Three-dimensional finite element modelling of all-ceramicrestorations based on micro-CT

Alvaro Della Bona a,*, Marcia Borba a, Paula Benetti a, Yuanyuan Duan b, Jason A. Griggs b

aUniversity of Passo Fundo, Post-graduate Program in Dentistry, Passo Fundo, RS, BrazilbDepartment of Biomedical Materials Science, University of Mississippi Medical Center, Jackson, MS, USA

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9

a r t i c l e i n f o

Article history:

Received 20 November 2012

Received in revised form

26 February 2013

Accepted 27 February 2013

Keywords:

Finite element analysis

Zirconia

Non-destructive testing

X-ray microtomography

a b s t r a c t

Objectives: To describe and apply a method of modelling dental crowns and three-unit fixed

partial dentures (FPD) for finite element analyses (FEA) from 3D images obtained using a

micro-CT scanner.

Methods: A crown and a three-unit fixed partial denture (FPD) made of a ceramic framework

(Y-TZP) and veneered with porcelain (VM9) were scanned using an X-ray micro-CT scanner

with a pixel size of 6.97 mm. Slice images from both structures were generated at each

0.034 mm and processed by an interactive image control system (Mimics). Different masks

of abutments, framework and veneer were extracted using thresholding and region growing

tools based on X-ray image brightness and contrast. 3D objects of each model were

incorporated into non-manifold assembly and meshed simultaneously. Volume meshes

were exported to the FEA software (ABAQUS), and the load-generated stress distribution was

analyzed.

Results: FEA models showed great shape resemblance with the structures. The use of non-

manifold assembly ensured matching surfaces and coinciding nodes between different

structural parts. For the crown model, tensile stresses were concentrated in the internal

surface of the core, near to the applied load. For the FPD model, the highest tensile stresses

were located in the framework, on the cervical area of connectors and pontic.

Conclusions: Valid 3D models of dental crown and FPD can be generated by combining micro-

CT scanning and Mimics software, emphasizing its importance as design tool in dental

research.

Clinical significance: The 3D FEA method described in this work is an important tool to predict

the stress distribution, assisting on structural design of dental restorations.

# 2013 Elsevier Ltd.

Available online at www.sciencedirect.com

journal homepage: www.intl.elsevierhealth.com/journals/jden

Open access under the Elsevier OA license.

1. Introduction

The clinical behaviour of restorative materials can be

estimated using in vitro and in vivo tests. Randomized clinical

trials can provide reliable information on the prognosis of

* Corresponding author at: Post-graduate Program in Dentistry, Dental

Fundo, RS, Brazil. Tel.: +55 54 3316 8395.E-mail address: dbona@upf.br (A. Della Bona).

0300-5712 # 2013 Elsevier Ltd.

http://dx.doi.org/10.1016/j.jdent.2013.02.014Open access under the Elsevier OA license.

prosthetic restorations. However, time is necessary to collect

data, the cost is high and a large number of volunteers is

required to obtain adequate statistical power.1,2 Thus, labora-

tory simulations are important tools to obtain fast and

standardized results.2 Although simplified specimens, such

as disks and micro-bars, used in these in vitro tests are useful

School, University of Passo Fundo, Campus I, BR285, km 171, Passo

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9 413

to determine materials strength and to predict local stresses

that could lead to clinical failure, they tend to underestimate

the influence of the restoration geometry in the stress

distribution.3,4

When specimens that simulate the shape of crowns and

fixed partial dentures (FPDs) are used, the mechanical

behaviour may be closer to the clinical situation, but the

evaluation of the stress distribution within complex geome-

tries is limited.5–7 This situation can be overcome using finite

element analysis (FEA), which is a fast and a relatively low cost

method used to investigate stress distribution and strain

patterns of complex structures, such as dental restorations.8

FEA can be used for two different purposes: (1) to understand

the failure behaviour of complex structures, or (2) to optimize

the experiments through the mathematical simulation and

selection of the best design to perform the test.9

The basic steps involved in this method are pre-processing,

solving and post-processing.10 The pre-processing stage

consists of geometric modelling of a structure, discrimination

of a model into smaller elements connected by nodes using

the proper selection of an element type and assigning the

material properties. The final step in pre-processing is the

application of external forces, pressure, thermal changes, or

other factors; and displacement constraints at specified

nodes.11 The computer software solves a set of simultaneous

equations with thousands of variables to achieve the desired

results. The post-processing stage consists on the graphical

presentation of results, including qualitative and numerical

results.

Pre-processing is a critical step, especially when anatomi-

cal shapes and layered structures are required. This stage is

usually time-consuming and is prone to errors due to

limitations of the geometry acquisition methods (i.e. manual

tracing of tooth sections, digitization of a plaster model).12,13

To overcome limits of computational power or difficulties

associated with complex geometry many studies simplified

the calculations using 3D models with coarse meshes14;

axisymmetric geometries15,16 or 2D models,17–19 which can

simulate the stress state at clinical failure. However, simplified

geometries could induce false predictions when inadvertently

applied.20,21 Thus, sophisticated techniques have been devel-

oped, in which an optimization of the model design is

performed from micro-computed tomography (micro-CT).22

Micro-CT is a non-destructive technology that allows

image acquisition with high spatial resolution.9,23 Therefore,

small objects such as teeth, dental implants, dental crowns

and FPDs could be accurately reproduced.5,12,24 The differ-

ences in the linear attenuation coefficient among the

materials that constitute the scanned structure are responsi-

ble for X-ray image contrast, which allows the identification of

the different layers.23,25 Important information on the internal

geometric properties and structural parameters of the speci-

men can be obtained. Thus, it is possible to generate models

with refined geometries, minimizing errors in the FEA and

reducing the risk of false predictions.9,12,22

Although previous studies reported the development of

valid and complex 3D element models using micro-

CT,5,12,13,21,22,26 there is still a lack of information related to

the modelling process of prosthetic restorations using this

methodology. Therefore, the objective of this study was to

describe the sequential software processing used to obtain a

three-dimensional finite element model of all-ceramic crowns

and FPD based on images provided by micro-CT scanning,

simulating the stress distribution of the restorations under

load.

2. Materials and methods

2.1. Micro-CT scanning

Scanning was performed using a SkyScan 1172 micro-CT

scanner with a 10 megapixel camera (Skyscan, Aartselaar,

Belgium). To produce the single-unit model, a monolithic

porcelain crown and a framework from a left upper first molar

crown were scanned. To produce the FPD model two parts

were scanned separately: (1) a stainless steel die simulating

prepared teeth and (2) a three-unit all-ceramic FPD (9 mm2

connector cross-section). Both crown and FPD were made by

an yttria partially stabilized zirconia-based (Y-TZP) ceramic

framework (Vita In-Ceram YZ, Vita Zahnfabrik, Germany) and

a feldspathic porcelain (Vita VM9, Vita Zahnfabrik, Germany).

The scanning parameters were: accelerating voltage of

100 kV, current of 100 mA, exposure time of 2950 ms per frame,

Al + Cu filter, and rotation step at 0.48 (1808 rotation). For the

metal dies, the X-ray beam was irradiated perpendicularly to

the preparation long axis and, for the dental restorations, the

beam was parallel to their long axis. The image pixel size was

6.97 mm. The X-ray projections were reconstructed to form a

3D model, which was saved as a stack of bmp-type files using

NRecon software (Skyscan, Aartselaar, Belgium). Beam hard-

ening correction of 80% and ring artefact correction of 7 were

used for the reconstruction.

2.2. Mesh generation

Tomography images of the structures were generated at each

0.034 mm and processed by an interactive medical image

control system (Mimics 13.0, Materialize, Belgium). Mimics

system imports all CT data in a wide variety of formats and

displays the objects in three views. The software presents

segmentation functions based on image density thresholds.12

2.2.1. Dental crownMasks of the framework and the veneer were obtained using

thresholding and region growing tools based on the image

value. The 3D object representing the zirconia framework was

subtracted from the monolithic porcelain crown object to

obtain a perfectly fitted veneer part. The mask of the master

die was created using Boolean operations by adding two

different masks: the internal space of the crown (cavity fill

tool) and a cylinder drawn at the bottom surface (Fig. 1).

2.2.2. Fixed partial dentureThe micro-CT files corresponding to the metal dies and the

FPD were processed separately to reduce the amount of

manual work necessary to built three different masks with

Mimics software. A mask of the dies was obtained though

brightness and contrast adjustment, and a 3D object was

produced and converted into a STL file. For the FPD,

Fig. 1 – Cross-section images of masks from different perspectives (A–C). 3D objects were created to represent the framework

(D), the veneer (E) and the die (F).

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9414

segmentation based on image density thresholding of differ-

ent value scale intensity levels was used to generate two

masks, corresponding to the framework and the veneering

layer. 3D objects were obtained for the framework and the

veneer. The metal dies STL file was imported to the FPD file

(Fig. 2A–C), making for a three-part final file: metal dies,

framework and veneer (Fig. 2D–F).

The masks of each part of the models were separately

converted into STL files (stereolithography, bilinear and

interplane interpolation algorithm), which are improper for

FEA because of the amount and shape of the triangles. Thus,

for both models (crown and FPD), the files of different parts

Fig. 2 – Cross-section images of dies, framework and veneer m

representing: (D) metal dies; (E) framework and (F) veneer.

were incorporated into non-manifold assembly in Mimics, and

edited simultaneously. The parts were remeshed with a

maximum geometrical error of 0.05%, maintaining the original

geometry. Wrapping and smoothing operations were used to

remove undesired sharp edges. The mesh quality was defined

by controlling triangle edge length, the ratio between height

and base of the triangles and removing sharp triangles using a

triangle filter, so that the file could be imported into the FEA

software without generating errors. Subsequently, the objects

were separated according to the original parts and volumetric

meshes were generated and imported by the FEA software

(ABAQUS V6.8, Simulia, USA).

asks from different perspectives (A–C) and 3D objects

Fig. 3 – Stress distribution in the core: top (A) and bottom (B)

images.

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9 415

2.3. Materials properties, boundary conditions, andanalysis

2.3.1. Dental crown

The final model was composed by tetrahedral elements

(compatible with 3D modelling) and three layers: (1) epoxy

resin die, with elastic/plastic behaviour similar to dentine; (2)

zirconia core (Y-TZP) and (3) porcelain layer (VM9).

The bottom surface nodes of abutment meshes were

constrained (no displacement) in the three spatial dimensions.

Interfaces between meshes were considered perfectly bonded

in Constraint Manager. An axial compressive load of 100 N was

uniformly applied in 10 nodes (10 N each) of a 2-mm diameter

area of the palatal cusp, simulating the opposing tooth contact

in a wear facet.

2.3.2. Fixed partial dentureThe final FPD model was composed of tetrahedral elements

and three layers: (1) metal dies (stainless steel); (2) ceramic

framework (Y-TZP) and (3) porcelain layer (VM9). Two

interfaces were created, between the metal dies and the

framework and between the framework and the porcelain

layer. The cement layer was neglected.

Nodes in the bottom surface of the dies were fixed in all

directions; no rotation or translation was allowed. A compres-

sive load, perpendicular to the restoration long axis, was

applied in the centre of the occlusal surface of the pontic. A

load of 200 N was distributed uniformly over 20 nodes located

in a circular area with 3 mm diameter.

The following considerations were made to facilitate the

FEA analyses: (1) the materials were considered to be isotropic

and homogeneous and to have a linear elastic behaviour; (2)

the effects of the periodontal ligament and pulp chamber were

not considered; (3) elastic modulus (E); and Poisson’s ratio (v)

were maintained constant. The values of the material

properties used to perform the analysis are presented in

Table 1.16,27,28

The stress distributions from the linear finite element

analyses were evaluated according to the location and

magnitude of the maximum first principal stress.

2.3.3. Verification of models accuracyPre-determined points were chosen and used as reference to

measure the dimension of the physical crown and FPD and the

dimension of the FEA models. A digital calliper was used to

measure the structures. The dimensions of the FEA models

were computed using the measuring tool of Mimics software.

The difference between the dimension of the physical

structure and the FEA model at the pre-determined points

were calculated to obtain the maximum dimensional error (%).

Table 1 – Materials properties attributed to the models.

Material E (GPa) n

Yttrium-partially stabilized zirconia-based

ceramic (Y-TZP)31

209 0.32

Feldspathic veneering ceramic (Vita VM9)31 67 0.21

Epoxy resin32 14.9 0.31

Stainless steel13 190 0.27

3. Results

The 3D model showed great physical resemblance with the

structure of the crown and FPD. Comparative measurements

revealed that the dimensional error of this micro-CT based

FEA modelling did not exceed 1.64%. The use of non-manifold

assembly ensured matching surfaces and coinciding nodes

between different parts.

For the crown model, tensile stresses were concentrated

mainly at the intaglio (cementation) surface of the core, in the

area directly opposed to the load site (Fig. 3), and in the

external surface of the veneer, near to the loading area (Fig. 4).

Stress distribution in the crown can be observed in Figs. 3 and

4.

For the FPD, the highest tensile stresses were located in the

cervical area of connectors and pontic within the framework

layer. Tensile stresses of lower magnitude were also found in

the margins of the copings and in the occlusal surface of the

connectors (Fig. 5). Similar stress distribution was observed

within the porcelain layer (Fig. 6).

4. Discussion

FEA represents a powerful tool to understand the mechanical

behaviour of all-ceramic crowns and FPDs and to optimize the

design of future tests.9 However, the analysis may be limited

by difficulties related to model generation.13 To overcome this

problem, the present study described a modelling technique,

combining micro-CT images and interactive medical image

control software, which resulted in valid 3D FEA models.

Fig. 4 – Stress distribution in the veneer: top (A) and bottom

(B) images.

Fig. 5 – Stress distribution in the FPD framework: lateral (A), cervical (B) and occlusal (C) images.

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9416

The micro-CT scanner was developed in the 1980s for

laboratory purposes on small samples and material experi-

ments and emerged as a potential key tool in dental research.

Many advantages are related to this technology: (1) relative

ease of using equipment and software; (2) fast and non-

destructive method9,26; (3) high resolution23; (4) 3D recon-

struction of complex structures (i.e. bone, root canal, dental

Fig. 6 – Stress distribution in the FPD porcelai

restorations); and (5) quantitative and visual measurements

for biomaterials.11,22–24 On the other hand, it is important to

emphasize that the micro-CT technique is sensitive to the

experience and knowledge of the operator. Individual param-

eters related to the scanning process (i.e. exposure time, filter,

rotation) and to the image reconstruction (i.e. beam hardening

and ring artefact) can influence dimensional results and

n layer: lateral (A) and cervical (B) images.

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9 417

produce significant errors.22,26,29 Despite the fact that some

systems are capable of reading micro-CT data and converting

them to a finite element model, many programs have limited

tools to select and edit the parts of interest. The Mimics

software was used as an interface between the micro-CT

scanning and the FEA software (ABAQUS) to fulfil the

requirements for creating accurate and highly detailed FE

models.30

It is worth mentioning that comparisons of the magnitude

of tensile stresses obtained for the crown model with the FPD

simulation were avoided because the stress state of cemented

restorations is known to be influenced by (1) restorations

design and processing; (2) ceramic thickness ratio; (3) elastic

modulus of the abutment material; and (4) cement thick-

ness.4,31–35 Different abutment materials for the crown and

FPD simulations were used for didactic purposes, simply

demonstrating the particularities on images obtainment from

scanning different materials. In addition, differences among

boundary conditions for both simulations are justified by the

fact that this research is part of a larger project that involves

mechanical testing of crowns and FPDs and the FEA design

corresponded to the physical test. However, the aim of the

present manuscript was solely to describe the technique used

to produce the FEA models.

The clinical failure of ceramic crowns was reported to

initiate from flaws and cracks existent at the cementation

(intaglio) surface directly opposed to the wear facets.4,32,36–38

Therefore, this area of the crown was expected to present

concentration of tensile stresses, which were observed in the

FEA results. Both clinical observations and FEA results suggest

that the stress state of the crown is determined by the

compressive loads applied to the occlusal surface, which

cause bending of the crown, producing tensile stresses at its

interface with the abutment. Thus, damage to the cementa-

tion surface, such as the damage produced by burs or

sandblasting, should be avoid. Tensile stresses were also

observed at the near-loading area in the veneer surface of the

crown, which is in agreement with data previous reported in

literature.8,39 However, clinical observations provided strong

evidence that catastrophic failures are unlikely to initiate from

the occlusal surface, thus tensile stress in this area does not

seem to be as critical for fracture development as the stresses

at the intaglio surface.4,32,36–38

Recent clinical investigations on all-ceramic restorations

reported higher number of bulk fractures (core and porcelain)

for alumina-based frameworks than for zirconia, which

presented a significant amount of veneer fractures (cracking,

chipping and delaminations) during a three-year follow-up

time.40,41 Several reasons have been reported in relation to the

origin of ceramic veneer fractures, which include restoration

design,42,43 ceramic–ceramic bonding conditions,44 loading

components,43 materials mechanical and thermal behaviour,

specifically residual stresses originated from the mismatch on

materials properties during the restoration processing.45

For FPDs, clinical investigations19,46 and FEA suggested that

the highest tensile stresses were located in the connectors’

cervical area.15,17,19,47 These results are in agreement with the

stress distribution observed in the present study for the FPD

model. Kelly et al.19 performed a fractographic analysis of all-

ceramic FPDs that failed in vivo and in vitro and observed that

in 70–78% the fracture initiated at the framework–veneer

interface, in the connector cervical area. Another study

investigated the fracture behaviour of all-ceramic zirconia-

based FPDs that failed clinically46; and the authors also

reported, for most cases, that the flaw origin was located on

the cervical area of the connectors, and, for one case, the flaw

origin was located at the margin of the crown. This finding is

also in agreement with the present FEA investigation, in which

tensile stresses were also observed at the crown margin.

It is important to notice that, in the present study, high

tensile stress concentration was not only located on the FPD’s

connectors but also in the cervical area of the pontic. These

results are related to the boundary conditions, not to the FE

model. The FPD geometry and the fact that the load was

applied in the centre of the pontic induced a stress distribution

similar to a three-point bending bar, in which a non-uniform

stress distribution is created. Thus, the maximum tensile

stress was located on the lower surface directly below the

applied load.19 A similar behaviour was observed in the

present study. The fact that the abutments were rigid in the

simulation also influenced the stress distribution. If rotation

and translation of the abutments were allowed, maximum

tensile stresses would, probably, be within the connector, in

the interface between porcelain and framework.19

Fischer et al.15 used FEA to evaluate the stress distribution of

all-ceramic FPDs produced with different framework materials

and connector cross-section dimensions. The authors observed

similar stress distribution among the framework materials.

Rotation of the model in the y-axis was allowed to simulate the

fisiologic movement of the teeth. Thus, the maximum principal

stress was located at the cervical area of the connectors and it

was possible to observe an increase of the tensile stress

concentration with the decrease of the connector size. As high

tensile stress concentration is located at the FPD’s connectors,

the restoration should be design with an appropriate connector

size and shape.48

To extrapolate the results observed with FEA to the clinical

situation it is important to consider the degree of reality in the

model and its validity, which refers to the accuracy of the

model to represent adequately the stress patterns within the

structures.5 Considering the degree of reality of the simula-

tion, it is important to emphasize that the FEA models

presented a few simplifications when compared with the

clinical situation: (1) materials were considered homogeneous,

isotropic and with a linear elastic behaviour; (2) the influence

of the cement layer was neglected; (3) the effect of periodontal

ligament was not considered; and (4) residual stresses induced

by the materials thermal mismatch were not considered.

Besides these factors, the flaws that were present in the

materials and the interface were not considered in the

simulation.

On the other hand, as the stress distribution observed for

the crown and the FPD was consistent with the results

reported in clinical studies, which demonstrated failure

originating from the cementation surface for the crowns

and from the connectors and pontic area for the FPD, the two

models produced in this study should be considered valid. It is

also true that there are no simple analytical solutions for

analyzing the stress distributions in specimens with complex

geometries.

j o u r n a l o f d e n t i s t r y 4 1 ( 2 0 1 3 ) 4 1 2 – 4 1 9418

5. Conclusion

Anatomically accurate three-dimensional finite element

models of a dental crown and 3-unit FPD can be generated

by combining micro-CT scanning and Mimics software

interactive tools.

Tensile stresses were observed in the crown at the near-

load area of the veneer and at the internal surface of the core.

In addition, for the applied load, the highest tensile stress

concentration in the FPD was located in the framework

material, on the cervical area of the connectors and pontic.

Conflict of interest

The authors declared that there is no conflict of interest.

Acknowledgements

The authors acknowledge theBrazilian Agencies FAPESP (2008/

58775-0), CAPES and CNPq (302364/2009-9) for the financial

support of the present research.

This investigation was also supported in part by research

grants DE013358 and DE017991 from the NIH-NIDCR.

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