S t r e s s e s at the d e n t i n o e n a m e l junction of h u m a n t e e t h - - A finite e l e m e n t i n v e s t i g a t i o n V i j a y K. G o e l , P h D , a S a t i s h C. K h e r a , B D S , D D S , M S , b J e f f r e y L. R a l s t o n , B S , c a n d K u a n g H. C h a n g , M S d

Colleges of Engineering and Dentistry, University of Iowa, Iowa City, Iowa A t h r e e - d i m e n s i o n a l , linear, elastic finite e l e m e n t m o d e l of a m a x i l l a r y first p r e m o l a r from longitudinal ground sections w a s d e v e l o p e d to i n v e s t i g a t e s t r e s s v a r i a t i o n in the e n a m e l and dentin adjacent to the d e n t i n o e n a m e l junction (DEJ). The effect of r e g i o n a l v a r i a t i o n in the contour o f the D E J on the s t r e s s patterns for e n a m e l and dentin w a s also analyzed. The n o r m a l ( c o m p r e s s i v e or tensile) and shear s t r e s s e s in the dentin and e n a m e l s u r f a c e s o f the D E J w e r e c o m p u t e d for a vertical load of 170 N acting on the entire o c c l u s a l surface of the model. The n o r m a l s t r e s s e s in dentin and e n a m e l w e r e m a x i m u m on the o c c l u s a l surface o f the m o d e l and d i m i n i s h e d along the buccal and l i n g u a l s u r f a c e s of the DEJ. H o w e v e r , the m a g n i t u d e of the n o r m a l s t r e s s e s i n c r e a s e d at the c e r v i c a l enamel, w h i c h also s h o w e d i n c r e a s e d v a l u e s for s h e a r s t r e s s distribution. The n o r m a l and s h e a r s t r e s s e s w e r e m a r k e d l y affected by the contour of the D E J and the t h i c k n e s s of e n a m e l in the occlusal third on the buccal and lingual surfaces. The results s u g g e s t e d that b e c a u s e the m e c h a n i c a l i n t e r l o c k i n g b e t w e e n e n a m e l and dentin in the c e r v i c a l region is w e a k e r than in other regions o f the DEJ, e n a m e l in this region m a y be s u s c e p t i b l e to b e l a t e d c r a c k i n g that could e v e n t u a l l y contribute to the d e v e l o p m e n t of c e r v i c a l caries. (J PROSTHET DENT 1991;66:451-9.)

D e n t i n accounts for the greatest bulk of the three calcified tissues in human teeth. It is also one of the major hard tissues in the body, second only to dental enamel in hardness. Dentin assists in the transmission of masticatory loads from the enamel on the occlusal surface to the root and indirectly to the periodontal complex. Any deterioration in the integrity of this tissue can alter this protective mechanism and contribute to clinical problems. For example, the excessive removal of dentin during cavity preparation compromises the adjacent enamel, which then can fracture without suitable restorative support. Cavity preparations with an excessively broad isthmus often contribute to fracture of the remaining tooth, 16 and endodontically treated teeth become brittle because of the loss of moisture 7 and nutrients to dentin and the dentinoenamel junction (DE J). The structural loss of enamel and dentin weakens the tooth, and reduction of nutrients can alter the biologic bond between the enamel and dentin.

Supported in part by a grant from the Graduate College of the University of Iowa and the Department of Operative Dentistry, College of Dentistry of the University of Iowa. aProfessor and Chairman, Department of Biomedical Engineering, College of Engineering. bprofessor, Department of Operative Dentistry. cPresently, Second year student, College of Medicine, University of Iowa. dpresently PhD student, Graduate College and Department of Mechanical Engineering, University of Iowa. 10/1/29079

THE JOURNALOF PROSTHETICDENTISTRY

There are documented differences in measurements of enamel and dentin for posterior teeth. A recent study reported substantial morphologic differences in functional and nonfunctional cusps, s These observations essentially confirmed that the thickness of enamel and dentin varied greatly in various areas and that the DEJ contour of the functional cusps was dramatically different from that of the nonfunctional cusps. This contour was concave in the occlusal third of the DEJ in the functional cusps of all teeth except the maxillary premolars that were concave in the nonfunctional buccal cusps. These cusps in the maxillary premolars were also the only nonfunctional cusps that were larger buccolingually than the functional cusps. Cervical lesions are also observed clinically on the buccal surface of posterior teeth? and the lesions could be carious or abrasion. The carious lesions develop as a result of a bacterial process, whereas abrasion lesions are generally attributed to mechanical action of prolonged toothbrushing, although stress has been associated with these lesions. 1°'12 Is there a relationship between the presence of these lesions and the unique characteristics of the DEJ and the thickness of enamel and dentin? This study used a three-dimensional finite element model to investigate the normal (tensile or compressive) and shear stresses in enamel and dentin along the DEJ that could be influenced by the contour of the DEJ. The study also compared changes in the stresses in a maxillary premolar by artificially altering the contour of the DEJ.

45].

G O E L E T AL

6B

M

I

-/° !i Ii

[I

\

?

V

d

/

S

L Fig. 1. Occlusal surface of premolar and approximate locations of planes for serial sectioning. Locations of sections No. 6 and 9 are identified by arrows. B, Buccal; D, distal; L, lingual; M, mesial.

MATERIALS

AND METHODS

A three-dimensional (3-D) mesh of an intact "normal" human maxillary first premolar was prepared by use of a technique described earlier. 13"15 Development of tooth model. A freshly extracted intact maxillary first premolar was embedded in epoxy resin at a specific orientation, and the outer surfaces of the resin block were machined into a cube. The cube was ground serially to expose tooth-resin sections perpendicular to the occlusal surface (Fig. 1). The amount of embedded tooth structure removed between sections varied from 0.1 to 0.5 mm and was precisely determined with a micrometer. Each ground section was photographed with the camera placed at a fixed distance and with its axis perpendicular to the section. A millimeter scale was placed adjacent to the section for recording the magnification. The photograph of a typical section, with the millimeter scale is shown in Fig. 2. The tracings from these photographs were digitized (Fig. 3) and these data from the serial sections were used to develop the a 3-D model. The present model differed from previous 3-D models prepared from digitized data of sections parallel to the occlusal surface. 15 The longitudinal sections in

452

Fig. 2. Section No. 9 with millimeter scale shows DEJ contour on buccal (left) and lingual surfaces.

Section Six

Section Nine

Fig. 3. Data from photographs of sections 6 and 9 after digitization for model. DEJ contour is identified by heavier line.

OCTOBER 1991

VOLUME 66

NUMBER 4

S T R E S S E S AT D E J OF H U M A N T E E T H

an

Section Six

Section Nine

Fig. 4. Digitized sections 6 and 9 for "artificial" model. Note DEJ contour in area of elements No. 5 and 5' as compared with contour in Fig. 3.

this study precisely focused on the demarcation of the DEJ (Fig. 2). The tooth model consisted of 14 longitudinal sections from mesial to distal surfaces. Section 4 was the first section to exhibit the total DEJ bucco-occluso-lingually. The elements along the DEJ were numbered from 1 through 19 for convenience (Figs. 3 and 4). Elements numbered 1 through 5 were on the buccal surface of the tooth, 6 through 12 on the occlusal surface, and 13 through 19 on the lingual surface. Elements with the same number in different sections were approximately in the same location in all sections. In sections without element numbers I and 19, enamel did not extend as far cervically. Linear, eight-nodal, isoparametric brick elements were used for the three-dimensional finite element model. A total of 491 elements, 229 for enamel and 262 for dentin, and 771 nodes were designated to develop the model. The periodontal ligament and alveolar bone surrounding the tooth were excluded in this model. Earlier studies demonstrated that the effect of periodontal tissues on the stresses in the tooth were negligible above the cervicoenamel junction (CEJ)} 3 The isotropic material properties (Young's modulus and Poisson's ratio) assigned to the enamel and dentin were based on literature designating 8.5 X 10 4 N/ram 2 and 0.33 for enamel and 1.98 x 10 4 N/mm 2 and 0.31 for dentin respectively 16 and were identical to earlier studies.13-15,17

The artificial tooth model. A slight alteration was made in the contour of the DEJ of the actual model in Fig. 3 to compare the effects of the contour of the DEJ or the

THE J O U R N A L OF P R O S T H E T I C D E N T I S T R Y

Fig. 5. Directions of planes along which normal (a,) and shear (s) stress were examined along DEJ.

thickness of enamel in the occlusal third of the buccal and lingual surfaces. The modification incorporated in the artificial model was to transform the properties of element 5 ~ from enamel to dentin (Fig. 4).

Loading of the models and parameters of stress analysis. A vertical load of 170 N was evenly distributed on the entire occlusal surface and appropriate nodes in the root region (Figs. 2 and 3) were secured to prevent rigid body motion of the model. The 170 N load was determined from the current literature establishing the normal chewing force as a third of the maximum biting force. 15 The stresses (Fig. 5) in dentin and enamel elements along the DEJ were computed with a finite element package, ANSYS (Swanson Analysis Inc., Huston, Pa.). The absolute value of the shear stress (s) only and the normal stress (~,) were recorded at the surface centroids of the dentin and enamel elements addressing each other along the DEJ. The finite element technique provides an approximate evaluation of stresses within these tissues, and this is especially true for the magnitude of shear stresses reported. A precise quantification of normal and shear stresses along the DEJ is arduous. One of the advantages of the finite element

453

O.

5

G O E L E T AL

151

15

Enamel a.

=E 10

10

, ~ , Enamel

(/) U,I nI=.

nl-

n-

rr < "r

Dentin

-r

Dentin

//P

I

I

!

I

I

•

'~ a.

I

I

|

I

I

I

I

|

|

I

I

I

Oent,n

-5

IE

Q. ,,.,.,

-5t J

// Enamel

(n u,i nJ