Mathematical analysis of tooth and restorationcontour using image analysis

Nabil Alhouria, David C. Wattsb, J. Fraser McCorda, Philip W. Smitha,*

aUnit of Prosthodontics, School of Dentistry, University of Manchester, Manchester M15 6FH, UKbUnit of Biomaterials Science, School of Dentistry, University of Manchester, Manchester, UK

Received 13 January 2004; accepted 8 June 2004

01do

16

KEYWORDSTooth contour;Image analysis;Crown restoration

09-5641/$ - see front matter Q 200i:10.1016/j.dental.2004.06.003

* Corresponding author. Tel.: C44-1-275-7822.E-mail address: psmith@fs1.den.m

Summary Objectives. The aim of this study was to develop a methodology forcomparison of the contour of artificial crowns in the mid bucco-lingual plane withtheir equivalent natural teeth on the opposing side of the same arch (antimeres)using a novel application of image analysis software. The objective was to determinewhether artificial crowns were overcontoured.

Methods. Specimens consisted of thin sections of silicone putty impressions of thebuccal and lingual surfaces of 55 full crown restorations and their natural antimericteeth. A thin slice of the putty was obtained in the mid-tooth bucco-lingual plane anda digital image was captured and this was analysed to produce a data set (x, y)representing the curvature of the tooth surface. Further analysis was performed inorder to describe the profile in optimum mathematical terms.

Results. The curves were best represented by three equations: yZaCbx(0.5),ln(y)ZaCbx2, and y2ZaCbx. In all equations parameter (b), which expresses thecontour curvature, was used as a deciding factor in comparing the degree of contourof the crown restorations with their natural antimeres. Most artificial crowns werefound to be either similarly or undercontoured when compared with their naturalantimeres. When overcontouring was present in the artificial crowns this tended tooccur on the lingual aspects of anterior and posterior crowns.

Significance. Simplifying tooth contour into a mathematical model can be useful indetermining whether restorations are overcontoured. Clinically, particular attentionshould be directed towards the lingual aspects of restorations which were more likelyto be overcontoured.Q 2004 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

4 Academy of Dental Materials

161-275-6629; fax: C44-

an.ac.uk (P.W. Smith).

Introduction

The contour of a tooth is an important aspect ofoverall dental aesthetics. It is defined in theGlossary of Prosthodontic Terms as the outline of

Dental Materials (2004) 20, 893–899

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. Published by Elsevier Ltd. All rights reserved.

N. Alhouri et al.894

the curving of the tooth, or the line representingthis outline [1]. The greatest convexity of toothcontour has been described, in previous literature,according to different positions in the dental arch.The crests of facial contours of all teeth were foundin the gingival third of the crown with a projectionof no more than 0.5 mm facially beyond thecementoenamel junction (CEJ) [2]. Betweenthe occlusal or incisal surface and the facial crest,the facial surface has a slight convexity. The buccalsurfaces of posterior mandibular teeth are convexbetween the gingival crests of curvature and theocclusal surfaces. Slight facial depressions existbetween the occlusal/incisal surface and thegingival crest of curvature in a vertical direction[3]. Similarly, the greatest convexity of the lingualsurfaces of some of the teeth is found in the gingivalthird of the crown. However, on mandibular molarsand possibly premolars, the lingual convexity isfound in the middle third of the crown. The lingualconvexity, it is considered, should protrude lin-gually only 0.5 mm beyond the CEJ in any toothexcept in the mandibular molars and premolarswhere this maximum convexity may extend to0.75–1 mm [3,4]. The cervical two thirds of aproximal surface of a tooth has been described asflat or slightly concave. The tooth is flat or slightlyconcave from the facial to lingual aspect, as well asfrom the level of proximal contact to the CEJ. Theexception is the distal proximal surface of themaxillary first molar, which is convex in shape, butcervically there is a concavity [3,4].

Many theories have been used to explain theneed for particular forms of axial contour of full andpartial coverage extracoronal restorations. It wasargued that many ideas regarding the contourssuggested for restorations were not based onscientific evidence, largely because artificialcrowns were constructed long before the aetiolo-gical role of dental plaque was known [5].

According to the ‘gingival protection theory’,convexities should be created in the cervical thirdof artificial crowns, to deflect food away from thefree gingivae. Food should, theoretically, pass overthe gingival crevice and onto the kertinized surfaceof the attached gingiva [2]. This theory, togetherwith the increased use of full-coverage veneercrowns led to an era of overcontoured restorations[6]. Many authors subsequently questioned therationale of the concept of the ‘gingival protectiontheory’, and concluded that crowns constructedaccording to this concept were likely to be over-contoured. Overcontoured crowns are consideredto promote, rather than prevent, gingival inflam-mation [7–10]. Perel [11] in a study on dogsreflected the same findings, demonstrating

increased levels of gingival inflammation andhyperplastic changes, which were associated withovercontoured restorations. Such changes wereobserved both at clinical and histological levels. Incontrast, undercontoured restorations were notassociated with any such pathological change.

In the ‘muscle-action theory’, the rationale ofmuscular molding and cleansing was used to explainthe observable clinical phenomena found aroundthe natural and artificial crowns [7,8]. According tothis concept, muscle action could be impaired whenintimate contact between the lips, cheeks, andtongue against gingivae is prevented by overcon-toured crowns. However, it has been demonstratedthat, in the absence of oral hygiene, ‘self-cleansing’mechanisms do nothing to prevent gingivitis [12,13].In the ‘anatomic (biologic) theory’, it was suggestedthat artificial crown contour should simulate themorphology of natural, healthy teeth [5].

Thus, duplication of the features of natural teethwhile constructing restorations might be con-sidered one of the goals of Restorative Dentistryand of Dental Materials Science. Morris [8] reportedthat the pre-operative shape of the embrasuresshould be reproduced provided the embrasurecontained a healthy papilla. Overcontouring prox-imal surfaces apical to contact areas might producesevere gingival inflammation. Parkinson [14] statedthat to minimise iatrogenic dental disease, artificialcrown form must approximate natural tooth mor-phology. If the curvature of the restoration exceedsnatural curvature, the restoration contradicts theinnate defensive capability of nature.

The aim of this study was to develop a scientificmethodology to mathematically compare the con-tour between artificial crowns and their naturalantimeres.

Materials and methods

Sample set and exclusion criteria

The sample set was obtained from a commercialDental Laboratory in the North of England whichtakes dental work from throughout the UK. Itconsisted of 55 full crown restorations and theirnatural antimeric teeth.

Full crowns were included in the study only iftheir antimeres were natural teeth and wereexcluded if the antimeres exhibited any of thefollowing:

†

Antimeres partially erupted † Antimeres with caries or restorations affecting

buccal or lingual surfaces

Figure 1 Thin bucco-lingual sections of silicone putty taken from an impression of a single crown and its naturalantimere.

Mathematical analysis of tooth contour 895

†

Antimeres with malformation or abnormalmorphology

†

Figure 2 An image showing buccal tooth contourderived from the thin section of silicone impression.

Antimeres with any defect in the casts resultingfrom either defects in the impression or sub-sequent laboratory techniques that might havean effect on the studied area.

Analysis of tooth contour

Impressions of buccal and lingual surfaces of the fullcrown restorations and their natural antimericteeth were made using addition cured siliconeputty (Vinyl Polysiloxane Provilw novo, putty, soft,fast set, Heraeus, Kulzer, Dormagen).

The putty impression was then sectioned in mid-buccal mid-lingual coronal plane perpendicular tothe mesiodistal diameter of the tooth, and a thinslice of the putty was obtained (Fig. 1). The slice ofpolyvinylsiloxane putty was then viewed under amicroscope with 6.5 magnification (Wild Leitz, WildHeerbrugg Ltd, 9435 Heerbrugg, Switzerland). Theslice of impression putty was positioned with astandardised orientation on the microscope stage.An image was taken (Fig. 2) using a digital camera(PEC3010, Pulnix, Basingstoke, UK), which had beenconnected to the microscope and to the computer.

The image was then analysed using SigmaScanSoftware (Sigma Scan Pro. Image Analysis, Version5.0.0 (Build number 3981) Copyrightq 1987–1999SPSS Inc.). The edges of the buccal and lingualsurfaces of the crown were tracked separately toproduce a profile curve. The SigmaScan softwarewas used to provide a text file with an orthogonaldata set (x, y) representing the curvature of eachsurface.

The text file was then imported to TableCurveSoftware (TableCurve 2D Windows v4.07, Copyright1989–1996 AISN Software Inc.). TableCurve wasused to produce an algebraic formula (equation),

which allowed the surface profile to be character-ised (Fig. 3). Equations were ranked within theprogram according to the fit of the curves.

The stages of analysing the tooth curvature arerepresented in Fig. 4.

Results

It was found that the curves (contour) of buccalsurfaces for all natural teeth in the study were bestrepresented by the following equation (EqB):

y Z a Cbx0:5

The curves (contour) of lingual surfaces for allanterior natural teeth in the study were bestrepresented by the equation (EqLa):

lnðyÞ Z a Cbx2

Figure 3 Tooth contour characterised, for orthogonalcoordinates (x,y), by algebraic formula: yZaCbx0.5. Inthis example: parameter aZ587.25; bZ21.89; r2Z0.9966.

Figure 5 Graphical representation of the equations ofcontour of buccal/lingual surfaces for anterior andposterior natural teeth. Curve a, lingual posterior;curve b, lingual anterior; curve c, buccal anterior; curved, buccal posterior.

N. Alhouri et al.896

The curves (contour) of lingual surfaces for allposterior natural teeth in the study were bestrepresented by the equation (EqLp):

y2 Z a Cbx

These equations were considered to be representa-tive equations of the curvatures (contour) ofnatural teeth.

Fig. 5 represents all equations of the contour ofbuccal and lingual surfaces of natural antimericanterior and posterior teeth.

The effects of different values of (a, b) onthe curvature of tooth contour

In order to know the effects of the different valuesof (a, b) on a graph representing EqB, a fixed valuewas given to parameter (b) with three differentvalues to parameter (a) (Fig. 6), and vice versa(Fig. 7).

It can be noticed from Fig. 6 that different valuesof parameter (a) do not have an effect on theshape of the graph (contour of the tooth) repre-senting EqB.

It can be noticed from Fig. 7 that different valuesof parameter (b) have an effect on the shape of thegraph (contour of the tooth) representing EqB. Thenegative values of parameter (b) make it moreconvex (or concave), whereas positive values makeit straighter.

Figure 4 Analysis of buccal and lingual contour ofartificial crowns and their natural antimeres.

The value of the parameter (b) inthe relevant equations

The mean value and standard deviation of par-ameter (b) in the equations representing thecontour of buccal and lingual surfaces for antimericnatural teeth versus full crown restorations in thestudy are presented in Table 1.

Figure 6 Graphical representation of the effectsof positive and negative values of parameter (a) in EqByZaCbx0.5. Curve a, parameter a positive; curve b,parameter a; curve c, parameter a negative.

Figure 7 Graphical representation of the effects ofpositive and negative values of parameter (b) in EqB yZaCbx0.5. Curve a, parameter b positive; curve b,parameter b; curve c, parameter b negative.

Table 2 The 95% limits of agreement of theparameter (b) for natural teeth.

95% limits of agreementof parameter (b)

Anterior teeth (buccal) (K3.07, 3.07)Anterior teeth (lingual) (K0.00000075,

0.00000075)Posterior teeth (buccal) (K7.73, 7.73)Posterior teeth (lingual) (K84.34, 84.34)

Mathematical analysis of tooth contour 897

Limits of agreements

In order to assess the limits of agreement in thepresent study, two teeth were selected randomlyfrom the sample. Ten images were taken forbuccal/lingual surfaces for each tooth. The imageswere then analysed and the values of theparameters (b) in the correspondent equationswere statistically analysed. The 95% limits ofagreements of the parameters (b) in the relevantequations were calculated as G2.26SD (Table 2).

The contour of the artificial crown would beconsidered similar to the contour of the naturalantimeric crown, if the differences in theparameter (b) of the relevant equation betweenthem are comparable to those found in themeasurement repetition.

Table 1 The statistical analysis of parameter (b) inEqB, EqLa and EqLp for full crown restorations andtheir natural antimeres.

b value inequations

Full crownmean (SD)

Natural antimeresmean (SD)

EqB for anteriorteeth

K23(3) K24(3)

EqB for posteriorteeth

K27(7) K28(7)

Eqla K0.000004(0.000001)

K0.000005(0.000002)

Elp K422(88) K441(134)

Comparison of the tooth contour betweenfull crowns and their natural antimeric teeth

The values of the parameter (b) of the equationsrepresenting buccal/lingual surfaces of fullcrown restorations (C)b were subtracted fromthose of the antimeric natural teeth (A)b as follows:(A)bK(C)bZb*.

If the resultant values of parameter (b*) did notexceed the 95% limits of agreement presented inTable 2, the contour of the full crown restorationwas regarded to be similar to the contour of theantimeric natural tooth. However, if the resultantvalue (b*) exceeded the 95% limits presented inTable 2, the contour of the full crown restorationwas not regarded to be similar to the contour of theantimeric natural tooth. When value (b*) waspositive the restoration was considered to beovercontoured, and conversely when (b*) wasnegative the crown was undercontoured.

The contour of full crown restorations

The values for (b*) were categorised according towhether they were overcontoured or undercon-toured. The results are presented in Table 3.

Discussion

Tooth contour has been studied previously usingoptical observation [2–4] or photographicapproaches [15]. The expressions ‘overcontouredand undercontoured’ of the tooth surfaces werederived from observational judgement of the nakedeye, or alternatively via metric assessment of thesurface prominence [2].

Shillingburg et al. [16] indicated that thecorresponding surfaces of the adjacent teeth, ifthey were in a normal position, make an excellentguide for judging the contours of the facial andlingual surfaces of wax patterns. It is also importantto evaluate the contour of the contralateral teeth

Table 3 The contour of full crown restorations as compared with their natural antimeres.

Tooth contour Similar Overcontour Undercontour

Anterior restoration (buccal) 18 (56.3%) 4 (12.5%) 10 (31.3%)Anterior restorations (lingual) 6 (18.8%) 8 (25%) 18 (56.3%)Posterior restorations (buccal) 16 (69.6%) 3 (13%) 4 (17.4%)Posterior restorations (lingual)a 10 (43.5%) 6 (26.1%) 5 (21.7%)

a Two values are missing.

N. Alhouri et al.898

(if present and sound) on dental casts, whenconstructing indirect restorations [17]. Further-more, the use of callipers was suggested tocompare tooth dimensions between measurementsof the study casts and final restorations [17].

This study used a mathematical method toevaluate and characterise tooth contour using animage analysis package. This novel method wasused to compare the surface contours of theartificial crowns and their natural antimeric teeth.Similarly, image analysis systems have been usedpreviously to analyse tooth shape variability ofbuccal surfaces [18]. The main factor in determin-ing the curvature of the surfaces of teeth was foundto be the value of parameter (b) in the relevantequation. Increasing negative values of parameter(b) in EqB, EqLa and EqLp indicates that the surfaceof the tooth is overcontoured, while increasingpositive values of parameter (b) indicates that thesurface of the tooth is undercontoured.

In the equations determined mathematicallyfrom this study:

(X) and (Y) are co-ordinates, variables

(a) and (b) are mathematical parameters where a is the intersection point between the curve andthe Y axis b represents the curvature value at each point ofthe curve.

In clinical terms therefore: parameter (a)becomes the intersection point between the toothcontour and gingival margin. Thus the (a) valuedepends on choosing the start point of themeasurement. Parameter (b) expresses the contourof curvature.

It has been suggested that the amount of toothpreparation can have an influence on the contour ofthe restoration [19]. There is a tendency even forexperienced operators to under prepare labialshoulders, both in laboratory and clinically.Seymour et al. [20] explained that this underpreparation leaves the technician facing adilemma: of either restoring the tooth to optimumcontour and thus compromise on material oraesthetic qualities. The second option is to use

the material in the recommended thickness andthereby overbuild the crown, thus compromising itsfinal contour and emergence profile.

In general, the contour of full crown restorationscompared with their antimeric natural teeth hadthe following trends:

†

Most of the full crown restorations had eithersimilar contour or were undercontoured com-pared with their antimeric natural teeth. Thisresult indicates that in this study, dentaltechnicians tended not to overcontour thesurfaces of full crown restorations. This resultfits in part with the recommendation of Tjanet al. [5] and Becker and Kaldahl [6].

†

The buccal contour of full crowns was similar totheir antimeric natural teeth in most cases forthe posterior crowns and in more than half of thecases for the anterior crowns.

†

If not similar, the buccal surface of anteriorfull crown was mostly made undercontouredcompared with the contour of their antimericnatural teeth.

†

The lingual aspects of the anterior full crownswere made undercontoured in more than half ofthe cases compared with the contour of theirantimeric natural teeth.

†

The lingual contour of the posterior full crownswas similar to their antimeric natural teeth injust less than the half of the cases.

It may be concluded that in this study artificialcrowns were either similarly contoured or under-contoured when compared with their naturalantimeres. This study suggests that it is valid thatdental technicians use unprepared antimeres as aguide for developing the contours artificial crowns.

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