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Introduction

In the past, the stress analysis of orthodonticforces and alveolar bone has been studied mainlyon models in which the bony structures havebeen replaced by wax and elastic materials.These materials do not have the characteristicsof the bony structure itself. The structure ofthese materials is totally different from bone andcan be considered as homogenous. An equallayer of wax is melted around plastic or metal

teeth in typodont set-ups, and the same holdstrue for elastic models in which the bonystructures are replaced by elastic materials(Caputo et al., 1974; Baeten, 1975; Brodsky et al.,1975; Gambrell and Allen, 1975; Chaconas et al.,1976). Depending upon their location in thearches, teeth might be surrounded by variousamounts of cancellous and cortical bone,resulting in a different resistance to appliedforce systems. Moreover, adjacent teeth and

surrounding bones may also influence theresistance. When applying orthopaedic forces tothe nasomaxillary complex, it is of importanceto analyse the effects upon the craniofacialskeleton and the dentition. Therefore, interestin biomechanics has resulted in a number ofanalytical and experimental investigations(Kragt et al., 1979, 1982, 1986; Dermaut andBeerden, 1981; Kragt and Duterloo, 1982,Kusy and Tulloch, 1986). The main purpose ofthat research was to study the overall effects

of various extra-oral traction appliances andthe resistance of the environment to the appliedforces. To understand the mechanical propertiesof these appliances, the relationship of the forcevector to the centre of resistance (Cre) of thenasomaxillary complex and the dentition has tobe considered. In former studies, model systemshave been used to determine the location of theCre of a tooth or a group of teeth (Burstoneet al., 1981; Dermaut and Vanden Bulcke, 1986;

European Journal of Orthodontics 23 (2001) 263273 2001 European Orthodontic Society

Location of the centre of resistance of the upper dentition

and the nasomaxillary complex. An experimental study

Toon Billiet, Guy de Pauw and Luc DermautDepartment of Orthodontics, University of Gent, Belgium

SUMMARY The purpose of this study was to investigate the initial displacement of the upperdentition and the nasomaxillary complex as a result of different directions of force application,and to determine the initial centres of resistance for both the upper dentition and thenasomaxillary complex.

A macerated human skull with a well-aligned upper arch was used as one experimentalmodel and Araldit 208 as a substitute for the periodontal ligament (PDL). Specificallydesigned antenna-headgear was developed in an attempt to create different points of forceapplication to simulate high-pull and horizontal traction, and orthopaedic force magnitudesof 8 N were applied to the upper dentition and the nasomaxillary complex. Double exposureholography was used to measure the initial displacement. Reproducibility of the techniquewas tested and found to be reliable.

According to the registered fringe patterns, the force application transmitted by the headgearresulted in complex displacement of facial bones. Pure translation of the maxilla and theupper dentition was observed when the force vector passed by in the area of the key-ridge.No obvious difference was found between the centre of resistance of the upper dentitionand the nasomaxillary complex. The location of two different centres of resistance couldnot be confirmed by measuring initial displacements on this macerated human skull.

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Dermaut et al., 1986a,b; Vanden Bulcke et al.,1987). These investigations provided insight intothe displacement characteristics of the dentitionto applied forces. In particular, the point of forceapplication was found to be an important factor

in tooth displacement. The location of the Creof the maxillary complex offers importantinformation with respect to the use of headgear-activators. Differences in the direction oforthopaedic forces, as well as the point of forceapplication may produce different displacementpatterns of the complex and stress distribution inthe maxillofacial sutures of the nasomaxillarycomplex. Kragt et al. (1982, 1986), Tanne et al.(1993), and Tanne and Matsubara (1996) reporteda difference in force distribution after application

of various force systems. These findings can beexplained by the differences in the locationand direction of force vectors relative to theCre of the nasomaxillary complex. According tothe literature, there is little evidence concerningthe location of the Cre. The experimentaldetermination of the Cre of the upper first molarand of the anterior teeth has already beencarried out (Dermaut et al., 1986a,b; Dermautand Vanden Bulcke, 1986; Vanden Bulcke et al.,1987). Teuscher (1986), and Stckli and Teuscher(1994) made a distinction between the Cre of the

upper dentition and of the maxilla. They definedthe Cre of the maxilla at the postero-superiorarea of the zygomaticomaxillary suture, whereasthe Cre of the upper dentition was situatedbetween the roots of the upper premolars. Thelocation of these points was determined byobserved changes in craniofacial morphologyevaluated on lateral cephalograms of differentpatients treated with an activator. The definedcentres of resistance have to be understood asaverage points. Moreover, the effect of normal

growth, which may differ from patient to patient,might also affect the position of these points.Initial stress analysis induced by headgear-activator therapy, might be investigated on askull by changing the point and direction of forceapplication. Initial displacement is the result ofthe resistance of the nasomaxillary complex todifferent force application systems in which thebiological parameters are left constant by usingthe same skull. Besides Teuscher (1986) and

Stckli and Teuscher (1994) a few other clinicalstudies have offered information on the local-ization of the Cre of the nasomaxillary complex.

Over the years, there has been an increasedinterest in studies in which extraoral traction has

been tested on different human skulls models.Strain gauges, photo-elastic models and finiteelement analysis are often used as measuringmethods (Caputo et al., 1974; Hata et al., 1987;Tanne et al., 1993). In a finite element study,Tanne et al. (1995) suggested that the Cre ofthe nasomaxillary complex was located on thepostero-superior ridge of the pterygomaxillaryfissure. Lee et al. (1997) concluded, in a laserholography study on a human dry skull, thata translation was reached when the point of

anterior force application was 15 mm above anddirected 20 degrees downwards to the occlusalplane along with palatal expansion.

The aim of this study was to investigate theinitial displacement of the upper dentition andthe nasomaxillary complex as a result of differ-ent directions of force, and to determine theinitial centres of resistance for both the upperdentition and the nasomaxillary complex.

In the present investigation a non-invasiveand highly accurate holographic method wasused which allowed the precise detection of

very subtle initial reactions of hard tissue afterforce application. From a clinical viewpoint,exact information on the possible effects offorce application is of outmost importance forthe orthodontist, since initial displacement maybe indicative.

Materials and methods

A macerated human skull (aged 16 years), withwell-aligned upper permanent teeth, was used as

the experimental model. The teeth were carefullyremoved from the skull and their bony socketscleaned with acetone to remove residue. Duringthis procedure an attempt was made to avoid anydamage to the alveolar bone. Only one skull wasused so that all biological and environmentalvariables were left constant except those tobe investigated. Since all parameters remainedunchanged, the only differences which weremeasured, were due to the differences in force

264 T. BILLIET ET AL.

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direction. The periodontal ligament (PDL) wasreplaced by a thin layer of resin (Araldit 208,CM Technics) injected into the empty sockets,following which the teeth were carefully

repositioned. This special resin, when mixed withthe harder 956 (CM Technics) at a ratio of 10to 1, displays nearly the same elastic propertiesas the human periodontium (Dijkman, 1969).In the present study, an artificial PDL was usedin an attempt to simulate more accurately thebiological situation. Although the elastic modulusof Araldit is not provided by the manufacturers,laboratory experiments have shown forces of60 kg/cm2, which is comparable to the valuesdescribed by Diemer and Hofmann (Dijkman,

1969). Orthodontic molar bands carryingheadgear tubes were cemented on the maxillaryfirst permanent molars and an identical tubewas glued directly to the maxillary bone. Anacrylic splint was fabricated to embrace theupper dentition and a rigid metal plate was fixedto the anterior part of the splint, in an attempt toregister accurately initial displacement by meansof holography (Figures 1 and 2). With a metalplate, an extension was made of the dentition.

For the same rotation it was obvious that thefurther away from the clasping point (point offixation), the larger the number of fringes. Themetal plate enabled improved visualization of

the differences between the various points offorce application. Two facebows, which alloweddifferent points of force application, were con-structed. In a first series of experiments a facebowwas used to register horizontal traction atdifferent vertical levels (Figure 3). For verticaltraction a second facebow was constructed toapply vertical forces on different sagittal positions(Figure 4). These last measurements were carriedout in a second experiment. Different hookswere soldered at various levels of the bows to

support a nylon wire and to create various pointsof force application.

The skull was fixed to a heavy metal support bya modelling compound shield covering the frontaland occipital bone. Traction was transmitted tothe hooks by means of a nylon wire attached toa weight carrier dish via wheels that could beadjusted to simulate high-pull and horizontaltraction. A force magnitude of 8 N was producedby placing a dish weight on the carrier.

CENTRE OF RESISTANCE AND UPPER DENTITION 265

Figure 1 Experimental set-up with antenna headgear, splint and metal plate; example of high-pulltraction to the dentition.

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In recent years, holography has been increas-ingly used in biomechanical research, especiallyin orthodontics. In this procedure, coherent

and monochromatic laser light is employed forrecording an object surface on a photosensitiveemulsion of the holographic plate. This plate isilluminated by a split laser beam; one beam (the

reference) is directed towards the holographicplate and the other reflected from the objectsurface. By superimposition of two coherentlight waves, one of which is reflected from theundeformed and the other from the deformedobject surface, spatial interference fields areformed by interference of these waves. In theplane of the hologram these fields are reducedto a system of interference fringes. This fringepattern yields information concerning themagnitude of the displacement at the surface

of the object and the direction of displacement.A 10 mW He-Ne laser ( = 0.6328 m) was usedand the laser beams were exposed on holographicplates (Agfa Gevaert) consisting of a highlysensitized emulsion that coated the glass plates.A double exposure technique was used. Theunloaded skull was exposed for 10 seconds, thedesired force was then applied for 10 minutesand the same holographic plate was thenexposed for a further 10 seconds. A relaxation


Figure 2 Example of horizontal traction to the maxilla.

Figure 3 Points of force application (17) to the maxillaand the dentition with horizontal traction.

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period of 15 minutes was allowed before the nexthologram was taken. A frontal hologram wastaken for each traction: seven points of forceapplication for the high-pull traction and sevenpoints for the horizontal traction. To test the

reliability of the method, five holograms fromsix different force systems were taken followingloading of 6 N. A minimal amount of force wasneeded to visualize the creation of fringes. Tomeasure displacements in a reproducible way, itwas found that a minimum force of 6 N wasneeded. In the final experiment, this force wasincreased to 8 N in an attempt to improve thevisualization of the amount and direction of thefringes.

Results

Reliability of the method

Since the quantitative calculation of the initialdisplacement of the upper dentition and thenasomaxillary complex uses the counting offringes with regard to a chosen reference point,the accuracy depends upon the visibility andoutline of the dark fringes. The fixation of theskull was tested under different loading andproved to be reliable. A series of five holograms

registering the application of an orthopaedicforce of 6 N under six different loading systems

showed a highly comparable fringe pattern. Thetotal amount of fringes over the whole lengthof the skull differed by a maximum of one unit(Table 1).

The analysis of the fringe patterns on the

maxillary complex and the upper dentition incase of high-pull and horizontal traction revealedthe following findings.

High-pull traction (Figure 4). A force applicationanterior to the key-ridge always created an initialcounterclockwise rotation of the dentition and ofthe maxillary complex indicated by the numberof fringes (Figure 5). Within one maxillofacialbone the fringe patterns showed regular images.In the sutures between the bones this regularpattern was interrupted, indicating that the

sutures transmitted orthopaedic forces resultingin differential displacement directions. When theforce vector approximated the presumed Cre,the magnitude of the rotational displacement wasless although a force direction through the Creshould create a translation. A force applicationposterior to the Cre again created a higher numberof fringes, indicating a clockwise rotation. Thedifference of the point of force applicationbetween the dental splint and the maxilla did notseem to be of great importance when comparingthe magnitudes of the initial displacement

(Figure 6). The rigid fixation of the dentitionby the maxillary splint seemed to transmit the


Table 1 Error of the method tested by comparing the magnitude of the initialdisplacement (106m) in 5 holograms (n = 5) taken from the same situation on3 randomly selected different points of force application (P1 P3).

x= mean displacement, r= range

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Figure 5 Example of a series of seven holograms illustrating the initial displacement of the nasomaxillarycomplex with high-pull traction on the dentition.

Figure 4 Points of force application (17) to the dentition and the maxilla withhigh-pull traction.

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applied forces directly to the maxilla without asignificant difference in initial displacement ofthe dentition.

Horizontal traction (Figure 3). The initialorthopaedic displacement of the maxilla afterhorizontal force application was comparablewith the displacement after high-pull traction asfar as the magnitude of the displacement wasconcerned.

A force application beneath the zygomaticprocess of the maxilla created a clockwiserotation of the maxilla, while a force applicationabove the zygomatic process resulted in acounter-clockwise rotation of the maxilla. The

smallest rotation was observed with a forcedirection just below the zygomatic process ofthe maxilla (Figure 7).

A typical circular fringe pattern as describedby Lee et al. (1997) was observed at the key-ridgeof the maxilla with high-pull, as well ashorizontal traction at different points of forceapplication (Figure 8). These circular fringeswere the result of a lateral translation of thecentre of the zygomatic arch.

By combining the force levels of horizontaland high-pull traction with the least fringes, theCre was constructed (Figure 9). Translation was

considered to occur in this experimental set-upwhere the least fringes were registered. Both theCre defined by forces applied to the splintedteeth and to the maxilla were located near thelower border of the zygomatic process of themaxilla. There were no significant differencesbetween the initial displacement of the upperdentition and the maxillary complex. Themagnitude as well as the direction of the initialdisplacement was comparable. The analysis of thefringe pattern could not distinguish a difference

between a dental and a skeletal Cre.

Discussion

The use of a macerated human skull as a modelto investigate the effect of force applicationon teeth and bone deals with the followinghypothesis: by applying a force on a tooth, thePDL is stretched on one side and squeezed onthe other. Bone apposition by the formation of


Figure 6 Diagram illustrating the magnitude of displacement for different points of forceapplication with high-pull traction on the dentition and the maxilla (CCW = counter-clockwiserotation; CW = clockwise rotation).

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bone spiculae and bone resorption on theopposite side might be the result. This biologicalphenomenon creates tooth movement andrebuilding of the alveolar process. Initial dis-placement registered on the skull might provide


Figure 8 Typical circular fringe pattern observed atdifferent force levels at the zygomatic area.

Figure 9 The Cre defined by the intersection of the actionlines after horizontal (HT) and high-pull (HPT) forceapplication inducing translation of the maxilla.

Figure 7 Diagram illustrating the magnitude of displacement for different points of forceapplication with horizontal traction on the dentition and the maxilla (CW = clockwiserotation; CCW = counter-clockwise rotation).

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an indication for the expected longitudinaleffect.

The influence of force application on thecraniofacial complex has been investigatedextensively in clinical and in vitro situations. It is

difficult to study the effect of the different forceparameters in the clinical situation. Therefore, inthe last decades, an attempt has been made toinvestigate the influence of orthopaedic forceson different in vitro models. In the present study,a macerated human skull was used to evaluatethe initial orthopaedic displacements of themaxilla and the upper dentition in a posteriordirection. The complex architecture of the skullwith combinations of trabecular and corticalbone, as well as sutures and teeth together with

changes in elasticity of all these structures, makethe dry skull a more valuable model than thoseconstructed by using photoelastic materials.Nevertheless, the absence of soft tissues in thesutures, and of the PDL, the macerating process,humidity and other factors may have consequencesin the biomechanical behaviour.

To approximate reality, Araldit was usedas a substitute for the PDL (Dijkman, 1969).

In previous studies the initial displacement ofteeth on a dry skull by headgear (Dermaut et al.,1986a,b) and by intrusive mechanics (Dermaut

and Vanden Bulcke, 1986) was found to becomparable to the clinical displacement (Wormset al., 1973; Nanda, 1981), indicating that theuse of a macerated skull might be a valuablemodel. The centre of rotation might be definedby the intersection of two displacement vectors(De Clerck et al., 1990; Govaert and Dermaut,1997). However, a recent study (De Pauw andDermaut, 1998), clearly showed that the useof the centre of rotation is susceptible to animportant error. Small differences in the direc-

tion of the displacement vectors may resultin a considerable change of the centre ofrotation. Therefore, in this study initial displace-ment vectors were used instead of centres ofrotation.

The magnitude and the direction of the initialdisplacement vector immediately after forceapplication will indicate the differential reactionsof the bones as a result of the force system used.A force application through the Cre of the

maxilla will create a pure translation, so anexact definition of the position of the Cre ofthe maxilla is important in order to obtainthe presumed maxillary displacement. Poulton(1959, 1967), Barton (1972), and Bench et al.

(1978) defined different displacements of themaxilla after headgear force application onpatients. According to Poulton (1959, 1967) theCre of the maxilla is situated at the apex of thesecond premolar in the maxilla. Bench et al.(1978) reported its position to be in the mostsuperior point of the fossa sphenopalatina, whileBarton (1972) linked the position of the Creof the maxilla to the number of teeth involved inthe appliance design. They all applied headgeartherapy to the upper first molars in different

patients. In the present experimental set-upheadgear traction was applied to a splint anddirectly to the maxilla in the same skull. Accordingto earlier experiments using laser measuringtechniques (Dermaut and Beerden, 1981; Dermautand Vanden Bulcke, 1986; Dermaut et al.,1986a,b) it has been found that bone displace-ments within a skull, after force application, aredue to displacements in the sutures, rather thanto bone bending within the same bone unit. Forpractical reasons tubes were glued on thealveolar process in the area of the first molars.

This location is not critical as the localisation ofthe Cre of the maxilla is determined by the pointof force application (facebow hooks) instead ofthe position of the tube. It is obvious thereforethat comparison of the findings is inappropriate.

Lee et al. (1997) in a comparable dryskull study applied anterior traction to a rapidmaxillary expansion appliance in an attempt totransmit the applied force to the entire maxilla.When the screw was activated and a protractionforce was exerted, the Cre of the maxilla was

reported to be located approximately in thesame area as that in this study. They, however,did not investigate the Cre of the upperdentition.

Teuscher (1986), and Stckli and Teuscher(1994), distinguished two centres of resistance:one for the maxilla and one for the dentition.By directing the extra-oral force vector betweenthe respective centres of resistance, differentialreaction patterns on the maxilla and the dentition


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might be expected. In this study, no cleardifference in initial displacement (magnitudeand direction) between maxilla and dentitionwas found.

Conclusions

The results of this investigation showed thatthe region of the Cre of the maxilla was situatedunderneath the zygomatic process of the maxillarycomplex. A force vector applied through thisregion induced initially nearly pure translation ofthe maxilla in high-pull as well as with posteriorhorizontal traction. The Cre of the maxilladefined by Teuscher was situated in a moreupward and posterior position. The localisation

of two different Cre as suggested by Teuscher(1986), and Stckli and Teuscher (1994) inactivator-headgear therapy could not be con-firmed by measuring initial displacements on amacerated human skull.

Address for correspondence

Professor Dr Luc DermautDepartment of OrthodonticsUniversity of GentDe Pintelaan 1859000 GentBelgium

References

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