REVIEW ARTICLE

Current status of researches on jaw movement andocclusion for clinical application

Eiichi Bando a,*, Keisuke Nishigawa b, Masanori Nakano c, Hisahiro Takeuchi b,Shuji Shigemoto b, Kazuo Okura b, Toyoko Satsuma b, Takeshi Yamamoto b

aThe University of Tokushima, 3-22 Yoshinohon-cho, Tokushima 770-0802, JapanbDepartment of Fixed Prosthodontics, Institute of Health Biosciences, The University of Tokushima Graduate School, JapancDepartment of Functional Oral Care and Welfare, Institute of Health Biosciences,The University of Tokushima Graduate School, Japan

Received 26 February 2009; received in revised form 8 April 2009; accepted 9 April 2009

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842. Evaluation of occlusal contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.1. Visualization methods for occlusal contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Japanese Dental Science Review (2009) 45, 83—97

KEYWORDSOcclusion;Jaw movement;Mandibular movement;Complementarymandibular movement;Tooth movement;Visualization

Summary Although many dentists agree that occlusion is one of the most important factors fordental clinics, evidence for this conclusion among contemporary clinical dental procedures is verylimited. The lack of appropriate measurement and recording methods for dental occlusion may beresponsible for this inconsistency. If transitional occlusal contact points on dentition duringfunctional jaw movement can be observed graphically, it will dramatically improve the realizationand evaluation of dental occlusion for both research and clinics. This technology is now available bycomputing the distance between the maxillary and mandibular occlusal surfaces during jawmovement. This visualization of occlusion requires a three-dimensional configuration record ofthe maxillary andmandibular dentitions and six-degree-of-freedom jawmovement data with a 10-mm accuracy level. We recently developed a new jaw-tracking device consisting of a pair of three-axis coils to satisfy these quality requirements. Improvement of three-dimensional digitizers with alaser beam system will be necessary for precise acquisition of the occlusal configuration. Foranalyses of occlusion and six-degree-of-freedom jaw movement, we propose two different math-ematical ideas to represent jaw movement. The first is mandibular movement, i.e. mandibularmotion against themaxilla, and the second is complementarymandibularmovement, i.e.maxillarymotion against the mandible. Eighteen-degree-of-freedom movement involving maxillary andmandibular teeth movements will be required for research in the near future.# 2009 Japanese Association for Dental Science. Published by Elsevier Ireland. All rights reserved.

* Corresponding author. Tel.: +81 88 654 5623; fax: +81 88 654 5623.E-mail address: bandou@lime.ocn.ne.jp (E. Bando).

ava i lab le at www.sc ienced i rect .com

journa l homepage: www.e lsevier .com/ locate / jdsr

1882-7616/$ — see front matter # 2009 Japanese Association for Dental Science. Published by Elsevier Ireland. All rights reserved.

doi:10.1016/j.jdsr.2009.04.001

2.2. Required accuracy for the evaluation of occlusal contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.3. Measurement of the configuration of occlusal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

2.3.1. Coordinate measuring instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862.3.2. Optical measuring instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872.3.3. Points at issue and future prospects for measurements of occlusal surfaces . . . . . . . . . . . . . . . 87

2.4. Measurement of jaw movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872.4.1. New jaw-tracking device with three-axis coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3. Jaw movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.1. Mandibular movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.1.1. Hinge axis and kinematic axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.1.2. Kinematic condylar point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.2. Complementary mandibular movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.3. Interrelationship of mandibular movement and complementary mandibular movement. . . . . . . . . . . . . 90

4. Reproduction of jaw movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915. Tooth movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936. Transition of the occlusal contact area during jaw movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.1. Designing the kinematic occlusal surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

84 E. Bando et al.

1. Introduction

In the Glossary of Prosthodontic Terms [1], occlusion isdefined as ‘‘the static relationship between the incising ormasticating surfaces of the maxillary or mandibular teeth ortooth analogues’’ and articulation is defined as ‘‘the staticand dynamic contact relationship between the occlusal sur-faces of the teeth during function’’. Since occlusion is some-times used in a broader sense [2], we refer to occlusion as acomprehensive statement of maxillary and mandibular den-titions that involves both the static relationship and dynamictransition expressed with six-degree-of-freedom movementin this review.

For general dentists, the diagnosis and treatment ofocclusion are common procedures in daily dental clinics.Posselt [3] stated that ‘‘occlusion is a basic principle indentistry’’ at the beginning of his book. In 1996, the NIHheld a Technology Assessment Conference to provide an‘‘assessment of management approaches to temporomandib-ular disorders (TMD)’’. In this conference, Kirveskari [4]reported about the interrelationship between occlusionand TMD, although the majority of studies have emphasizedthat there is a lack of sufficient scientific evidence to confirmsuch an interrelationship [5]. In Japan in 1989, the AichiDental Association began a campaign to ‘‘keep twenty teethat the age of eighty’’. This campaign, designated the 8020movement, has been conducted by the Japan Dental Associa-tion and the Ministry of Health, Labour and Welfare [6,7].During this campaign, the significant roles of mastication,chewing and swallowing in physical and mental health cameto be recognized. In elderly people in particular, the activ-ities of daily living and even cognitive symptoms could beimproved by healthy mastication, which strongly suggeststhat oral health is truly indispensable to maintain a goodquality of life [8].

Although many dentists agree that occlusion is a signifi-cant factor for dental treatment, Carlsson [9] reported thatthere is very limited evidence for the definition and evalua-tion of occlusion among dental procedures. One possiblereason for this inconsistency is the lack of appropriate

recording methods for dental occlusion. If occlusal contactpoints associated with dynamic jaw movement can be visua-lized graphically, it will improve the quality of dental treat-ment as well as dental research [10]. In this review, wepropose technologies and describe the points at issue, cur-rent state and future prospects for the visualization of dentalocclusion. Fundamental principles to evaluate six-degree-of-freedom jaw movement and occlusion are also described.

2. Evaluation of occlusal contacts

2.1. Visualization methods for occlusal contacts

Several dental materials and devices, such as articulatingpaper, thin silk ribbon, occlusal indicator wax, siliconeimpression material, Dental Prescale1 and T-Scan1, are usedfor inspection of occlusal contacts [11—20]. Articulatingpaper, thin silk ribbon, wax and silicone impression materialpossess fine sensitivity for detecting occlusal contacts. Den-tal Prescale1 [21] is a thin film that detects occlusal forceloading via microcapsules that develop color images underdestructive force. Consequently, Dental Prescale1 candetect not only occlusal contact points but also the strengthof the occlusal force. T-Scan1 [22] uses an electric pressure-sensitive film with mesh grid lines and sequentially detectsthe transition of occlusal force loading in each grid point.

Although all these methods have fine validity for inspect-ing occlusal contacts, a film or some other material must beplaced between the maxillary and mandibular dentitionsduring the detection of occlusal contacts. This substantialproperty of these methods prevents the inspection of occlu-sal contacts during mastication and sleep-associated brux-ism. Such analyses can be achieved by visualization ofocclusal contacts using three-dimensional configurationrecords of the occlusal surfaces on the maxillary and man-dibular dentitions and high precision six-degree-of-freedomjaw movement data (Fig. 1) [23—27]. By computing theminimum distance between the maxillary and mandibulardentitions, the transition of occlusal points during mastica-tion can be observed by computer graphics (Fig. 2) [23,24].

Figure 1 Block diagrams of the visualization system for occlusal contacts. Digitization of the 3D configuration of occlusal surfaces isoperated with six-degree-of-freedom jaw movement data. These data are computed to evaluate the minimum distances between themaxillary and mandibular occlusal surfaces as the occlusal contacts.

Visualization of occlusion 85

Technically, real-time representation of contact points asso-ciated with jaw movement is possible by using a high-per-formance computer system.

2.2. Required accuracy for the evaluation ofocclusal contacts

The reports described below may lead to a consensus for therequired accuracy level for the evaluation of occlusal teethcontacts. Muhlemann and Herzog [28] reported the long-itudinal effects of excessively high gold inlays attached tothe left maxillary first premolar of a 14-year-old girl for 9months. In that study, the mobility of the restored tooth didnot show any remarkable differences with a 0.3-mm high gold

Figure 2 Examples of visualized occlusal contacts. The left figure sright-side gum chewing. The graphics present a jaw position that is aclosing movement. The minimum clearance areas between the occlusfigure shows a panoramic display of the occlusal clearances during

inlay, while an immediate increase was observed with a 0.75-mm high inlay. Schaerer and Stallard [29] studied the effectsof occlusal interferences by EMG recordings and multipleradio transmitters to detect occlusal contacts in three sub-jects. In their report, the interferences on the opposite sideto the chewing side were associated with significantly largernumbers of occlusal contact times compared with the chew-ing side. The effects of these interferences were alsodetected by the EMG activities, but the locations of theinterferences could not be distinguished based on the EMGdata. Noble and Martin [30] investigated the effects of 0.5—1.0-mm excessively high metal inlays that were attached toten patients. They reported that such interference increasedthe mobility of the adjacent and antagonistic teeth as much

hows computer graphics of the dentition during the 7th stroke ofpart by 1 mm from the maximum intercuspation during the jawal surfaces are indicated as the occlusal contact areas. The rightpeanut chewing on the right side.

86 E. Bando et al.

as that of the restored teeth. Hagiwara and Kobayashi [31]reported that metal inlays with 100-mm interferenceincreased nocturnal bruxism and affected hormone secretionpatterns. Tanaka [32] studied the effects of different heightsof full veneer metal restorations that were temporarilycemented on the mandibular first molars of adult volunteers.In that study, most of the subjects complained of difficultieswith articulation for restorations of �35 mm and EMG ana-lyses of the masticator muscles supported these feelings ofdifficulty. Hasegawa et al. [33] insisted that cautious clinicalprocedures for dental restoration allow occlusal adjustmentat the maximum intercuspation within an error level of10 mm. Ikeda [34] studied the relationship between occlusalinterference and the teeth threshold level. A thin metalinterference was attached to the subject’s molar teethand the chronological effects on the pulp threshold levelwere evaluated using an electric testing apparatus. In thatstudy, significant changes in the teeth threshold levels werefound 2 days after the interference was attached, andadjustment of the interferences caused correspondingchanges in the threshold levels. Ikeda et al. [35] concludedthat occlusal interference could be a cause of hypersensitivedentin and that occlusal adjustment should be considered asa suitable aid for such cases. A discrimination test with silverfoil thickness suggested that the sensor threshold level of theperiodontal ligament was 10—35 mm for intact molar teeth[36]. Other discrimination tests with aluminum and silver foilreported threshold levels of 8—30 mm and even the poorestsensitivity was still better than 60 mm in all subjects [37].Halperin et al. [38] suggested that the thickness of anocclusal registration strip should be <21 mm.

Based on the above-described reports, we suggest that themaximum error of occlusal adjustment for crown restorationshould be <10 mm [10]. Furthermore, this accuracy levelshould also apply to the precision required for visualization ofocclusal contacts.

Figure 3 Optical measuring instrument (Optimet-Optical Metrologaccuracy of the current instrument is not sufficient for evaluation o

2.3. Measurement of the configuration ofocclusal surfaces

Digitization of occlusal surfaces is utilized for the fabricationof prosthetic appliances with CAD/CAM systems. CEREC 3D[39] adopts both an optical impression system that performsdirect measurements of intraoral structures and a laserscanner system that is used for indirect measurements of acast stone model. The optical impression system is a veryhandy system, but is only currently applied formeasurementsof limited areas. The laser scanner system requires multipleprocesses, but can measure wider areas, such as wholedentition. General industrial technologies and devices arealso available for indirect measurements.

Direct measurement technologies that enable more accu-rate and rapid acquisition of the configuration of wholedentition are required. However, such technologies havenot yet been developed and the current indirect measure-ment technologies still have some associated practical pro-blems.

2.3.1. Coordinate measuring instrumentA recently developed coordinate measuring instrument witha touch sensor probe has sufficient accuracy to performindirect measurements of occlusal surfaces for evaluationof occlusal contacts [23]. Since the touch probe detects onetarget point at a time, themechanical structure of the devicerequires a long operation period.

For digitization of the occlusal surfaces of maxillary andmandibular dentitions with 250-mm mesh grids, 50,000target points need to be measured. The automatic controlprogram of the device requires 55—60 h to complete thedigitization of dentition surfaces. Use of 100-mm and 25-mm mesh grids requires 6.25-fold and 100-fold longeroperation periods, respectively, and such measurementsare not practical.

y Ltd.). The optical sensor enables high-speed scanning, but thef occlusion.

Figure 4 Block diagrams of the jaw-tracking device with amagnetic field system. A three-axis coil in the primary sensor unitis driven by an alternating current to generate a magnetic field.Next, a three-axis coil in the secondary sensor unit detects theintensity of this magnetic field to derive six-degree-of-freedommovement data.

Visualization of occlusion 87

2.3.2. Optical measuring instrumentOpticalmeasuring technologies involve a variety of techniquessuch as use of line scanners [40], laser triangulation [41], themoire scale [42] and holography [43,44]. In general, opticalmeasuring instruments enable high-speed scanning comparedwith the touch sensor instrument. Laser triangulation is acommon industrial technology that projects a laser beam ontothe target item. By determining the angles between theprojected and reflected rayswith optical sensors, the distanceis calculated from the triangular relationships. According tothe manufacturer’s specifications [41], these devices havevery high precision. However, in practical measurements ofa cast stone model, the complicated configuration of theocclusal surface seems to cause random reflections of theprojected ray that lead to unavoidable errors. Therefore,multiple scanning is indispensable for precise measurementsof the configuration of an occlusal surface with this instru-ment. A confocal laser scanner can detect the reflected rayfrom the target item through the exact same optical path asthe projected laser beam [41]. In this manner, a laser scannercan perform more stable measurements than a triangulationscanner. The IMPRESSION Dental Scanner (Optimet-OpticalMetrology Ltd.) is the newest optical measuring instrumentand uses a rugged holography technique with incoherent light(Fig. 3). To scan the cast stone model of dentition with a 250-mm mesh grid from five different directions, a total of onemillion target points are measured. This instrument performssuch measurements within approximately 400 s and is muchquicker than the above-described coordinate measuringinstrument. The specifications of the instrument indicate thatthe accuracy of the system is 20 mm [45]. Since the requiredaccuracy for evaluation of occlusion is 10 mm, we are expect-ing improvements in the accuracy of this system. Currently,however, this instrument is the most practical option forvisualization of occlusal contacts.

2.3.3. Points at issue and future prospects formeasurements of occlusal surfacesAs mentioned above, the mechanical instrument with thetouch sensor probe has a high accuracy but is time-consuming,while the optical measuring instrument enables high-speedscanning but has inferior accuracy. Another possible method ismicro-CTof a cast stonemodel. Kamegawa et al. [46] reportedthat the accuracy of micro-CT is 50—60 mm and that thetechnique requires about 800 s to scan a cast model. Sincethis micro-CT is not used for in vivo measurements, radio-protection is not necessary. The disadvantages of this methodare its insufficient accuracy and thehighprice of theCTdevice.

To perform practical measurements of occlusal surfaces,the present objective is to improve the accuracy of theoptical measuring instrument to a sufficient level for evalua-tion of occlusion. The overall goal is to develop a directmeasuring technology that enables intraoral measuring withsufficient accuracy and speed. If such a device can be devel-oped, it can replace the impression technique for dentalprostheses and may lead to dramatic changes in clinicaldental procedures.

2.4. Measurement of jaw movement

Gates and Nicholls [47] reported decreases in mandibularwidth in the protrusive and jaw opening positions. When the

micro-deformation of the mandible is ignored, jaw move-ment can be represented by six independent parameters, i.e.six-degree-of-freedom jaw movement.

In 1934, McCollum and Stuart [48] devised the firstrecording technique for six-degree-of-freedom jaw move-ment using a pantograph tracing method (Gnathograph).Early in 1960, electric six-degree-of-freedom jaw-trackingdevices with rotary transmitters were developed [49].Since then, many types of jaw-tracking devices have beendeveloped and used in clinics as well as in research [50—62]. Currently, the manufactured products of these jaw-tracking devices have a variety of transducers such asoptical sensors [40], measuring styli and flags [63] andultrasound sensors [64]. However, the designed accuracyof most of these jaw-tracking devices is around 100 mm andthey are not sufficient for use in the evaluation of occlusalcontacts.

2.4.1. New jaw-tracking device with three-axis coilsCurrently, a new jaw-tracking device with a pair of three-axis coils is under development. This jaw-tracking device hasa potentially acceptable accuracy for evaluation of occlusalcontacts (Fig. 4). The three-axis coil is a combination ofthree coils that cross at right-angles to one another. Thesethree coils have the same central point and each coil corre-sponds with the x—y—z axes of rectangular coordinates. Oneset of coils, i.e. the primary coil unit, is driven by analternating current to create a magnetic field. The otherset of coils, i.e. the secondary coil unit, detects the intensityof the magnetic field and the signals from the secondary coilunit are used tomeasure the relative positions of the two coilunits. For measurements of six-degree-of-freedom jawmovement, the primary coil unit is attached to themaxillarydentition, and the secondary coil unit is attached to themandibular dentition. The coil units are 21.0-mm cubes andweigh 7.0 g (Fig. 5). Calibration studies revealed that thepositioning and posturing resolutions of this device are 3.8-mm translation with 0.0001-degree rotation around themaximum intercuspal position and 48-mm translation with

Figure 5 Three-axis coil sensors. These sensor units have threecoils with the same central point that cross at right angles to oneanother. The left panel shows the primary sensor unit generatingthe magnetic field and the secondary sensor unit that arecurrently in use. The right panel shows the new secondary sensorunit under development. The performance of the new sensor unitis improved by more than 10-fold compared with the currentlyused sensor unit and provides sufficient accuracy for analysis ofocclusal contacts.

88 E. Bando et al.

0.034-degree rotation around the maximum jaw openingposition [65,66].

A prototype of the new coil unit with a micro-fineelectric wire is also shown in Fig. 5. This sensor unit isminiaturized to a 13.0-mm cube, and the resolution isimproved by approximately 10-fold compared with thatof the previous coil unit [67]. Since the intensity of themagnetic field decreases in proportion to the third powerof the distance, the resolution of this device is not iso-tropic. However, within the space around the maximumintercuspal position, this device can provide sufficientaccuracy for evaluation of occlusal contacts. The smallsize of the coil unit enables intraoral use, and the devicecan be applied for the measurement of jaw movementduring nocturnal bruxism (Fig. 6) [68].

Figure 6 Intraoral sensor units. The small sizes of the sensorunits enable intraoral use of these instruments. This system canperform measurements of jaw movement during sleep bruxismand the obtained data are used for graphic presentation of theocclusal contacts.

3. Jaw movement

Since occlusion has a close relationship with jaw movement,comprehension of jaw movement is indispensable for under-standing the contemporary concepts of dental occlusion. Ingeneral, jaw movement is equivalent to mandibular move-ment, i.e. the motion of the mandible against the maxilla.However, in clinical practice, the motion of the maxillaagainst the mandible is frequently recorded for evaluationof jaw movement. For example, the Gothic arch tracingtechnique uses a tracing plate connected to the mandibleand a stylus connected to the maxilla [69]. With this combi-nation, the jaw movement pathway on the tracing plate doesnot represent the mandibular movement but the maxillarymovement pathway during lateral excursion of the tracingplate on the mandible. When the tracing plate is attached tothe maxilla and the stylus is attached to the mandible, asimilar pathway is drawn on the plate. The shapes of thesetwo pathways appear to have point symmetry, but moredetailed differences are actually present between the twotraces. Such differences should be considered for clinicalevaluation of jaw movement and occlusion.

We propose the idea that the term jawmovement involvestwo different concepts. The first concept is mandibularmovement, i.e. mandibular motion against the maxilla,and the second concept is complementary mandibular move-ment, i.e. maxillary motion against the mandible [70,71].

3.1. Mandibular movement

Fig. 7 shows the shape of the mandibular border movementarea at various points of the mandible [72]. The bordermovement area at the incisal point [73,74] is well knownas the ‘‘Posselt figure’’ or ‘‘Swedish banana’’. At the molarpoint, the frontal width of the border movement area is

Figure 7 Borders of the mandibular movement pathway atvarious reference points on the mandible. The border mandib-ular movement at the incisal point is known as Posselt’s figure.The vertical size of this area is shortened at the molar points andmost convergent at the condylar points.

Figure 8 Hinge axis and kinematic axis. Mandibular openingand closing movements while maintaining a retruded mandibularposition create simple rotation around an imaginary axis. Thisrotation axis is called the hinge axis. The sagittal mandibularmovement pathway converges at a point around the condylarhead and makes a simple curve. The lateral axis that passes thispoint is called the kinematic axis. Generally, the kinematic axis isfound at the upper front direction relative to the hinge axis. HA,hinge axis; KA, kinematic axis.

Visualization of occlusion 89

almost the same as that of the incisal point, while the verticalsize is decreased. At the condylar point, the vertical size ofthis area has almost disappeared. This convergence of man-dibular movement is a key point for analyses of jaw move-ment and designing articulators that reproduce jawmovement.

3.1.1. Hinge axis and kinematic axisThe upper part of the posterior border during the opening andclosing movements of the mandible within the sagittal planecan be represented as a simple rotation around an imaginaryaxis. This rotation axis is called the hinge axis or transversehorizontal axis.

Within the sagittal movement of the mandible, there is anaxis where the jaw movement pathway has the least thick-ness and traces a simple curve. Kohno [75—77] named thisaxis the kinematic axis, while Yatabe et al. [78,79] referredto the same axis as the kinematic center. Generally, thekinematic axis is found at the upper forward area of thehinge axis (Fig. 8) [75].

3.1.2. Kinematic condylar pointFor all movements of the mandible, including lateral move-ments, there are points at which the mandibular movementpathway shows convergence and has the least thickness. Thispoint is called the kinematic condylar point and one suchpoint is found at the central area of each condylar head [72].Fig. 9 shows the border movement pathway on the pointsalong the kinematic axis. At the points on the outer area ofthe condylar head, the lateral movement pathway takes theupper backward direction while the inner point does not takethis direction. A pantograph and some other tracing sensordevices have been designed to record the condylar move-ments at the outer point of the condylar head. Consequently,it should be noted that the condylar movements recordedwith these devices are not consistent with the actual move-ments of the condylar head. At the points on the inner area ofthe condylar head, the lateral movement pathway takes anupper direction compared with the sagittal movement.

Figure 9 Kinematic condylar point. All the mandibular movementhave the least vertical thickness at a certain point in the condylar hefound at the central area of the condylar head on both sides. At the opass through the upper backward space of the sagittal movement patat the upper space of the sagittal movement pathway.

Since the kinematic axis [75] and the kinematic condylarpoint [72] are defined independently, the kinematic condylarpoint may not always be on the kinematic axis. In general,however, the kinematic condylar point is rarely apart fromthe kinematic axis.

3.2. Complementary mandibular movement

Fig. 10 shows the same jaw movement as that in Fig. 7, butrepresented as the maxillary movement pathway againstthe mandible, i.e. the complementary mandibular move-ment. The vertical sizes of the border movement pathway

pathways, including lateral excursion, make a convergence andad. This point is named the kinematic condylar point and can beuter point of the condylar head, the lateral movement pathwayshway. At the inner point, the lateral movement pathway is found

Figure 10 Mandibular movement and complementary mandib-ular movement. The complementary mandibular movementpathway is observed using the samemovement as themandibularmovement pathway shown in Fig. 7. The most convergent pointsof these pathways are found at the centers of the condylar headfor the mandibular movement and the articular tubercle for thecomplementary mandibular movement.

90 E. Bando et al.

of the complementary mandibular movement aredecreased at closer points to the condylar head. However,the closest convergence point of the complementary man-dibular movement is found at the central area of thearticular tubercle, while the mandibular movement showsthe highest convergence at the center of the condylar head[80].

3.3. Interrelationship of mandibular movementand complementary mandibular movement

This subsection describes the appropriate format for six-degree-of-freedom movement recording for analysis andevaluation of jaw movement. One of the common methodsfor representing three-dimensional movement is to draw aprojection figure of the involved point pathway on the hor-izontal, sagittal and frontal planes. The following are exam-ples for numerical expression of the jaw position andformulae for calculating the target point pathway at thisjaw position. WhenO(X,Y,Z) is substituted for the rectangularcoordinates on the maxilla and o(x,y,z) is substituted for therectangular coordinates on the mandible, the jaw position isexpressed as follows [81].

Maxillary coordinates Mandibular coordinates

x y z

X l1 l2 l3Y m1 m2 m3

Z n1 n2 n3

li, mi, ni (i = 1, 2, 3): direction cosines of the coordinate axes;O(X0,Y0,Z0): translation of the mandibular movement origin;o(x0,y0,z0): translation of the complementary mandibular movementorigin.The mandibular movement at any point (x,y,z) of themandible is expressed by:

X ¼ l1x þ l2y þ l3zþ X0

Y ¼ m1x þm2y þm3zþ Y0

Z ¼ n1x þ n2y þ n3zþ Z0

The complementary jaw movement at any point (X,Y,Z) isexpressed by:

x ¼ l1X þm1Y þ n1Z þ x0

y ¼ l2X þm2Y þ n2Z þ y0

z ¼ l3X þm3Y þ n3Z þ z0

Therefore, the origins of each set of coordinates areexpressed by the following formulae:

x0 ¼ �ðl1X0 þm1Y0 þ n1Z0Þy0 ¼ �ðl2X0 þm2Y0 þ n2Z0Þz0 ¼ �ðl3X0 þm3Y0 þ n3Z0ÞOn the rectangular coordinates, the six-degree-of-freedommovement involves three-degree-of-freedom parameters forthe translation of the origin and three-degree-of-freedomparameters for the rotation around each axis. Since the sumsof the squares in each line and each row equal one and theinner products between each direction cosine equal zero, thedegree-of-freedom data of these nine direction cosines addup to three.

For evaluation of occlusion, such analyses of the move-ment pathway at representative points is useful. However,the spatial movement of the whole occlusal surface on thedentition should also be considered. As described above, themovement of a rigid body can be expressed by the spatialrelationship of two rectangular coordinates. When a rigidbody is moved from one place to another place, this move-ment is mathematically equivalent to the relative positionbetween one pair of rectangular coordinates. Drawing path-ways on any two same points on these two coordinatesreveals that there are points at which the length of thepathway makes the minimum distance. By connecting thesepoints, a straight line is drawn corresponding to each move-ment. The movement between these two coordinates canthen be divided into the translation along this line and therotation around the same line. The idea of this singular linehelps us to figure out the spatial movement of the dentitionfrom one jaw position to another position. Mathematically, astraight line in rectangular coordinates involves four-degree-of-freedom parameters. The translation along this line deci-des one-degree-of-freedom parameter and rotation aroundthe line regulates the remaining one-degree-of-freedomparameter. Therefore, a total of six-degree-of-freedommovement parameters are contained in the motion alongthis line. Suzuki [82] designated this line the intermaxillaryaxis. The same line is also called the helical axis or screw axisin physics.

In 1980, Spoor and Veldpaus [83] introduced a technicaluse for the helical axis. Subsequently, analyses of jaw move-ment using this axis have been reported in dental studies[82,84—87]. The idea of the intermaxillary axis is helpful forunderstanding the solid geometry of six-degree-of-freedom

Figure 12 Representation of the interrelationship betweenmandibular movement and complementary mandibular move-ment with the intermaxillary axis. Mandibular movement withtranslation t and rotation u around the intermaxillary axis isequivalent to complementary mandibular movement with trans-lation �t and rotation �u around the same axis. The intermax-illary axis represents the spatial relationship between two jawpositions and also mediates the interrelationship between themandibular movement and the complementary mandibularmovement.

Figure 11 Representation of jaw movement with the inter-maxillary axis. Translation along and rotation around the inter-maxillary axis represent bodily movement of the mandible.

Visualization of occlusion 91

movement (Fig. 11) [88]. The eigenvector of the revolutionmatrix indicates the direction of the intermaxillary axis. Theinterrelationship between the mandibular movement andcomplementary mandibular movement can be expressed asthe reversed translation and rotation movement along thisaxis (Fig. 12) [88].

4. Reproduction of jaw movement

Articulators are instruments designed to perform mechan-ical reproduction of jaw movement using cast stone modelsof dentition. More detailed observation of occlusion thanintraoral inspection in static jaw positions is enabled withthese instruments. The types of articulators are classifiedinto condylar path articulators, which are designed to imi-tate the anatomical structure of the temporomandibularjoint, and non-condylar path articulators, which are devel-oped independently of the anatomical form of the humanbody. The condylar path articulators are further divided intoarcon-type articulators, which possess an adjustablemechanism for the condylar path on the maxillary part ofthe articulator, and non-arcon-type articulators, which havethe same mechanism on the mandibular part. Since thearcon-type articulators have a more similar mechanism tothe anatomical structure, this type of articulator is believedto have better properties. Some textbooks suggest a theorythat, since the condylar path of non-arcon-type articulatorsis mounted on the mandibular parts, the inclination of thecondylar guidance cannot be the same during the openingand closing operations of the articulator (Fig. 13) [89].However, this theory is not based on the differences betweenmandibular movement and complementary mandibularmovement, and is certainly misleading. Since arcon-typearticulators reproduce mandibular movement, i.e. mandib-

ular movement against the maxilla, condylar guidanceshould bemounted on themaxillary part. On the other hand,non-arcon-type articulators (condylar type articulators)have condylar guidance on the mandibular part, meaningthat this type of articulator is designed to reproduce thecomplementary mandibular movement. In that sense, theinclination of the condylar guidance should be mounted onthe mandibular part and the inclination of this guidanceshould be obtained from observation of the complementarymandibular movement.

For reproduction of the terminal hinge movement, i.e.simple rotation around a hinge axis, the mandibular move-ment and complementary mandibular movement can beexpressed as a reversed movement around the same axison the articulator. However, for reproduction of more com-plicated jaw movements, i.e. a combination of translationand rotation, the condylar guidance of arcon-type articula-tors should rationally trace the movement of the kinematiccondylar points, while that of non-arcon-type articulatorsshould follow the complementary kinematic condylar points.

In addition, most articulators have incisal guidance withthe combination of an incisal pin on the maxillary part and anincisal table on the mandibular part. Therefore, this type ofincisal guidance is designed to reproduce the complementarymandibular movement. The adjustable mechanism of typicalarcon-type articulators consists of condylar guidance thatreproduces the mandibular movement and incisal guidancethat reproduces the complementary mandibular movement.This inconsistency of the mechanism may confuse the usageof such articulators.

It can be said that the current design of incisal guidancethat reproduces the complementary mandibular movement ispractically useful. In laboratory work, operations with anadjustable articulator are frequently performed with hand-

Figure 13 Arcon-type and non-arcon (condylar)-type articulators. Some textbooks insist that the inclination of the condylarguidance of non-arcon-type articulators is altered with the opening operation of the articulator. This idea is misleading and does nottake account of the differences between the mandibular and complementary mandibular movements (Redrawn from Rosenstiel SF,Land MF, Fujimoto J. Contemporary fixed prosthodontics. 2nd ed., St Louis: Mosby. 1995; p. 23).

92 E. Bando et al.

ling of the maxillary part. Therefore, we consider that non-arcon-type articulators with a complete mechanism forreproducing the complementary mandibular movement havebetter properties for clinical usage.

Figure 14 Reproduction of jawmovement with a HEXAPOD robot. Cstage reproduce six-degree-of-freedom jaw movement. The masticagenerated occlusal surface for crown restoration.

Most condylar path articulators have a relatively simplemechanism that performs the reproduction of static jawpositions. However, these instruments cannot reproducedynamic jaw movements during mastication involving chew-

ast stonemodels that are attached to a precise micro-positioningtory movement of a patient was utilized to design the functional

Visualization of occlusion 93

ing and swallowing. The dynamic duplicator developed byBeck and Morrison [49] and the Case Gnathic Replicatordeveloped by Messerman [50] and Gibbs et al. [51] weredesigned to observe such dynamic jaw movements as themotions of cast stone models.

Aparallel link systemisusedas themechanismtocontrol thestage position with six rods connecting the base and the stage.The expansion and contraction of these six rods preciselymanage the stage position for six-degree-of-freedom move-ment under high-performance computer operation. Nishigawaet al. [90] reported an indirect FGPmethod with a parallel linksystem. In this report, functional jaw movements of a patientincluding mastication were reproduced with a parallel linkrobot to create a functionally generated path for a dentalprosthesis (Fig. 14). Ikawa et al. [91] reported a different typeof jawmovementreproductionsystemusingasimulationrobot.

5. Tooth movement

Thus far, this review article has been based on the assumptionthat all teeth are tightly fixed to the maxilla and mandibleand make two rigid bodies. In practice, however, each toothhas its own mobility and undergoes a relatively large range ofmovement under occlusal force loading during functional jawmovements. Such tooth movement is found not only in loadedteeth, but also in adjacent teeth without direct occlusalcontact (Fig. 15) [92,93]. The magnitude of the tooth move-ment is around 100 mm [94], which is 10-fold larger than theexpected error level for a dental prosthesis. Therefore, infurther analyses of occlusion, we should not ignore such alarge range of tooth movement.

The movement of a maxillary tooth against the maxillainvolves a set of six-degree-of-freedom parameters. Themovement of an antagonistic tooth against the mandibleinvolves another set of six-degree-of-freedom parameters.With these additional six-degree-of-freedom jaw movement

Figure 15 Movement of the right maxillary first premolar. The ttooth (right maxillary canine) is shown. The coronal shape of the tocoordinate measuring instrument. The root form is created by 3Dmeasured with a six-degree-of-freedom motion detector with a mthe translation and rotation around the helical axis are enlarged by50-fold larger than the tooth shape.

parameters, analyses involving a total of eighteen-degree-of-freedom parameters will be required for rigorous evaluationof occlusion and jaw movement.

6. Transition of the occlusal contact areaduring jaw movement

When a pair of occlusal facets with flat contact at themaximum intercuspation make an excursion, how can bethe interrelationship between these facets at the new jawposition be evaluated? Mathematically, the possible rela-tionship is one or several combinations of flat contact,disengagement and interference. To maintain flat contactduring the excursive movement from the maximum inter-cuspation, the intermaxillary axes between every set ofsequential jaw positions need to be identical [95]. Suchmovement, i.e. the combination of translation and rotationwith flat contact, can be seen during the attachment of abolt with a nut. However, observation of the excursive jawmovements during grinding and chewing reveals that theintermaxillary axis rarely maintains the same position(Fig. 16) [82]. Theoretically, therefore, if the occlusal sur-faces of dentition maintain rigid bodies during six-degree-of-freedom movement, the occlusal facets with flat contactat themaximum intercuspation cannotmaintain flat contactat an eccentric occlusal position.

Nakao [96,97] studied the occlusal contact area duringlateral excursion using a silicone impression material. Inthese reports, the maximum contact area on the occlusalfacets was observed at the maximum intercuspal position,and the contact area gradually decreased according to therange of lateral excursion. Okubo and Bando [24] reportedsix-degree-of-freedom movement analyses for visualizationof occlusal contacts. In that study, the same results wereobtained for most teeth, except for the canines, which couldhave a broader contact area at eccentric occlusal positions.

ooth movement during occlusal force loading on the adjacentoth was obtained by measuring the cast stone model with a 3Dreconstruction from spiral CT images. Tooth movement was

agnetic field coil system. In these graphics, the magnitudes of50-fold, such that the magnification of the tooth movement is

Figure 16 Intermaxillary axes during left-side border jaw movement. These graphics show intermaxillary axes between themaximum intercuspation and the jaw positions during left-side border jaw movement. The locations of the intermaxillary axes varywith the transition of the jaw position and never stay in the same place.

94 E. Bando et al.

Therefore, it can be speculated that the flat contacts ofocclusal facets at the maximum intercuspation do not dis-appear at the very initial phase of excursive movement andthat the area of these flat contacts gradually decreasesthrough the excursion. This sequential transition of theocclusal contact area can be performed by micro-movementsof teeth on the alveolar bone during excursive movement.

6.1. Designing the kinematic occlusal surface

Several ideas have been proposed for the ideal occlusalcontact pattern and occlusal guidance at the eccentricocclusal position. Mutually protected occlusion is a sugges-tion that immediate disengagement of the posterior toothcontact occurs in the excursive movement of the mandible.With bilaterally balanced occlusion, the occlusal contacts atthe maximum intercuspation keep engaging at eccentricocclusal positions [98]. The present article does not discussthe issue that occlusal guidance should have better proper-ties as the ideal occlusion. The aim of this chapter is todescribe the required conditions for designing occlusal sur-faces that can maintain flat contacts at both centric andeccentric occlusal positions. Such occlusion will be requiredfor cases requiring prostheses for both antagonistic canineteeth.

As mentioned above, occlusal facets with flat contacts atthe maximum intercuspation make flat contact, disengage-ment or interference at eccentric occlusal positions. Remov-ing the interference at eccentric occlusal positions cannot bethe solution, since it may cause disengagement of the facetsat the maximum intercuspation. If the maxillary and man-dibular dentitions are rigid bodies during six-degree-of-free-dommovement, it is impossible to design occlusal facets thatmaintain flat contacts at centric and eccentric occlusalpositions. Therefore, to find a practical solution for the abovequestion, it is necessary to design occlusal facets thatmake the minimum magnitude of interference at eccentric

positions [99]. These occlusal facets are obtained by tracingthe movement pathways of the optional points on the occlu-sal surface and designated the occlusal reference surface[95,100].

7. Conclusions

Although many clinical experiences indicate the signifi-cance of occlusion for dental practice, there is only verylimited scientific evidence for this conclusion in clinicalprocedures for the determination of dental occlusion [9]. Ifthe dynamic transition of occlusal contacts can observedvisually, it will be helpful for providing scientific solutionsfor clinical problems with dental occlusion. For morerigorous analyses of dental occlusion, eighteen-degree-of-freedom analyses will be required that involve three-dimensional configuration data for the maxillary and man-dibular dentitions, six-degree-of-freedom jaw movementand six-degree-of-freedom maxillary and mandibular teethmovements that are associated with deformation of thejaw bones and alveolar tissues.

High-performance computers are indispensable for theseanalyses, and such computers have already been popular-ized. Therefore, the practical problem will be the measure-ment of tooth micro-movements [93,101]. The initial step forthese analyses is to develop high-speed measuring technol-ogy for occlusal surfaces with sufficient accuracy. The opera-tion of these occlusal configurations with six-degree-of-freedom jaw movement data will provide a graphical pre-sentation of occlusal contact during functional jaw move-ment. If such graphical analyses are established, they will besufficiently valid for improvement of dental research andclinical practice.

In future, when eighteen-degree-of-freedom analysesinvolving micro-deformation of jaw structures have beendeveloped, they will be helpful for solving the current con-fusion about dental occlusion. In addition, we believe that

Visualization of occlusion 95

they will be helpful for improving the quality of life ofpatients through dental practices that are based on scientificevidence of dental occlusion.

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