Won-suk Oh Tae-Ju Oh Ju-mi Park
Authors’ affiliations: Won-suk Oh, Department of Biologic and Materials Sciences, University of Michigan School of Dentistry, Ann Arbor, MI, USA Tae-Ju Oh, Department of Periodontics and Oral Medicine, University of Michigan School of Dentistry, Ann Arbor, MI, USA Ju-mi Park, Department of Prosthodontics, Chonbuk National University School of Dentistry, Research Institute of Clinical Medicine Chonbuk National University-Biomedical, Research Institute of Chonbuk National University Hospital, Jeonju, South Korea Corresponding author: Ju-mi Park, DDS, MS, PhD Professor, Department of Prosthodontics, Chonbuk National University School of Dentistry, 664-14 Deokjin-dong 1-ga, Deokjin-gu, Jeonju, Jeonbuk, 561-756, South Korea Tel.: 82 63 250 2030 Fax: 82 63 250 2218 e-mail: [email protected]
Impact of implant support on mandibular free-end base removable partial denture: theoretical study
Key words: bending moment, force, implant, removable partial denture, support Abstract Objectives: This study investigated the impact of implant support on the development of shear force and bending moment in mandibular free-end base removable partial dentures (RPDs). Material and methods: Three theoretical test models of unilateral mandibular free-end base RPDs were constructed to represent the base of tooth replacement, as follows: Model 1: first and second molars (M1 and M2); Model 2: second premolar (P2), M1, and M2; and Model 3: first premolar (P1), P2, M1, and M2. The implant support located either at M1 or M2 sites. The occlusal loading was concentrated at each replacement tooth to calculate the stress resultants developed in the RPD models using the free-body diagrams of shear force and bending moment. Results: There was a trend of reduction in the peak shear force and bending moment when the base was supported by implant. However, the degree of reduction varied with the location of implant support. The moment reduced by 76% in Model 1, 58% in Model 2, and 42% in Model 3, when the implant location shifted from M1 to M2 sites. Conclusions: The shear forces and bending moments subjected to mandibular free-end base RPDs were found to decrease with the addition of implant support. However, the impact of implant support varied with the location of implant in this theoretical study.
Date: Accepted 21 November 2014 To cite this article: Oh W-s, Oh T-J, Park J-m. Impact of implant support on mandibular free-end base removable partial denture: theoretical study. Clin. Oral Impl. Res. 27, 2016, e87–e90 doi: 10.1111/clr.12534
The design of a mandibular free-end base removable partial denture (RPD) should embrace a stress-releasing concept to avoid torque force driven against the abutment tooth (McCracken 1963; Mericske-Stern 2009). This may require a specific design of direct retainer and location of the rest to induce axial force direction (Monteith 1984). However, a rotational movement of the freeend base is unavoidable with the fulcrum line developed from different compressibility of the ridge mucosa and the periodontal ligament of tooth (Cecconi et al. 1971; Thompson et al. 1977; Frank et al. 2004; Muraki et al. 2004). This mismatch of tissue characteristics may induce a high degree of forces and bending moments developed in the freeend base prostheses (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997; Korioth et al. 1998). One strategy of enhancing the support and stability of the base is to use the tooth roots (Firtell et al. 1979; Castleberry 1990; McDermott & Grasso 1990; Ben-Ur et al. 1994). Other benefits of using this overdenture concept include more favorable stress distribution pattern, preservation of alveolar
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
bone of the ridge, and enhancement of patient’s comfort and mastication. However, the success rates of the endodontically compromised tooth roots seating underneath the base vary with high risk of caries development, root fracture, and periodontal breakdown (Koller et al. 2011). The use of dental implants may substitute the role of tooth roots in enhancing the support and stability of RPDs. Depending on the implant location, the free-end base RPDs can be converted into Kennedy Class 3 and eliminate the development of fulcrum line (Ganz 1991; Keltjens et al. 1993; Kuzmanovic et al. 2004; Al-Johany & Andres 2008; Koller et al. 2011; Liu et al. 2012). The common location of implants is posterior to abutment tooth in replacing functions of key teeth such as canine, premolars, and molars (Al-Johany & Andres 2008). Although failures were reported, the success rates of the implants were found to be more predictable than when using the tooth roots (Ben-Ur et al. 1994; Tandlich et al. 2007; Kaufmann et al. 2009; Minoretti et al. 2009; Bortolini et al. 2011; El Mekawy et al. 2012). However, the effect of implant support on the biomechanical
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Oh et al Impact of implant support on RPDs
aspects of denture design has not been investigated scientifically. Thus, the purpose of this theoretical study was to investigate the impact of implant support on the development of shear forces and bending moments in the free-end base of RPDs.
the coordinate axis (Gere & Timoshenko 1997). Secondly, the shear forces and bending moments acting on each segment of the beam of base between the points of several concentrated occlusal loads were obtained using the free-body diagrams, as follows (Fig. 3) (Gere & Timoshenko 1997): For the first segment of the beam,
(a)
(b)
Methods Three theoretical free-body test models representing unilateral mandibular free-end base RPDs were constructed to represent the base of tooth replacement, as follows: Model 1: first and second molars (M1 and M2); Model 2: second premolar (P2), M1, and M2; and Model 3: first premolar (P1), P2, M1, and M2. The cantilever free-end bases represented the sum of mesiodistal dimension of each replacement tooth (0.7 cm for P1, 0.7 cm for P2, 1.2 cm for M1, and 1.0 cm for M2) and were subjected to multiple concentrated vertical occlusal forces at the center of each replacement tooth (50 N for P1, 50 N for P2, 100 N for M1, and 150 N for M2) (Figs 1 and 2) (Powers & Sakaguchi 2006; Aras et al. 2009). Each model of the base represented cantilever beam having anterior support by the tooth (P2 in Model 1, P1 in Model 2, and canine in Model 3) and received additional support of implant either at M1 or M2 sites (Fig. 2). The tooth support was designed to resist displacement and to permit vertical rotation of the base. The implant support was to resist the vertical rotational movement and to permit displacement of the base. Thus, the test design
(a)
V ¼ AY
V ¼ AY P1 M ¼ AY x P1 ðx a1 Þ ða1 \x\a2 Þ
(c)
V ¼ BY þP3 M ¼ BY ðLxÞP3ðLb3 xÞ ða2 \x\a3 Þ Fig. 2. The theoretical test Models 1, 2, and 3 demonstrating location of tooth and implant supports. Note multiple vertical occlusal forces concentrated at the center of each replacement tooth: 50 N at P1, 50 N at P2, 100 N at M1, and 150 N at M2. (a) Model 1; M1 and M2, (b) Model 2; P2, M1, and M2, (c) Model 3; P1, P2, M1, and M2.
of base was pinned against the tooth and rolled against the implant to simulate the free-body movement of vertical rotation of a beam (Gere & Timoshenko 1997). The test was conducted mathematically to obtain stress resultants of shear forces and bending moments distributed along the beam of base. For the cantilever beam of base presenting no implant support, the shear forces and bending moments were calculated using the free-body diagram and equations of equilibrium, as follows (Gere & Timoshenko 1997):
X
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Clin. Oral Impl. Res. 27, 2016 / e87–e90
3
4
For the third segment of the beam,
X
Fig. 1. The theoretical test Models 1, 2, and 3 demonstrating base length as represented by sum of each replacement tooth (0.7 cm for P1, 0.7 cm for P2, 1.2 cm for M1, and 1.0 cm for M2): (a) Model 1; M1 and M2, (b) Model 2; P2, M1, and M2, (c) Model 3; P1, P2, M1, and M2. Note the arrows indicating the center of each tooth.
ð0\x\a1 Þ
For the second segment of the beam,
(b)
(c)
M ¼ AY x
Fvert ¼ 0 P V ¼ 0
1
M ¼ 0 M Px ¼ 0
2
where F = force, P = load, V = shear force, M = bending moment, and x = distance from the free-end of the beam to the cross section where the V and M are being determined. For the beam of base receiving additional support of implant, the sign conventions for shear forces and bending moments were first used to calculate the vertical forces subjected to each unit of support (AY = vertical force at tooth A; BY = vertical force at implant B). The forces were positive or negative according to the direction along
5
For the fourth segment of the beam, V ¼ BY
M ¼ BY ðL xÞ
ða3 \x\LÞ
6
where L = length and x = distance [x = a1 in (3), x = a2 in (4), and x = a3 in (5)].
(a)
(b)
(c)
Fig. 3. Free-body diagrams of shear force and bending moment for a tooth-implant supported beam loaded by multiple concentrated occlusal forces. (a) Beam of base with concentrated loads, (b) shear force diagram, (c) Bending moment diagram.
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Oh et al Impact of implant support on RPDs
Table 1. The peak shear force (N) developed in each test model Implant location
Model 1
Model 2
Model 3
No implant M1 M2
250 425 100
300 292.3 96.3
350 270 111.3
site, the moments were found to decrease by 88% in Model 1 and 87% in Models 2 and 3. However, the effect of implant support on the decrease of moment varied; with shifting the implant location from M2 to M1 sites, the moments were found to increase by 325% in Model 1, 140% in Model 2, and 72% in Model 3.
Table 2. The peak bending moment (Ncm) developed in each test model Implant location
Model 1
Model 2
Model 3
No implant M1 M2
315 165 38.8
510 165 68.8
735 165 97.6
Results The details of the peak shear forces and peak bending moments for all test models are described in Tables 1 and 2. There are no means and standard deviations of the data because of the theoretical study conducted by mathematical calculation. The peak shear forces were, in general, higher when the bases received no additional support of implant. Among those having no implant support, the highest force was found in Model 3, intermediate in Model 2, and lowest in Model 1. The shear forces were the lowest when the implant located at M2 site in all test models. When compared to those receiving no implant support, the forces were lower by 60% in Model 1 and 68% in Models 2 and 3. Interestingly, the highest force was developed in Model 1 when the implant located at M1 site. However, the forces decreased with the shift of implant support from M1 to M2 sites by 76% in Model 1, 67% in Model 2, and 58% in Model 3. The peak bending moments were much higher in models receiving no implant support. The highest moment was found in Model 3, intermediate in Model 2, and lowest in Model 1. The moments decreased when the base received additional support of implant; when the implant is located at M2
Discussion The shear force is a measure of stress acting in transverse direction to the occlusal plane and may cause a bending or fracture of the base at the site of peak force development (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997; Korioth et al. 1998). The shear forces were higher in the models of base receiving no implant support. The peak forces were found at the pivot point of abutment tooth and became higher with an increase of occlusal force and base length. Thus, free-end base RPDs may pose higher risk of failure in the supporting elements of denture and abutment tooth (Cecconi et al. 1971; Thompson et al. 1977; Monteith 1984; Frank et al. 2004; Muraki et al. 2004). The shear forces greatly reduced when the models of base received implant support at M2 site. However, the pattern of force distribution was not consistent when the implant support shifted to M1 site. The force was rather increased in Model 1, although a force reduction was found in Models 2 and 3. This may relate to the short distance between the supports of tooth and implant in Model 1. The peak forces developed at the site of implant location subjecting the base under higher tension of bending moment (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997). The bending moment is a resultant of shear force as a function of distance and may negatively affect the stability of free-end base RPDs (Gere & Timoshenko 1997; Tandlich et al. 2007). When a high moment develops, the base is prone to rotate, bend, and/or displace against the supporting elements of denture
(Monteith 1984; Muraki et al. 2004). The abutment tooth can be at risk for the loss of periodontal stability, in particular, when combined with the base demonstrating multiple occlusal units as presented in Model 3. The addition of implant support reduced the bending moments developed in the base in this study. However, the effect of implant support was not consistent, but varied with the location of implant. In fact, the bending moment was the lowest when the implant was placed at M2 site, eliminating the free-end segment of base in all test models. Within the limits of this theoretical study, mandibular free-end base RPDs were found to develop high shear forces and bending moments in the supporting elements of base. While the forces and moments were significantly reduced with the addition of implant support, the force and moment reduction varied with implant location as reference to base length. Thus, a further research needs to be investigated to optimize the location of implant support in designing RPDs.
Conclusion The high shear forces and bending moments subjected to mandibular free-end base RPDs were found to decrease with the addition of implant support. However, the impact of implant support varied with implant location in this theoretical study. A further research needs to be conducted to investigate the biomechanically most advantageous location of implant support in designing RPDs.
Funding This research was carried out without funding.
Conflict of interests No conflict of interests declared.
References Al-Johany, S.S. & Andres, C. (2008) ICK classification system for partially edentulous arches. Journal of Prosthodontics 17: 502–507. Aras, K., Hasanreiso glu, U. & Shinogaya, T. (2009) Masticatory performance, maximum occlusal force, and occlusal contact area in patients with bilaterally missing molars and distal extension removable partial dentures. International Journal of Prosthodontics 22: 204–209.
Ben-Ur, Z., Gorfil, C. & Aviv, I. (1994) Use of roots to establish favorable removable partial denture design: case reports. Quintessence International 25: 173–176. Bortolini, S., Natali, A., Franchi, M., Coggiola, A. & Consolo, U. (2011) Implant-retained removable partial dentures: an 8-year retrospective study. Journal of Prosthodontics 20: 168–172.
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Brunski, J.B. (1988) Biomechanics of oral implants: future research directions. Journal of Dental Education 52: 775–787. Castleberry, D.J. (1990) Philosophies and principles of removable partial overdentures. Dental Clinics of North America 34: 589–592. Cecconi, B.T., Asgar, K. & Dootz, E. (1971) Fit of the removable partial denture base and its effect on abutment tooth movement.
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Oh et al Impact of implant support on RPDs Journal of Prosthetic Dentistry 25: 515–519. El Mekawy, N.H., El-Negoly, S.A., Grawish, Mel.-A. & El-Hawary, Y.M. (2012) Intracoronal mandibular Kennedy Class I implant-tooth supported removable partial overdenture: a 2-year multicenter prospective study. International Journal of Oral Maxillofacial Implants 27: 677–683. Firtell, D.N., Herzberg, T.W. & Walsh, J.F. (1979) Root retention and removable partial denture design. Journal of Prosthetic Dentistry 42: 131–134. Frank, R.P., Brudvik, J.S. & Noonan, C.J. (2004) Clinical outcome of the altered cast impression procedure compared with use of a one-piece cast. Journal of Prosthetic Dentistry 91: 468–476. Ganz, S.D. (1991) Combination natural tooth and implant-borne removable partial denture: a clinical report. Journal of Prosthetic Dentistry 66: 1–5. Gere, J.M. & Timoshenko, S.P. (1997) Shear force and bending moment. In: Gere, J.M., ed. Mechanics of Materials, 4th edition, 267–302. Boston: PWS Publishing. Kaufmann, R., Friedli, M., Hug, S. & MericskeStern, R. (2009) Removable dentures with implant support in strategic positions followed for up to 8 years. International Journal of Prosthodontics 22: 233–241. Kayacan, R., Ballarini, R. & Mullen, R.L. (1997) Theoretical study of the effects of tooth and implant mobility differences on occlusal force
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transmission in tooth/implant supported partial prostheses. Journal of Prosthetic Dentistry 78: 391–399. Keltjens, H.M., Kayser, A.F., Hertel, R. & Battistuzzi, P.G. (1993) Distal extension removable partial dentures supported by implants and residual teeth: considerations and case reports. International Journal of Oral Maxillofacial Implants 8: 208–213. Koller, B., Att, W. & Strub, J.R. (2011) Survival rates of teeth, implants, and double crown-retained removable dental prostheses: a systematic literature review. International Journal of Prosthodontics 24: 109–117. Korioth, T.W., Chew, C.B. & Chung, D.H. (1998) Effect of implant number on transverse bending moments during simulated unilateral loading of mandibular fixed-detachable prostheses. Journal of Oral Implantology 24: 93–96. Kuzmanovic, D.V., Payne, A.G. & Purton, D.G. (2004) Distal implants to modify the Kennedy classification of a removable partial denture: a clinical report. Journal of Prosthetic Dentistry 92: 8–11. Liu, R., Kaleinikova, Z., Holloway, J.A. & Campagni, W.V. (2012) Conversion of a partial removable dental prosthesis from kennedy class II to class III using a dental implant and semiprecision attachments. Journal of Prosthodontics 21: 48–51. McCracken, W. (1963) A philosophy of partial denture treatment. Journal of Prosthetic Dentistry 13: 889–900.
McDermott, I.G. & Grasso, J.E. (1990) Removable partial overdentures. Clinical considerations. Dental Clinics of North America 34: 611–629. Mericske-Stern, R. (2009) Removable partial dentures. International Journal of Prosthodontics 22: 508–511. Minoretti, R., Triaca, A. & Saulacic, N. (2009) The use of extraoral implants for distal-extension removable dentures: a clinical evaluation up to 8 years. International Journal of Oral Maxillofacial Implants 24: 1129–1137. Monteith, B.D. (1984) Management of loading forces on mandibular distal-extension prostheses. Part I: evaluation of concepts for design. Journal of Prosthetic Dentistry 52: 673–681. Muraki, H., Wakabayashi, N., Park, I. & Ohyama, T. (2004) Finite element contact stress analysis of the RPD abutment tooth and periodontal ligament. Journal of Dentistry 32: 659–665. Powers, J.M. & Sakaguchi, R.L. (2006) Mechanical properties. In: Powers, J.M., ed. Craig’s Restorative Dental Materials, 12th edition, 52–53. St. Louis: Mosby Elsevier. Tandlich, M., Ekstein, J., Reisman, P. & Shapira, L. (2007) Removable prostheses may enhance marginal bone loss around dental implants: a longterm retrospective analysis. Journal of Periodontology 78: 2253–2259. Thompson, W.D., Kratochvil, F.J. & Caputo, A.A. (1977) Evaluation of photoelastic stress patterns produced by various designs of bilateral distalextension removable partial dentures. Journal of Prosthetic Dentistry 38: 261–273.
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Authors’ affiliations: Won-suk Oh, Department of Biologic and Materials Sciences, University of Michigan School of Dentistry, Ann Arbor, MI, USA Tae-Ju Oh, Department of Periodontics and Oral Medicine, University of Michigan School of Dentistry, Ann Arbor, MI, USA Ju-mi Park, Department of Prosthodontics, Chonbuk National University School of Dentistry, Research Institute of Clinical Medicine Chonbuk National University-Biomedical, Research Institute of Chonbuk National University Hospital, Jeonju, South Korea Corresponding author: Ju-mi Park, DDS, MS, PhD Professor, Department of Prosthodontics, Chonbuk National University School of Dentistry, 664-14 Deokjin-dong 1-ga, Deokjin-gu, Jeonju, Jeonbuk, 561-756, South Korea Tel.: 82 63 250 2030 Fax: 82 63 250 2218 e-mail: [email protected]
Impact of implant support on mandibular free-end base removable partial denture: theoretical study
Key words: bending moment, force, implant, removable partial denture, support Abstract Objectives: This study investigated the impact of implant support on the development of shear force and bending moment in mandibular free-end base removable partial dentures (RPDs). Material and methods: Three theoretical test models of unilateral mandibular free-end base RPDs were constructed to represent the base of tooth replacement, as follows: Model 1: first and second molars (M1 and M2); Model 2: second premolar (P2), M1, and M2; and Model 3: first premolar (P1), P2, M1, and M2. The implant support located either at M1 or M2 sites. The occlusal loading was concentrated at each replacement tooth to calculate the stress resultants developed in the RPD models using the free-body diagrams of shear force and bending moment. Results: There was a trend of reduction in the peak shear force and bending moment when the base was supported by implant. However, the degree of reduction varied with the location of implant support. The moment reduced by 76% in Model 1, 58% in Model 2, and 42% in Model 3, when the implant location shifted from M1 to M2 sites. Conclusions: The shear forces and bending moments subjected to mandibular free-end base RPDs were found to decrease with the addition of implant support. However, the impact of implant support varied with the location of implant in this theoretical study.
Date: Accepted 21 November 2014 To cite this article: Oh W-s, Oh T-J, Park J-m. Impact of implant support on mandibular free-end base removable partial denture: theoretical study. Clin. Oral Impl. Res. 27, 2016, e87–e90 doi: 10.1111/clr.12534
The design of a mandibular free-end base removable partial denture (RPD) should embrace a stress-releasing concept to avoid torque force driven against the abutment tooth (McCracken 1963; Mericske-Stern 2009). This may require a specific design of direct retainer and location of the rest to induce axial force direction (Monteith 1984). However, a rotational movement of the freeend base is unavoidable with the fulcrum line developed from different compressibility of the ridge mucosa and the periodontal ligament of tooth (Cecconi et al. 1971; Thompson et al. 1977; Frank et al. 2004; Muraki et al. 2004). This mismatch of tissue characteristics may induce a high degree of forces and bending moments developed in the freeend base prostheses (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997; Korioth et al. 1998). One strategy of enhancing the support and stability of the base is to use the tooth roots (Firtell et al. 1979; Castleberry 1990; McDermott & Grasso 1990; Ben-Ur et al. 1994). Other benefits of using this overdenture concept include more favorable stress distribution pattern, preservation of alveolar
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
bone of the ridge, and enhancement of patient’s comfort and mastication. However, the success rates of the endodontically compromised tooth roots seating underneath the base vary with high risk of caries development, root fracture, and periodontal breakdown (Koller et al. 2011). The use of dental implants may substitute the role of tooth roots in enhancing the support and stability of RPDs. Depending on the implant location, the free-end base RPDs can be converted into Kennedy Class 3 and eliminate the development of fulcrum line (Ganz 1991; Keltjens et al. 1993; Kuzmanovic et al. 2004; Al-Johany & Andres 2008; Koller et al. 2011; Liu et al. 2012). The common location of implants is posterior to abutment tooth in replacing functions of key teeth such as canine, premolars, and molars (Al-Johany & Andres 2008). Although failures were reported, the success rates of the implants were found to be more predictable than when using the tooth roots (Ben-Ur et al. 1994; Tandlich et al. 2007; Kaufmann et al. 2009; Minoretti et al. 2009; Bortolini et al. 2011; El Mekawy et al. 2012). However, the effect of implant support on the biomechanical
e87
Oh et al Impact of implant support on RPDs
aspects of denture design has not been investigated scientifically. Thus, the purpose of this theoretical study was to investigate the impact of implant support on the development of shear forces and bending moments in the free-end base of RPDs.
the coordinate axis (Gere & Timoshenko 1997). Secondly, the shear forces and bending moments acting on each segment of the beam of base between the points of several concentrated occlusal loads were obtained using the free-body diagrams, as follows (Fig. 3) (Gere & Timoshenko 1997): For the first segment of the beam,
(a)
(b)
Methods Three theoretical free-body test models representing unilateral mandibular free-end base RPDs were constructed to represent the base of tooth replacement, as follows: Model 1: first and second molars (M1 and M2); Model 2: second premolar (P2), M1, and M2; and Model 3: first premolar (P1), P2, M1, and M2. The cantilever free-end bases represented the sum of mesiodistal dimension of each replacement tooth (0.7 cm for P1, 0.7 cm for P2, 1.2 cm for M1, and 1.0 cm for M2) and were subjected to multiple concentrated vertical occlusal forces at the center of each replacement tooth (50 N for P1, 50 N for P2, 100 N for M1, and 150 N for M2) (Figs 1 and 2) (Powers & Sakaguchi 2006; Aras et al. 2009). Each model of the base represented cantilever beam having anterior support by the tooth (P2 in Model 1, P1 in Model 2, and canine in Model 3) and received additional support of implant either at M1 or M2 sites (Fig. 2). The tooth support was designed to resist displacement and to permit vertical rotation of the base. The implant support was to resist the vertical rotational movement and to permit displacement of the base. Thus, the test design
(a)
V ¼ AY
V ¼ AY P1 M ¼ AY x P1 ðx a1 Þ ða1 \x\a2 Þ
(c)
V ¼ BY þP3 M ¼ BY ðLxÞP3ðLb3 xÞ ða2 \x\a3 Þ Fig. 2. The theoretical test Models 1, 2, and 3 demonstrating location of tooth and implant supports. Note multiple vertical occlusal forces concentrated at the center of each replacement tooth: 50 N at P1, 50 N at P2, 100 N at M1, and 150 N at M2. (a) Model 1; M1 and M2, (b) Model 2; P2, M1, and M2, (c) Model 3; P1, P2, M1, and M2.
of base was pinned against the tooth and rolled against the implant to simulate the free-body movement of vertical rotation of a beam (Gere & Timoshenko 1997). The test was conducted mathematically to obtain stress resultants of shear forces and bending moments distributed along the beam of base. For the cantilever beam of base presenting no implant support, the shear forces and bending moments were calculated using the free-body diagram and equations of equilibrium, as follows (Gere & Timoshenko 1997):
X
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Clin. Oral Impl. Res. 27, 2016 / e87–e90
3
4
For the third segment of the beam,
X
Fig. 1. The theoretical test Models 1, 2, and 3 demonstrating base length as represented by sum of each replacement tooth (0.7 cm for P1, 0.7 cm for P2, 1.2 cm for M1, and 1.0 cm for M2): (a) Model 1; M1 and M2, (b) Model 2; P2, M1, and M2, (c) Model 3; P1, P2, M1, and M2. Note the arrows indicating the center of each tooth.
ð0\x\a1 Þ
For the second segment of the beam,
(b)
(c)
M ¼ AY x
Fvert ¼ 0 P V ¼ 0
1
M ¼ 0 M Px ¼ 0
2
where F = force, P = load, V = shear force, M = bending moment, and x = distance from the free-end of the beam to the cross section where the V and M are being determined. For the beam of base receiving additional support of implant, the sign conventions for shear forces and bending moments were first used to calculate the vertical forces subjected to each unit of support (AY = vertical force at tooth A; BY = vertical force at implant B). The forces were positive or negative according to the direction along
5
For the fourth segment of the beam, V ¼ BY
M ¼ BY ðL xÞ
ða3 \x\LÞ
6
where L = length and x = distance [x = a1 in (3), x = a2 in (4), and x = a3 in (5)].
(a)
(b)
(c)
Fig. 3. Free-body diagrams of shear force and bending moment for a tooth-implant supported beam loaded by multiple concentrated occlusal forces. (a) Beam of base with concentrated loads, (b) shear force diagram, (c) Bending moment diagram.
© 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Oh et al Impact of implant support on RPDs
Table 1. The peak shear force (N) developed in each test model Implant location
Model 1
Model 2
Model 3
No implant M1 M2
250 425 100
300 292.3 96.3
350 270 111.3
site, the moments were found to decrease by 88% in Model 1 and 87% in Models 2 and 3. However, the effect of implant support on the decrease of moment varied; with shifting the implant location from M2 to M1 sites, the moments were found to increase by 325% in Model 1, 140% in Model 2, and 72% in Model 3.
Table 2. The peak bending moment (Ncm) developed in each test model Implant location
Model 1
Model 2
Model 3
No implant M1 M2
315 165 38.8
510 165 68.8
735 165 97.6
Results The details of the peak shear forces and peak bending moments for all test models are described in Tables 1 and 2. There are no means and standard deviations of the data because of the theoretical study conducted by mathematical calculation. The peak shear forces were, in general, higher when the bases received no additional support of implant. Among those having no implant support, the highest force was found in Model 3, intermediate in Model 2, and lowest in Model 1. The shear forces were the lowest when the implant located at M2 site in all test models. When compared to those receiving no implant support, the forces were lower by 60% in Model 1 and 68% in Models 2 and 3. Interestingly, the highest force was developed in Model 1 when the implant located at M1 site. However, the forces decreased with the shift of implant support from M1 to M2 sites by 76% in Model 1, 67% in Model 2, and 58% in Model 3. The peak bending moments were much higher in models receiving no implant support. The highest moment was found in Model 3, intermediate in Model 2, and lowest in Model 1. The moments decreased when the base received additional support of implant; when the implant is located at M2
Discussion The shear force is a measure of stress acting in transverse direction to the occlusal plane and may cause a bending or fracture of the base at the site of peak force development (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997; Korioth et al. 1998). The shear forces were higher in the models of base receiving no implant support. The peak forces were found at the pivot point of abutment tooth and became higher with an increase of occlusal force and base length. Thus, free-end base RPDs may pose higher risk of failure in the supporting elements of denture and abutment tooth (Cecconi et al. 1971; Thompson et al. 1977; Monteith 1984; Frank et al. 2004; Muraki et al. 2004). The shear forces greatly reduced when the models of base received implant support at M2 site. However, the pattern of force distribution was not consistent when the implant support shifted to M1 site. The force was rather increased in Model 1, although a force reduction was found in Models 2 and 3. This may relate to the short distance between the supports of tooth and implant in Model 1. The peak forces developed at the site of implant location subjecting the base under higher tension of bending moment (Brunski 1988; Gere & Timoshenko 1997; Kayacan et al. 1997). The bending moment is a resultant of shear force as a function of distance and may negatively affect the stability of free-end base RPDs (Gere & Timoshenko 1997; Tandlich et al. 2007). When a high moment develops, the base is prone to rotate, bend, and/or displace against the supporting elements of denture
(Monteith 1984; Muraki et al. 2004). The abutment tooth can be at risk for the loss of periodontal stability, in particular, when combined with the base demonstrating multiple occlusal units as presented in Model 3. The addition of implant support reduced the bending moments developed in the base in this study. However, the effect of implant support was not consistent, but varied with the location of implant. In fact, the bending moment was the lowest when the implant was placed at M2 site, eliminating the free-end segment of base in all test models. Within the limits of this theoretical study, mandibular free-end base RPDs were found to develop high shear forces and bending moments in the supporting elements of base. While the forces and moments were significantly reduced with the addition of implant support, the force and moment reduction varied with implant location as reference to base length. Thus, a further research needs to be investigated to optimize the location of implant support in designing RPDs.
Conclusion The high shear forces and bending moments subjected to mandibular free-end base RPDs were found to decrease with the addition of implant support. However, the impact of implant support varied with implant location in this theoretical study. A further research needs to be conducted to investigate the biomechanically most advantageous location of implant support in designing RPDs.
Funding This research was carried out without funding.
Conflict of interests No conflict of interests declared.
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