. A simple experiment involving an interocclusal record material illustrates the suggested format for positional analysis.

MATHEMATICAL CONSIDERATIONS

The maxillary and mandibular members of an arcon articulator can be considered two rigid bodies in space. Any interfering material or procedure that causes an altered intercast relationship results in a change in position of one member of the articulator relative to the other. Such a displacement of one rigid body relative to a second involves two basic considerations*: (1) the description of the initial static positions of the two bodies under consideration and (2) the description of the end result of a displacement of one of the objects relative to the other.

The first of these descriptive problems can be solved by assigning a three-dimensional Cartesian coordinate system to the maxillary member. The origin of the coordinate system is placed at the intercondylar housing midpoint (ICP). The maxillary member is chosen to be the fixed body. Therefore, its x (anterior- posterior), y (mediolateral), and z (superior-inferior) axes define the standard, or global, coordinate system. The second object, the mandibular member, is arbitrarily assigned its own, or local, coordinate system. Similar to the maxillary portion of the articulator, the mandibular member’s origin is located at the intercondylar analogue midpoint.

A comprehensive description of the displacement of the local (mandibular) coordinate system relative to the global (maxillary) system can be accomplished by

JULY 1983 VOLUME 50 NUMBER 1

MANDIBULAR DISPLACEMENT ANALYSIS

1 Transverse Axis

Anterior Mirror/Arbor

Assembly

g$\\j @I

I

k Right Mirror/Arbor Assembly

Anterior- Posterior Axis

Fig. 1. Superior view of maxillary member of modified articulator.

considering three positional alterations: the displace- positional alteration can be described by means of ment of the local origin relative to the global origin, the arbitrarily selecting one of the local system’s axes as an change in attitude of one of the local coordinate axes axis of orientation and assigning it a unit vector. The relative to its global analogue, and the degree of unit vector of an axis is a parameter of its attitude in angular rotation of any normal to the selected axis (that spaoz9 This quantity represents a vector of magnitude is, the screw rotation of the axes). 1 that originates from the global origin and is parallel

The displacement of the local origin relative to the to the selected axis of orientation. Because the magni- global origin can be described as a vector quantity. tude of the unit vector is 1 and it displaces from the When a vector is represented by a directed line origin, its components are each equal to the cosine of segment, the initial point of which is the global origin, the vector’s angle to each respective coordinate axis. it is called a position vector.* The formula for a position Therefore, the formula for a unit vector would be given vector would be given by: by:

where V = V,i + V.j = V,k V = the position vector V, = displacement along the x axis V, = displacement along the y axis V, = displacement along the z axis

where N = N,i + Nj + N,k N = the unit vector N, = cos (alpha); where alpha = angle

of N with the x axis N, = cos (beta); where beta =: angle

of N with the y axis Because the mandibular member’s ICP is the local origin, its displacement from the global (maxillary) origin can be defined by:

N, = CDS (gamma); where gamma = angle of N with the z axis

where VlCP = V,i + VA + V,k V,, V,, and V, represent displacements along the global coordinate system axes

The change in attitude of one of the local coordinate axes relative to its global counterpart is analogous to the familiar aeronautic terms pitch and yaw when applied to the central axis of an aircraft. Such a

Because the vector quantities N,, N2, and N3 are derived from the angles formed by the unit vector with the coordinate axes, they are termed direction cosines. As a matter of convenience the arbitrary orientation axis chosen for displacement analysis was the intercondylar analogue axis, or transverse axis, of the mandibular member. Therefore, the resulting unit vector would be defined by:

THE JOURNAL OF PROSTHETIC DEN’ITSTRY 55

HART ET AL

Transverse Axis

1 Right Mirror/Arbor

1 Assembly.

Er kl

- yEd-jj In Place

I

Fig. 2. Posterior view of maxillary member of modified articulator.

Table I. Means (in millimeters) and standard deviations (in parentheses) of the coefficients of ICP position vectors

Time Without screen With screen

(hr) V,’ V, V, V. V, V,

1 -1.65 -1.35 -0.82 -1.64 -1.35 -0.82 (0.04) (0.01) (0.03) (0.01) (0.02) (0.03)

6 -1.53 -1.14 -1.02 -1.80 -1.14 -0.96 (0.89) (0.02) (0.06) (0.01) (0.02) (0.06)

24 -1.82 -1.07 -0.96 -1.80 -1.14 -0.96 (0.06) (0.04) (0.16) (0.02) (0.01) (0.03)

48 -1.81 -1.16 -1.02 -1.77 -1.16 -0.97 (0.03) (0.03) (0.07) (0.03) (0.03) (0.04)

N. *rd”wcne axis = N,i = Nj = N,k where N,, Nz, and NJ are, respectively, the

x, y, and z direction cosines of the transverse axis unit vector

The final positional alteration to consider is the degree of angular rotation of any normal to the chosen axis. This quantity is simply the amount of screw rotation undertaken by the axis of orientation. In aeronautic terms, such an attitude change is labeled roll. It can be defined and measured by determining the angular change of a normal to the displaced axis with a selected global coordinate plane. Therefore, if the local y axis is described by its unit vector, its rotation may be measured by the angle between the local x axis and the global xy plane. In terms of the articulator example, this would be analogous to measuring the angle formed by the displaced mandibular (local) anterior-posterior axis and the maxillary (global) horizontal plane. This value will be labeled theta.

Therefore, the displacement of the mandibular portion of an arcon articulator relative to the maxillary member can be described by: (1) displacement of mandibular ICP described by the ICP position vector, (2) orientation of the intercondylar analogue axis represented by the transverse axis unit vector (pitch and yaw), and (3) pure rotation of the transverse axis (roll).

EXPERIMENTAL DESIGN

A device was constructed to permit the determination of mandibular articulator member displacement of ICP position vector, transverse axis unit vector, and transverse axis rotation. This was accomplished by evaluating the parameters of ICP displacement, pitch, yaw, and roll of one articulator member relative to the other. A Whip-Mix articulator (Whip-Mix Corp., Louis- ville, Ky.) was modified to record displacements during interocclusal registration.

The condylar housings were removed from the maxillary member and the condylar analogues were removed from the mandibular portion. This produced a floating articulator situation similar to a Buhnergraph or Vericheck (Denar Corp., Anaheim, Calif.). The point of intersection between the maxillary intercondylar housing axis (transverse axis or y axis) and the anterior-posterior axis (x axis) was determined. A 1.5 mm viewport was drilled at this point. A 1.9 mm single cross-hair microscope reticle was epoxied to the periph- ery of the viewport with its cross-hair elements positioned coincident with the anterior-posterior and transverse axes (Fig. 1). The vertical position of the cross hair was observable from the posterior aspect of the articulator (Fig. 2). Any displacements of ICP could be detected by three-dimensional tracking of the cross hair. The tracking was performed with two traveling microscopes and three dial gauges (Fig. 3). The first microscope viewed the cross hair from the superior aspect. The microscope was movable along the x and y axes by means of two-dimensional rack-and-pinion assemblies. Two 0.01 mm dial gauges measured anterior-posterior and left-right movement of the microscope rack-and-pinion assembly. Any x and y component displacements of ICP could be determined by manipulating the microscope in such a manner as to produce observed coincidence between its objective cross-hair reticle and the ICP cross hair. The second microscope was positioned posterior to the reticle and was capable of manipulation along the x (left to right) and z (superior-inferior) axes. A single dial gauge was positioned on the second rack-and-pinion assembly to measure superior-inferior movement of the microscope.

56 JULY 1983 VOLUME 50 NUMBER 1

The : deter vertic its hc

z axis component displacement of ICP could be ained by manipulating the microscope until its al cross hair was centered on the ICP reticle and Kzontal cross hair was colinear with the trans- axis scribe of the ICP reticle. Thus, any displace- of the maxillary member’s ICP could be found by

verse ment

Fig. 3. A, View of two traveling microscopes tracking ICP reticle. B, Modified maxillary member of articulator with interocclusal record in place.

determining the net movement of the x, y, and z gauges. The position vector of the mandibular could subsequently be determined by applyinl appropriate calculations.

Each condylar housing was replaced by a surface mirror assembly. The reflective surfaces (

: dial ICP

g the

first- If the

THE JOURNAL OF PROSTHETIC DENTISTRY 57

I I Left Mirror/Arbor

flTran.sverse Axi{ Assembly

I Anterior Mirror

Fig. 4. Anterior view of maxillary member of modified articulator.

mirrors were positioned perpendicular to the maxillary transverse axis (Fig. 4). Therefore, the optical axis of each mirror was coincident with the transverse axis. A third mirror was positioned at the anterior border of the maxillary member. The optical axis of the anterior mirror was coincident with the anterior-posterior axis of the maxillary member (Fig. 5). Thus, the optical axes of all three mirrors intersected at ICP (Fig. 1). A 35 mm slide projector was positioned 3 meters away from the left mirror so that its optical axis was colinear with the transverse axis. A second projector was similarly placed so that its optical axis was colinear with the anterior-posterior axis in the undisplaced condition (Fig. 6). An aluminum clipboard with a 1 mm centered hole was positioned in front of each projector. Each clipboard was positioned perpendicular to the optical axis of its respective projector with the 1 mm hole centered. Each projector projected the image of a cross hair through the hole in the clipboard and against the front surface of the appropriate mirror. Any deviation in mirror position could be determined by measuring, on the surface of the clipboard, the displacement of the reflected cross-hair image from the projector’s optical axis. The transverse axis projection system allowed detection of any pitch and yaw of the maxillary transverse axis (Fig. 7). The mandibular transverse axis unit vector could then be computed by application of the appropriate trigonometric calculations. The anterior axis projection system was used to determine the degree of any roll of the maxillary member.

EXPERIMENTAL PROCEDURE The effect of fabric screens (Ramitec, Premier

Dental Products Co., Morristown, Pa.) on the dimen-

58

HART ET AL

sional stability of polyether interocclusal records (Coe Laboratories, Inc., Chicago, Ill.) was determined. The casts of one subject were chosen for this experiment. The decision to use one subject’s cast allowed for minimization of experimental variability. Polyether maxillary and mandibular impressions were made of a 27-year-old man. The individual presented with a Class I occlusion, minimal restorations, and no temporomandibular joint disease, A hinge axis locator was used to determine the location of the kinematic axis. A face-bow transfer to the unmodified articulator was then performed with the use of the located axis. Centric relation records were made at three levels of anterior openings by means of a disoccluding jig and acrylic records. The consistency of these records was con- firmed by using the split-cast technique.” After the casts were mounted, a 10 mm X 25.4 mm machined nut was embedded in the lingual land area of the mandibular cast. A 24 mm silver/copper disk was luted to the palatal area of the maxillary cast with epoxy glue. A machine screw was threaded into the nut. The head of the screw engaged the metal disk and acted as a limitation to closure. This limiting assembly was set to an arbitrary height that allowed for noncontact of the occlusal surfaces of the teeth (thus simulating use of a disoccluding jig).. Epoxy glue was then applied to the threads of the nut to prevent variation during experimental manipulation.

Multiple occlusal registrations of the articulated casts were made. Every odd-numbered registration used the polyether registration material alone. Each even-numbered registration used a commercial fabric screen (Coe Laboratories, Inc.) in conjunction with the polyether registration material. A total of 60 registrations were performed. All procedures involved hinge axis closure of the articulator. The degree of closure was rendered consistent by the limiting screw assembly. In each case the manufacturer’s recommendations were followed exactly. The catalyst and base were proportioned according to mass. Each record was placed in a 100% humidity, 27” C oven for the first 5 minutes before being subjected to further manipulation. All storage was performed in a room-temperature environment.

The maxillary assembly of the modified (floating) articulator was weighted so as to balance its gravita- tional force at a midcast position. Each record was placed in the device 1 hour, 6 hours, 24 hours, and 48 hours after initial mix time. With each proceeding, the x, y, and z positions of the ICP were recorded by means of the microscope assemblies (Fig. 7). The positions of the projected cross hairs on the anterior and lateral

JULY 1983 VOLUME 50 NUMBER 1

I Anterior

I Mirror /Arbor

Assembly

Left Mirror

Transverse Axis

I

I Right Side View of Maxillary Assembly

With Right Mirror/Arbor Removed

Fig. 5. Lateral view of maxillary member of modified articulator.

$ Recording Surface

. . .

---_-_-_-- .+------ ---- --- --

1

” . I \ I

Anterior Projector 1 Posterior i Microscope I

I-

i 3m

I

cj I

Lateral Projector -+I

-4

E c9

View of Apparatus from Superior Aspect (some detail omitted for clarity)

Fig. 6. Aeronautic parameters of pitch, yaw, and roll as applied to modified maxillary member of Whip-Mix articulator.

clipboards were recorded directly on graph paper. The data were refined into mandibular ICP position vector, mandibular transverse axis unit vector, and mandibular transverse axis rotation.

RESULTS

The means and standard deviations for the refined data were calculated. The values for the coefficients of

the ICP position vector are presented in Table I. Paired t-tests revealed that there was a significant difference (p = .05) between the first hour determination and all subsequent measurements for all three coefficients in both fabric and no-fabric groups. Unpaired t-tests between the screen and no-screen groups revealed no significant difference at p = .05.

The values for the coefficients of the transverse axis


HART ET AL

+ PITCH

9 + YAW

Fig. 7. Diagrammatic representation of portion of apparatus used to determine pitch, yaw, and roll.

unit vector are presented in Table II. No significant differences among any of the coefficients were noted at any of the measurement periods. In addition, there were no differences & = .05) noted in unit vector coefficients between the screen and no-screen groups.

Finally, the degrees of transverse axis rotation are presented in Table III. Once again, no significant differences were observed either on a temporal basis or between the screen and no-screen groups.

DISCUSSION

This investigation suggested that the use of fabric screens neither improves nor diminishes the in vitro accuracy or stability of polyether registration material. This conclusion pertains to interocclusal records performed with a disoccluding stop. When the fabric screen is used under simulated oral conditions, it does not contribute to the dimensional stability of the polyether registration material. Further, when a sec- ondary disoccluding interference is used, such as a Lucia jig, the fabric screen does not significantly alter the eventual positioning of the mandibular cast on the articulator.

The suggested format for description of mandibular displacement and the simple experiment demonstrating its application represent a research potential and diverse clinical applications. The ability to record

mandibular displacement suggests several possible applications.

Investigations involving the variability of hinge axis and centric relation records could be designed to generate usable data. The specific nature of distortion in such procedures could be more fully understood if we were able to analyze the intracranial position vector, the hinge axis unit vector, and the hinge axis rotation. An intracranial position vector could be calculated by the simple vector addition of the left and right vertical pantograph table scribes’ position vectors at centric relation.

The format of displacement analysis presented has been applied to computer graphic modeling of the experimental data (Apple Computer, Inc., Cupertino, Calif.). By applying three-dimensional transformation matrices (based on hinge axis position vector, unit vector, and rotation) to three-dimensional mapping of the dentition, the relationships among dental morphol- ogy, temporomandibular joint anatomy, and mandibular displacement could be investigated with greater clarity. The surface geometry of an interfering incline could, for example, be related directly to condylar displacement, or the condylar avoidance path. Motion studies could also be rendered more comprehensive by using a vector analysis format of description. Abler’ extrapolated envelopes of motion from three-dimensional data. The converse is also possible, as long as a temporal reference is included in the envelopes’ paths of motion. Because envelopes of motion are really planar intercepts of various mandibular axes, the appropriate values for instantaneous displacements could be derived from such traces.

A standardized format of mandibular displacement analysis would be of great benefit in comparing similar investigations. A review of the dental literature revealed that the ability to compare data from different investigations involving mandibular displacement remained singularly elusive.

CONCLUSION

A format for mandibular displacement was presented. The total displacement of the mandibular member of an arcon articulator relative to the maxillary portion may be described by the following three entities:

1. Position vector of the intercondylar analogue midpoint (ICP) given by:

V=V,i+Vj+V&

where V,., V,, and V, are, respectively, the anterior-

60 JULY 1983 VOLUME 50 NUMBER 1

MANDIBULAR DISPLACEMENT ANALYSIS

Table If. Means and standard deviations of the coefficients of transverse axis direction cosines (no units)

Time (hr)

Without screen

N* N,

With screen

N* N3

1 -0.0147 1.0000 0.0087 -0.0113 (0.0002) (0.0000) (0.0005) (0.0010)

6 -0.0108 1 .oooo 0.0075 -0.0107 (0.0008) (0.0001) (0.0008) (0.0011)

24 -0.0154 1 .oooo 0.0055 -0.0107 (0.0010) (0.0001) (0.0004) (0.0010)

48 -0.0165 1 .oooo 0.0086 -0.0161 (0.0007) (0.0001) (0.0007) (0.0008)

Top number is direction cosine mean; number in parentheses is the standard deviation of direction cosine.

posterior, left-right, and superior-inferior components of ICP displacement.

2. Unit vector of the mandibular member’s transverse axis as defined by:

N=N,i+Nj+N&

1 .oooo 0.0064 (0.0001) (0.0003) 1 .oooo 0.0041

(0.0001) (0.0008) 1.0000 0.0046

(0.0001) (0.0005) 1.0000 0.0032

(0.0001) (0.0010)

Table III. Means (in degrees) and standard deviations (in parentheses) of the transverse axis rotational position

Time fhr) Without screen With screen

where N,, N?, and N, are the direction cosines of the unit vector. This is analogous to aeronautic terms pitch and yaw of the transverse axis.

3. Pure rotation of the transverse axis, or theta. The rotation of the intercondylar axis is synonomous to the aeronautic parameter of roll.

A device based on this descriptive format was designed and constructed for the purpose of evaluating displacements caused by interocclusal recording media. A simple experiment demonstrated that fabric mesh screens have no significant effect (p = -05) on polyether interocclusal records (when no occlusal contact is permitted). Finally, several potential applications of the derived vector format of mandibular displacement were discussed.

I would like to express my appreciation to Mr. Telasphore Janovicz, Jr., for his contribution to construction of the instrument array and to Mr. John Jones for the graphic arts.

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REFERENCES 1. Abler, J. N.: Design and Analysis of a Clinical System to

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10.

1 3.30 3.34 (0.06) (0.04)

6 3.50 3.63 (0.06) (0.03)

24 3.60 3.65 (0.04) (0.04)

48 3.40 3.42 (0.06) (0.08)

ments of young adults recorded by intraorally placed Iight- emitting diodes. J PRO~THET DENT 42689, 1979. Jankelson, B.: Neuromuscular aspects of occlusal effects of occiusal position on the physiology and dysfunction of the mandibular musculature. Dent Clin North Am 23:157, 1979. Lewin, A., Lemmer, J., and Vanrensburg, L.: The measurement of jaw movement. Part II. J PROSTHET DENT 36~312, 1976. Messerman, T.: A concept of jaw function with a related clinical application, J PROSTHET DENT 13:130, 1963. Lundeen, H. C., Shryock, E. F., and Gibbs, C. H.: An evaluation of mandibular border movements: Their character and significance. J PR~.STHET DENT 40:442, 1978. PurcelI, E. J.: Calculus With Analytic Geometry. Englewood Cliffs, N.J., 1978, Prentice-Hall, Inc., p 621. Rogers, D. F., and Adams, A. J.: Mathematical Elements for Computer Graphics. New York, 1976, McGraw-Hii1 Book Co., Inc., pp 55-59. Schwarz, W. D., and Gear, V. D.: Accurate location and relocation of casts on articulators. J PROSTHET DENT 34~695, 1975.

2. Waysenson, B., and Salomon, J.: Three-dimensional record- ReQrtnt requests to: ings of envelopes of motion related to mandibular movements. J DR. TIMOTHY 0. HART PROSTHET DENT 38:52, 1977. 6124 SHERIDAN RD.

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a proposed format for mandibular displacement analysis in fixed prosthodontics

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