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Effects of design on stress distribution of intracoronal gold restorations
Eight intracoronal and extracoronal designs for gold restorations with different tapers to the lateral walls were investigated to determine the most efficient design in distributing occlusal stresses. It was found that the occlusal wall of an inlay cavity with a 7° taper and no bevel resulted in a better stress distribution than a cavity preparation with a greater taper or a long bevel. It was shown further that a wide inlay preparation resulted in less stress if the cusps were protected by gold.
Effects of design on stress distribution of intracoronal gold restorations Jean William Farah, PhD Joseph B. Dennison, DD S, MS John M. Powers, PhD, Ann Arbor, M ich ■
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The cast gold restoration has long been advoca ted for the rehabilitation of teeth with extensive caries and severely weakened remaining tooth structure. The internal design of a cavity prep aration for cast gold is more closely related to the success of the restoration than that for many other restorative materials. This investigation is an attempt to study the effect of lateral wall taper and cavosurface bevel on the stress distribution under the occlusal portion of a cast gold restor ation.
tenance of this seal during prolonged clinical function may, in many cases, be related to such factors as deflection of the gold under stress, thickness of the gold in areas of stress concen tration, uniform distribution of stresses along the gold-cement-tooth structure interface, and the bulk of remaining dentin in areas where stress might concentrate along adjacent tooth struc ture.
Materials and methods Review of the literature The intracoronal retention of a gold casting de pends on the degree of taper or inclination of the lateral walls of the cavity preparation from the path of insertion. A variation between 5° and 10° of taper on each wall is accepted in standard texts to be consistent with complete seating of the cast ing and adequate retention.1'3 The adaptation of the margin of a cast gold re storation is related to the cavosurface angle and its modification by the placement of a bevel. Much has been written concerning the necessity for bevel placement in accomplishing optimum adaptation at this interface.2'6 Adaptation of the margin does, however, remain a complex clinical problem to evaluate and is complicated by the use of a thin film of a suitable dental cement to establish a final margin seal. Satisfactory main-
The finite element method was used to investi gate the effects of the design of the lateral occlu sal wall of the cavity preparation for a cast gold restoration. The finite element method is a com puterized stress analysis method by which the stresses, as well as displacements, throughout the model under investigation can be calculated.7 To obtain the stresses and displacements, two constants are needed: the modulus of elasticity, E, and Poisson’s ratio, v. These are readily avail able in the dental literature and are presented in the Table. When these constants, as well as the type of loading, are fed into the computer as inT able ■ E la stic co n sta n ts fo r g o ld , enam el, and d e n tin .
Enamel Dentin Gold
Young's modulus (E) MN/m2
Poisson's ratio (u)
82,800 18,600 77,200
0.33 0.31 0.33
JA D A , V o l. 94, J u n e 1977 ■ 1151
Fig 1 ■ Four intracoronal cavity designs. A, with 7° taper (design 1); B, with 7° taper and 13° bevel (design 2); C, with 7° taper and 23° bevel (design 3); and D, with 15° taper (design 4).
put, an output is obtained that includes all the stresses, as well as displacements. Eight different designs (Fig 1 to 3) were inves tigated under identical loading conditions: an occlusal inlay cavity with a 7° taper to the lateral wall and no bevel, a 7° taper with a 13° bevel at the cavosurface margin, a 7° taper with a 23° bev el at the cavosurface margin, an occlusal inlay cavity with a 15° taper and no bevel, a wider prep aration with a 7° taper and no bevel, a wider prep aration with a 33° bevel to protect the tip of the cusp, an occlusal onlay preparation to protect the cusp by a long external bevel, and an occlu sal preparation with a thin shoulder on the outer incline of the cusp and a short bevel. The first molar with slightly idealized mor phology and with the various inlays and onlays described was subjected to a 222-N load. Half
the load (111 N) acted along the cuspal incline, and the other half (111 N) was at the height of the cusp tip (Fig 4 to 6). The stresses throughout the tooth, as well as the gold restoration, were computed, with special emphasis on the stresses at the gold-tooth structure interface.
Results The distributions of compressive stresses in the tooth structure adjacent to the restoration are shown in Figures 4 to 6. In design 1 (Fig 4A), the highest value of the compressive stress was 7.5 MN/m2 and occurred in enamel near the dentinoenamel junction. In design 2 (Fig 4B), the stress was highest (10 MN/m2) near the cavosurface
A
B
Fig 3 ■ Two extracoronal cavity designs. A, with occlusal onlay prep Fig 2 ■ Two intracoronal cavity designs. A, with 7° taper and no bevel
aration to protect cusp by long external bevel (design 7); and B, same as
(design 5); and B, with 7° taper and cusp protection (33° bevel, design 6).
A, but using thin shoulder on outer incline of cusp and short bevel (de sign 8).
1152 ■ JAD A, V ol. 94, J u n e 1977
Fig 4 ■ Compressive stresses at the gold-tooth structure interface. Lines perpendicular to outline of restor ation represent magnitude and direction of stress.
margin. In design 3 (Fig 4C), the stress distribu tion was similar to that in design 2, but slightly greater and nearer to the occlusal margin. Figure 4C (design 4) shows approximately the same stress distribution as in design 2. In design 5 (Fig 5A), the taper was 7°, but a wider preparation than that in design 1 was chosen. The stress was highest in enamel at the occlusal surface, reach ing a value of 19 MN/m2 and decreasing slowly toward the pulpal floor. In design 6 (Fig 5B), where the cusp was protected, the maximum stresses were located near the dentinoenamel junction and were substantially lower (6.5 MN/ m2) than those in design 5. In designs 7 and 8 (Fig 6A and B), the stresses were quite uniform ly distributed and were dramatically lower (ap proximately 1 MN/m2) than those in other de
signs. In all these designs, the stresses at the pul pal floor were uniform and did not exceed 1 MN/ m 2.
Discussion The results obtained from the first four cavity designs (Fig 4) indicate that the design with a 7° taper to the lateral occlusal wall and no bevel exhibited the least amount of compressive stress. As the inclination of the lateral wall was in creased (design 4) and with the addition of a ca vosurface bevel of greater inclination (designs 2 and 3), the stress increased accordingly., On the average, the compressive stress was 24% higher in design 2 and approximately 33% higher
Fig 5 ■ Compressive stresses at gold-tooth structure interface.
Fig 6 ■ Compressive stresses at gold-tooth structure interface.
Lines perpendicular to outline of restoration represent magnitude
Lines perpendicular to outline of restoration represent magnitude and direction of stress.
and direction of stress.
Farah— D e n n is o n — P o w e rs: DESIGN OF IN TR A C O R O N A L R E STO R ATIO N S ■ 1153
in designs 3 and 4, when compared with design 1. It is deduced that in the preparation of the occlu sal portion of a Class I gold restoration, the taper should be kept to a minimum (<7°) and the bevel away from the point of load application. Sub stantially lower compressive stresses (6.5 MN/ m2) were encountered in a large preparation when the cusp was onlaid with gold (design 6) as compared with design 5 (Fig 5), where the stress was 19 MN/m2. This substantiates the advantage of cuspal protection in teeth with ex tensive caries with undermining of cuspal areas. When the cusp was completely protected on the buccal or lingual surface, the average com pressive stress was significantly lower (1 MN/m2) and more uniformly distributed (Fig 6). No dif ference in the stress distribution was observed between designs 7 and 8. For teeth in which cus pal support is weakened, a properly designed gold restoration can be used to evenly distribute the occlusal stresses. In the final design of a gold inlay, many fac tors must be taken into consideration. In a con servative preparation, the buccolingual width of both the isthmus area and the box should be kept reasonably narrow to avoid the weaken ing of cuspal support and the accumulation of excessive stress at the cavosurface margin (com pare designs 1 and 5). Since gold alloys are rela tively ductile restorative materials, margin adap tation of the restoration can be greatly enhanced by the creation of an acute cavosurface angle or bevel on which the gold can be finished and bur nished to place. Although adaptation and mar ginal seal can be improved by making the angle of this bevel more acute (a greater angle from the line of draw), results in this,study (designs 1, 2, and 3) indicate that stresses concentrate as the bevel gets longer and thus approaches the point of occlusal loading. This could result in deflec tions of the thin gold bevel and breakage of the cement bond with concurrent leakage. An in crease of the taper on the lateral walls from 7° (design 1) to 15° (design 4) will not only reduce the frictional resistance against the casting so vitally needed for retention, but also will increase the stress concentration (Fig 4A, D) and change its location from the dentinoenamel junction to the cavosurface enamel. It is a measure that could weaken the restoration and should be con traindicated. Protection of the cuspal tip in a wide inlay preparation is well supported by the results of this study (designs 5 through 8). In preparations where the cusp has been weakened by caries or 1154 ■ JADA, Vol. 94, June 1977
a previously placed restorative material, com plete onlay of the cusp with extension onto the external surface of the tooth will both reduce the amount of stress accumulation (designs 5, 6, and 8) and also uniformly distribute the load away from an already weakened dentinoenamel junction (designs 6 and 8). There appears to be little value to the use of design 8 over design 7 when protecting a cusp with gold, at least as far as stress distribution is concerned. However, the creation of a short external wall with approxim ately a 15° total extracoronal taper, a flat shoul der perpendicular to the line of draw, and a short uniform outer bevel should improve retention form, resistance form, and margin adaptation, respectively, and improve the durability of such a major restorative procedure.
Conclusions Within the limitations of an axisymmetric de sign, used for the molar model evaluated in this study, it can be concluded that the lateral walls of an inlay preparation will result in less stress if both the taper of the wall and the inclination of the cavosurface bevel are minimal. A wide inlay preparation will result in less stress if cusps are protected by the gold. Finally, in a wide inlay preparation, onlay of the cusps with gold and ex tension onto the lateral external surface will func tion better in distributing the stresses than ter mination of the bevel at the cuspal tip.
Dr. Farah is assistant research scientist in the department of dental materials, School of Dentistry, the University of Michi gan, Ann Arbor, 48109. Dr. Dennison is associate professor of dentistry in the departments of dental materials and operative dentistry, and Dr. Powers is associate professor of dentistry in the department of dental materials, School of Dentistry, the Uni versity of Michigan. Address requests for reprints to Dr. Farah. 1. Charbeneau, G.T., and others. Principles and practice of operative dentistry. Philadelphia, Lea & Febiger, 1975, p 363. 2. Sturdevant, C.M., and others. The art and science of oper ative dentistry. New York, McGraw-Hill Book Co., 1968. 3. Smith, G.E., and Grainger, D A. Biomechanical design of extensive cavity preparations for cast gold. JADA 89:1152 Nov 1974. 4. Fisher, D.W., and others. Photoelastic analysis of inlay and onlay preparations. J Prosthet Dent 33:47 Jan 1975. 5. Barnes, J.E. The production of inlay cavity bevels. Br Dent J 137:379, Nov 19, 1974. 6. Rosenstiel, E. To bevel or not to bevel? Br Dent J 138:389 May 20, 1975. 7. Farah, J.W.; Hood, J.A., and Craig, R.G. Effects of cement bases on the stresses in amalgam restorations. J Dent Res 54:10 Jan-Feb 1975.
Effects of design on stress distribution of intracoronal gold restorations Jean William Farah, PhD Joseph B. Dennison, DD S, MS John M. Powers, PhD, Ann Arbor, M ich ■
■
■
The cast gold restoration has long been advoca ted for the rehabilitation of teeth with extensive caries and severely weakened remaining tooth structure. The internal design of a cavity prep aration for cast gold is more closely related to the success of the restoration than that for many other restorative materials. This investigation is an attempt to study the effect of lateral wall taper and cavosurface bevel on the stress distribution under the occlusal portion of a cast gold restor ation.
tenance of this seal during prolonged clinical function may, in many cases, be related to such factors as deflection of the gold under stress, thickness of the gold in areas of stress concen tration, uniform distribution of stresses along the gold-cement-tooth structure interface, and the bulk of remaining dentin in areas where stress might concentrate along adjacent tooth struc ture.
Materials and methods Review of the literature The intracoronal retention of a gold casting de pends on the degree of taper or inclination of the lateral walls of the cavity preparation from the path of insertion. A variation between 5° and 10° of taper on each wall is accepted in standard texts to be consistent with complete seating of the cast ing and adequate retention.1'3 The adaptation of the margin of a cast gold re storation is related to the cavosurface angle and its modification by the placement of a bevel. Much has been written concerning the necessity for bevel placement in accomplishing optimum adaptation at this interface.2'6 Adaptation of the margin does, however, remain a complex clinical problem to evaluate and is complicated by the use of a thin film of a suitable dental cement to establish a final margin seal. Satisfactory main-
The finite element method was used to investi gate the effects of the design of the lateral occlu sal wall of the cavity preparation for a cast gold restoration. The finite element method is a com puterized stress analysis method by which the stresses, as well as displacements, throughout the model under investigation can be calculated.7 To obtain the stresses and displacements, two constants are needed: the modulus of elasticity, E, and Poisson’s ratio, v. These are readily avail able in the dental literature and are presented in the Table. When these constants, as well as the type of loading, are fed into the computer as inT able ■ E la stic co n sta n ts fo r g o ld , enam el, and d e n tin .
Enamel Dentin Gold
Young's modulus (E) MN/m2
Poisson's ratio (u)
82,800 18,600 77,200
0.33 0.31 0.33
JA D A , V o l. 94, J u n e 1977 ■ 1151
Fig 1 ■ Four intracoronal cavity designs. A, with 7° taper (design 1); B, with 7° taper and 13° bevel (design 2); C, with 7° taper and 23° bevel (design 3); and D, with 15° taper (design 4).
put, an output is obtained that includes all the stresses, as well as displacements. Eight different designs (Fig 1 to 3) were inves tigated under identical loading conditions: an occlusal inlay cavity with a 7° taper to the lateral wall and no bevel, a 7° taper with a 13° bevel at the cavosurface margin, a 7° taper with a 23° bev el at the cavosurface margin, an occlusal inlay cavity with a 15° taper and no bevel, a wider prep aration with a 7° taper and no bevel, a wider prep aration with a 33° bevel to protect the tip of the cusp, an occlusal onlay preparation to protect the cusp by a long external bevel, and an occlu sal preparation with a thin shoulder on the outer incline of the cusp and a short bevel. The first molar with slightly idealized mor phology and with the various inlays and onlays described was subjected to a 222-N load. Half
the load (111 N) acted along the cuspal incline, and the other half (111 N) was at the height of the cusp tip (Fig 4 to 6). The stresses throughout the tooth, as well as the gold restoration, were computed, with special emphasis on the stresses at the gold-tooth structure interface.
Results The distributions of compressive stresses in the tooth structure adjacent to the restoration are shown in Figures 4 to 6. In design 1 (Fig 4A), the highest value of the compressive stress was 7.5 MN/m2 and occurred in enamel near the dentinoenamel junction. In design 2 (Fig 4B), the stress was highest (10 MN/m2) near the cavosurface
A
B
Fig 3 ■ Two extracoronal cavity designs. A, with occlusal onlay prep Fig 2 ■ Two intracoronal cavity designs. A, with 7° taper and no bevel
aration to protect cusp by long external bevel (design 7); and B, same as
(design 5); and B, with 7° taper and cusp protection (33° bevel, design 6).
A, but using thin shoulder on outer incline of cusp and short bevel (de sign 8).
1152 ■ JAD A, V ol. 94, J u n e 1977
Fig 4 ■ Compressive stresses at the gold-tooth structure interface. Lines perpendicular to outline of restor ation represent magnitude and direction of stress.
margin. In design 3 (Fig 4C), the stress distribu tion was similar to that in design 2, but slightly greater and nearer to the occlusal margin. Figure 4C (design 4) shows approximately the same stress distribution as in design 2. In design 5 (Fig 5A), the taper was 7°, but a wider preparation than that in design 1 was chosen. The stress was highest in enamel at the occlusal surface, reach ing a value of 19 MN/m2 and decreasing slowly toward the pulpal floor. In design 6 (Fig 5B), where the cusp was protected, the maximum stresses were located near the dentinoenamel junction and were substantially lower (6.5 MN/ m2) than those in design 5. In designs 7 and 8 (Fig 6A and B), the stresses were quite uniform ly distributed and were dramatically lower (ap proximately 1 MN/m2) than those in other de
signs. In all these designs, the stresses at the pul pal floor were uniform and did not exceed 1 MN/ m 2.
Discussion The results obtained from the first four cavity designs (Fig 4) indicate that the design with a 7° taper to the lateral occlusal wall and no bevel exhibited the least amount of compressive stress. As the inclination of the lateral wall was in creased (design 4) and with the addition of a ca vosurface bevel of greater inclination (designs 2 and 3), the stress increased accordingly., On the average, the compressive stress was 24% higher in design 2 and approximately 33% higher
Fig 5 ■ Compressive stresses at gold-tooth structure interface.
Fig 6 ■ Compressive stresses at gold-tooth structure interface.
Lines perpendicular to outline of restoration represent magnitude
Lines perpendicular to outline of restoration represent magnitude and direction of stress.
and direction of stress.
Farah— D e n n is o n — P o w e rs: DESIGN OF IN TR A C O R O N A L R E STO R ATIO N S ■ 1153
in designs 3 and 4, when compared with design 1. It is deduced that in the preparation of the occlu sal portion of a Class I gold restoration, the taper should be kept to a minimum (<7°) and the bevel away from the point of load application. Sub stantially lower compressive stresses (6.5 MN/ m2) were encountered in a large preparation when the cusp was onlaid with gold (design 6) as compared with design 5 (Fig 5), where the stress was 19 MN/m2. This substantiates the advantage of cuspal protection in teeth with ex tensive caries with undermining of cuspal areas. When the cusp was completely protected on the buccal or lingual surface, the average com pressive stress was significantly lower (1 MN/m2) and more uniformly distributed (Fig 6). No dif ference in the stress distribution was observed between designs 7 and 8. For teeth in which cus pal support is weakened, a properly designed gold restoration can be used to evenly distribute the occlusal stresses. In the final design of a gold inlay, many fac tors must be taken into consideration. In a con servative preparation, the buccolingual width of both the isthmus area and the box should be kept reasonably narrow to avoid the weaken ing of cuspal support and the accumulation of excessive stress at the cavosurface margin (com pare designs 1 and 5). Since gold alloys are rela tively ductile restorative materials, margin adap tation of the restoration can be greatly enhanced by the creation of an acute cavosurface angle or bevel on which the gold can be finished and bur nished to place. Although adaptation and mar ginal seal can be improved by making the angle of this bevel more acute (a greater angle from the line of draw), results in this,study (designs 1, 2, and 3) indicate that stresses concentrate as the bevel gets longer and thus approaches the point of occlusal loading. This could result in deflec tions of the thin gold bevel and breakage of the cement bond with concurrent leakage. An in crease of the taper on the lateral walls from 7° (design 1) to 15° (design 4) will not only reduce the frictional resistance against the casting so vitally needed for retention, but also will increase the stress concentration (Fig 4A, D) and change its location from the dentinoenamel junction to the cavosurface enamel. It is a measure that could weaken the restoration and should be con traindicated. Protection of the cuspal tip in a wide inlay preparation is well supported by the results of this study (designs 5 through 8). In preparations where the cusp has been weakened by caries or 1154 ■ JADA, Vol. 94, June 1977
a previously placed restorative material, com plete onlay of the cusp with extension onto the external surface of the tooth will both reduce the amount of stress accumulation (designs 5, 6, and 8) and also uniformly distribute the load away from an already weakened dentinoenamel junction (designs 6 and 8). There appears to be little value to the use of design 8 over design 7 when protecting a cusp with gold, at least as far as stress distribution is concerned. However, the creation of a short external wall with approxim ately a 15° total extracoronal taper, a flat shoul der perpendicular to the line of draw, and a short uniform outer bevel should improve retention form, resistance form, and margin adaptation, respectively, and improve the durability of such a major restorative procedure.
Conclusions Within the limitations of an axisymmetric de sign, used for the molar model evaluated in this study, it can be concluded that the lateral walls of an inlay preparation will result in less stress if both the taper of the wall and the inclination of the cavosurface bevel are minimal. A wide inlay preparation will result in less stress if cusps are protected by the gold. Finally, in a wide inlay preparation, onlay of the cusps with gold and ex tension onto the lateral external surface will func tion better in distributing the stresses than ter mination of the bevel at the cuspal tip.
Dr. Farah is assistant research scientist in the department of dental materials, School of Dentistry, the University of Michi gan, Ann Arbor, 48109. Dr. Dennison is associate professor of dentistry in the departments of dental materials and operative dentistry, and Dr. Powers is associate professor of dentistry in the department of dental materials, School of Dentistry, the Uni versity of Michigan. Address requests for reprints to Dr. Farah. 1. Charbeneau, G.T., and others. Principles and practice of operative dentistry. Philadelphia, Lea & Febiger, 1975, p 363. 2. Sturdevant, C.M., and others. The art and science of oper ative dentistry. New York, McGraw-Hill Book Co., 1968. 3. Smith, G.E., and Grainger, D A. Biomechanical design of extensive cavity preparations for cast gold. JADA 89:1152 Nov 1974. 4. Fisher, D.W., and others. Photoelastic analysis of inlay and onlay preparations. J Prosthet Dent 33:47 Jan 1975. 5. Barnes, J.E. The production of inlay cavity bevels. Br Dent J 137:379, Nov 19, 1974. 6. Rosenstiel, E. To bevel or not to bevel? Br Dent J 138:389 May 20, 1975. 7. Farah, J.W.; Hood, J.A., and Craig, R.G. Effects of cement bases on the stresses in amalgam restorations. J Dent Res 54:10 Jan-Feb 1975.