avity
depth
on stresses
in a restored
t
Vijay K. Gael, PhD,a Satish C. Khera, BDS, DDS, MS,b Senthil Gurusami, MS,” and Robert C. S. Chen, DDS, MSd University of Iowa, Colleges of Engineering and Dentistry, Iowa City, Iowa Restorative procedures commonly replace lost tooth structure, but redistribution of functional stresses after treatment is not fully understood. Many restorative methods are dictated by the integrity of the remaining tooth structure, because sparse tooth structure can lead to fracture. It is essential to prevent fractures by having a clear concept of the designs for cavity preparations, and to anticipate the stresses of mastication on the remaining tooth structure. Knowledge of various internal parameters of cavity designs would facilitate selection of the appropriate cavity preparation for a specific clinical situation. Three cavity designs and restorations were examined in this study for stresses using the finite element technique. After placement of restorative materials, the dentin experienced a dramatic change in stress gradient immediately below the pulpal wall, and this response was magnified in deeper cavity preparations. Enamel also exhibited major alterations in the stress gradient in all three designs of cavity preparations. The combination of the changes can cause cracks in the remaining tooth structure, leading to cusp fracture immediately adjacent to the deepest portion of the cavity. (J PROSTHET DENT 174-83.)
estorative dental procedures are necessary to ensure tooth function, relieve dental pain, and prevent pulpal pathology. The clinical procedure involves preparing a cavity of appropriate dimensions with respect to isthmus width and pulpal depth. However, in class II mesial, occlusal, and distal (MOD) cavity preparations, gingival depth and the thickness of dentin between mesial and distal axial walls are also important criteria during cavity preparati0n.l The dimensions are dictated primarily by the extent of carious lesion or trauma, and the prepared cavity is then restored with the appropriate restorative material such as cast gold, amalgam, composite resin, or porcelain. The major considerations after restoring the tooth are the health of the remaining tooth structure, its function, and the potential for fracture. Numerous studies2-12 have confirmed a correlation between cuspal fractures of the restored teeth, tooth morphology, and allied cavity parameters. Nadalll recommended cavity preparations with a narrow occlusal outline and a shallow pulpal floor to reduce failure. Blaser et a1.12 investigated the fracture potential of prepared teeth and
This investigation was supported by funds from the Graduate College and the Weeg Computing Center at the University of Iowa. “Professor and Chairman, Department of Biomedical Engineering, College of Engineering. bProfessor, Department of Operative Dentistry, College of Dentistry. CBiomedical Engineer, Engineering Department, Ford Motor Co., Dearborn, Mich. dGraduate student, Department of Oral Biology, University of Michigan, School of Dentistry, Ann Arbor, Mich. IO/A/29658
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the internal dimensions of the MOD cavity preparation, and discovered that the width of the isthmi of MOD cavity preparations did not substantially weaken the teeth if the pulpal depth was shallow. However, the damage to the remaining tooth structure was dramatically increased if the pulpal depth was increased and the cavity width remained narrow. Khera et al? reported similar conclusions regarding the depth of the cavity preparation, after an analyses of stresses on the remaining tooth structure using the finite element technique. The stress distribution in a normal tooth was compared with tooth models of different cavity preparations. In a normal tooth, the stresses were predominantly compressive in response to an axial compressive load, but in the model with a wide and deep cavity preparation, tensile stresses were recorded at the pulpal wail. These, combined with heavy compressive stresses in the immediately adjacent area, can cause greater damage to the remaining tooth structure compared with a normal tooth or a tooth with a narrow and shallow cavity preparation. This change in the type of stresses, from compression to tension, is responsible for an increased fracture potential of a tooth with wide and deep cavity preparations. The experimental studies have also demonstrated that these dimensions of a cavity preparation, usually necessitated by large carious lesions, diminish the fracture resistance of the prepared tooth.1°-12 These studies were commonly performed on extracted teeth without standardization of the size, age, biochemical, or morphologic differences between samples or variations in the thickness or the contour of the remaining enamel and dentin. This study was conducted to review the effects of dimensional variables and to address the following: (1) Do the dimensions of the cavity preparation that alter the stress distribution within a prepared tooth also
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(B) Constant
Parameters
MD:IT::l
(C) Variable
Parameters
D-O.70 PD:GD:
9.703.0
D-O.85 PD:GD: rO.&:l .O
D-1.0 PD:GD:
:l .03 .0
Fig. 1. Various tooth landmarks and cavity preparation rameters between three cavity designs (B) and variable
change the stresses in a restored tooth? (2) What are the clinical implications resulting from stress changes associated with these variables? The main objective was to investigate a restored tooth by examining the stress distribution resulting from the size of the cavity preparation. This study specifically examined the effect of cavity depth on the stress distribution in a restored tooth. The finite element technique was used because the conventional experimental techniques were incapable of an in-depth analysis of stress distribution within a complex, asymmetric, and irregular three-dimensional structure such as the tooth.
IAL
AND
METHODS
A three-dimensional finite element model of a mandibular second premolar was developed. The data for the model with cavity designs were grouped into three categories: (1) generation of the three-dimensional geometry of the intact tooth and a tooth with various cavity designs; (2) properties of the dental tissues and the restorative mate-
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in this study (A). Constant parameters (C).
pa-
rial; and (3) magnitude, distribution, and direction of the chewing force. The technique of the three-dimensional finite element models based on the geometrical data from an actual tooth was reported ear1ier.i One mandible, with normal tooth morphology, shape of the alveolar crest, and the alignment of dentition, was selected from IO human mandibles. The mandible was sectioned vertically so that it extended from the mesial surface of the first premolar to the distal surface of the third molar. Duplicates of the specimen were made with Die Keen (Columbus Dental, St. Louis, MO.) die cast material. Different cavity designs of explicit dimensions were prepared on the duplicates to evaluate class II MOD cavity preparations of three different internal parameters. Each cavity preparation had an isthmus width (IW)-to-intercuspal width (CW) ratio of 0.25, and the thickness of the remaining dentin and the mesiodistal (MD) dimension of the tooth was 0.5 (Fig. 1). These constant parameters were sustained. The ratio of the pulpal depth to gingival depth (PD/GD) was the only variable between the three designs.
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GQEL
ET AL
Enamel = section
6-7
Section 7-6
Fig. 2. Digitization of serial sections to prepare three-dimensional with different cavity designs.
I. Material properties assigned to dental tissues and restorative material in this study
Table
Tissue/ restorative material
Enamel Dentin Periodontal ligament Alveolar bone Restorative material (type I gold alloy)
Young’s modulus E(N/mm2)
8.4 x 104* 2.0 x 104* 1750* 3.4 x 103 7.7 x 1047
Poisson’s ratio
0.33* 0.31* 0.45* 0.33* 0.33$
E, Young’s modulus of elasticity; N, Newton. *Atmaram GH, Mohammed H. Estimation of physiological stresses in a natural tooth considering fibrous PDL structure. J Dent Res 1981;60:873-7. KI’Brien WJ, Ryge G. An outline of dental materials. 1st ed. Philadelphia: WB Saunders Co: 1978:402. $Farah JW, Craig RG. Distribution of stresses in porcelain-fused-to-metal and porcelain jacket crowns. J Dent Res 1975;54:255-61.
Pulpal depth wasdetermined by measuringfrom the buccal cusp tip to the pulpal wall, while gingival depth was measuredfrom the buccal cusptip to gingival wall (Fig. 1). This ratio for design 1 (D.70) was 0.7; for design 2 (D.85) it was0.85; and for design3 (D1.O) it was 1 where both the pulpal and the gingival wall were at the samelevel (Fig. 1). The original specimenand the three duplicates were embedded in an epoxy resin block in a known orientation. All of the six facesof the block were ground to ensureorthog176
model of normal tooth
onality. A global Cartesian coordinate system was established on the resin block. Serial photographs of the horizontal ground sectionswere obtained using a photographic technique at approximately 0.5 mm intervals and were then recorded. The tracings of the morphologic geometry, the contour, and the thicknessof the enameland dentin wereobtained from thesephotographs.The tracings were then divided into rectangles of appropriate sizesso that the geometry of each section was duplicated (Fig. 2). Eight nodal linear isoparametricelementswere formed by correspondingnodesof the adjacent section. In this manner three-dimensionalfinite element (FE) modelsof a normal unpreparedmandibular secondpremolar and the same tooth with three cavity designswere formulated. The prepared cavities in the FE modelswere restored with a type I gold alloy. The physical properties of the dental tissues and the properties of the restorative material for this model are presentedin Table I. A uniform axial masticatory force of 170 N wasdistributed on the entire occlusalsurface of the model for this study. This procedure wasselectedto compare our method with that of earlier studiesand to confirm that the depth of cavity preparation altered stresseswithin the prepared tooth and that it had a similar effect on the completed restoration. Three boundaries were imposed for three models of a normal tooth: “crown,” “root,” and “bone + lig.” In the
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z-coordinate section # 5.098
1
5.047 --N--m_-
3.274 3.152
---=+m+------2
\
I I \
/
3.033 2.915 2.655
Fig. 3. Locations
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\/
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“crown” model, the tooth geometry modeled was to the cervical section (section no. 13, Fig. 3) and the nodes were fixed in all directions. The complete tooth was modeled in the “root” model, and the nodes in contact with the periodontal ligament (sections 14 to 23, Fig. 3) were fixed. The entire tooth, periodontal ligament, and the surrounding alveolar bone were included in the “bone + lig” model. The outermost nodes of sections 14 to 25 (Fig. 3) of the alveolar bone region were also fixed. The number of elements and nodes used for the three normal tooth models are presented in Table II. The execution times and the expense for the three-dimensional finite element models increase phenomenally as the number of elements and the nodes are raised. Therefore the execution costs were controlled without sacrificing the accuracy by restricting these numbers, such as by choosing one of the three models. Since the region above the cervical section is critical in
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sections and Z coordinates. this study, the disparity of the stresses between the three models was compared. No significant difference in stresses was recorded for the “root” and “bone + lig” models.13 The stress results for the normal and restored tooth models were from the “root” finite element models. The ANSYS finite element package (Swanson Analysis Systems, Inc., Huston, Pa.) was used for this study.
RESULTS The stress distribution in the normal tooth has been described in earlier reports,14-16 so sample data for the three normal tooth models are included to justify using the “root” model for analyzing stresses: D.70 (PDIGD = 0.70); D.85 (PD/GD = 0.85); and D1.O (PD/GD = 1.0). The applied load was compressive, but both the compressive stress and the tensile stress were included in the analysis. The predicted stresses in various models were compared in two steps. First, the stress distribution in elements of various
177
GOEL
Tensile 5-6
’
8-9
1
I
-15
-10
I
0
-5
Section
Numbers 1
ET AL
Stresses
(A)
Enamel
Legend: I 5
0 CROWN MODEL A ROOT MODEL + BONE f LIG. MODEL
I 10
Dentin
1
10
NEWTONS/mm2 Fig. 4. Comparisonof stresspatterns in normal tooth (buccolingual direction) shownby “crown,” “root,” and “bone + lig.” models.
Table
II. Breakdown of number of elementsand nodesused in configuration of three finite element models of a normal
tooth No. of elements Model
Crown Root Bone
+
lig
Enamel
Dentin
176 176 176
205 546 546
tooth sections cut by a specific horizontal (buccolingual) section was studied. The buccolingual plane progresses acrosslines “A-A,” “B-B,” “C-C,” “D-D,” and “E-E” in sections “5-6,” “6-7,” “7-8, ” “8-9,” and “9-10” (Fig. 2). Second, the variation of the maximum compressiveand tensile stresseswas compared along the axial direction of a tooth model. For example, Fig. 4 displays the variation of compressiveand tensile stressesalong line E-E (section 9-10) for the three normal tooth models: 0-“crown,” A-“root,” and +-“bone + lig.” The dotted vertical lines
178
Ligament
BIXIC?
No. of nodes
308
554 1190 1792
385
define the dentinoenameljunction The predicted stresses for the “root” and “bone + lig” modelswere in agreement with each other. The correspondingstressescomputed using the “crown” model revealed a dramatic departure, compared with the “root” and the “bone + lig.” models, especiallyin the enamel.The regional variation of stresses in the enameland dentin along the axial direction, respectively, are presentedin Fig. 5. The “crown” model alsoexhibited a different stresspattern for enamelin the axial direction than did the other two models.The predicted com-
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329
330
331
Element
332
333
334
335
MODEL
A ROOT
MODEL
+ BONE
+ LIG.
MODEL
Numbers
Notations: BS
E
D
D
E Ls
E D R BS LS
= ; = = z
Compressive 328
329
330
331
Element
Fig. 5. Comparison models.
of stress patterns
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pressive stresses in dentin were similar for the three models, but the tensile stresses in dentin along sections 9-10 and lo-11 for the “crown”mode1 differed substantially from those for the other two models. Since the stress distribution predicted by using the “root” and “bone + lig” models was similar at all section levels, the “root” model was used for further analysis. The stress departures following restoration in comparison to those in the normal tooth was an examination designed to assess the stress distribution along the buccolingual plane of the sections, in the axial direction for the normal tooth and the restoration with a PD/GD ratio of 1 (Dl). The subtle differences for the other two restorative designs were then compared with the Dl results. The sections surrounding the restorative material are 5-6 to 7-8 (Fig. 3). Furthermore, section 7-8 is just above the gingival wall of the preparation and section 8-9 is located immediately below. The variations in compressive and tensile stresses along the buccolingual lines throughout the enamel and dentin after restoration (A) compared with those in the normal tooth (0) are shown in Fig. 6. The mnemonics for different regions are: BS-buccal side; LS-lingual side; E-enamel; D-dentin; and R-restoration. The effect of restoration on the stresses was not significant at section 9-10, a section 1 mm below the gingival floor of the cavity preparation (Fig. 6). The effect of restoring a cavity with a dental material is highly localized adjacent to the restoration. The stress deviation after a restoration (dotted line) compared with that in the normal tooth (solid line) is exhibited in Fig. 7 for maximum compressive and tensile stresses
THE
333
Enamel Dentin Restoration Buccal Side Lingual Side
tooth (axial direction)
shown by the three
along the axial direction, both in the enamel and dentin region. The compressive stresses in the restored tooth (Dl) revealed maximum variation in both enamel and dentin in sections 6-7 to 8-9 when compared with the normal tooth model. The compressive stresses in enamel were increased at section 6-7 (Fig. 6), but were reduced at section 8-9 compared with those in the normal tooth. The corresponding changes in the dentin were complementary to the variation in enamel (Fig. 6) and the stresses in the restored tooth model returned to normal at section 9-10 and below. The variation of maximum compressive and tensile stresses in the axial direction for the three restoration designs (D.7, D.85, Dl) are shown in Fig. 8, A and B, respectively. The variation in percent difference in maximum compressive stresses in the restored tooth models and the corresponding stresses in the normal tooth model from section 6-7 to section 8-9 is displayed in Table III. This is expressed as ga’-rrb’/aa-ub where ua and cb are the stresses at sections 6-7 and 8-9 of a normal tooth and ga’ and ab’ are the corresponding stresses for a restored tooth (Fig. 7, A). These differences indicate the severity of the stress departures in the region surrounding the restoration as compared with the normal tooth. The percent changes in both the enamel and dentin regions are displayed in Table III. A percentage stress gradient departure in the enamel region (difference of numbers in a column; difference between points a’ and b’ in Fig. 8, A), with respect to the normal tooth, was 36% for Dl model as compared with 42 % for D.85 and 30 % for D.7 model (Table III). The cor-
179
GOEL
0 NORMAL
ET AL
TOOTH
A DESIGN 3 (D 1.0~ROOT
MODEL
Notations:
E = Enamel D=Deniin
Compressive Stresses Bucc.4 A-A side
-2
f$
Tensile Stresses
R=Restoration Buccal Sid.5
Lingual
Q
SECTION
A-A
S-6
-4
--
R
-2
SECTION
6-7
-4
2
-5
0 1 c-c
0
c-c
R
4
-5
SECTION
7-B 0
-21
E D I
0-i
I
D-D
D-D 0:
E-E
I
41
I
Q E
E-E
Fig. 6. Compressive and tensile stresses along buccolingual lines at various section levels with restorative materials (R) in cavity design 3 D-l. Restorative material is present in sections 5-6, 6-7, and 7-8 only.
responding changes in the dentin region were 32 % , 27 % , and 23 % , respectively. These observations demonstrated the critical role of the depth of the cavity preparation in the stress gradient for enamel and dentin after restoration. The results strongly suggested that the deeper the prepared cavity, the greater the changes in the stress gradient in the dentin. The changes in the stress gradient could initiate fracture of the remaining cusps, possibly starting in dentin, immediately adjacent to the deepest portion of the cavity preparation, according to the study by Bell et a1.17
180
DISCUSSION IMPLICATIONS
AND
CLINICAL
Dental tissues respond biologically to stresses and strains imposed during mastication. 14-16 Compromised teeth from extensive carious lesions or large restorations tend to weaken and are prone to further trauma. The stresses in teeth associated with these conditions may lead to cuspal fracture and may require complex or expensive restorations, while the restorative procedures can alter the stress distribution patterns in the remaining tooth structure and may cause failure of the restoration. For these reasons, it
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a
b
-
5-6
7
-
6-7
-
-
7-0
-
-
8-9
-
Legend:
-
0 NORMAL TOOTH A DESIGN D-l .Q-430
- 9-10
Section
Stresses
(A) Enamel
Numbers *
Dentin
NEWTONS/mm2
Fig. 7. Compressiveand tensile stressesin enameland dentin at various section levels in normal tooth and after cavity preparation D-l, as analyzed by “root model.”
is essentialto understand the stressesfor a normal tooth or a tooth with a special restorative design.A comparisonof the stressesbetween models can confirm the reasonsfor failure while identifying the region that has the propensity for failure. An experimental approach is desirablefor such investigations since the traditional experimental methods7-10, l2 do not allow monitoring tissueor material stresses at different levels becauseof the biologic complexity of the teeth. The experiments are limited to overall strength data of teeth with and without restorations. Numerous studies have reported such data,?-12including the stressdistributions within the tooth structure using the photoelastic technique,18-2’but all of these techniques have strengths, limitations, and complexities. The finite elementtechnique iswell suited to investigate stressesin complex structures like the human tooth,21V26 and the validity of the computed results has been confirmed in the biomechanicsliterature and specifically for dental applications.l, 14-16, 21-31A number of two-dimensional and three-dimensional finite element studies with the stressdistributions of normal and restored tooth modelshave beenreported.‘, 14-17, 22-26 This researchdealswith the biomechanicsof a restored tooth and is an extension of
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the previously reported studies.l,14-16 The model for this investigation replicates the three-dimensional tooth geometry, sincethe model is basedon the actual geometry of the tooth, including its tissues,derived from the serial photography technique. It allowsan understanding of the regional stressvariations related to cavity designsand restorations. The stressesin a tooth with a restoration are related to various factors: the properties of the restorative material, the cavity designand restoration, and the bond strength at the restoration/dentinal tissue interface, etc. This study examined the stressdistributions of enameland dentin for a restored tooth as a function of cavity depth, while the values for other parameters were sustained. The cavity isthmus width and interaxial dentin width in a class II MOD cavity preparation were standardized. The material properties for the enameland dentinal tissueswere documented representative values (Table I) and were identical to thosein earlier reports.14-16 The three-dimensionalfinite element modelsdeveloped for the analysiswere linear, and the bond between the restorative material and the dental tissue was consideredideal. Clinically this is unrealistic. The stressesin the normal tooth and restored tooth mod-
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GOEL
Compressive
ET AL
Tensile Stresses
Stresses 5-6
Tooth
(A) Enamel 6-7
Normal Tooth
7-6 6-9
f -5 Section Numbers i
’
1
I
5
lo
Legend: 0 DESIGN D-0.704OOT A DESIGN D-0.8543001 + DESIGN D-l .OO--ROOT @ NORMALTOOTH
(W
Dentin
Normal Tooth
IO-ll,,,,
-4
-5 0 NEWTONS/mm*
0
Fig. 8. Comparison
of compressive by the “root
and tensile model.”
-12-
normal
tooth analyzed
5
10
stresses among three cavity designs and
Table III. Percentage change in maximum compressive stresses following restoration same location in normal tooth model; Difference below section 8-9 was negligible Design Section
No.
5-6
6-7 7-8 8-9 Total % difference
Enamel
0.7
Design Dentin
25.6
-14.6 9.8
20.7
-4.1 30.1
24.4
-21.7 42.4
-
els were analyzed for an axial compressive load of 170 N distributed over the occlusal surfaces of the models. This study discovered that with the restorative materials harder than dentin but more flexible than enamel the predicted compressive stresses in dentin surrounding the restoration were increased compared with those in the normal tooth except immediately below the cavity floor. This finding was especially noticeable for the cavity preparations with deep pulpal floor, such as models D.85 and Dl (Fig. 8). The stresses in these models revealed an increase in the dentin adjacent to the cavity floor, so it is essential to appreciate how critical the remaining dentin is in restorative procedures. This tissue provides fundamental support to the restoration, including mechanical retention
182
Enamel
in comparison
with stresses at Design
0.85 Dentin
1
Enamel
-11.1 9.6 27.3
Dentin
-22.1
16.5
10.2 32.3
-19.4 35.9
from undercuts and the “box form” of the prepared cavity. The lesser the amount of the remaining dentin, the greater the stress gradient and thus the greater the potential for fracture. This greater stress gradient, from immediately above the floor of the prepared cavity to just below it, can initiate fracture of the cusps or failure at the restorationtooth interface. The latter may contribute to microieakage, possibly leading to recurrent decay or corrosion of the restorative material.27z 28 The abrupt change, from dentin prior to cavity preparation to the restorative material after restoration, is responsible for this phenomenon. This development can also contribute to the dislodgment of implants that replace body joints, such as a hip prosthesis and elbow joint arthroplasty.2g-33 These results suggested that the unfavorable stresses in FEBRUARY
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a cavity preparation varied significantly with the depth of the cavity and the change in the materials. However, this theory is based on the assumption that the bond at the restorative material/dentinal interface was perfect, which is improbable. If the restoration is dislodged from its mechanical interlocking, the stress concentration effects of the cavity preparation may dominate. The effect of cavity depth on the stresses in a prepared tooth illustrated that the deeper the cavity, the more unfavorable the stress distributioqr and this effect is magnified if the bond is incomplete. Under these circumstances, the deeper cavities are undesirable. However, a dentist is repeatedly forced to prepare deep preparations due to caries. Nevertheless, the dentist should be aware of the prolonged effects of the changing stress gradient immediately adjacent to the deepest portion of the cavity. These situations demand critical clinical evaluation because these teeth are more appropriately restored with metal castings or etched porcelain restorations using bonding agents.
SUMMARY ,This study indicated that an unfavorable stress gradient was evident in the dentinal cavity floor of a restored tooth compared with an intact natural tooth. This change in the stress gradient can initiate fracture of the cusps. If the fracture occurs at the restoration-tooth interface, the microleakage would also be greater with deeper cavity preparations. REFERENCES 1. Khera SC, Gael VK, Chen RCS, Gurusami SA. A three-dimensional finite element model. Oper Dent 1988;13:128-37. 2. Vale WA. Cavity preparation. Irish Dent Rev 1956;2:33-41. 3. Vale WA. Cavity preparation and further thoughts on high speed. Br Dent J 19X+107:333-46. Eakle WS, Maxwell EH, Braly BV. Fractures of posterior teeth in adults. J Am ‘Dent Assoc 1986;112:215-8. Cave1 WT, Kelsey WP, Blankenau RJ. An in viva study of cuspal fracture. J PROSTHETDENT 1985;53:38-42. Lagouvardos P, Sourai P, Douvitsas G. Coronal fractures in posterior teeth. Oper Dent 1989;14:28-32. Mondelli J, Stengall L, Ishikirma A, Delima-Navarro MF, Socres FB. Fracture strength of human teeth with cavity preparations. J PROSTHET DENT 1980;43:419-22. 8. Re GJ, Norling BK, Draheim RN. Fracture strength of molars containing three surface amalgam restorations. J PROSTHET DENT 1982;47: 183-7. 9. Re GJ, Draheim RN, Norling BK. Fracture resistance of mandibular molars with occlusal Class I amalgam preparations. J Am Dent Assoc 1981;103:580-3. 10. Larsen TD, Douglas WH, Geistfeld RE. Effects of prepared cavities on the strength of teeth. Oper Dent 1981;6:2-5. 11. Nadal R. Amalgam restoration: cavity preparation, condensing and finishing. J Am Dent Assoc 1962;65:66-77.
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12. Blaser PK, Lund MR, Cochran MA, Potter RH. Effects of designs of Class i1 preparations on resistance to fracture. Oper Dent 198%8x6-10. 13. Gurusami SA. Stresses in human teeth-an application of the finite element technique. Master’s Thesis. Iowa City, Iowa: University of Iowa Graduate College, 1985. 14. Goel VK, Khera SC, Gurusami SA, Chen RCS. Effect of cavity design on stresses in first molar [Abstract]. J Dent Res i985;64:350. 15. Goel VK, Khera SC, Singh K. The clinical implications of the response of enamel and dentin to masticatory loads. 3 PROSTHET DENT 1990; 64:446-54. 16. Goel VK, Khera SC, Ralston JL, Chang KH. Stresses at the dentinoenamel junction of human teeth-a finite element investigation. J PROSTHET DENT 1991;66:451-9. 17. Bell JG, Smith MC!, dePont JJ. Cuspal failures of MOD restored teeth. Aust Dent J 1982;27:283-7. 18. El-Ebrashi MK: Craig RG, Peyton FA. Experimental stress analysis of dental restorations. Part I. Two-dimensional photoelastic stress analysis of inlays. J PROSTHET DENT 1967;17:277-91. 19. Fisher DW, Caputo AA, Shillingburg HT Jr, Duncanson MG. Photoelastic analysis of inlay and onlay preparations. J PROSTHET DENT 1975;33:47-53. 20. Farah JW, Dennison JB, Powers JM. Effects of design on stress distribution in intracoronal gold restorations. J Am Dent Assoc 1977;94: 1151-4. 21. Farah JW, Craig RG, Sikarski DL. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomechanics 1973;6:511-20. 22. Thrasher RW, Saito GE. The stress analysis of human teeth. 3 Biomechanics 1973;6:443-9. 23. Rubin C, Krishnamurthy N, Capilouto E, Yi H. Stress analysis of the human tooth using a three-dimensional finite element model. J Dent Res 1983;62:82-5. 24. deVree JHP, Peters MCRB, Plasschaert AJM. The influence of modification of cavity design on distribution of stresses in a restored molar. J Dent Res 1984;63:1217-20. 25. Yettram AL, Wright KWJ, Picard HM. Finite element stress analysis of crowns of normal and restored teeth. J Dent Res 1976;55:1004-11. 26. Williams KR, Edmundson JT, Rees JS. Finite element method stress analysis of restored teeth. Dent Mat 1987;3:200-6. 27. D&and T. Marginal failure of amalgam Class II restoration. J Dent Res 1977;56:481-5. 28. Anusavice KJ. Quality evaluation of dental restorations. Criteria for placement and replacement. Chicago: Quintessence Books, 198928-9. 29. Rohlmann A, Mlissner U, Bergmann G, Kiilber R. Finite element analysis and experimental investigation in a femur with hip endoprosthesis. J Biomechanics 1983;16:727-42. 30. Goel VK, Blair WF. Biomechanics of the elbow joint. Automedica 1985;6:119-38. 31. Goel VK, Lee I-K, Blair WF. Effect of the Coonrad eibow prosthesis cm stress in humerus. Clin Biomech 1989;4:11-6. 32. Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomechanics 1983;16:385-410. 33. Goel VK, Lee I-K, Blair WF. Stress distribution in the ulna following a hinged elbow arthoplasty-a finite element analysis. J Arthroplasty 1989;4:163-71.
Reprintrequests to: DR. SATISH C.KHERA PROFESSOR,DEPARTMENT OPERATIVEDENTISTRY COLLEGEOFDENTISTRY UNIVERSITY OF IOWA IOWA CITY.IA 52242
OF
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depth
on stresses
in a restored
t
Vijay K. Gael, PhD,a Satish C. Khera, BDS, DDS, MS,b Senthil Gurusami, MS,” and Robert C. S. Chen, DDS, MSd University of Iowa, Colleges of Engineering and Dentistry, Iowa City, Iowa Restorative procedures commonly replace lost tooth structure, but redistribution of functional stresses after treatment is not fully understood. Many restorative methods are dictated by the integrity of the remaining tooth structure, because sparse tooth structure can lead to fracture. It is essential to prevent fractures by having a clear concept of the designs for cavity preparations, and to anticipate the stresses of mastication on the remaining tooth structure. Knowledge of various internal parameters of cavity designs would facilitate selection of the appropriate cavity preparation for a specific clinical situation. Three cavity designs and restorations were examined in this study for stresses using the finite element technique. After placement of restorative materials, the dentin experienced a dramatic change in stress gradient immediately below the pulpal wall, and this response was magnified in deeper cavity preparations. Enamel also exhibited major alterations in the stress gradient in all three designs of cavity preparations. The combination of the changes can cause cracks in the remaining tooth structure, leading to cusp fracture immediately adjacent to the deepest portion of the cavity. (J PROSTHET DENT 174-83.)
estorative dental procedures are necessary to ensure tooth function, relieve dental pain, and prevent pulpal pathology. The clinical procedure involves preparing a cavity of appropriate dimensions with respect to isthmus width and pulpal depth. However, in class II mesial, occlusal, and distal (MOD) cavity preparations, gingival depth and the thickness of dentin between mesial and distal axial walls are also important criteria during cavity preparati0n.l The dimensions are dictated primarily by the extent of carious lesion or trauma, and the prepared cavity is then restored with the appropriate restorative material such as cast gold, amalgam, composite resin, or porcelain. The major considerations after restoring the tooth are the health of the remaining tooth structure, its function, and the potential for fracture. Numerous studies2-12 have confirmed a correlation between cuspal fractures of the restored teeth, tooth morphology, and allied cavity parameters. Nadalll recommended cavity preparations with a narrow occlusal outline and a shallow pulpal floor to reduce failure. Blaser et a1.12 investigated the fracture potential of prepared teeth and
This investigation was supported by funds from the Graduate College and the Weeg Computing Center at the University of Iowa. “Professor and Chairman, Department of Biomedical Engineering, College of Engineering. bProfessor, Department of Operative Dentistry, College of Dentistry. CBiomedical Engineer, Engineering Department, Ford Motor Co., Dearborn, Mich. dGraduate student, Department of Oral Biology, University of Michigan, School of Dentistry, Ann Arbor, Mich. IO/A/29658
174
the internal dimensions of the MOD cavity preparation, and discovered that the width of the isthmi of MOD cavity preparations did not substantially weaken the teeth if the pulpal depth was shallow. However, the damage to the remaining tooth structure was dramatically increased if the pulpal depth was increased and the cavity width remained narrow. Khera et al? reported similar conclusions regarding the depth of the cavity preparation, after an analyses of stresses on the remaining tooth structure using the finite element technique. The stress distribution in a normal tooth was compared with tooth models of different cavity preparations. In a normal tooth, the stresses were predominantly compressive in response to an axial compressive load, but in the model with a wide and deep cavity preparation, tensile stresses were recorded at the pulpal wail. These, combined with heavy compressive stresses in the immediately adjacent area, can cause greater damage to the remaining tooth structure compared with a normal tooth or a tooth with a narrow and shallow cavity preparation. This change in the type of stresses, from compression to tension, is responsible for an increased fracture potential of a tooth with wide and deep cavity preparations. The experimental studies have also demonstrated that these dimensions of a cavity preparation, usually necessitated by large carious lesions, diminish the fracture resistance of the prepared tooth.1°-12 These studies were commonly performed on extracted teeth without standardization of the size, age, biochemical, or morphologic differences between samples or variations in the thickness or the contour of the remaining enamel and dentin. This study was conducted to review the effects of dimensional variables and to address the following: (1) Do the dimensions of the cavity preparation that alter the stress distribution within a prepared tooth also
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(B) Constant
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MD:IT::l
(C) Variable
Parameters
D-O.70 PD:GD:
9.703.0
D-O.85 PD:GD: rO.&:l .O
D-1.0 PD:GD:
:l .03 .0
Fig. 1. Various tooth landmarks and cavity preparation rameters between three cavity designs (B) and variable
change the stresses in a restored tooth? (2) What are the clinical implications resulting from stress changes associated with these variables? The main objective was to investigate a restored tooth by examining the stress distribution resulting from the size of the cavity preparation. This study specifically examined the effect of cavity depth on the stress distribution in a restored tooth. The finite element technique was used because the conventional experimental techniques were incapable of an in-depth analysis of stress distribution within a complex, asymmetric, and irregular three-dimensional structure such as the tooth.
IAL
AND
METHODS
A three-dimensional finite element model of a mandibular second premolar was developed. The data for the model with cavity designs were grouped into three categories: (1) generation of the three-dimensional geometry of the intact tooth and a tooth with various cavity designs; (2) properties of the dental tissues and the restorative mate-
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in this study (A). Constant parameters (C).
pa-
rial; and (3) magnitude, distribution, and direction of the chewing force. The technique of the three-dimensional finite element models based on the geometrical data from an actual tooth was reported ear1ier.i One mandible, with normal tooth morphology, shape of the alveolar crest, and the alignment of dentition, was selected from IO human mandibles. The mandible was sectioned vertically so that it extended from the mesial surface of the first premolar to the distal surface of the third molar. Duplicates of the specimen were made with Die Keen (Columbus Dental, St. Louis, MO.) die cast material. Different cavity designs of explicit dimensions were prepared on the duplicates to evaluate class II MOD cavity preparations of three different internal parameters. Each cavity preparation had an isthmus width (IW)-to-intercuspal width (CW) ratio of 0.25, and the thickness of the remaining dentin and the mesiodistal (MD) dimension of the tooth was 0.5 (Fig. 1). These constant parameters were sustained. The ratio of the pulpal depth to gingival depth (PD/GD) was the only variable between the three designs.
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GQEL
ET AL
Enamel = section
6-7
Section 7-6
Fig. 2. Digitization of serial sections to prepare three-dimensional with different cavity designs.
I. Material properties assigned to dental tissues and restorative material in this study
Table
Tissue/ restorative material
Enamel Dentin Periodontal ligament Alveolar bone Restorative material (type I gold alloy)
Young’s modulus E(N/mm2)
8.4 x 104* 2.0 x 104* 1750* 3.4 x 103 7.7 x 1047
Poisson’s ratio
0.33* 0.31* 0.45* 0.33* 0.33$
E, Young’s modulus of elasticity; N, Newton. *Atmaram GH, Mohammed H. Estimation of physiological stresses in a natural tooth considering fibrous PDL structure. J Dent Res 1981;60:873-7. KI’Brien WJ, Ryge G. An outline of dental materials. 1st ed. Philadelphia: WB Saunders Co: 1978:402. $Farah JW, Craig RG. Distribution of stresses in porcelain-fused-to-metal and porcelain jacket crowns. J Dent Res 1975;54:255-61.
Pulpal depth wasdetermined by measuringfrom the buccal cusp tip to the pulpal wall, while gingival depth was measuredfrom the buccal cusptip to gingival wall (Fig. 1). This ratio for design 1 (D.70) was 0.7; for design 2 (D.85) it was0.85; and for design3 (D1.O) it was 1 where both the pulpal and the gingival wall were at the samelevel (Fig. 1). The original specimenand the three duplicates were embedded in an epoxy resin block in a known orientation. All of the six facesof the block were ground to ensureorthog176
model of normal tooth
onality. A global Cartesian coordinate system was established on the resin block. Serial photographs of the horizontal ground sectionswere obtained using a photographic technique at approximately 0.5 mm intervals and were then recorded. The tracings of the morphologic geometry, the contour, and the thicknessof the enameland dentin wereobtained from thesephotographs.The tracings were then divided into rectangles of appropriate sizesso that the geometry of each section was duplicated (Fig. 2). Eight nodal linear isoparametricelementswere formed by correspondingnodesof the adjacent section. In this manner three-dimensionalfinite element (FE) modelsof a normal unpreparedmandibular secondpremolar and the same tooth with three cavity designswere formulated. The prepared cavities in the FE modelswere restored with a type I gold alloy. The physical properties of the dental tissues and the properties of the restorative material for this model are presentedin Table I. A uniform axial masticatory force of 170 N wasdistributed on the entire occlusalsurface of the model for this study. This procedure wasselectedto compare our method with that of earlier studiesand to confirm that the depth of cavity preparation altered stresseswithin the prepared tooth and that it had a similar effect on the completed restoration. Three boundaries were imposed for three models of a normal tooth: “crown,” “root,” and “bone + lig.” In the
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z-coordinate section # 5.098
1
5.047 --N--m_-
3.274 3.152
---=+m+------2
\
I I \
/
3.033 2.915 2.655
Fig. 3. Locations
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\/
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“crown” model, the tooth geometry modeled was to the cervical section (section no. 13, Fig. 3) and the nodes were fixed in all directions. The complete tooth was modeled in the “root” model, and the nodes in contact with the periodontal ligament (sections 14 to 23, Fig. 3) were fixed. The entire tooth, periodontal ligament, and the surrounding alveolar bone were included in the “bone + lig” model. The outermost nodes of sections 14 to 25 (Fig. 3) of the alveolar bone region were also fixed. The number of elements and nodes used for the three normal tooth models are presented in Table II. The execution times and the expense for the three-dimensional finite element models increase phenomenally as the number of elements and the nodes are raised. Therefore the execution costs were controlled without sacrificing the accuracy by restricting these numbers, such as by choosing one of the three models. Since the region above the cervical section is critical in
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sections and Z coordinates. this study, the disparity of the stresses between the three models was compared. No significant difference in stresses was recorded for the “root” and “bone + lig” models.13 The stress results for the normal and restored tooth models were from the “root” finite element models. The ANSYS finite element package (Swanson Analysis Systems, Inc., Huston, Pa.) was used for this study.
RESULTS The stress distribution in the normal tooth has been described in earlier reports,14-16 so sample data for the three normal tooth models are included to justify using the “root” model for analyzing stresses: D.70 (PDIGD = 0.70); D.85 (PD/GD = 0.85); and D1.O (PD/GD = 1.0). The applied load was compressive, but both the compressive stress and the tensile stress were included in the analysis. The predicted stresses in various models were compared in two steps. First, the stress distribution in elements of various
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GOEL
Tensile 5-6
’
8-9
1
I
-15
-10
I
0
-5
Section
Numbers 1
ET AL
Stresses
(A)
Enamel
Legend: I 5
0 CROWN MODEL A ROOT MODEL + BONE f LIG. MODEL
I 10
Dentin
1
10
NEWTONS/mm2 Fig. 4. Comparisonof stresspatterns in normal tooth (buccolingual direction) shownby “crown,” “root,” and “bone + lig.” models.
Table
II. Breakdown of number of elementsand nodesused in configuration of three finite element models of a normal
tooth No. of elements Model
Crown Root Bone
+
lig
Enamel
Dentin
176 176 176
205 546 546
tooth sections cut by a specific horizontal (buccolingual) section was studied. The buccolingual plane progresses acrosslines “A-A,” “B-B,” “C-C,” “D-D,” and “E-E” in sections “5-6,” “6-7,” “7-8, ” “8-9,” and “9-10” (Fig. 2). Second, the variation of the maximum compressiveand tensile stresseswas compared along the axial direction of a tooth model. For example, Fig. 4 displays the variation of compressiveand tensile stressesalong line E-E (section 9-10) for the three normal tooth models: 0-“crown,” A-“root,” and +-“bone + lig.” The dotted vertical lines
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Ligament
BIXIC?
No. of nodes
308
554 1190 1792
385
define the dentinoenameljunction The predicted stresses for the “root” and “bone + lig” modelswere in agreement with each other. The correspondingstressescomputed using the “crown” model revealed a dramatic departure, compared with the “root” and the “bone + lig.” models, especiallyin the enamel.The regional variation of stresses in the enameland dentin along the axial direction, respectively, are presentedin Fig. 5. The “crown” model alsoexhibited a different stresspattern for enamelin the axial direction than did the other two models.The predicted com-
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329
330
331
Element
332
333
334
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MODEL
A ROOT
MODEL
+ BONE
+ LIG.
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Numbers
Notations: BS
E
D
D
E Ls
E D R BS LS
= ; = = z
Compressive 328
329
330
331
Element
Fig. 5. Comparison models.
of stress patterns
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pressive stresses in dentin were similar for the three models, but the tensile stresses in dentin along sections 9-10 and lo-11 for the “crown”mode1 differed substantially from those for the other two models. Since the stress distribution predicted by using the “root” and “bone + lig” models was similar at all section levels, the “root” model was used for further analysis. The stress departures following restoration in comparison to those in the normal tooth was an examination designed to assess the stress distribution along the buccolingual plane of the sections, in the axial direction for the normal tooth and the restoration with a PD/GD ratio of 1 (Dl). The subtle differences for the other two restorative designs were then compared with the Dl results. The sections surrounding the restorative material are 5-6 to 7-8 (Fig. 3). Furthermore, section 7-8 is just above the gingival wall of the preparation and section 8-9 is located immediately below. The variations in compressive and tensile stresses along the buccolingual lines throughout the enamel and dentin after restoration (A) compared with those in the normal tooth (0) are shown in Fig. 6. The mnemonics for different regions are: BS-buccal side; LS-lingual side; E-enamel; D-dentin; and R-restoration. The effect of restoration on the stresses was not significant at section 9-10, a section 1 mm below the gingival floor of the cavity preparation (Fig. 6). The effect of restoring a cavity with a dental material is highly localized adjacent to the restoration. The stress deviation after a restoration (dotted line) compared with that in the normal tooth (solid line) is exhibited in Fig. 7 for maximum compressive and tensile stresses
THE
333
Enamel Dentin Restoration Buccal Side Lingual Side
tooth (axial direction)
shown by the three
along the axial direction, both in the enamel and dentin region. The compressive stresses in the restored tooth (Dl) revealed maximum variation in both enamel and dentin in sections 6-7 to 8-9 when compared with the normal tooth model. The compressive stresses in enamel were increased at section 6-7 (Fig. 6), but were reduced at section 8-9 compared with those in the normal tooth. The corresponding changes in the dentin were complementary to the variation in enamel (Fig. 6) and the stresses in the restored tooth model returned to normal at section 9-10 and below. The variation of maximum compressive and tensile stresses in the axial direction for the three restoration designs (D.7, D.85, Dl) are shown in Fig. 8, A and B, respectively. The variation in percent difference in maximum compressive stresses in the restored tooth models and the corresponding stresses in the normal tooth model from section 6-7 to section 8-9 is displayed in Table III. This is expressed as ga’-rrb’/aa-ub where ua and cb are the stresses at sections 6-7 and 8-9 of a normal tooth and ga’ and ab’ are the corresponding stresses for a restored tooth (Fig. 7, A). These differences indicate the severity of the stress departures in the region surrounding the restoration as compared with the normal tooth. The percent changes in both the enamel and dentin regions are displayed in Table III. A percentage stress gradient departure in the enamel region (difference of numbers in a column; difference between points a’ and b’ in Fig. 8, A), with respect to the normal tooth, was 36% for Dl model as compared with 42 % for D.85 and 30 % for D.7 model (Table III). The cor-
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GOEL
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ET AL
TOOTH
A DESIGN 3 (D 1.0~ROOT
MODEL
Notations:
E = Enamel D=Deniin
Compressive Stresses Bucc.4 A-A side
-2
f$
Tensile Stresses
R=Restoration Buccal Sid.5
Lingual
Q
SECTION
A-A
S-6
-4
--
R
-2
SECTION
6-7
-4
2
-5
0 1 c-c
0
c-c
R
4
-5
SECTION
7-B 0
-21
E D I
0-i
I
D-D
D-D 0:
E-E
I
41
I
Q E
E-E
Fig. 6. Compressive and tensile stresses along buccolingual lines at various section levels with restorative materials (R) in cavity design 3 D-l. Restorative material is present in sections 5-6, 6-7, and 7-8 only.
responding changes in the dentin region were 32 % , 27 % , and 23 % , respectively. These observations demonstrated the critical role of the depth of the cavity preparation in the stress gradient for enamel and dentin after restoration. The results strongly suggested that the deeper the prepared cavity, the greater the changes in the stress gradient in the dentin. The changes in the stress gradient could initiate fracture of the remaining cusps, possibly starting in dentin, immediately adjacent to the deepest portion of the cavity preparation, according to the study by Bell et a1.17
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DISCUSSION IMPLICATIONS
AND
CLINICAL
Dental tissues respond biologically to stresses and strains imposed during mastication. 14-16 Compromised teeth from extensive carious lesions or large restorations tend to weaken and are prone to further trauma. The stresses in teeth associated with these conditions may lead to cuspal fracture and may require complex or expensive restorations, while the restorative procedures can alter the stress distribution patterns in the remaining tooth structure and may cause failure of the restoration. For these reasons, it
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a
b
-
5-6
7
-
6-7
-
-
7-0
-
-
8-9
-
Legend:
-
0 NORMAL TOOTH A DESIGN D-l .Q-430
- 9-10
Section
Stresses
(A) Enamel
Numbers *
Dentin
NEWTONS/mm2
Fig. 7. Compressiveand tensile stressesin enameland dentin at various section levels in normal tooth and after cavity preparation D-l, as analyzed by “root model.”
is essentialto understand the stressesfor a normal tooth or a tooth with a special restorative design.A comparisonof the stressesbetween models can confirm the reasonsfor failure while identifying the region that has the propensity for failure. An experimental approach is desirablefor such investigations since the traditional experimental methods7-10, l2 do not allow monitoring tissueor material stresses at different levels becauseof the biologic complexity of the teeth. The experiments are limited to overall strength data of teeth with and without restorations. Numerous studies have reported such data,?-12including the stressdistributions within the tooth structure using the photoelastic technique,18-2’but all of these techniques have strengths, limitations, and complexities. The finite elementtechnique iswell suited to investigate stressesin complex structures like the human tooth,21V26 and the validity of the computed results has been confirmed in the biomechanicsliterature and specifically for dental applications.l, 14-16, 21-31A number of two-dimensional and three-dimensional finite element studies with the stressdistributions of normal and restored tooth modelshave beenreported.‘, 14-17, 22-26 This researchdealswith the biomechanicsof a restored tooth and is an extension of
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the previously reported studies.l,14-16 The model for this investigation replicates the three-dimensional tooth geometry, sincethe model is basedon the actual geometry of the tooth, including its tissues,derived from the serial photography technique. It allowsan understanding of the regional stressvariations related to cavity designsand restorations. The stressesin a tooth with a restoration are related to various factors: the properties of the restorative material, the cavity designand restoration, and the bond strength at the restoration/dentinal tissue interface, etc. This study examined the stressdistributions of enameland dentin for a restored tooth as a function of cavity depth, while the values for other parameters were sustained. The cavity isthmus width and interaxial dentin width in a class II MOD cavity preparation were standardized. The material properties for the enameland dentinal tissueswere documented representative values (Table I) and were identical to thosein earlier reports.14-16 The three-dimensionalfinite element modelsdeveloped for the analysiswere linear, and the bond between the restorative material and the dental tissue was consideredideal. Clinically this is unrealistic. The stressesin the normal tooth and restored tooth mod-
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GOEL
Compressive
ET AL
Tensile Stresses
Stresses 5-6
Tooth
(A) Enamel 6-7
Normal Tooth
7-6 6-9
f -5 Section Numbers i
’
1
I
5
lo
Legend: 0 DESIGN D-0.704OOT A DESIGN D-0.8543001 + DESIGN D-l .OO--ROOT @ NORMALTOOTH
(W
Dentin
Normal Tooth
IO-ll,,,,
-4
-5 0 NEWTONS/mm*
0
Fig. 8. Comparison
of compressive by the “root
and tensile model.”
-12-
normal
tooth analyzed
5
10
stresses among three cavity designs and
Table III. Percentage change in maximum compressive stresses following restoration same location in normal tooth model; Difference below section 8-9 was negligible Design Section
No.
5-6
6-7 7-8 8-9 Total % difference
Enamel
0.7
Design Dentin
25.6
-14.6 9.8
20.7
-4.1 30.1
24.4
-21.7 42.4
-
els were analyzed for an axial compressive load of 170 N distributed over the occlusal surfaces of the models. This study discovered that with the restorative materials harder than dentin but more flexible than enamel the predicted compressive stresses in dentin surrounding the restoration were increased compared with those in the normal tooth except immediately below the cavity floor. This finding was especially noticeable for the cavity preparations with deep pulpal floor, such as models D.85 and Dl (Fig. 8). The stresses in these models revealed an increase in the dentin adjacent to the cavity floor, so it is essential to appreciate how critical the remaining dentin is in restorative procedures. This tissue provides fundamental support to the restoration, including mechanical retention
182
Enamel
in comparison
with stresses at Design
0.85 Dentin
1
Enamel
-11.1 9.6 27.3
Dentin
-22.1
16.5
10.2 32.3
-19.4 35.9
from undercuts and the “box form” of the prepared cavity. The lesser the amount of the remaining dentin, the greater the stress gradient and thus the greater the potential for fracture. This greater stress gradient, from immediately above the floor of the prepared cavity to just below it, can initiate fracture of the cusps or failure at the restorationtooth interface. The latter may contribute to microieakage, possibly leading to recurrent decay or corrosion of the restorative material.27z 28 The abrupt change, from dentin prior to cavity preparation to the restorative material after restoration, is responsible for this phenomenon. This development can also contribute to the dislodgment of implants that replace body joints, such as a hip prosthesis and elbow joint arthroplasty.2g-33 These results suggested that the unfavorable stresses in FEBRUARY
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a cavity preparation varied significantly with the depth of the cavity and the change in the materials. However, this theory is based on the assumption that the bond at the restorative material/dentinal interface was perfect, which is improbable. If the restoration is dislodged from its mechanical interlocking, the stress concentration effects of the cavity preparation may dominate. The effect of cavity depth on the stresses in a prepared tooth illustrated that the deeper the cavity, the more unfavorable the stress distributioqr and this effect is magnified if the bond is incomplete. Under these circumstances, the deeper cavities are undesirable. However, a dentist is repeatedly forced to prepare deep preparations due to caries. Nevertheless, the dentist should be aware of the prolonged effects of the changing stress gradient immediately adjacent to the deepest portion of the cavity. These situations demand critical clinical evaluation because these teeth are more appropriately restored with metal castings or etched porcelain restorations using bonding agents.
SUMMARY ,This study indicated that an unfavorable stress gradient was evident in the dentinal cavity floor of a restored tooth compared with an intact natural tooth. This change in the stress gradient can initiate fracture of the cusps. If the fracture occurs at the restoration-tooth interface, the microleakage would also be greater with deeper cavity preparations. REFERENCES 1. Khera SC, Gael VK, Chen RCS, Gurusami SA. A three-dimensional finite element model. Oper Dent 1988;13:128-37. 2. Vale WA. Cavity preparation. Irish Dent Rev 1956;2:33-41. 3. Vale WA. Cavity preparation and further thoughts on high speed. Br Dent J 19X+107:333-46. Eakle WS, Maxwell EH, Braly BV. Fractures of posterior teeth in adults. J Am ‘Dent Assoc 1986;112:215-8. Cave1 WT, Kelsey WP, Blankenau RJ. An in viva study of cuspal fracture. J PROSTHETDENT 1985;53:38-42. Lagouvardos P, Sourai P, Douvitsas G. Coronal fractures in posterior teeth. Oper Dent 1989;14:28-32. Mondelli J, Stengall L, Ishikirma A, Delima-Navarro MF, Socres FB. Fracture strength of human teeth with cavity preparations. J PROSTHET DENT 1980;43:419-22. 8. Re GJ, Norling BK, Draheim RN. Fracture strength of molars containing three surface amalgam restorations. J PROSTHET DENT 1982;47: 183-7. 9. Re GJ, Draheim RN, Norling BK. Fracture resistance of mandibular molars with occlusal Class I amalgam preparations. J Am Dent Assoc 1981;103:580-3. 10. Larsen TD, Douglas WH, Geistfeld RE. Effects of prepared cavities on the strength of teeth. Oper Dent 1981;6:2-5. 11. Nadal R. Amalgam restoration: cavity preparation, condensing and finishing. J Am Dent Assoc 1962;65:66-77.
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12. Blaser PK, Lund MR, Cochran MA, Potter RH. Effects of designs of Class i1 preparations on resistance to fracture. Oper Dent 198%8x6-10. 13. Gurusami SA. Stresses in human teeth-an application of the finite element technique. Master’s Thesis. Iowa City, Iowa: University of Iowa Graduate College, 1985. 14. Goel VK, Khera SC, Gurusami SA, Chen RCS. Effect of cavity design on stresses in first molar [Abstract]. J Dent Res i985;64:350. 15. Goel VK, Khera SC, Singh K. The clinical implications of the response of enamel and dentin to masticatory loads. 3 PROSTHET DENT 1990; 64:446-54. 16. Goel VK, Khera SC, Ralston JL, Chang KH. Stresses at the dentinoenamel junction of human teeth-a finite element investigation. J PROSTHET DENT 1991;66:451-9. 17. Bell JG, Smith MC!, dePont JJ. Cuspal failures of MOD restored teeth. Aust Dent J 1982;27:283-7. 18. El-Ebrashi MK: Craig RG, Peyton FA. Experimental stress analysis of dental restorations. Part I. Two-dimensional photoelastic stress analysis of inlays. J PROSTHET DENT 1967;17:277-91. 19. Fisher DW, Caputo AA, Shillingburg HT Jr, Duncanson MG. Photoelastic analysis of inlay and onlay preparations. J PROSTHET DENT 1975;33:47-53. 20. Farah JW, Dennison JB, Powers JM. Effects of design on stress distribution in intracoronal gold restorations. J Am Dent Assoc 1977;94: 1151-4. 21. Farah JW, Craig RG, Sikarski DL. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J Biomechanics 1973;6:511-20. 22. Thrasher RW, Saito GE. The stress analysis of human teeth. 3 Biomechanics 1973;6:443-9. 23. Rubin C, Krishnamurthy N, Capilouto E, Yi H. Stress analysis of the human tooth using a three-dimensional finite element model. J Dent Res 1983;62:82-5. 24. deVree JHP, Peters MCRB, Plasschaert AJM. The influence of modification of cavity design on distribution of stresses in a restored molar. J Dent Res 1984;63:1217-20. 25. Yettram AL, Wright KWJ, Picard HM. Finite element stress analysis of crowns of normal and restored teeth. J Dent Res 1976;55:1004-11. 26. Williams KR, Edmundson JT, Rees JS. Finite element method stress analysis of restored teeth. Dent Mat 1987;3:200-6. 27. D&and T. Marginal failure of amalgam Class II restoration. J Dent Res 1977;56:481-5. 28. Anusavice KJ. Quality evaluation of dental restorations. Criteria for placement and replacement. Chicago: Quintessence Books, 198928-9. 29. Rohlmann A, Mlissner U, Bergmann G, Kiilber R. Finite element analysis and experimental investigation in a femur with hip endoprosthesis. J Biomechanics 1983;16:727-42. 30. Goel VK, Blair WF. Biomechanics of the elbow joint. Automedica 1985;6:119-38. 31. Goel VK, Lee I-K, Blair WF. Effect of the Coonrad eibow prosthesis cm stress in humerus. Clin Biomech 1989;4:11-6. 32. Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomechanics 1983;16:385-410. 33. Goel VK, Lee I-K, Blair WF. Stress distribution in the ulna following a hinged elbow arthoplasty-a finite element analysis. J Arthroplasty 1989;4:163-71.
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