RESEARCH. Key Words: crown-implant ratios, proximal bone-to-implant contact. Journal of Oral Implantology 425

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1 RESEARCH Crown-to-Implant Ratios of Short-Length Implants Hardeep Birdi, DMD, MS 1 * John Schulte, DDS, MSD 1 Alejandro Kovacs, DDS, MS 1 Meghan Weed, RDH 2 Sung-Kiang Chuang, DMD, MD 3 Excessive crown-implant ratios have been cited in the literature as being detrimental to longterm implant survival. However, unfavorable crown-implant ratios have not yet been established. The primary aim of this study was to determine the crown-implant ratios of single-tooth implant-supported restorations on short-length implants in a clinical practice, and to evaluate the health of these implants via mesial and distal first bone-to-implant contact levels. Additionally, the relationship between crown-implant ratios and proximal first bone-to-implant contact levels will be evaluated. In this retrospective cohort study, the cohort was composed of 194 patients who possessed at least 1 single 5.7 mm or 6mm length plateau design implant-supported restoration that had been surgically placed between February 1997 and December A chart review was performed to acquire the most recent radiographs in which both the entire crown and the implant were visible. The length of the crown and implant was measured directly from the radiographs using consistent magnification to calculate the crown-implant ratio. Mesial and distal first bone-toimplant contact levels were measured using 3 times magnification and were mathematically corrected for distortion. The last available radiograph was used to measure bone levels. Follow-up time was calculated from the day of implant placement to the date of the last available radiograph. Statistical analyses with analysis of variance mixed models were used. Data from 309 single implant-supported fixed restorations were tabulated and included in the study. The mean (SD) follow-up time was 20.9 (23.2) months, with a range of 15.6 to months. The mean crown length (SD) was 13.4 (2.6) mm, with a range of 6.2 to 21.7 mm. The mean (SD) crown-implant ratio was 2.0 (0.4) and ranged from 0.9 to 3.2. The average mesial and distal first bone-to-implant contact levels (SD) measured from the radiographs were 20.2 (0.7) mm and 20.2 (0.9) mm, respectively. No statistically significant relationship was observed between increasing crown-implant ratios and decreasing mesial and distal first bone-to-implant contact levels around the implant with P values of.94 and.57, respectively. In this investigation, mesial and distal first bone-to-implant contact levels on short-length implants fall within the established guidelines for success. Also, there are no associations between crown-implant ratios and first bone-to-implant contact levels. Key Words: crown-implant ratios, proximal bone-to-implant contact 1 University of Minnesota School of Dentistry, Minneapolis, Minn. 2 Implant Dentistry Center, Boston, Mass. 3 Department of OMFS, Massachusetts General Hospital and the Harvard School of Dental Medicine, Boston, Mass. * Corresponding author, bobbirdi@gmail.com DOI: /AAID-JOI-D Journal of Oral Implantology 425

2 Crown-to-Implant Ratios INTRODUCTION The use of endosseous dental implants as tooth replacements has become an accepted treatment modality in dentistry today. As a result, clinicians often use certain guidelines associated with natural teeth and apply them to implant dentistry. One of these guidelines is crown-to-root ratio. The crown-to-root ratio is defined as the physical relationship between that portion of the tooth within the alveolar bone and that portion not within alveolar bone, as determined by a radiograph. 1 The crown-toroot ratio is determined by dividing the length of the tooth coronal to the bone by the length of the root that resides in bone (Figure 1). Dentists use the crown-to-root ratio as an important prognostic indicator to determine the suitability of a tooth to act as an abutment for a fixed or removable partial denture. Furthermore, the crown-to-root ratio is used as a prime indicator of the long-term prognosis of a given tooth. 2 4 It extrapolates the biomechanical concept of a class I lever for evaluating abutment teeth with the fulcrum lying in the middle portion of the root residing in alveolar bone. As progressive bone loss occurs, the fulcrum moves apically, and as a result, the tooth is more susceptible to harmful lateral occlusal forces. 5 Newman et al 6 reinforce this by stating that because of disproportionate crown-to-root ratios and the reduced root surface available for periodontal support, the periodontium may be more susceptible to injury by occlusal forces. McGuire and Nunn 7 in a prospective 8 year study on predicting tooth loss for 100 periodontal patients also concluded that an unfavorable crown-toroot ratio is a significant factor for clinicians to consider when predicting the long-term prognosis for a tooth. Prosthodontic textbooks consider the ideal crown-to-root ratio for a potential FIGURE 1. Crown-to-root ratio calculated. abutment supporting a fixed or removable partial denture to be 1:2 or smaller. 2 4 However, crown-to-implant ratio guidelines have not yet been established. Misch 8 states that the crown-to-implant ratio should not be considered the same way as a crown-toroot ratio. He further states that an implant does not rotate around a center located twothirds down the endosteal/root portion and affirm that implant length is not related to mobility and does not affect its resistance to lateral force. Many studies have addressed the issue of implant length as a predictor of implant survival. These publications have expressed conflicting results Excessive crown-toimplant ratios have been cited in the literature as being detrimental to long-term implant survival Conversely, disproportionate crown-to-implant ratios have been associated with high implant survival, especially with short implants Anitua et al 18 found the 5 year retrospective survival rate of 532 short (7 and 8.5 mm) implants to be 99.2%. Schulte et al 19 conducted a retrospective case series study and found the 426 Vol. XXXVI/No. Six/2010

3 Birdi et al crown-to-implant ratios of 889 plateau-design single-tooth implants to be 1.3 on average, with an average survival rate of 98.2% over 2.3 years. The 5 accepted and recognized criteria for implant success were established in 1986 by Albrektsson et al. 36 Smith et al 37 later reinforced these criteria and made reference to Adell et al 38 in establishing that the mean bone loss for Branemark osseointegrated implants was 1.5 mm in the first year, followed by a mean bone loss of 0.1 mm per year. Zarb et al 39 also further refined the criteria for implant success in the Toronto Consensus Report in Therefore, based on the criteria established in the literature, to be considered successful, an implant must meet the following requirements: 1. The resultant implant support does not preclude the placement of a planned functional and esthetic prosthesis that is satisfactory to both patient and dentist. 2. No pain, discomfort, altered sensation, or infection is attributable to the implants. 3. Individual unattached implants are immobile when tested clinically. 4. The mean vertical bone loss is less than or equal to 1.5 mm in the first year and less than 0.2 mm annually thereafter. Today, implants are placed with both nonsubmerged and submerged approaches. With submerged implants, it is safe to assume that the highest possible first boneto-implant contact at the time of implant placement would occur at the top of the implant-abutment connection. Therefore, with this level used as a baseline, measurements of subsequent first bone-toimplant contact levels can be related to vertical bone loss as stated above. Hence, the primary aims of this study were to determine the crown-to-implant ratios of single implant-supported restorations on short-length plateau-design implants in a clinical practice, and to evaluate the success of these implants via mesial and distal first bone-to-implant contact levels. Additionally, the relationship between crown-to-implant ratios and proximal first bone-to-implant contact levels was to be evaluated. MATERIALS AND METHODS Study design and sample A retrospective cohort study design was utilized to address the specific aims of this investigation. The sample used in this study was derived from a population of patients who had been treated with 5.7 mm or 6 mm length plateau design implants (Bicon, Boston, Mass) placed by practitioners at the Implant Dentistry Center at Faulkner Hospital (IDC-FH), in Boston, Massachusetts, between February 1997 and December All subjects who had 1 or more single-tooth 5.7 mm or 6 mm long plateau-design implants placed and restored (cement retained, nonsplinted) with use of the locking-taper design were eligible for inclusion in the study. A total of 309 implants placed in 194 patients met the inclusion criteria. Implants were placed by a periodontist, 2 oral surgeons, and a prosthodontist. They were subsequently restored by 2 general dentists and a prosthodontist. Informed consent was attained from all patients who participated in the study. A chart review was conducted to attain the most recent digital periapical radiographs in which the entire crown and the implant were visible. Accurate measurements of periapical radiographs have been demonstrated in the literature to be reliable. 40 All radiographs were made using the paralleling technique. Periapical radiographs taken with the paralleling technique minimize the problem of dimensional distortion; however, some minor distortion may still exist. 41 Vertical distortion occurs equally in the crown and the implant of the radiograph, and because the crown-toimplant ratio is not dependent on absolute values, the effect of vertical distortion on a Journal of Oral Implantology 427

4 Crown-to-Implant Ratios FIGURE 2. Summary of radiographic measurements. ratio is minimal. 42 Radiographs with gross distortion and inadequate contrast and displaying poor definition of crown and implant outlines were eliminated from the study, along with all other data pertaining to these implants. No other exclusion criteria were utilized in this investigation. Crown-to-implant ratios were measured using a software program (DIGORA, Soredex, Tuusula, Finland) measuring tool in conjunction with a magnification tool. Each image was measured from the bottom of the implant to the crown base and then from the crown base to its highest point. The mesial and distal first bone-toimplant contact levels were measured from the top of the implant-abutment connection to the highest level of bone-to-implant contact. All measurements were recorded to the nearest 0.1 mm (Figure 2). Descriptive variables Descriptive variables were grouped into the following categories: 1. Demographics: The gender and age of the patient at the time of implant placement were recorded. 2. Implant Variables: The implant width and location and the type of tooth replaced were recorded. 3. Surgical Staging: The staging of implant surgery (1-stage or 2-stage) was recorded. Outcome variables Crown-to-implant ratios were calculated by dividing the digital length of the crown by the digital length of the implant. The time between implant placement and the date of last follow-up was used to calculate the follow-up time. Statistical analysis A Microsoft Excel database (Microsoft, Redmond, Wash) was used to tabulate all data recorded from the chart review. SAS statistical software (SAS Institute, Cary, NC) was utilized to evaluate the data and to perform 428 Vol. XXXVI/No. Six/2010

5 Birdi et al Variable Average Follow-up Time, mo TABLE 1 Follow-up time and crown-to-implant ratios Average Radiographic Crown Length, mm Average Radiographic Implant Length, mm Average Crown-to- Implant Ratio Value :1 SD Range the statistical analyses. Descriptive statistics were calculated for all descriptive variables. Statistical analyses with analysis of variance (ANOVA) mixed models were used to evaluate any relationship between crown-toimplant ratios and the highest mesial and distal bone-to-implant contact levels measured from the most recent radiograph in which the entire crown and implant were visible. RESULTS During the study interval from February 1997 to December 2005, a total of 309 singletooth implants from 194 patients were measured and investigated. The measured results are summarized in Tables 1 and 2. The mean (SD) follow-up time for each implant was 20.9 (23.2) months, with a range of 15.6 to months. The mean measured crown length (SD) was 13.3 (2.6) mm, with a range of 6.2 to 21.7 mm. The mean (SD) measured implant length was 6.8 (0.5) mm. Thus, the mean (SD) crown-to-implant ratio calculated was 2.0 (0.4) and ranged from 0.9 to 3.2. The distribution of the measured crown-to-implant ratios is shown graphically in Figure 3. More than 93% of the implants TABLE 2 Average proximal first bone-to-implant contact levels Variable Average Mesial First Bone Contact Level, mm Average Distal First Bone Contact Level, mm Value SD Median restored had crown-to-implant ratios of equal to or greater than 1.5, and more than 45% of restored implants possessed crownto-implant ratios of equal to or greater than 2.0 (Figure 4). Average mesial and distal first bone-to-implant contact levels (SD) measured from the digital radiographs were 20.2 (0.7) mm and 20.2 (0.9) mm, respectively. The descriptive statistics are summarized in Table 3. The mean age of the sample was 61.3 years (range, 21 to 88 years) with even distribution between males and females. The implants were spread almost equally between the maxilla and the mandible (45.0% and 55.0%, respectively), and were placed predominantly in the posterior regions (93.2%). Implant diameters varied between 5 and 6 mm, with most being 5 mm in diameter (71.2%). The types of teeth replaced were predominantly premolars (32.7%) and molars (60.5%). Nearly all implants were placed with a 2-stage surgical regimen (96.1%). Statistical analyses utilizing ANOVA mixed models were used to evaluate any relationship between crown-to-implant ratios and proximal first bone-to-implant contact levels. No statistically significant relationships were found between increasing crown-to-implant ratios and decreasing mesial and distal first bone-to-implant contact levels around the implant, with P values of.94 and.57, respectively. DISCUSSION The aims of this study were (1) to determine the crown-to-implant ratios of single-tooth Journal of Oral Implantology 429

6 Crown-to-Implant Ratios FIGURE 3. Frequency of crown-to-implant ratios. short-length plateau-design implant-supported restorations, (2) to interpret the success of these implants via mesial and distal first bone-to-implant contact levels, and (3) to evaluate any relationship between crown-to-implant ratios and proximal first bone-to-implant contact levels. The average crown-to-implant ratio found in this study (2.0:1) far surpasses what FIGURE 4. Crown-to-implant ratio of greater than 2. TABLE 3 Descriptive statistics Variable N % Demographics Mean age (n 5 187) 61.3 Minimum 20.6 Maximum 88.0 Gender (n 5 194) Male Female Implant variables Jaw location (k 5 309) Maxilla Mandible Anteroposterior location (k 5 309) Anterior Posterior Jaw and anteroposterior location (k 5 309) Anterior maxilla Posterior maxilla Anterior mandible Posterior mandible Implant diameter (k 5 309) 5.0 mm mm Type of tooth replaced (k 5 309) Incisor Canine Premolar Molar Surgical staging Staging of implant surgery (k 5 306) One stage Two stage Vol. XXXVI/No. Six/2010

7 Birdi et al clinicians believe would be favorable for natural teeth. In many instances, a tooth with a crown-to-root ratio of 2.0:1 would be recommended for extraction and replacement. However, the results of this study suggest that a crown-to-implant ratio of 2.0:1 and even greater can produce a stable favorable outcome. Crown-to-implant ratios of such large magnitude have not been cited in the literature thus far. Blanes et al 20 evaluated 192 nonsubmerged ITI implants and reported a mean (SD) clinical crown-toimplant ratio of 1.77 (0.56), with 51 implants exhibiting crown-to-implant ratios greater than or equal to 2.0. The crown height in that study was measured from the top of the crestal bone in contact with the implant to the top of the crown; thus the implant length was measured from the bottom of the fixture to the top of the crestal bone in contact with the implant. This is termed the clinical crown-to-implant ratio. The anatomic crown-to-implant ratio that was measured in the present study is measured from the bottom of the fixture to the implant-abutment connection and then from that point to the top of the crown. This is an important difference because of the fact that an implant of conventional length (.10 mm) may exhibit a large crown-to-implant ratio if the crestal bone has remodeled to a level far below the implant-abutment connection. It is important to mention that only 13.5% of the restorations utilized in the mentioned study were single-tooth nonsplinted restorations. Rokni et al 21 also reported crown-toimplant ratios of sintered porous-surfaced implants. That study included 198 implants (5 12 mm in length) and reported a mean (SD) anatomic crown-to-implant ratio of 1.5 (0.4), with 78.9% of the implants having crown-to-implant ratios between 1.1 and 2.0. However, calculations of the crown-to-implant ratios were based on measurements of articulated diagnostic casts; this represents a prime difference from the present study. Another purpose of this study was to determine the success of the implants investigated by interpreting mesial and distal first bone-to-implant contact levels. Accepted criteria for implant success state that the mean vertical bone loss of a successful implant should be less than or equal to 1.5 mm in the first year and then less than 0.2 mm annually thereafter With the top of the implant-abutment connection used as a baseline, both mesial and distal first bone-to-implant contact levels were measured at 0.2 mm over an average follow-up time of 20.9 months, which helps to establish implant success. All implant sites were devoid of pain and infection, and all implants were able to be restored and were immobile. Thus the success of the implants was further established. The final purpose of this investigation was to assess any relationship between crown-to-implant ratios and proximal first bone-to-implant contact levels. In this study, no statistically significant relationship was found between increasing crown-to-implant ratios and decreasing mesial and distal first bone-to-implant contact levels when analysis of variance mixed models were used. Therefore, a larger crown-to-implant ratio did not correlate with decreased first boneto-implant contact levels. Rokni et al 21 also found no association between crown-toimplant ratios and first bone-to-implant contact levels, but did find an association between decreasing first bone-to-implant contact levels and increasing implant length, as well as splinting of restorations. Blanes et al, 20 however, did find a positive correlation between increasing crown-to-implant ratios and increasing first bone-to-implant contact levels over 1 year. Higher clinical crown-toimplant ratios showed lower average bone loss when compared with lower crown-toimplant ratios. This again may be attributed to the design of the nonsubmerged implants, the clinical crown-to-implant calcula- Journal of Oral Implantology 431

8 Crown-to-Implant Ratios tions, or the fact that most of the restorations were splinted. The limitations of this study include those associated with the retrospective design, lack of clinician calibration, investigation of only plateau-design implants, and follow-up duration. Future studies undertaken to investigate the influence of crown-to-implant ratios on clinical performance should include numerous implant designs, additional controls, and studies of longer duration. CONCLUSION The results of this study suggest that crownto-implant ratios do not affect the success of short-length plateau-design implants. The average (SD) crown-to-implant ratio found in this study was 2.0 (0.4), which would be deemed unfavorable for a tooth. The average (SD) mesial and distal first bone-toimplant contact levels of 0.2 (0.7) mm and 0.2 (0.9) mm, respectively, establish the health and success of these implants. Furthermore, no associations between crown-to-implant ratio and first bone-to-implant contact levels were found. ABBREVIATIONS ANOVA: analysis of variance REFERENCES 1. The glossary of prosthodontic terms, 8th ed. J Prosthet Dent. 2005;94: Schillingburg HT, Hobo S, Whitsett LD, Jacobi R, Brackett SE. Fundamentals of Fixed Prosthodontics. 3rd ed. Chicago, Ill: Quintessence; 1997: Rosenstiel SF, Land MF, Fujimoto J. Contemporary Fixed Prosthodontics. 4th ed. St. Louis, Mo: Elsevier; 2006: Car AB, McGivney GP, Brown DT. McCracken s Removable Partial Prosthodontics. 11th ed. St. Louis, Mo: Elsevier; 2004: Grossmann Y, Sadan A. The prosthodontic concept of crown-to-root ratio: a review of the literature. J Prosthet Dent. 2005;1993: Newman NG, Takei HH, Carranza AC. Carranza s Clinical Periodontology. 9th ed. St. Louis, Mo: Elsevier; 2002: McGuire MK, Nunn ME. Prognosis versus actual outcome. III. The effectiveness of clinical parameters in accurately predicting tooth survival. J Periodontol. 1996;67: Misch CE. Contemporary Implant Dentistry. 3rd ed. St. Louis, Mo: Elsevier; 2008: Wyatt CC, Zarb GA. Treatment outcomes of patients with implant supported fixed partial prostheses. Int J Oral Maxillofac Implants. 1998;13: Higuchi KW, Folmer T, Kultje C. Implant survival rates in partially edentulous patients: a 3-year prospective multicenter study. J Oral Maxillofac Surg. 1995;53: Friberg B, Jemt T, Lekholm U. Early failures in 4,641 consecutively placed Branemark dental implants: a study from stage I surgery to the connection of completed prostheses. Int J Oral Maxillofac Implants. 1991;6: Winkler S, Morris HF, Ochi S. Implant survival to 36 months as related to length and diameter. Ann Periodontol. 2000;5: Mericske-Stern R. Overdentures with roots or implants for elderly patients: a comparison. J Prosthet Dent. 1994;72: Grunder U, Polizzi G, Goene R, et al. A 3-year prospective multicenter follow-up on the immediate and delayed-immediate placement of implants. Int J Oral Maxillofac Implants. 1999;14: Snauwaert K, Duyck J, van Steenberghe D, Quirynen M, Naert I. Time dependent failure rate and marginal bone loss of implant supported prostheses: a 15-year follow-up study. Clin Oral Investig. 2000;4: Friberg B, Jemt T, Lekholm U. Early failures in 4,641 consecutively placed Branemark dental implants: a study from stage 1 surgery to the connection of completed prostheses. Int J Oral Maxillofac Implants. 1991;6: van Steenberghe D, Lekholm U, Bolender C, et al. Applicability of osseointegrated oral implants in the rehabilitation of partial edentulism: a prospective multicenter study on 588 fixtures. Int J Oral Maxillofac Implants. 1990;5: Anitua E, Orive G, Aguirre JJ, Andía I. Five-year clinical evaluation of short dental implants placed in posterior areas: a retrospective study. J Periodontol. 2008;79: Schulte J, Flores AM, Weed M. Crown-toimplant ratios of single tooth implant-supported restorations. J Prosthet Dent. 2007;98: Blanes RJ, Bernard JP, Blanes ZM, Belser UC. A 10-year prospective study of ITI dental implants placed in the posterior region. II: influence of the crown-toimplant ratio and different prosthetic treatment modalities on crestal bone loss. Clin Oral Implants Res. 2007;18: Rokni S, Todescan R, Watson P, Pharoah M, Adegbembo AO, Deporter D. An assessment of crownto-root ratios with short sintered porous-surfaced implants supporting prostheses in partially edentulous patients. Int J Oral Maxillofac Implants. 2005;20: Teixeira ER, Wadamoto M, Akagawa Y, Kimoto T. Clinical application of short hydroxylapatite-coated dental implants to the posterior mandible: a five-year survival study. J Prosthet Dent. 1997;78: Vol. XXXVI/No. Six/2010

9 Birdi et al 23. Renouard F, Nisand D. Short implants in the severely resorbed maxilla: a 2-year retrospective clinical study. Clin Implant Dent Relat Res. 2005;7(suppl 1):S104 S Feldman S, Boitel N, Weng D, Kohles SS, Stach RM. Five-year survival distributions of short-length (10 mm or less) machine surfaced and Osseotite implants. Clin Implant Dent Relat Res. 2004;6: ten Bruggenkate CM, Asikainen P, Foitzik C, Krekeler G, Sutter F. Short (6-mm) nonsubmerged dental implants: results of a multicenter clinical trial of 1 to 7 years. Int J Oral Maxillofac Implants. 1998;13: Tawil G, Younan R. Clinical evaluation of short, machined-surface implants followed for 12 to 92 months. Int J Oral Maxillofac Implants. 2003;18: Gentile MA, Chuang SK, Dodson TB. Survival estimates and risk factors for failure with mm implants. Int J Oral Maxillofac Implants. 2005;20: Grant BT, Pancko FX, Kraut RA. Outcomes of placing short dental implants in the posterior mandible: a retrospective study of 124 cases. J Oral Maxillofac Surg. 2009;67: Tawil G, Aboujaoude N, Younan R. Influence of prosthetic parameters on the survival and complication rates of short implants. Int J Oral Maxillofac Implants. 2006;21: Fugazzotto PA. Shorter implants in clinical practice: rationale and treatment results. Int J Oral Maxillofac Implants. 2008;23: Fugazzotto PA, Beagle JR, Ganeles J, Jaffin R, Vlassis J, Kumar A. Success and failure rates of 9 mm or shorter implants in the replacement of missing maxillary molars when restored with individual crowns: preliminary results 0 to 84 months in function. A retrospective study. J Periodontol. 2004;75: Deporter D, Ogiso B, Sohn DS, Ruljancich K, Pharoah M. Ultrashort sintered porous-surfaced dental implants used to replace posterior teeth. J Periodontol. 2008;79: Neves FD, Fones D, Bernardes SR, Prado CJ, Neto AJF. Short implants an analysis of longitudinal studies. Int J Oral Maxillofac Implants. 2006;21: Arlin ML. Short dental implants as a treatment option: results from an observational study in a single private practice. Int J Oral Maxillofac Implants. 2006;21: Maló P, de Araújo Nobre M, Rangert B. Short implants placed one-stage in maxillae and mandibles: a retrospective clinical study with 1 to 9 years of followup. Clin Implant Dent Relat Res. 2007;9: Albrektsson T, Zarb G, Worthington P, Eriksson AR. The long-term efficacy of currently used dental implants: a review and proposed criteria of success. Int J Oral Maxillofac Implants. 1986;1: Smith DE, Zarb GA. Criteria for success of osseointegrated endosseous implants. J Prosthet Dent. 1989;62: Adell R, Lekholm U, Rockier B, Branemark P-I. A 15-year study of osseointegrated implants in the treatment of the edentulous jaw. Int J Oral Surg. 1981;10: Zarb GA, Albrektsson T. Consensus report: towards optimized treatment outcomes for dental implants. J Prosthet Dent. 1998;80: Gher ME, Richardson AC. The accuracy of dental radiographic techniques used for evaluation of implant fixture placement. Int J Periodontics Restorative Dent. 1995;15: Langlais RP, Rodriguez IE, Maselle I. Principles of radiographic selection and interpretation. Dent Clin North Am. 1994;38: Langland OE, Sippy FH, Morris CR, Langlais RP. Principles and Practice of Panoramic Radiology. 2nd ed. Philadelphia, Pa: WB Saunders; 1992: Journal of Oral Implantology 433

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