3d finite element model and cervical lesion formation in

8/9/2019 3D Finite Element Model and Cervical Lesion Formation In

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tooth structure. When mastication is not ideal, lateral

forces appear which cause the tooth to bend. This

produces larger tensile stresses acting on the CEJ,

causing disruption of the bonds between the hydroxy-

apatite crystals and leading to separation of the enamel

from the dentine (1). Although many investigators

(1719) have supported this theory, only a few biome-

chanical studies have demonstrated the role of tooth

flexure in the development of abfraction lesions (20

23). Previous finite element (18) and strain-gauge

studies (19) have found that stresses concentrated in

the thin cervical enamel area, and the magnitude of

these stresses exceeded the known failure stresses for

enamel. Improved computer and modelling techniques

render the finite element method (FEM) a very reliable

and accurate approach in biomechanical applications.

The aim of this study was to develop a FEM of the

first maxillary premolar in order to compare the stressprofiles in the buccal and palatal cervical regions. The

premolar was chosen because a previous study con-

firmed that every third premolar was affected by some

form of NCCL (3), and a two-rooted tooth was never

used as model for studying an NCCL. This study used a

3D FEM to investigate stress distribution and compare

the changes in the stresses in normal occlusion and in

malocclusion. The hypothesis in this study was that

there were no differences in the stress profiles between

the tooth in normal occlusion and in malocclusion.

Materials and methods

An intact human maxillary first premolar was first

embedded in red epoxy resin using a previously

prepared cube-shaped mould (Palavit G)*. The edges

of the casting resin defined the global orientation of the

specimen. The tooth was sectioned perpendicular to the

long axis, in 13 mm intervals by a precise saw with

water cooling system (ISOMETTM 1000 Precision Saw).

Advancing to cross-sectioning, fixed point has been

marked at the bottom of fixating device. The point has

been kept visible at all photographs and served as areference in the x- and y-coordinate system (in-plane

coordinate system). Besides, z-coordinate has been

determined knowing the distance between each cross-

section (13 mm), and their sequence. Each of the

20 sections was digitally photographed (Fujifilm, Fine-

Pix S1 Pro). The 3D geometry of the tooth was

reconstructed from these cross-sections by using the

computer program AutoCAD Mechanical Desktop

(v. 40). CAD software was used to create new curves

based on the contours of cross-sectional morphologies.

Knowing the distance of each thus created entity from

the reference point, the curves produced were used in

lofting of finally reconstructed surfaces that defined

each morphological entity (dentine, enamel, periodon-

tal ligament and bone tissue). When constructing the

aforementioned curves, it was of particular importance

to take care of the starting point of each curve. The line

joining these points had to be as straight as possible in

order to avoid twisting of the reconstructed surface.

The outline of the periodontal ligament 03 mm

wide, and the surrounding alveolar bone was generated

using the outline of the tooth as a guide. The dimen-

sions of the periodontal ligament and surrounding bonewere derived from the literature (24, 25). The solid

model was transferred into a FEM program NASTRAN

(v. 2002); a 3D mesh was created, and the stress

distribution analysis was performed. Boundary condi-

tions have been established on surrounding bone. It has

been estimated that if sufficient amount of bone

material were modelled around the tooth, boundary

conditions applied far enough from force application

point would not significantly influence the stress

distribution in different part of the tooth. Therefore,

the bone is clamped (all displacements fixed), thus

preventing rigid body displacements in directions of all

three coordinate axes. Furthermore, this corresponds to

physical conditions, where the displacement of the rest

of the structure is negligible. Besides, it was necessary

to restrict the motion of tooth in a direction normal to

the neighbouring teeth. This has been implemented in

the model through appropriate boundary conditions

(prevented displacement in the direction of normal to

the joint contact surface). In the analysis, it has been

judged that it is not required to model the contact with

neighbouring teeth by applying specialized contact

elements. Contact modelling would unnecessary in-crease the complexity of the model without signifi-

cantly influencing the final results, as the scope of the

research is not the detailed modelling of contact area

itself.

*Heraus Kulzer GmbH, Wehrheim, Germany.Buehler Ltd, Lake Bluff, IL, USA.

Fuji Photo Film Co. Ltd, Tokyo, Japan.AutoDesk Inc., San Rafael, CA, USA.MSC Software Corporation, Santa Ana, CA, USA.

3 D F E M A N D C E R V I C A L L E S I O N F O R M A T I O N 505

2005 Blackwell Publishing Ltd, Journal of Oral Rehabilitation 32; 504510


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Four-nodded tetrahedral elements were applied in

the discretization of the tooth morphology, resulting in

1 684, 512 elements and 246, 510 nodes with 739,

530 degrees of freedom. The mechanical properties of

the enamel, dentine, bone and periodontal ligaments

are shown in Table 1. The materials of the various

tooth structures were assumed to be isotropic, homo-

geneous and elastic, as they remained under applied

loads. In case I (normal occlusion), the three forces

were applied on the occlusal surface. The forces were

acted at the palatinal incline of the buccal cusp, at the

buccal incline of the palatal cusp, and at the palatinal

incline of the palatinal cusp (Fig. 1a). In case II

(malocclusion) the force was applied at the buccal

incline of the palatal cusp (Fig. 1b). During the

analysis, the model of the tooth was loaded with a

total force of 200 N, which is assumed to be a normal

chewing load. The chewing forces produced by mas-

tication are reported to range from approximately

37 to 40% of the maximum bite force (26). The load

vectors were applied in the direction normal to the

surface in order to simulate the contact with antag-

onistic teeth. To estimate the stress field in the models,

maximum and minimum principal stress (r1 and r2)

were analysed. The sign of principal stress with

maximal absolute value was instrumental in defining

the tensile or compressive nature of loading at eachelement to be examined.

Results

Figures 2 and 3 show differences in the stress distri-

bution between the two models under different

loading conditions. Two typical cases have been

considered: the tooth under normal occlusion and

the tooth under malocclusion. The results are presen-

ted as maximum and minimum principal stresses.

Positive and negative values indicate that the corres-

ponding regions are subjected to tensile or compres-

sive stresses, respectively. A detailed description of the

stress distribution was based on two sections. One was

Table 1. Physical properties of the materials used in the study

Material

Youngs

modulus (GPa)

Poissons

ratio Reference

Enamel 80 03 Rees et al. (4)

Dentine 186 031 Eskitascioglu et al. (37)

Pulp 00021 0

45 Lin et al. (38)

Periodontal

ligament

00689 045 Eskitascioglu et al. (37)

Bone tissue 12 03 Eskitascioglu et al. (37)

Fig. 1. Contact points at the occlusal surface. Case I (normal

occlusion) (a), case II (malocclusion) (b).

Fig. 2. Stress distribution in the

tooth with normal occlusion (case I).

Arrows show places and directions of

the force application. Minimum

principal stresses in longitudinal

midline section (a). Minimum prin-

cipal stresses in horizontal plane at

the cemento-enamel junction (CEJ)

(b). Maximum principal stresses in

longitudinal midline section (c).

Maximum principal stresses in hori-

zontal plane at the CEJ (d).

J . B O R C I C et al.506



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longitudinal midline section and the other was hori-zontal plane at the CEJ (Figs 2 and 3). In case I, larger

compressive stresses were found inside the enamel at

the area where the force was applied and in the

cervical enamel and dentine. Tensile stresses were

found in the fissure system and in the adjacent area

of the enamel, and at the vestibular surface of the

buccal cusp. In case II, larger compressive stresses

were also found inside the enamel at the target area,

and in the palato-cervical enamel and dentine. Tensile

stresses were found inside the enamel in the fissure

system and in the adjacent area as well as at the

vestibular surface of the buccal cusp, and in the

bucco-cervical enamel.

Table 2 shows the values of the maximum and

minimum principal stress values in the cervical regions

for case I and II. In case I, the peak values for the

principal stress ranged from )259 to +225 MPa in the

cervical areas. Case II shows signification variation in

stress values. This case was selected because it vaguely

resembles traumatic load. In this case, results show

increase in stress values to be reaching compressive

stress of 501

947 MPa in palatal region and tensile stressof 824 MPa in buccal region. The reason for this is the

prominent bending of the tooth.

It is apparent from the above results that the response

of the structure is different if asymmetrical loading is

considered. Under the same loading, the deformation

caused by tensile stresses, was observed at the cervical

region on the opposite side of the loading point. The

tooth in malocclusion (case II) shows significant weak-

ening in the continuity of the structure of the hard

dental tissues, and this causes the increase of the

stresses in the cervical region.

Discussion

This study predicted dramatic variations in the com-

pressive and tensile stress values in the enamel and

dentine at the cervical area in two different models.

This area has a weak mechanical bond between enamel

and dentine because of the lack of a scalloping pattern

of CEJ. In theory, any occlusal contact that can

generate tensile stress at the cervical area has a

Table 2. The peak principal stressvalues of the cervical regions for

various load conditions

Case I Case II

Maximum

principal

stress (MPa)

Minimum

principal

stress (MPa)

Maximum

principal

stress (MPa)

Minimum

principal

stress (MPa)

Bucco-cervical

region

+2248 )111478 +824 )0658

Palato-cervical

region

)15411 )259085 )30636 )501947

Fig. 3. Stress distribution in thetooth in malocclusion (case II).

Arrow show place and direction of

the force application. Minimum pri-

ncipal stresses in longitudinal mid-

line section (a). Minimum principal

stresses in horizontal plane at the

cemento-enamel junction (CEJ) (b).

Maximum principal stresses in lon-

gitudinal midline section (c). Maxi-

mum principal stresses in horizontal

plane at the CEJ (d).




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possibility to create a cervical lesion. When lateral loads

were applied, tensile stresses generated on the cervical

areas were higher than when vertical loads were

applied at the same areas (20). The malocclusion with

heavy lateral occlusal force generated much higher

tensile stress on the tooth, which may have caused a

higher prevalence of cervical lesions. The increase in

the load did not cause a change in the overall stress

pattern but increased the values. The loading to which

the tooth was subjected may have caused cracks in the

tooth, but not necessarily its immediate failure. It is

notable that the large tensile stress was concentrated at

the cervical region on the buccal side in the model

where occlusion was not ideal. The oblique force

loaded on the palatal cusp produced distortion of the

tooth and caused enamel at the cervical region to

stretch. Various studies (1, 20, 27, 28) have shown that

a lateral force causes bending of the tooth and thattensile stress acting on the tooth brings out the

disruption of chemical bonds between the enamel

crystals. This chipped enamel can accelerate the devel-

opment of caries when dentine is exposed to the oral

cavity environment. It can also be mechanically abra-

ded by brushing into V-shaped notches as suggested by

some authors (27). Dentine exposed by cracked enamel

can also lead to increased sensitivity. Other areas along

the DEJ are presumably not as severely affected

because of stronger mechanical bonds between enamel

and dentine. Klahn et al. (29) confirmed by the

photoelastic method that an oblique force loaded on

the tooth causes stress concentration at the cervical

line. Darendeliler et al. (30) showed that the shear

stresses both of which were smaller than the maximum

compressive-yield stresses, generated fracture of the

tooth. The results of the present study are in agreement

with those observations. When the tooth is compres-

sively loaded, displacements do not appear to be

significant because of the rather large compressive

yield strength. It is apparent from above results that

during normal mastication, where forces are loaded on

the occlusal surface almost vertically and evenly, thecompressive stress appeared in the enamel in the

cervical region. The situation is different if the asym-

metrical loading is considered, when the tensile stress

occurs at the side opposite of the loading point. In the

present study, large tensile stress appeared on the

enamel surface near the cervical line at the side

opposite the loading point. Lee et al. (20) and Lee and

Eakle (27) argued that a lateral occlusal force produced

compressive stress on the side towards which the tooth

bent, and tensile stress on the opposite side. Spears et al.

(31) showed that a vertical force loaded at one tip of

the lingual cusp of the mandibular second premolar

produces tensile stress at the lingual enamel on the

cervical region. Tanaka et al. (1) demonstrated that an

occlusal force loaded on the lingual tip of the premolar

produces the tensile strain at the cervical region on the

buccal side, which leads to plastic deformation of the

enamel surface.

A few studies (32, 33) confirmed that NCCLs

occurred in elderly people more frequently in the

cervical areas of mandibular functional cusps and

maxillary nonfunctional cusps. These observations

suggest that the pattern, character, and magnitude of

stresses caused by masticatory loads are associated with

the development of cervical carious and abrasion

lesions as contributing factors. Perhaps the influenceof these factors becomes evident over a long period of

time, and thus the development of these lesions is

observed more frequently in the elderly (21). Clinical

studies have found that abfraction lesions are rarely

found palatally (34). It is possible that erosive dietary

acids could work in tandem with cervical stresses

generated by occlusal loads. Combination of acidic

substances, tooth brushing, and stresses can cause more

damage than any of these acting alone (35). Fluids

containing naturally occurring erosive agents are

cleared from palatal sites six times more quickly than

from buccal and labial sites because of the influence of

salivary flow (36).

To obtain better understanding of the cervical

lesions, which is obviously important for the clinical

treatment and restoration of damage, analyses of

stress distribution in the teeth under various loading

conditions are highly desirable. So far in the literature

available, there has been no detailed investigation of

stress distribution in a premolar with two roots. This

study implies a role of occlusal forces in noncarious

lesions. The occlusal force leaning against the tooth

axis causes the tooth to bend, and higher tensilestresses are produced on the cervical region. If oblique

force loading on teeth is the major cause of cervical

lesions, further attention should be paid to the

importance of the occlusal adjustment for the treat-

ment of cervical tooth defects.

The results of this study must be interpreted with a

certain amount of caution. Only bone tissue has been

modelled and most of the researches modelled enamel




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as isotropic and not orthotropic. The FEM model

represented a static situation at the moment of load

application and not an actual clinical situation.

Assumptions related to material properties of simulated

structures (such as isotropy, homogeneity, and linear

elasticity) are not usually absolute representations of

the structure. In reality, the loading of the structure is

more dynamic and cyclic. However, this study provides

a biomechanical explanation for the clinical variation

seen in the presentation of NCCLs.

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Correspondence: Josipa Borcic, MSc, DDS, Vere Bratonje 23, 51 000

Rijeka, Croatia.

E-mail: [email protected]



3d finite element model and cervical lesion formation in

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