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The convergence angle of tooth preparations for complete crowns
The convergence angle of tooth preparations for complete crowns P. J. B. Leempoel, D.D.S., Ph.D.,* Ph. L. M. Lemmens, D.D.S.,** P. A. Snoek, D.D.S.,*** and M. A. van ‘t Hof, Ph.D.**** University of Nijmegen, Faculty of Dentistry, Nijmegen, The Netherlands
F
actors that influence the retention of complete gold crowns may be categorized as (1) the preparation, (2) the restoration, and (3) the cement.‘” This article discusses the influence of the convergence angle of tooth preparations on the retention of an artificial crown. The convergence angle can be defined as the angle made by the opposite walls of a preparation.4 The tooth preparations for the clinical research had provided sufficient retention inasmuch as all restorations were still present after 5 years without recementing. According to Gabe15the best retention was created by preparing the axial walls as nearly parallel as possible. Later investigations by J$rgenserP suggested that the ideal angle was 5 to 10 degrees, and an angle greater than 10 degrees decreased retention by 50%. Other researchers2z7-9recommended convergence angles between 10 and 16 degrees, on the basis of laboratory studies. More recently, Snoek and KSyser,‘O Eames et al.,” and Mack12 demonstrated that these laboratory figures are difficult to achieve under clinical conditions. Snoek and Kgyser” concluded that a convergence angle of 12 to 30 degrees was often used and that these angles were acceptable because they did not lead to failures. These findings agreed with those of Nordlander and Weir.‘) Mack12 believed the disparity between laboratory research and clinical application could be explained by the experience of the dentist. MATERIAL
AND
METHODS
Working dies of cast crown preparations were randomly selected from the 285 laboratory models of two dentists. The restorations had been inserted 5 to 10 years before and were still functioning adequately in the mouth. The teeth were prepared without retention grooves. The total number of randomly selected dies was 132. The distribution by tooth and arch is listed in Table I.
*Senior Prosthodontist, Department of Occlusal Reconstruction. **Staff Member, Department of Cariology. ***Assistant Professor, Department of Occlusal Reconstruction. ****Senior Statistical Consultant, Department of Statistical Consultation.
414
Table I. Distribution and dental arch Dentist
Maxilla Mandible
Total
of 132 dies by tooth Dentist 2
1
Premolar’
Molar
Premolar
Molar
Total
16 8 24
18 19 37
24 14 38
14 19 33
72 60 132
Table II. Mean convergence angle, standard
deviation, and systematic difference for 132 dies of tooth preparations Observer
1
Mean SD (degrees)
View Buccal
21.3
8.5
Proximal
21.9
7.6
Observer 2
Systematic difference (degrees)
Mean SD (degrees) 20.4 20.9
8.6 7.5
0.9 1.0
Table III. Pearson correlation between the
two observers for buccal and proximal view View
Observer 1 Observer
2
Measurement error (degrees)
Buccal
Proximal
0.89 0.97 2.0
0.94 0.96 1.6
One photograph was made of the buccal surface and the proximal surface of the preparation to measure the convergence angle (Fig. 1). The negatives were mounted in a D-Mac (D-Mac Ltd., Glasgow, U.K.) registration device, consisting of a slide projector, measurement table, and position registration equipment. The projector was adjusted on a Xl8 linear magnification with a viewer and a reticle. The position of the center of the reticle was expressed in coordinates and registered in tenths of a millimeter. Two points were designated on the mesial and the distal surfaces for the
buccal-view photograph. A proximal-view photograph recorded the buccal and lingual surfaces of the tooth
OCTOBER
1987
VOLUME
58
NUMBER
4
CONVERGENCE
ANGLE
OF TOOTH
PREPARATIONS
Fig.
1.
Setup for photographs.
Table IV. Distribution of the mean convergence preparations by two dentists
angles (degrees + SD) of 132 dies of tooth
Premolar
Molar Proximal
Buccal
Dentist 1 Maxilla Mandible Dentist 2 Maxilla Mandible
Table V. Distribution
SD
Mean
SD
Mean
SD
Mean
SD
17.5 14.3
4.5 6.8
14.6 16.7
5.0 3.7
21.6 24.3
6.1 8.1
21.4 24.6
4.1 7.0
17.5 15.1
6.3 6.2
20.4 16.5
7.9 4.3
20.0 31.3
6.6 8.4
23.4 29.2
6.0 7.0
of the overall
convergence
angle (OCA) (degrees k SD) of 132 dies Dentist
1
Premolar
2
Premolar
Molar
Molar
OCA
SD
OCA
SD
OCA
SD
OCA
SD
16.0 15.5
3.1 4.1
21.5 24.4
3.8 6.6
19.0 15.8
6.3 4.0
21.7 30.2
5.7 6.8
preparation (Fig. 2). These points were located on the straight portion of the contour in the center of the surface. The buccal and proximal coordinates were recorded from each die. Two dentists performed the measurements independently. RESULTS The interobserver agreement can be seen in Tables II and III. Table II demonstrates that observer 1 measured systematically larger angles than observer 2 (paired t-test; p < .Ol). Table III confirmed the measurement error and the interobserver correlation was satisfactory. The average value of both observers on the same view of each die was then used for further analysis.
THE JOURNAL
Proximal
Mean
Dentist
Maxilla Mandible
Buccal
OF PROSTHETIC
DENTISTRY
A description of the data base of the mean convergence angles is presented in Table IV. The results displayed a wide variety in mean angles, ranging from 14.3 to 31.3 degrees, and when the standard deviation was considered the range was even more impressive. The overall convergence angle (OCA) and/or the mean of the angle in buccal view and the angle in proximal view is reported in Table V. Analysis of variance illustrated a significant specific tooth effect (@< .OOOl), dental arch effect, and an interaction between tooth type and arch (9, = .03). The influence of the skill between dentists was not appreciable. The calculation of the differences is presented in Table VI. The table indicates that the molar tooth has
415
LEEMPOEL
ET AL
dies measured revealed a surprising range in the convergence angles (15.5 to 30.2 degrees). The mandibular molar preparations had the greatest convergence angle. The design of mandibular molar preparations should be the subject of additional research. . REFERENCES 1
2
3.
Fig. 2. Approximal view photograph with measured (a, b, c, d).
points
to be
4. 5.
Table VI. Differences in overall convergence angle (degrees) because of tooth and dental arch Maxilla Premolar Molar Tooth effect
17.5 21.6 4.1
Mandible 15.6 27.3 11.7
Jaw effect 1.9 -5.7
6.
7. 8.
9.
the largest difference OCA (11.7 degrees) and the mandibular molars are 5.7 degrees more convergent. DISCUSSION OCAs of 15.5 degrees to 30.2 degrees provide sufficient retention for a complete artificial crown. These results contradict the recommendations of the laboratory studies of Pickard,’ Smith,2 and El-Ebrashi et al.* However, they agree with the results of Snoek,‘ONordlander and Weir,13 and Ohm and Silness.‘4 The mandibular molar preparation recorded the greatest OCA. Although the retention of the crowns was suitable clinically, the height of the preparation also influences retention. I5 Retention grooves are recommended to increase the retention in mandibular molars when these teeth are used as abutments. Weed and Baez16indicated that the preparation of grooves was also important to increase the resistance of the crown against rotating forces. Periodontists have advocated supragingival margins that result in shorter preparations occlusogingivally, decreasing retention. This could be compensated by a smaller convergence angle and the addition of retention grooves.
10.
11.
12.
13.
14. 15.
16.
Kaufman EG, Coelho AB, Colin L. Factors influencing the retention of cemented gold castings. J PROSTHETDENT 1961; 11:487-502. Smith BGN. The effect of the surface roughness of prepared dentin on the retention of castings. J PROSTHETDENT 1970; 23:187-98. Lorey RE, Myers GE. The retentive quality of bridge retainers. J Am Dent Assoc 1968;76:568-72. Rosenstiel E: The taper of inlay and crown preparations, a contribution to dental terminology. Br Dent 1975;139:436-8. Gabel AB. The american textbook of operative dentistry. 9th ed. Philadelphia: Lea & Febiger, 1954;377. Jfirgensen KD. The relationship between retention and convergence angle in cemented veneer crowns. Acta Odontol Stand 1955;13:35-40. Pickard HM. A manual of operative dentistry. London: Oxford University Press, 1961;93. El-Ebrashi MK, Craig RG, Peyton FA. Experimental stress analysis of dental restorations. Part IV. The concept of parallelism of axial walls. J PRO~THETDENT 1969;22:346-53. Dodge WW, Weed RM, Baez RJ, Buchanan RN. The effect of convergence angle on retention and resistance form. Quintessence Int 1985;16:191-4. Snoek PA, KIyser AF. De convergentiehoek van de schouderloze volledige kroonpreparatie. Ned Tijdschr Tandheelkunde 1973; 80:398-400. Eames WB, O’Neal SJ, Monteiro J, Miller C, Roan JD, Cohen KS. Techniques to improve the seating of castings. J Am Dent Assoc 1978;96:432-7. Mack PJ. A theoretical and clinical investigation into the taper achieved on crown and inlay preparations. J Oral Rehabil 1980;7:255-65. Nordlander J, Weir D. Taper and length of crown preparations by general practice residents [Abstract]. J Dent Res 1985; 64377. Ohm E, Silness J. The convergence angle in teeth prepared for artificial crowns. J Oral Rehabil 1978;5:371-5. Maxwell AW, Blank LW, Pelleu GB. Crown preparations and the retention and resistance of gold castings [Abstract]. J Dent Res 1985;64:377. Weed RM, Baez RJ. A method for determining adequate resistance form of complete cast crown preparations. J PR~STHET DENT 1984;52:330-4.
Reprint requests to: DR. Ph. J. B. LEEMPOEL UNIVERSITYOF NIJMEGEN FACULTYOF DENTISTRY PHILIPSVAN LEYDENLAAN25 6525 EX NIJMEGEN THE NETHERLANDS
CONCLUSION A method was developed to measure the convergence angle on dies of complete crown preparations. The 132 416
OCTOBER
1987
VOLUME
58
NUMBER
4
F
actors that influence the retention of complete gold crowns may be categorized as (1) the preparation, (2) the restoration, and (3) the cement.‘” This article discusses the influence of the convergence angle of tooth preparations on the retention of an artificial crown. The convergence angle can be defined as the angle made by the opposite walls of a preparation.4 The tooth preparations for the clinical research had provided sufficient retention inasmuch as all restorations were still present after 5 years without recementing. According to Gabe15the best retention was created by preparing the axial walls as nearly parallel as possible. Later investigations by J$rgenserP suggested that the ideal angle was 5 to 10 degrees, and an angle greater than 10 degrees decreased retention by 50%. Other researchers2z7-9recommended convergence angles between 10 and 16 degrees, on the basis of laboratory studies. More recently, Snoek and KSyser,‘O Eames et al.,” and Mack12 demonstrated that these laboratory figures are difficult to achieve under clinical conditions. Snoek and Kgyser” concluded that a convergence angle of 12 to 30 degrees was often used and that these angles were acceptable because they did not lead to failures. These findings agreed with those of Nordlander and Weir.‘) Mack12 believed the disparity between laboratory research and clinical application could be explained by the experience of the dentist. MATERIAL
AND
METHODS
Working dies of cast crown preparations were randomly selected from the 285 laboratory models of two dentists. The restorations had been inserted 5 to 10 years before and were still functioning adequately in the mouth. The teeth were prepared without retention grooves. The total number of randomly selected dies was 132. The distribution by tooth and arch is listed in Table I.
*Senior Prosthodontist, Department of Occlusal Reconstruction. **Staff Member, Department of Cariology. ***Assistant Professor, Department of Occlusal Reconstruction. ****Senior Statistical Consultant, Department of Statistical Consultation.
414
Table I. Distribution and dental arch Dentist
Maxilla Mandible
Total
of 132 dies by tooth Dentist 2
1
Premolar’
Molar
Premolar
Molar
Total
16 8 24
18 19 37
24 14 38
14 19 33
72 60 132
Table II. Mean convergence angle, standard
deviation, and systematic difference for 132 dies of tooth preparations Observer
1
Mean SD (degrees)
View Buccal
21.3
8.5
Proximal
21.9
7.6
Observer 2
Systematic difference (degrees)
Mean SD (degrees) 20.4 20.9
8.6 7.5
0.9 1.0
Table III. Pearson correlation between the
two observers for buccal and proximal view View
Observer 1 Observer
2
Measurement error (degrees)
Buccal
Proximal
0.89 0.97 2.0
0.94 0.96 1.6
One photograph was made of the buccal surface and the proximal surface of the preparation to measure the convergence angle (Fig. 1). The negatives were mounted in a D-Mac (D-Mac Ltd., Glasgow, U.K.) registration device, consisting of a slide projector, measurement table, and position registration equipment. The projector was adjusted on a Xl8 linear magnification with a viewer and a reticle. The position of the center of the reticle was expressed in coordinates and registered in tenths of a millimeter. Two points were designated on the mesial and the distal surfaces for the
buccal-view photograph. A proximal-view photograph recorded the buccal and lingual surfaces of the tooth
OCTOBER
1987
VOLUME
58
NUMBER
4
CONVERGENCE
ANGLE
OF TOOTH
PREPARATIONS
Fig.
1.
Setup for photographs.
Table IV. Distribution of the mean convergence preparations by two dentists
angles (degrees + SD) of 132 dies of tooth
Premolar
Molar Proximal
Buccal
Dentist 1 Maxilla Mandible Dentist 2 Maxilla Mandible
Table V. Distribution
SD
Mean
SD
Mean
SD
Mean
SD
17.5 14.3
4.5 6.8
14.6 16.7
5.0 3.7
21.6 24.3
6.1 8.1
21.4 24.6
4.1 7.0
17.5 15.1
6.3 6.2
20.4 16.5
7.9 4.3
20.0 31.3
6.6 8.4
23.4 29.2
6.0 7.0
of the overall
convergence
angle (OCA) (degrees k SD) of 132 dies Dentist
1
Premolar
2
Premolar
Molar
Molar
OCA
SD
OCA
SD
OCA
SD
OCA
SD
16.0 15.5
3.1 4.1
21.5 24.4
3.8 6.6
19.0 15.8
6.3 4.0
21.7 30.2
5.7 6.8
preparation (Fig. 2). These points were located on the straight portion of the contour in the center of the surface. The buccal and proximal coordinates were recorded from each die. Two dentists performed the measurements independently. RESULTS The interobserver agreement can be seen in Tables II and III. Table II demonstrates that observer 1 measured systematically larger angles than observer 2 (paired t-test; p < .Ol). Table III confirmed the measurement error and the interobserver correlation was satisfactory. The average value of both observers on the same view of each die was then used for further analysis.
THE JOURNAL
Proximal
Mean
Dentist
Maxilla Mandible
Buccal
OF PROSTHETIC
DENTISTRY
A description of the data base of the mean convergence angles is presented in Table IV. The results displayed a wide variety in mean angles, ranging from 14.3 to 31.3 degrees, and when the standard deviation was considered the range was even more impressive. The overall convergence angle (OCA) and/or the mean of the angle in buccal view and the angle in proximal view is reported in Table V. Analysis of variance illustrated a significant specific tooth effect (@< .OOOl), dental arch effect, and an interaction between tooth type and arch (9, = .03). The influence of the skill between dentists was not appreciable. The calculation of the differences is presented in Table VI. The table indicates that the molar tooth has
415
LEEMPOEL
ET AL
dies measured revealed a surprising range in the convergence angles (15.5 to 30.2 degrees). The mandibular molar preparations had the greatest convergence angle. The design of mandibular molar preparations should be the subject of additional research. . REFERENCES 1
2
3.
Fig. 2. Approximal view photograph with measured (a, b, c, d).
points
to be
4. 5.
Table VI. Differences in overall convergence angle (degrees) because of tooth and dental arch Maxilla Premolar Molar Tooth effect
17.5 21.6 4.1
Mandible 15.6 27.3 11.7
Jaw effect 1.9 -5.7
6.
7. 8.
9.
the largest difference OCA (11.7 degrees) and the mandibular molars are 5.7 degrees more convergent. DISCUSSION OCAs of 15.5 degrees to 30.2 degrees provide sufficient retention for a complete artificial crown. These results contradict the recommendations of the laboratory studies of Pickard,’ Smith,2 and El-Ebrashi et al.* However, they agree with the results of Snoek,‘ONordlander and Weir,13 and Ohm and Silness.‘4 The mandibular molar preparation recorded the greatest OCA. Although the retention of the crowns was suitable clinically, the height of the preparation also influences retention. I5 Retention grooves are recommended to increase the retention in mandibular molars when these teeth are used as abutments. Weed and Baez16indicated that the preparation of grooves was also important to increase the resistance of the crown against rotating forces. Periodontists have advocated supragingival margins that result in shorter preparations occlusogingivally, decreasing retention. This could be compensated by a smaller convergence angle and the addition of retention grooves.
10.
11.
12.
13.
14. 15.
16.
Kaufman EG, Coelho AB, Colin L. Factors influencing the retention of cemented gold castings. J PROSTHETDENT 1961; 11:487-502. Smith BGN. The effect of the surface roughness of prepared dentin on the retention of castings. J PROSTHETDENT 1970; 23:187-98. Lorey RE, Myers GE. The retentive quality of bridge retainers. J Am Dent Assoc 1968;76:568-72. Rosenstiel E: The taper of inlay and crown preparations, a contribution to dental terminology. Br Dent 1975;139:436-8. Gabel AB. The american textbook of operative dentistry. 9th ed. Philadelphia: Lea & Febiger, 1954;377. Jfirgensen KD. The relationship between retention and convergence angle in cemented veneer crowns. Acta Odontol Stand 1955;13:35-40. Pickard HM. A manual of operative dentistry. London: Oxford University Press, 1961;93. El-Ebrashi MK, Craig RG, Peyton FA. Experimental stress analysis of dental restorations. Part IV. The concept of parallelism of axial walls. J PRO~THETDENT 1969;22:346-53. Dodge WW, Weed RM, Baez RJ, Buchanan RN. The effect of convergence angle on retention and resistance form. Quintessence Int 1985;16:191-4. Snoek PA, KIyser AF. De convergentiehoek van de schouderloze volledige kroonpreparatie. Ned Tijdschr Tandheelkunde 1973; 80:398-400. Eames WB, O’Neal SJ, Monteiro J, Miller C, Roan JD, Cohen KS. Techniques to improve the seating of castings. J Am Dent Assoc 1978;96:432-7. Mack PJ. A theoretical and clinical investigation into the taper achieved on crown and inlay preparations. J Oral Rehabil 1980;7:255-65. Nordlander J, Weir D. Taper and length of crown preparations by general practice residents [Abstract]. J Dent Res 1985; 64377. Ohm E, Silness J. The convergence angle in teeth prepared for artificial crowns. J Oral Rehabil 1978;5:371-5. Maxwell AW, Blank LW, Pelleu GB. Crown preparations and the retention and resistance of gold castings [Abstract]. J Dent Res 1985;64:377. Weed RM, Baez RJ. A method for determining adequate resistance form of complete cast crown preparations. J PR~STHET DENT 1984;52:330-4.
Reprint requests to: DR. Ph. J. B. LEEMPOEL UNIVERSITYOF NIJMEGEN FACULTYOF DENTISTRY PHILIPSVAN LEYDENLAAN25 6525 EX NIJMEGEN THE NETHERLANDS
CONCLUSION A method was developed to measure the convergence angle on dies of complete crown preparations. The 132 416
OCTOBER
1987
VOLUME
58
NUMBER
4