Sf

Fa

b

c

a

A

R

R

2

A

K

M

F

D

T

O

P

0d

d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) e47–e55

avai lab le at www.sc iencedi rec t .com

journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls /dema

equential software processing of micro-XCT dental-imagesor 3D-FE analysis

lávia P. Rodriguesa,∗, Jianying Lib, Nick Silikasc, Rafael Y. Ballestera, David C. Wattsc

Department of Dental Materials, School of Dentistry, University of São Paulo, São Paulo, BrazilSchool of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, UKBiomaterials Science Research Group, School of Dentistry, The University of Manchester, Manchester, UK

r t i c l e i n f o

rticle history:

eceived 26 September 2008

eceived in revised form

6 January 2009

ccepted 2 February 2009

eywords:

icro-XCT

EA

ental-images

eeth

cclusal loading

a b s t r a c t

Objectives. The aim was to describe a sequential software processing of �-XCT molar-images

for 3D-FE tooth/restoration model geometries based on a representative molar tooth, giving

attention on each step of data-processing. This paper first gives an overview of a sequential

processing and then applies the resulting model to the particular case.

Methods. An intact mandibular molar was scanned using a micro-XCT instrument (1072,

SkyScan, Belgium) in which 960 slices were obtained. Sixty-three non-adjacent bitmap slices

were then optimally selected for model-creation. Enamel/dentin boundaries were clarified,

for each slice, using image control-system software (ScanIP, Simpleware), generated a file

which was sequentially converted into a mesh in a reconstruction software (ScanFE, Simple-

ware) and posteriorly converted into a STL-file (triangulated-2D-stereolithography). This was

imported into a FE-software package (Patran, MSC.Software, USA) and all elements were re-

meshed. From these elements, surfaces were created and exported to another FE-software

(Hypermesh, Altair Hyperworks) to build the dental-cavities. Finally, the volumetric-mesh

was created and the model was imported back to FE-software to apply the boundary-

conditions, material-properties and initiate post-processing (using Patran and Marc, MSC

Software). To demonstrate the use of the resulting model, this was applied to the particular

case of a Class I restoration subjected to distributed loading. The analysis was performed

as linear and structural and outputs of maximum principal (MP) and maximum shear (MS)

stresses were then evaluated.

Results. A 3D-model of a mandibular molar was processed without generating errors in the

FE-package used. The maximum deviation between the tooth and the model was less than

0.1%. Stress concentrations were found at the surface where the load was applied and in

the vicinity of the tooth–composite interface.

Significance. The described procedure is a successful method able to produce a highly detailed

3D finite element model of restored molar teeth with any cavity configuration and combi-

nation of restorative materials and this method can also be used for other biological or

biomaterials applications.

© 2009 Academy

∗ Corresponding author at: Departamento de Materiais Dentários, Facurestes, 2227, Cidade Universitária, CEP 05508-900 São Paulo, SP, Brazil.

E-mail addresses: flapiro@usp.br, flapiro@gmail.com (F.P. Rodrigues)109-5641/$ – see front matter © 2009 Academy of Dental Materials. Puoi:10.1016/j.dental.2009.02.007

of Dental Materials. Published by Elsevier Ltd. All rights reserved.

ldade de Odontologia, Universidade de São Paulo, Av. Prof. LineuTel.: +55 11 3091 7840x222; fax: +55 12 3951 5904..blished by Elsevier Ltd. All rights reserved.

l s 2

e48 d e n t a l m a t e r i a

1. Introduction

In recent years, there has been an increasing interest inachieving an optimal cavity preparation design and optimalrestorative materials to minimize the stress developed bypolymerisation shrinkage and/or occlusal loading [1–19]. Nodefinitive guidelines are available yet with regard to the opti-mal cavity preparation design and restorative materials to beused [18]. Studies based on laboratory experiments may givethe answers to these questions. However, a major problem isperformance on live subjects. Moreover, in view of the vari-ability of the mechanical properties and shape of the teeth,and since it is virtually impossible to obtain physical mea-surements of stresses within a tooth structure, finite elementmethods (FEM) are useful tools to achieve a representation ofreality with calculation of these complex stresses. These indi-cate mechanical aspects of biomaterials and human tissuesthat can hardly be measured in vivo [20,21]. Recently, someauthors have investigated FE optimisation methods for cavitypreparation [6,22].

FEM were introduced into dental research in 1973 [23] toshow internal stresses. Structures are divided into a numberof shaped elements with individual stress/strain characteris-tics [10,17]. Determination of these parameters was achievedwhile the structure was exposed to external force, pressure,thermal change, or other factors. By solving the deformationof all the small elements simultaneously, the deformation ofthe structure as a whole can be assessed [17]. On that basispredictions can be made about failure [18,20]. Previous stud-ies have reported different techniques to create 2D and 3D FEmodels of teeth. Teeth were digitized with several types ofscanning device or even conventional computational tomog-raphy scans (CT-scan) in which the images were converted into3D prototyping or 3D-CAD systems [24]. More simply, contoursof dental tissues were paper traced or obtained with graphicssoftware programs [25]. Templates were then used to createthe FE computerized model and most of them meshed withless detail reproduction [26].

Researchers have recently shown an increased interest invirtual FE-models and simulations associated with sophis-ticated techniques, in which an iterative optimization ofthe model design has been performed from X-ray micro-computed tomography (�XCT). Refinements have been madein geometry acquisition by recreation and digitization of pla-nar outlines of the spatial anatomy [10,24,27]. The principleconsists in reconstructing the linear attenuation coefficient,within an object, from the attenuation measurements of anX-ray beam passing through the sample at different viewingangles. Differences in linear attenuation coefficient among tis-sues are responsible for X-ray image contrast, which allowsquantitative analysis to be made [28].

FEM have been used to evaluate the status of restored teeth[3,5,29–34] including the tooth, interface and composite stressand strain under simulated clinical conditions [29]. The com-bination of �-XCT data with FE analysis result in models finer

in texture than those previously reported. By employing thistechnology, the aim of this study was to describe sequen-tial software processing of �-XCT molar-images for 3D-FEtooth/restoration model geometries based on a representative

5 ( 2 0 0 9 ) e47–e55

molar tooth, giving attention on each step of data-processing.This paper first gives an overview of a sequential processingand then applies the resulting model to the particu-lar case of a Class I restoration subjected to distributedloading.

2. Materials and methods

The tooth (a lower second molar) was selected based on itslack of carious lesions, and absence of abnormalities, and alsoits ‘approximate symmetry’, which could simplify interpreta-tion of results of a sound and prepared cavities tooth modelfor FE analysis. Thus, the sound tooth model could serve as acontrol.

To develop a 3D-FE model based upon actual geometricdimensions, sequential software processing was performed.

2.1. Acquisition of teeth shape data from micro-XCTscanning

A micro-XCT was used in this study (Model 1072, Skyscan, Kon-tich, Belgium) for scanning the molar tooth. This instrumentis a X-ray micro-computer tomographic unit composed by thescanner coupled to a workstation. The hardware used to pro-cess these data in the current study were a Dell Precisionworkstation PWS 450 Intel® Xeon (4 Gb CPU, 3.06 GHz), whichhas a dedicated software for micro-XCT: SkyScan 1072® soft-ware (Skyscan, Belgium); and a Dell Precision workstation PWS390 Intel® Core (4 Gb CPU, 2.13 GHz) with TView® and NRecon®

(Skyscan, Belgium).The equipment was adjusted to scan the whole tooth, with

a beam accelerating voltage of 102 kV and X-ray beam cur-rent of 96 �A. Initially (using SkyScan 1072 software), a totalof 1020 Tag Image File Format (TIFF) 16-bit images, with ver-tical and horizontal resolution of 1336 dpi and 2 Mb size file,were obtained. Using NRecon® software, the region of inter-esting was then selected to generate 960 horizontal layers ofthe inner structure of the tooth (transversal slices) with mag-nification of 14.3 pixels at 1024 × 1024 resolution, each as 1 Mbbitmap files. Two frames were taken for 180◦ rotation per 0.45◦

frame angle and 4 s of exposure time per frame.The recorded slices were then reduced to sixty-three, which

were chosen manually, according to the morphological simi-larities that could be noticed among files thumbnails. Thesefiles were then organized in the same directory and checkedusing TView® to check if there were any areas with artefactsand/or defects which need to be removed or non-selectedfor the next step. To facilitate the visualization and worka-bility, these bitmap were cropped with Adobe® Photoshop®

7.0 (Adobe Systems Incorporated, USA), or in any other soft-ware with the same tool for decreasing the file size from 1 Mbto 280 kb and 554 × 508 resolution and also to focus on thearea of interesting. ‘Un-painting’ also could be done if therewere still some artefacts around this area, which could addparts that does not exist in the tooth. These sixty-three non-

adjacent bitmap slices were then used for the reconstructionprocess to generate the 3D-FE model-creation, with an equalseparation distance of 0.152 mm (Fig. 1), described in the nextsection.

d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) e47–e55 e49

Fig. 1 – Reconstruction process, generating 63 non-adjacent bitmap slices. The levels (from 1 to 10) were divided only fori

2c

Ebcowsbmgavhaieaimrsc

2

TFtd

llustrative purposes.

.2. Segmentation: dentin and enamel ‘masks’reation

namel and dentin outer shapes, which appeared as visibleoundaries on the sixty-three bitmap slices, were accuratelylarified following tooth segmentation pixel-by-pixel for eachne, using image control-system software (ScanIP®, Simple-are, UK). This software imports a stack of images from �-XCT

lices in a wide variety of software formats (in this case asitmap files), allowing steps of visualization and assisted seg-entation based on image density thresholding of different

ray scale intensities corresponding to the degree of miner-lization. The segmentation was then used to generate theolumes (binary volumes) that are called masks, which defineow the objects fill the space. This step is not fully automatednd the segmentation can be continued manually (via paint-ng and unpainting tools, in the same way they can be doneasier in Adobe Photoshop® if it is necessary). Thus, enamelnd dentin corresponding masks were created by graduallynterpolation, extraction, and filling of the borders during seg-

entation, changing the threshold values of two-dimensionalegions on the imported stack of images, modified until theyhowed a satisfactory mask. This ScanIP® file is sequentiallyonverted into a mesh in ScanFE® (Fig. 2).

.3. Reconstruction for the 3D-FE model generation

he reconstruction available in NRecon® is inappropriate forE analysis. This is normally used for checking volumes foropological studies. To create a 3D-FE model from the stepescribed before, the ScanIP® file with all segmented masks

was imported into ScanFE® reconstruction software (Simple-ware), generating a mesh of the entire image volume usingtriangulated 2D shell-elements (STL-stereolithography file),which is meshed model with information in the form requiredto generate it from its underlying image and mask data. Eachmask created in ScanIP® is reproduced and displayed in thesame colour within the meshed volume as a separate part inScanFE®. The reconstruction runs in few minutes, dependingon the number of slices and masks. The STL files had a totalof 485,726 nodes and 974,464 elements, which are too largeand for use in FEA obtaining the geometry and for processinganalysis [10,35] because of their aspect ratio and connectivityof the triangles. So these files were then imported into Patran®

(MSC Software, USA) and the elements were then re-meshed toreduce mesh density, maintaining the tooth shape. From thesenew shell elements, surfaces were created (Fig. 3) and exportedto another FE software (Hypermesh®, Altair Hyperworks, USA).

2.4. Cavity design and volumetric mesh

The first step using Hypermesh® was the re-establishmentof the congruency of the dentin–enamel junction, which waslost during the previously re-meshing process. Once congru-ency was achieved, tooth cavities using ‘cutting planes’ werethen developed (Fig. 4a). Using the same software, 3D solidscorresponded to enamel, dentin and pulp were also created(Fig. 4b).

The final mesh of this model consisted of four-node iso-parametric tetrahedral elements (Tet4), with a mean edgelength of 0.20 mm. The number of nodal points was limitedto 37,985 associated with 201,506 elements. Finally, the vol-

e50 d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) e47–e55

Fig. 2 – (A) Examples of segmentation steps: manual unpaint and automatic painting and interpolating using Scan IP®,are,

Simpleware, UK. (B) Reconstruction using Scan FE®, Simplew

umetric mesh (four-node isoparametric tetrahedral elements)was created and the model was imported back in Patran® soft-ware to apply the boundary-conditions, material-propertiesand initiate FE processing (using Patran® and Marc®, MSC soft-ware). Tooth dimensions measured by using a digital caliperwere checked with the model ones.

2.5. Boundary-conditions, material-properties andanalysis

To demonstrate the use of the resulting model, this wasapplied to the particular case of a Class I restoration sub-

jected to distributed loading (Fig. 5). All nodes on the lowersurface of the tooth were constrained in all directions (X,Y and Z), preventing rigid body displacement, in agreementwith previous studies [5,9,17,36,37]. Thus it was assumed that

Fig. 3 – FE remeshed model and surfaces generated. (Left) The w(A), enamel (B), dentin (C) and pulp (D).

UK.

the overall stress distribution in the coronal portion was onlymarginally affected by the root area, under the simulatedboundary-conditions [17,38]. At all interfaces, the nodes wereshared.

The occlusal distributed loading was simulated accordingto precedents from the literature [3,29,39]. A uniform loadingwas applied at a pressure (stress) of 10.48 MPa, correspondingto 890 N distributed over 84.9 mm2 molar occlusal face area[37]. The component materials were all considered homoge-neous, linear, elastic and isotropic [34] and their propertiesare presented in Table 1. The material colours for each group(enamel, dentin, pulp and composite) were arbitrarily selected

from the FE software.

The analysis was performed as linear and structural. Theoutputs of maximum principal (MP) and maximum shear (MS)stresses were then evaluated.

hole tooth remeshed. (Right) Surfaces of the whole tooth

d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) e47–e55 e51

Fig. 4 – (a) Tooth cavities generation using ‘cutting planes’ and (b) 3D solids corresponded to enamel, dentin and pulp.

F dition ns (X

3

Aetcr(

ig. 5 – Class I restoration and corresponding boundary-conodes on the bottom surface were constrained in all directio

. Results

3D model of a mandibular molar was processed without gen-rating errors in the FE package used. The single real molar

ooth selected clearly determined the shape and geometri-al dimensions of the model tooth, also allowing variations,epresenting model cavity preparation. Dimensions checkedlength and diameter) from FE model were very close to those

Table 1 – Elastic properties of the materials.

Material Elastic modulus (GPa)

Enamel 80.0Dentin 15.0Pulp 0.002Resin–composite 25.0

ns. The model was subjected to distributed loading and all, Y and Z).

measured by using a digital calliper, presented the geome-try of the tooth very well. The maximum deviation betweenthe intact tooth and the corresponding model was less than0.1%.

Characteristics stress patterns in the tooth under occlusal

force were observed. From FEM investigation on the stressesgenerated by uniform loading of this tooth model, it wasevident that the stress-patterns generated in the compos-ite material and tooth tissues were truly 3D (followed all 3D

Poisson’s ratios Reference

0.30 Rees and Jacobsen (1995) [12]0.31 Ausiello et al. (2002) [3]0.45 Barink et al. (2003) [5]0.30 Ausiello et al. (2001) [29]

e52 d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) e47–e55

ss at

Fig. 6 – Maximum principal stress and maximum shear stre

contours of the model), which suggested the potential of themodel for being versatile (Fig. 6), which can be used for sim-ulating any structural loading (such as occlusal loading andshrinkage).

Stress concentrations were found at the surface where theload was applied and in the vicinity of the tooth–compositeinterface, especially at the deepest and sharpest regions of

the occlusal face. Stress concentration at the dentin–enameljunction (DEJ) was also identified. Convex areas raised lessconcentrated stresses than concave areas around enamel(cavosurface angle).

molar Class I cavity interface and onto the composite.

4. Discussion

It is widely recognized that FEM has proven itself asan extremely powerful tool in addressing a wide rangeof biomedical problems, mainly when complex geome-tries are involved [19]. Software has been developed to

assist in the generation of FE models for attending thecomplexity and spatial relationship of objects and/or tis-sues representation. One of the possibilities is the use ofsome sophisticated techniques as �-XCT scanning associated

2 5

ws

utetnttl[pcC(up[Ttt

btsctegscft

oc�

iaprcFeto

pftwXdb�

d

[o

d e n t a l m a t e r i a l s

ith intermediate software before performing FE analy-is.

Conventional scanners and profile projectors have beensed to generate 3D-models for biomedical researches relatedo bone behavior, but they still required much manual work orven resulted in coarser meshes [18,40]. Prior studies in den-istry, aiming to achieve a model from image processing, haveoticed the importance of stress distributions in a normalooth and the effect of different cavity designs all on the sameooth. Some 3D-models have been prepared from contourine teeth [41], duplicate casts [42], and dental plaster models29], with different cavity designs, which were sectioned andhotographed [42], laser scanned, digitized using a charge-oupled device camera attached to a stereomicroscope [26] orT scanned. The detailed contours of the areas of interesting

mainly enamel, dentin and pulp chamber) were not directlysed to create a 3D-image, but traced onto millimeter-gradedapers [42] or obtained with a graphics software program

25] with lines added to simulate different tooth preparations.hese were then digitized with a scanning device and the rela-

ive relationships of the serial longitudinal or parallel sectionso the occlusal or proximal faces were established.

Micro-XCT was developed in 1980s for in vitro studies ofone structures [28]. By obtaining 2D slices and interpolatinghe 2D information into a 3D model, this visualizes and mea-ures complete 3D structures without sample preparation orhemical fixation [43]. The first study in 2001 to apply thisechnique to restored teeth, developed a 3D tooth-map andxported this to FE software for stress analysis [18]. When theenerated images were directly used, the coordinate system totack the contours was identical to that of the scanning pro-ess and the cross-sections were automatically fixed, whichacilitated few errors in the 3D mesh in comparison with otherechniques.

�-XCT software is straightforward to use, but experiencedperator and good judgment will be the main key for the suc-ess of the study. There are some artifacts and noise from-XCT data, which can be corrected by filtering when the

mages are reconstructed [35]. During reconstruction, which isnon-linear operation, any noise in the small signal areas canroduce significant errors [43]. Hence the software incorpo-ates tools to eliminate noise. Exposure times affect the imageontrasting and can also influence dimensional results. WithEM software, the difficulties are directly related to the experi-nce and knowledge of the operator and the specific problemo be solved. In developing an FE model, some specific trainingr expert collaboration is required.

The validity of a FE model refers to the possibility of it torocess with efficiency, fastness and coherence all answersront to mechanical loadings, which consequently makes ito represent adequately the stress and strain patterns bothithin the materials and their interfaces. The use of the �-CT also helps generate a detailed model [18]. However, CTata must be interpreted carefully because the accuracy coulde influenced by the image threshold value [44]. Nevertheless,-CT has sufficient accuracy to evaluate crown adaptation and

efects in crown restorations [20].

�-XCT is contributing to many non-invasive studies18,24,28] but the literature is sparse on 3D-FE constructionf models and the difficulties of this process. Most software

( 2 0 0 9 ) e47–e55 e53

has the same tools but their interfaces vary considerably inease of use. The main advantages of using �-XCT in dentistryare:

• Relative ease of using equipment and software. Sophis-ticated visualization tools (shades, wireframe 3Dviews,section views, etc.) and different filters, highlighting porosi-ties and defects on the materials, interfaces failures, etc.

• Rapid and non-destructive method [35,45]. No requirementfor staining of the object—which can affect the organizationof the investigated structure.

• Superior resolution compared to existing digital dental sys-tems [28]. The maximum deviation between the original CTimage and reconstructed surface solids can be less than0.6% [19,46]; but this also depends on several factors, suchas artifacts, beam hardening, exposure time, instrumentmodel, etc.

• 3D-reconstruction from root canals [47], crowns and othersamples where the shape is more important than 3D-FEmodel generation [20]; the surface areas or volumes of den-tal tissues can also be obtained.

• Quantitative and visual measurements for biomaterials(metals, ceramics, and polymers), including bio-histologicalmaterials [20]; also in vitro caries research [28].

In the present study, sequential software processing of �-XCT dental-images to optimize 3D-FE analysis was performed.The model was an exact replica of a second molar tooth bythe combined used of �-XCT and numerical analysis soft-ware, generating a valid 3D-FE model with the possibility ofany cavity preparation, boundary-conditions and material-properties. To demonstrate the use of the resulting model,this was applied to the particular case of a Class I restora-tion subjected to distributed loading and the stress patternwas analyzed.

The findings corroborated [10] the advantages of using‘STL’ files as a standard format for data transmition fromCAD to systems such as the rapid prototyping [24] and finiteelement packages [10,17,19,46,48], because of their uncompli-cated procedure, with minimal manual intervention. However,to achieve congruency between these different tissues, metic-ulous work is still required [10].

Since teeth have many structural details or ‘defects’,including fissures, cuspal anatomy variations, enamel anoma-lies, it is not realistic to incorporate too many of such details ina model, which would lose its generality. In the present proce-dure, definition and biological tissue could be lost if the stepsof importing-exporting, segmentation, and meshing proce-dures were not done with caution.

During 2D and/or 3D mesh generation, the presence ofsharp regions makes adaptation of the elements difficult. Thesoftware tries to deform the elements to fit the geometry.This is the rationale for using triangulated and tetrahedralelements instead of quadrilateral ones for meshing complexshape structures. Depending on the geometry, they may notbe meshed because of a generated error. Thus, usually during

segmentation and meshing procedures, if some areas irrele-vant to the study present a non-definite shape, which does notallow meshing, these areas can be automatically or manuallysmoothed, if possible. Thus, it is at the step of segmentation,

l s 2

r

e54 d e n t a l m a t e r i a

when it is best to decide what is really important to simulatein terms of dental anatomy.

For reasons of computational efficiency, the anatomicdetail of the dentin–enamel junction (DEJ), well captured viathe CT reconstruction, was reduced to create a smoother junc-tion, in accordance with other studies [19]. The definition ofjunctions in CT-images, such as the DEJ, must be accurate. Alljunctions, between two different materials or even surfaces orsolids, sometimes need to be reconstructed ‘manually’. Whenthe smoothing tools are insufficient for a good result, it is ben-eficial to work with pixel precision, not just with thresholdtools. As dental tissues are not isotropic and homogeneous,threshold automatic tools can be non-sufficient to define someareas as DEJ, making them not uniform or well-smooth. In thiscase, some manual work is required to guarantee the fidelityof the model in this area.

The development of this 3D-FE model was part of ongoingresearch into stress states of bonded restorations subjectedto polymerization shrinkage and/or occlusal loading. In thisstudy, only the occlusal distributed loading was simulated.FE models predict a variety of parameters [20]; some of themare connected with stress patterns within the structure butdoes not predict failure [18] unless modeling the initiation andpropagation of cracks themselves [19]. The present results areconsistent with prior studies using 3D-FE models which usedFEM as a powerful tool for generating [10,11,18] and analyzingthe mechanical behavior of complex structures [29].

When the loading was applied, stress effects were revealedat the cavosurface angle and DEJ. Examination of the stresscontours highlighted regions of particular interest. The stressconcentrating effect of corners is an established issue andareas of high stress were generally expected in these regions.

Geometry acquisition and 3D modeling based on �-XCTdata can still be considered at a pioneering stage [11,45,48].Using this technique to obtain realistic 3D-FE models of teethand cavity preparations, further investigations are in progressto evaluate different isthmus widths and the thickness ofresidual inter-axial dentin on teeth with various cavity designsand modes of loading. A possible limitation of this approachmay be the range of chemical elements that can be investi-gated, since their absorption edge must be within the X-rayenergy range of the beam line [45]. Moreover, the sequence ofsoftware used was found workable by the authors, who do notsuggest that this is the only feasible approach to this problem.

5. Conclusion

The purpose of the current study was to describe sequen-tial software processing of �-XCT molar-images for optimized3D-FE tooth/restoration model geometries based on of molarteeth, giving attention on each step of processing data. Thedescribed procedure is a successful method able to pro-duce a highly detailed 3D finite element model of restoredmolar teeth with any cavity configuration and combination

of restorative materials and this method can also be usedfor other biological or biomaterials applications. The studydevelops further understanding of this new technology whichassociates �-XCT data and FEM.

5 ( 2 0 0 9 ) e47–e55

Acknowledgements

Based in part on abstract no. 106894, presented at the 86thIADR meeting in Toronto, July 4, 2008. The authors acknowl-edge Dr. Alex S. Fok for his support in the use of Scan IPand Scan FE packages, in the School of Mechanical, Aerospaceand Civil Engineering, The University of Manchester, Manch-ester, United Kingdom. This study was supported in part byFAPESP (Fundacão de Amparo à Pesquisa do Estado de SãoPaulo, Brazil), process no. 6/00186-3.

e f e r e n c e s

[1] Hubsch P, Middleton J, Knox J. The influence of cavity shapeon the stresses in composite dental restorations: a finiteelement study. Comput Methods Biomech Biomed Eng2002;5:343–9.

[2] Asmussen E, Munksgaard EC. Bonding of restorative resinsto dentine: status of dentine adhesives and impact on cavitydesign and filling techniques. Int Dent J 1988;38:97–104.

[3] Ausiello P, Apicella A, Davidson CL. Effect of adhesive layerproperties on stress distribution in compositerestorations—a 3D finite element analysis. Dent Mater2002;18:295–303.

[4] Ausiello P, Davidson CL, Cascone P, DeGee AJ, Rengo S.Debonding of adhesively restored deep Class II MODrestorations after functional loading. Am J Dent1999;12:84–8.

[5] Barink M, Van der Mark PC, Fennis WM, Kuijs RH, KreulenCM, Verdonschot N. A three-dimensional finite elementmodel of the polymerization process in dental restorations.Biomaterials 2003;24:1427–35.

[6] Couegnat G, Fok SL, Cooper JE, Qualtrough AJ. Structuraloptimization of dental restorations using the principle ofadaptive growth. Dent Mater 2006;22:3–12.

[7] de Trey E, Lutz F. Effect of the shape of the cavity and thesealant system on the adaptive quality of the proximalanterior filling margins. SSO Schweiz MonatsschrZahnheilkd 1977;87:737–51.

[8] Feilzer AJ, De Gee AJ, Davidson CL. Setting stress incomposite resin in relation to configuration of therestoration. J Dent Res 1987;66:1636–9.

[9] Hubsch PF, Middleton J, Knox J. A finite element analysis ofthe stress at the restoration–tooth interface, comparinginlays and bulk fillings. Biomaterials 2000;21:1015–9.

[10] Magne P. Efficient 3D finite element analysis of dentalrestorative procedures using micro-CT data. Dent Mater2007;23:539–48.

[11] Magne P, Tan DT. Incisor compliance following operativeprocedures: a rapid 3D finite element analysis usingmicro-CT data. J Adhes Dent 2008;10:49–56.

[12] Rees JS, Jacobsen PH. The effect of interfacial failure arounda class V composite restoration analysed by the finiteelement method. J Oral Rehabil 2000;27:111–6.

[13] Borkowski K, Kotousov A, Kahler B. Effect of materialproperties of composite restoration on the strength of therestoration–dentine interface due to polymerizationshrinkage, thermal and occlusal loading. Med Eng Phys

2007;29:671–6.

[14] Kahler B, Kotousov A, Borkowski K. Effect of materialproperties on stresses at the restoration–dentin interface ofcomposite restorations during polymerization. Dent Mater2006;22:942–7.

2 5

analysis. J Endod 2007;33:727–31.

d e n t a l m a t e r i a l s

[15] Kahler B, Kotousov A, Melkoumian N. On material choiceand fracture susceptibility of restored teeth: an asymptoticstress analysis approach. Dent Mater 2006;22:1109–14.

[16] Kahler B, Kotousov A, Swain MV. On the design of dentalresin-based composites: a micromechanical approach. ActaBiomater 2008;4:165–72.

[17] Magne P, Belser UC. Rationalization of shape and relatedstress distribution in posterior teeth: a finite element studyusing nonlinear contact analysis. Int J Periodont Restor Dent2002;22:425–33.

[18] Verdonschot N, Fennis WM, Kuijs RH, Stolk J, Kreulen CM,Creugers NH. Generation of 3D finite element models ofrestored human teeth using micro-CT techniques. Int JProsthodont 2001;14:310–5.

[19] Ichim I, Li Q, Loughran J, Swain MV, Kieser J. Restoration ofnon-carious cervical lesions. Part I. Modelling of restorativefracture. Dent Mater 2007;23:1553–61.

[20] Wakabayashi N, Ona M, Suzuki T, Igarashi Y. Nonlinear finiteelement analyses: advances and challenges in dentalapplications. J Dent 2008;36:463–71.

[21] Fennis WM, Kuijs RH, Barink M, Kreulen CM, Verdonschot N,Creugers NH. Can internal stresses explain the fractureresistance of cusp-replacing composite restorations? Eur JOral Sci 2005;113:443–8.

[22] Shi L, Fok AS, Qualtrough A. A two-stage shape optimizationprocess for cavity preparation. Dent Mater 2008.

[23] Farah JW, Craig RG, Sikarskie DL. Photoelastic and finiteelement stress analysis of a restored axisymmetric firstmolar. J Biomech 1973;6:511–20.

[24] Shimizu Y, Usui K, Araki K, Kurosaki N, Takanobu H,Takanashi A. Study of finite element modeling from CTimages. Dent Mater J 2005;24:447–55.

[25] Magne P, Douglas WH. Design optimization and evolution ofbonded ceramics for the anterior dentition: a finite-elementanalysis. Quintessence Int 1999;30:661–72.

[26] Magne P, Douglas WH. Interdental design of porcelainveneers in the presence of composite fillings: finite elementanalysis of composite shrinkage and thermal stresses. Int JProsthodont 2000;13:117–24.

[27] Cattaneo PM, Dalstra M, Melsen B. The finite elementmethod: a tool to study orthodontic tooth movement. J DentRes 2005;84:428–33.

[28] Clementino-Luedemann TN, Kunzelmann KH. Mineralconcentration of natural human teeth by a commercialmicro-CT. Dent Mater J 2006;25:113–9.

[29] Ausiello P, Apicella A, Davidson CL, Rengo S. 3D-finiteelement analyses of cusp movements in a human upperpremolar, restored with adhesive resin-based composites. JBiomech 2001;34:1269–77.

[30] Katona TR, Winkler MM, Huang J. Stress analysis of abulk-filled class-V chemical-cured dental composite

restoration. J Biomed Mater Res 1996;31:445–9.

[31] Kinomoto Y, Torii M, Takeshige F, Ebisu S. Polymerizationcontraction stress of resin composite restorations in amodel class I cavity configuration using photoelasticanalysis. J Esthet Dent 2000;12:309–19.

( 2 0 0 9 ) e47–e55 e55

[32] Versluis A, Douglas WH, Cross M, Sakaguchi RL. Does anincremental filling technique reduce polymerizationshrinkage stresses? J Dent Res 1996;75:871–8.

[33] Versluis A, Tantbirojn D, Douglas WH. Distribution oftransient properties during polymerization of alight-initiated restorative composite. Dent Mater2004;20:543–53.

[34] Versluis A, Tantbirojn D, Pintado MR, DeLong R, DouglasWH. Residual shrinkage stress distributions in molars aftercomposite restoration. Dent Mater 2004;20:554–64.

[35] Kato A, Ohno N. Construction of three-dimensional toothmodel by micro-computed tomography and application fordata sharing. Clin Oral Invest 2008.

[36] Ausiello P, Rengo S, Davidson CL, Watts DC. Stressdistributions in adhesively cemented ceramic andresin–composite class II inlay restorations: a 3D-FEA study.Dent Mater 2004;20:862–72.

[37] Arola D, Galles LA, Sarubin MF. A comparison of themechanical behavior of posterior teeth with amalgam andcomposite MOD restorations. J Dent 2001;29:63–73.

[38] Goel VK, Khera SC, Ralston JL, Chang KH. Stresses at thedentinoenamel junction of human teeth—a finite elementinvestigation. J Prosthet Dent 1991;66:451–9.

[39] Anusavice KJ. Phillips: dental materials. 11th ed. Elsevier;2005. p. 800.

[40] Akagawa Y, Sato Y, Teixeira ER, Shindoi N, Wadamoto M. Amimic osseointegrated implant model for three-dimensionalfinite element analysis. J Oral Rehabil 2003;30:41–5.

[41] Kubota K, Natori M, Sasaki K. Three-dimensionalmeasurement study of the maximum protuberance andcervical line of the upper molars. J Nihon Univ Sch Dent1994;36:58–66.

[42] Khera SC, Goel VK, Chen RCS, Gurusami SA. AThree-dimensional finite element model. Oper Dent1988;13:128–37.

[43] SkyScan. SkyScan 1072-Desktop X-raymicrotomograph-instruction manual; 1998–2001. p. 61.

[44] Kakaboura A, Rahiotis C, Watts D, Silikas N, Eliades G.3D-marginal adaptation versus setting shrinkage inlight-cured microhybrid resin composites. Dent Mater2007;23:272–8.

[45] De Santis R, Mollica F, Prisco D, Rengo S, Ambrosio L,Nicolais L. A 3D analysis of mechanically stresseddentin–adhesive–composite interfaces using X-raymicro-CT. Biomaterials 2005;26:257–70.

[46] Ichim IP, Schmidlin PR, Li Q, Kieser JA, Swain MV. Restorationof non-carious cervical lesions. Part II. Restorative materialselection to minimise fracture. Dent Mater 2007;23:1562–9.

[47] Cheng R, Zhou XD, Liu Z, Hu T. Development of a finiteelement analysis model with curved canal and stress

[48] Li J, Li H, Shi L, Fok AS, Ucer C, Devlin H, et al. Amathematical model for simulating the bone remodelingprocess under mechanical stimulus. Dent Mater2007;23:1073–8.