680
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
IN
BONE
AND IMPLANTS
PADHYE
ET AL
Stress Distribution in Bone and Implants in Mandibular 6-Implant-Supported Cantilevered Fixed Prosthesis: A 3D Finite Element Study Omkar Vinayak Padhye, MDS,* Manisha Herekar, MDS,† Viraj Patil, MDS,† Shahnawaz Mulani, MDS,‡ Megha Sethi, MDS,* and Aquaviva Fernandes, MDS†
vast improvement in the treatment of completely edentulous patients over a traditional complete denture is a removable overdenture supported by 2 to 4 implants. The option of restoring the completely edentulous jaws with a fixed replacement offers even greater psychological benefits to the patient.1 The complete implant-supported fixed restoration can halt posterior bone loss associated with edentulism and provides fewer prosthetic complications compared with removable restorations.2,3 Misch proposed 5 treatment options for fixed rehabilitation of the completely edentulous mandible. Treatment option 1 proposes 4 to 6 implants between mental foramina and a distal cantilever to replace posterior teeth; the arch form and position of mental foramina are important criteria when 4 to 6 implants are placed in the anterior segment to replace the entire mandibular arch.4 In treatment option 2,
A
Purpose: The purpose of the study was to evaluate by a 3dimensional finite element analysis the load transmission to periimplant bone by a framework supported by 6 implants placed in an edentulous mandible and to compare the stress distribution for varying cantilever lengths. Methodology: A computerized model of the anterior segment of a mandible with a 6-implant-supported bridge was created in software. The length of the cantilever segment was considered as 10, 15, and 20 mm. A 150 N load was applied to the terminal point of the cantilever segment, and Von Mises stresses were analyzed along implants, framework, and bone.
Results: When the cantilever length was increased from 10 to 20 mm, the stress increased 79.66% in the framework, 68.16% in implants, and 59.96% and 52.81% in cortical and cancellous bones, respectively. Conclusion: The greatest amount of stress was seen around the distalmost region of the distal-most implant. The framework absorbed the maximum amount of stresses followed by the implants, cortical bone, and cancellous bone. Extension of the cantilever beyond 15 mm could lead to greater stress in the lingual cortical plate, which could compromise the integrity of the implants. (Implant Dent 2015;24:680–685) Key Words: cantilever, mandibular fixed prosthesis, dental implants
*Postgraduate Student, Department of Prosthodontics, Maratha Mandal’s NGH Institute of Dental Sciences and Research Centre, Belgaum, India. †Professor, Department of Prosthodontics, Maratha Mandal’s NGH Institute of Dental Sciences and Research Centre, Belgaum, India. ‡Senior Lecturer, Department of Prosthodontics, Aditya Dental College, Beed, India.
5 to 7 implants are used; the additional distal implant is placed above the mental foramina. In treatment option 3, 5 to 7 implants are used with a unilateral cantilever; treatment options 4 and 5 permit the placement of 6 to 9 implants and have the primary advantage of totally eliminating cantilevers.5 Cantilevers in implant dentistry are beneficial when anatomical limitations preclude the ideal placement of implants. The additional masticatory units that may be provided by the cantilever arm can provide function and esthetics
that would otherwise be unachievable. The length of the cantilever is determined by the A-P spread of implants and force factors such as parafunction, crown height, masticatory dynamics, bone density in implanted areas, and implant design.6,7 The use of 6 implants placed in the interforaminal region of an ovoid arch provides an adequate A-P spread.8–10 However, cantilevers may adversely affect the biomechanics of implant restorations.3 It has been demonstrated that the bite force of patients with implant
Reprint requests and correspondence to: Omkar Vinayak Padhye, MDS, 1/30, Calpana C.H.S., Ghantali, Naupada, Sahayog Mandir Road, Thane (West), Maharashtra 400602, India, Phone: +91-9820909981, Fax: +91-22-25376459, E-mail: omkar_padhye@ yahoo.com ISSN 1056-6163/15/02406-680 Implant Dentistry Volume 24 Number 6 Copyright © 2015 Wolters Kluwer Health, Inc. All rights reserved. DOI: 10.1097/ID.0000000000000300
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015
ET AL
Fig. 1. A, Complete model showing framework, 6 implants, and mandibular bone block. B, Complete meshed model, side view. C, Complete meshed model, rear view. D, Model showing the point of load application and constrained ends.
prostheses was comparable with or higher than that of the natural dentition.7 The biomechanics of implant-supported fixed prostheses play an important role in the longevity of the bone around dental implants.8 Falk et al11 stated that an occlusal interference in the cantilevered segment resulted in an increase in vertical bending stress at the distal cantilever joint. Previously, implant cantilever recommendations were primarily based on empiricism.10,12,13 The current literature proposes varying lengths of cantilever for treatment option 1. Several recommendations have been made for cantilever length treatment planning.10,14–18 The purpose of this study was to evaluate by a 3-dimensional (3D) finite element analysis (FEA) the load transmission to periimplant bone by a framework
supported by 6 implants placed in the interforaminal region of an edentulous mandible and to compare the stress distribution by varying lengths of the cantilevered segments.
METHODOLOGY A computerized 3D finite element model of the anterior segment of a human mandible with an implantsupported bridge was created in ANSYS 10 software to analyze and compare the stresses transmitted to the periimplant bone and the implants. The basic mandible model consisted of a curved beam with a 15 mm radius, 69.0 mm in length, 14.0 mm in height, and 6.0 mm in width. This beam was covered with a 1.0-mm-thick layer on the buccal, occlusal, and lingual surfaces and a 3.0 mm layer at the base
Table 1. Elastic Properties of Materials Used for FEA Model Material Titanium (abutment, implant) Cancellous/spongy bone Cortical bone Co-Cr alloy (framework)
Elastic Modulus (E) (GPa)
Poisson Ratio (m)
110 1.37 13.7 218
0.35 0.3 0.3 0.33
Reference 8 20 20 8
Elastic properties of materials such as elastic modulus (E) and Poisson ratio (m) assigned to different material compounds of the finite element model were determined from the literature to study stress distribution.8,20
681
to simulate cortical bone; the final external dimensions were 71.0 3 18.0 3 8.0 mm. It was not necessary to build a model of the entire mandible. By doing so, one has the advantage of reducing the modeling and calculation time.8,9 A second beam 71.0 mm long, 4.0 mm high, and 6.0 mm wide was added in connection to the abutments to simulate the Co-Cr framework. The attachment of the second beam to the abutments is considered to be rigid. The length of this beam was modified as per the cantilever segment to be studied. The length of the cantilever segment was considered as 10, 15, and 20 mm from the distal part of the terminal implant to the terminal point of the Co-Cr superstructure (Fig. 1A). Six cylindrical implants were modeled, 11.5 mm long. The implant diameter in the incisor region (2 implants) was 3.5 mm, and the implant diameter in the canine (2 implants) and bicuspid region (2 implants) was 4.0 mm. The implants were positioned at a distance of 3.0 mm from each other. Abutments were also modeled with diameter equal to that of the corresponding implant. All the abutments were modeled with an equal height of 4.0 mm. The abutments were screwed and considered as rigidly fixed to the implant body. The FEA model assumed a state of optimal osseointegration, which means that the cortical and trabecular bones are assumed to be 100% osseointegrated with the implant surface for refinement of the mesh.18 An average occlusal force of 150 N was determined from the literature.8,9,18 The ends were constrained, and the load was applied along the distal portion of the cantilever to assess stress distribution. The final meshed model comprised 167,188 elements and 31,359 nodes (Fig. 1, B and C). The constraints at the end of the bone segment and force application on top of the Co-Cr framework roughly approximate the complex balance between masticatory forces and their reactions (Fig. 1D). All materials were presumed linear elastic, homogeneous, and isotropic.17,18 The cortical and cancellous bones were modeled as having elastic properties of a D2-type bone.19 The corresponding elastic properties such as Young’s modulus (E) and Poisson ratio (m) were
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
682
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
IN
BONE
AND IMPLANTS
Fig. 2. A, Von Mises stress distribution pattern on application of load at the distal-most point on cantilever. B, Stress distribution along implants. C, Stress distribution along the Co-Cr framework. D, Stress distribution along the cortical bone. E, Stress distribution along the cancellous bone. F, Compressive forces seen acting along the distal implants, tensile forces along the anterior implants.
determined from (Table 1).8,20
the
literature
RESULTS All the parameters required to load the model and produce stress patterns
were fed to the computer program. On application of forces along the distal terminal point of the model, Von Mises stress patterns were obtained as contour lines (Fig. 2A). Stress concentration in all the configurations was seen at the distolingual
PADHYE
ET AL
aspect of the distal-most implants. Stresses were more of the compressive type along the distolingual region, while the buccal, mesial, and distal sides demonstrated more tensile stresses (Fig. 2B). Stresses decreased for implants away from the point of application of the load. There was a generalized increase in the amount of stresses experienced by the implants as the length of the cantilever arm increased (Fig. 3A). The prosthetic framework was bearing the maximum amount of stress. The stresses were concentrated at the point attachment of framework to the distal abutment (Fig. 2C). The Von Mises stress values increased linearly as the length of the framework increased beyond the support of distal implant (Fig. 3B). In the cortical bone, stresses were concentrated at the crest along the crestal module of the implants (Fig. 2D), whereas in the cancellous bone section, stresses were distributed along the whole length of the implant body along the distolingual region (Fig. 2E). An increasing trend in the amount of stresses experienced by the cortical and cancellous bones was evident when the length of the cantilever arm was increased (Fig. 3, C and D). The implants closest to the cantilever showed compressive stresses, whereas the implants in the incisor region showed tensile stresses opposite to the direction of load application (Fig. 2F).
DISCUSSION
Fig. 3. Von Mises stress distribution around (A) implants, (B) Co-Cr framework, (C) cortical bone, and (D) cancellous bone.
The distribution of loads applied to implant-supported prostheses depends on the number, arrangement, placement, design, and stiffness of the implants used, as well as on the shape and stiffness of the prosthesis and type of bone.13,20–22 In this study, the effect of cantilever length on stress distribution around the periimplant bone was studied by the application of occlusal loads on the distal-most point of the cantilever arm at 10, 15, and 20 mm on a computer model. The results suggest that at every 5-mm increment of cantilever length, there was a generalized increase in the amount of stresses on all structures (prosthesis, bone: cortical and cancellous, and implant). The maximum
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
ET AL
stresses were borne by the Co-Cr framework and then by the implants, cortical bone, and cancellous bone in descending order, respectively. For all configurations studied, which can be compared with a class 1 lever, the maximum concentration of stresses around implants was seen near the distolingual region, which was a common finding.12,14,23,24 Tensile stresses were seen in the buccal and mesial regions and were similar to results published in a study of tilted distal implants with a 5 mm cantilever arm.9,24 There was an increase in the amount of stress by 41.03% when the length of the cantilever arm was extended from 10 to 15 mm and a 29.17% additional increase on further increasing the cantilever to 20 mm. There was a 68.16% total increase in the amount of stress levels when the cantilever arm is extended from 10 to 20 mm. This implies that the stresses on implants increase with increase in the length of the lever arm, which was evident from this study and a previous similar study.8 The most distal implant acts as the fulcrum of a class 1 lever, and therefore it is subjected to greater compression forces while the intermediary implants suffer tension.23 It is recommended that the arches of free-end prosthesis with implants within the interforaminal region be connected in a rigid manner, so that the implants on one side may help balance tensions generated on the other.25,26 Contrary to this, if implant placement in mandible is beyond the interforaminal region, the framework should be segmented to allow for flexure movement of the mandibular arch.5,27 In the prosthetic framework, the maximum stress concentration was seen at the position where it connects the distal-most implant. The framework stresses increased considerably by 49.58% at 15 mm; then, there was an additional 33.37% stress increase when the cantilever was increased by 5 mm. The total percentage stress increase when the cantilever arm extended from 10 to 20 mm was 79.66%. The use of an alloy with high modulus of elasticity transmits less stress to the surrounding bone, itself bearing the maximum amount of stresses.28 Co-Cr framework allowed for more even distribution of
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015 load with decreased bulk and reduced cost when cantilevers are present, compared with gold alloy or silverpalladium framework, which demonstrate accurate fitting framework and ease in casting but with less flexure strength.8,14,28–30 In this study, Co-Cr framework demonstrated compression along the length of the cantilever arm and tensile stresses from a point mesial to the implant in canine region with maximum tensile stress evident at the buccal surface of crest module of incisor implants, cortical bone, and cancellous bone. The tensile stresses were well within the failure stress limits of the bone; this implies that the material of the framework plays a decisive role in determining the length of the cantilever.31,32 Biomechanics of an osseointegrated system suggest that forces applied to an implant are modified by the specific implant geometry, material, or design affecting the interfacial load transferred to the surrounding bone.29 Also, the density of the available bone in an edentulous site is a determining factor in treatment planning, implant design selection, surgical approach, healing time, and initial progressive bone loading during prosthetic reconstruction. In this study, a D-2 bone block was used to simulate a mandible because it is the most common variant in the anterior mandible.19 It was assumed that the models were homogeneous and isotropic.17,18 Cylindrical flat implants without abutment housing and prosthetic screws were considered for study.24 Moreover, ideal conditions were established, such as single-point loading on framework, 100% contact between bone and implant, and perfect fit of the implants, abutments, and prosthetic bars (absence of gap or frictional coefficient), as the main intent of the study was to study the cantilever length of the framework and its effect on bone. As this study was comparative in nature, such assumptions would not interfere in the aims because they were present in all models. Simplifications are present and are common in any study of implant dentistry that uses FEA.28,31,33–36 The area of bone around the distalmost implant bores the maximum amount of stresses; the amount decreased
683
while traveling to the symphyseal region. In every situation, the stresses tended to be concentrated at the crest of the cortical bone along the distolingual aspect of the implant closest to the point of application of the load. There was a 35.25% increase in cortical bone stress levels when increasing the length of the cantilever arm from 10 to 15 mm and an additional 26.08% increase when the arm was further extended to 20 mm. Stresses increased by 59.96% when the cantilever arm increased in length from 10 to 20 mm. Also, the magnitude of stresses in the cortical bone was approximately 10 times greater than that seen in the cancellous bone, which can be explained by the higher modulus of elasticity of cortical bone, which therefore bears more stress.13,14 The stresses would be underestimated in the study, as the implants were modeled as flat cylinders; to counter this, the bone margins were not modeled physiologically.9,33 It has been reported that overloading of implants resulted in increased bone resorption around the implant crestal module and a decreased percentage of mineralized bone tissue in the cortex.37 The modeled mandible and framework connected to each other by implants displayed a composite beam structure, with a multitude of difference in physical properties between both structures (Table 1). The mandible being a biological structure tends to alter its physical properties depending on the stresses exerted on it; contrary to this, the Co-Cr framework does not display any change in its physical properties. The implant-abutment assembly, which acts as connector between the 2 beams, gains significance in the given situation as it transfers the stresses from framework to bone. Optimum design and number of implants that would dissipate the forces to the bone become key factors in considering the length of the cantilever arm.23 Excessive cantilever length has shown to produce greater stresses, which may decrease the bone density around the implant crestal module and lead to crater-like defects.38,39
CONCLUSION Under the conditions of this study, the following conclusions were drawn:
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
684
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
1. The stress location and distribution pattern were very similar in the 3 models with variable cantilever lengths. 2. Regardless of the length of the cantilever arm, the greatest amount of stress in the prosthesis was seen around the distal-most implant, and the value decreased as the measurements traveled along the length of the mandible towards anterior symphysis. 3. The Co-Cr framework absorbed the maximum amount of stresses followed by the titanium implants, cortical bone, and cancellous bone bearing the least. 4. Extension of the cantilever beyond 15 mm could lead to greater stresses in the periimplant region, which could jeopardize the integrity of the implant-bone interface. The cantilever arm of an implantsupported prosthesis framework is easily controlled by the dentist; to keep the length of the cantilever arm to a minimum in the prescription to the dental technician is a procedure that should not be neglected.
DISCLOSURE The authors claim to have no financial interest, either directly or indirectly, in the products or information listed in the article.
REFERENCES 1. Humphris GM, Healey T, Howell RA, et al. The psychological impact of implantretained mandibular prosthesis. Int J Oral Maxillofac Implants. 1995;10:437–444. 2. Wright P, Glantz P, Randow K, et al. The effects of fixed and removable implant-stabilized prostheses on posterior mandibular residual ridge resorption. Clin Oral Implants Res. 2002;13:169–174. 3. Goodacre CJ, Bernal G, Rungcharassaeng K, et al. Clinical complications with implant and implant prostheses. J Prosthet Dent. 2003;90:121–132. 4. Adell R, Lekholm U, Rockler B, et al. A 15-year study of osseointegrated implants in the treatment of the edentulous jaws. Int J Oral Surg. 1981;10:387–416. 5. Misch CE. The completely edentulous mandible: Treatment plans for fixed restorations. In: Misch CE, ed. Contemporary
IN
BONE
AND IMPLANTS
Implant Dentistry. 3rd ed. St. Louis, MO: C.V. Mosby; 2008:314–326. 6. Rodriguez AM, Aquilino SA, Lund PS. Cantilever and implant biomechanics: A review of the literature, Part 2. J Prosthodont. 1994;3:114–118. 7. Haroldson T, Carlsson GE. Bite force and oral function in patients with osseointegrated oral implants. Scand J Dent Res. 1977;85:200. 8. Rubo JH, Souza EA. Finite element analysis of stress in bone adjacent to dental implants. J Oral Implantol. 2008;34:248–255. 9. Bellini CM, Romeo D, Galbusera F, et al. Comparison of tilted versus non-tilted implant-supported prosthetic designs for the restoration of the edentulous mandible: A biomechanical study. Int J Oral Maxillofac Implants. 2009;24:511–517. 10. English CE. Critical A-P spread. Implant Soc. 1990;1:2–3. 11. Falk H, Laurell L, Lundgren D. Occlusal interferences and cantilever joint stress in implant-supported prosthesis occluding with complete dentures. Int J Oral Maxillofac Implants. 1990;5:70–77. 12. Rangert B, Jemt T, Jörneus L. Forces and moments on Brånemark implants. Int J Oral Maxillofac Implants. 1989;4:241–247. 13. Skalak R. Biomechanical considerations in osseointegrated prostheses. J Prosthet Dent. 1983;49:843–848. 14. Jacques LB, Moura MS, Suedam V, et al. Effects of cantilever length and framework alloy on the stress distribution of mandibular-cantilevered implant-supported prostheses. Clin Oral Implants Res. 2009;20:737–741. 15. English CE. The mandibular overdenture supported by implants in the anterior symphysis: A prescription for implant placement and bar prosthesis design. Dent Implantol Update. 1993;4:1–3. 16. English CE. Prosthodontic prescriptions for mandibular implant overdentures. Dent Implantol Update. 1996;7:1–4. 17. Bellini CM, Romeo D, Galbusera F, et al. A finite element analysis of tilted versus non-tilted implant configuration in the edentulous maxilla. Int J Prosthodont. 2009;22:155–157. 18. Bevilacqua M, Tealdo T, Pera F, et al. Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths. Int J Prosthodont. 2008;21:539–542. 19. Misch CE. Density of bone: Effect on treatment plans, surgical approach, healing and progressive loading. Int J Oral Implantol. 1990;6:23–31. 20. Greco GD, Jansen WC, Landre J, et al. Stress analysis on the free-end distal extension of an implant-supported mandibular complete denture. Braz Oral Res. 2009;23:175–181.
PADHYE
ET AL
21. Bidez MW, Misch CE. Force transfer in implant dentistry: Basic concepts and principles. J Oral Implantol. 1992;18: 264–274. 22. Bidez MW, Misch CE. Issues in bone mechanics related to oral implants. Implant Dent. 1992;1:289–294. 23. Misch CE. Clinical biomechanics in implant dentistry. Misch CE, ed. Dental Implant Prosthetics. 1st ed. St. Louis, MO: C.V. Mosby; 2005:309–321. 24. Fazi G, Tellini S, Vangi D, et al. Three-dimensional finite element analysis of different implant configurations for a mandibular fixed prosthesis. Int J Oral Maxillofac Implants. 2011;26:752–759. 25. Jemt T. Failures and complications in 391 consecutively inserted fixed prostheses supported by Brånemark implants in edentulous jaw: A study of treatment from the time of prosthesis placement to the first annual checkup. Int J Oral Maxillofac Implants. 1991;6:270–276. 26. Skalak R. Aspects of biomechanical considerations. In: Brånemark PI, Zarb GA, Albreksson T, eds. Tissue-Integrated ProsthesesdOsseointegration in Clinical Dentistry. Chicago, IL: Quintessence; 1985:117–128. 27. Omar R, Wise MD. Mandibular flexure associated with muscle force applied in retruded axis position. J Oral Rehabil. 1981;8:209–221. 28. Sertgoz A. Finite element analysis study of the effect of superstructure material on stress distribution in an implant-supported fixed prosthesis. Int J Prosthodont. 1997;10:19–27. 29. Cibirka RM, Razzoog ME, Lang BR, et al. Determining the force absorption quotient for restorative materials used in implant occlusal surfaces. J Prosthet Dent. 1992;67:361–364. 30. Silva GC, Mendonça JA, Lopes LR, et al. Stress patterns on implants in prostheses supported by four or six implants: A three-dimensional finite element analysis. Int J Oral Maxillofac Implants. 2010;25:239–246. 31. Geng JP, Tan KBC, Liu GR. Application of finite element analysis in implant dentistry: A review of the literature. J Prosthet Dent. 2001;85:585–598. 32. Van Oosterwyjck H, Duyck J, Vander Sloten J, et al. The influence of bone mechanical properties and implant fixation upon bone loading around oral implants. Clin Oral Implants Res. 1998;9: 407–418. 33. Zampelis A, Rangert B, Heijl L. Tilting of splinted implants for improved prosthodontic support: A two-dimensional finite element analysis. J Prosthet Dent. 2007;97:35–43. lar A, Aydin C, Ozen J, et al. 34. Cag Effects of mesiodistal inclination of implants
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
ET AL
on stress distribution in implant-supported fixed prostheses. Int J Oral Maxillofac Implants. 2006;21:36–44. lu H, Akça K. Comparative 35. Iplikçiog evaluation of the effect of diameter, length and number of implants supporting threeunit fixed partial prostheses on stress distribution in the bone. J Dent. 2002;30:41–46. 36. Van Staden RC, Guan H, Loo YC. Application of finite element method in
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015 dental research. Comput Methods Biomech Biomed Engin. 2006;9:257–270. 37. Hoshaw SJ, Brunski JB, Cochran GVB. Mechanical loading of Brånemark implants affects interfacial bone modeling and remodeling. Int J Oral Maxillofac Implants. 1994;9:345–360. 38. Suedam V, Capello Souza EA, Jacques LB, et al. Effect of abutment’s height and framework alloy on the load
685
distribution of mandibular cantilevered implant-supported prosthesis. Clin Oral Implants Res. 2009;20:196–200. 39. Papavasiliou G, Kamposiora P, Bayne SC, et al. Three-dimensional finite element analysis of stress-distribution around single tooth implants as a function of bony support, prosthesis type, and loading during function. J Prosthet Dent. 1996;76:633–640.
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
IN
BONE
AND IMPLANTS
PADHYE
ET AL
Stress Distribution in Bone and Implants in Mandibular 6-Implant-Supported Cantilevered Fixed Prosthesis: A 3D Finite Element Study Omkar Vinayak Padhye, MDS,* Manisha Herekar, MDS,† Viraj Patil, MDS,† Shahnawaz Mulani, MDS,‡ Megha Sethi, MDS,* and Aquaviva Fernandes, MDS†
vast improvement in the treatment of completely edentulous patients over a traditional complete denture is a removable overdenture supported by 2 to 4 implants. The option of restoring the completely edentulous jaws with a fixed replacement offers even greater psychological benefits to the patient.1 The complete implant-supported fixed restoration can halt posterior bone loss associated with edentulism and provides fewer prosthetic complications compared with removable restorations.2,3 Misch proposed 5 treatment options for fixed rehabilitation of the completely edentulous mandible. Treatment option 1 proposes 4 to 6 implants between mental foramina and a distal cantilever to replace posterior teeth; the arch form and position of mental foramina are important criteria when 4 to 6 implants are placed in the anterior segment to replace the entire mandibular arch.4 In treatment option 2,
A
Purpose: The purpose of the study was to evaluate by a 3dimensional finite element analysis the load transmission to periimplant bone by a framework supported by 6 implants placed in an edentulous mandible and to compare the stress distribution for varying cantilever lengths. Methodology: A computerized model of the anterior segment of a mandible with a 6-implant-supported bridge was created in software. The length of the cantilever segment was considered as 10, 15, and 20 mm. A 150 N load was applied to the terminal point of the cantilever segment, and Von Mises stresses were analyzed along implants, framework, and bone.
Results: When the cantilever length was increased from 10 to 20 mm, the stress increased 79.66% in the framework, 68.16% in implants, and 59.96% and 52.81% in cortical and cancellous bones, respectively. Conclusion: The greatest amount of stress was seen around the distalmost region of the distal-most implant. The framework absorbed the maximum amount of stresses followed by the implants, cortical bone, and cancellous bone. Extension of the cantilever beyond 15 mm could lead to greater stress in the lingual cortical plate, which could compromise the integrity of the implants. (Implant Dent 2015;24:680–685) Key Words: cantilever, mandibular fixed prosthesis, dental implants
*Postgraduate Student, Department of Prosthodontics, Maratha Mandal’s NGH Institute of Dental Sciences and Research Centre, Belgaum, India. †Professor, Department of Prosthodontics, Maratha Mandal’s NGH Institute of Dental Sciences and Research Centre, Belgaum, India. ‡Senior Lecturer, Department of Prosthodontics, Aditya Dental College, Beed, India.
5 to 7 implants are used; the additional distal implant is placed above the mental foramina. In treatment option 3, 5 to 7 implants are used with a unilateral cantilever; treatment options 4 and 5 permit the placement of 6 to 9 implants and have the primary advantage of totally eliminating cantilevers.5 Cantilevers in implant dentistry are beneficial when anatomical limitations preclude the ideal placement of implants. The additional masticatory units that may be provided by the cantilever arm can provide function and esthetics
that would otherwise be unachievable. The length of the cantilever is determined by the A-P spread of implants and force factors such as parafunction, crown height, masticatory dynamics, bone density in implanted areas, and implant design.6,7 The use of 6 implants placed in the interforaminal region of an ovoid arch provides an adequate A-P spread.8–10 However, cantilevers may adversely affect the biomechanics of implant restorations.3 It has been demonstrated that the bite force of patients with implant
Reprint requests and correspondence to: Omkar Vinayak Padhye, MDS, 1/30, Calpana C.H.S., Ghantali, Naupada, Sahayog Mandir Road, Thane (West), Maharashtra 400602, India, Phone: +91-9820909981, Fax: +91-22-25376459, E-mail: omkar_padhye@ yahoo.com ISSN 1056-6163/15/02406-680 Implant Dentistry Volume 24 Number 6 Copyright © 2015 Wolters Kluwer Health, Inc. All rights reserved. DOI: 10.1097/ID.0000000000000300
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015
ET AL
Fig. 1. A, Complete model showing framework, 6 implants, and mandibular bone block. B, Complete meshed model, side view. C, Complete meshed model, rear view. D, Model showing the point of load application and constrained ends.
prostheses was comparable with or higher than that of the natural dentition.7 The biomechanics of implant-supported fixed prostheses play an important role in the longevity of the bone around dental implants.8 Falk et al11 stated that an occlusal interference in the cantilevered segment resulted in an increase in vertical bending stress at the distal cantilever joint. Previously, implant cantilever recommendations were primarily based on empiricism.10,12,13 The current literature proposes varying lengths of cantilever for treatment option 1. Several recommendations have been made for cantilever length treatment planning.10,14–18 The purpose of this study was to evaluate by a 3-dimensional (3D) finite element analysis (FEA) the load transmission to periimplant bone by a framework
supported by 6 implants placed in the interforaminal region of an edentulous mandible and to compare the stress distribution by varying lengths of the cantilevered segments.
METHODOLOGY A computerized 3D finite element model of the anterior segment of a human mandible with an implantsupported bridge was created in ANSYS 10 software to analyze and compare the stresses transmitted to the periimplant bone and the implants. The basic mandible model consisted of a curved beam with a 15 mm radius, 69.0 mm in length, 14.0 mm in height, and 6.0 mm in width. This beam was covered with a 1.0-mm-thick layer on the buccal, occlusal, and lingual surfaces and a 3.0 mm layer at the base
Table 1. Elastic Properties of Materials Used for FEA Model Material Titanium (abutment, implant) Cancellous/spongy bone Cortical bone Co-Cr alloy (framework)
Elastic Modulus (E) (GPa)
Poisson Ratio (m)
110 1.37 13.7 218
0.35 0.3 0.3 0.33
Reference 8 20 20 8
Elastic properties of materials such as elastic modulus (E) and Poisson ratio (m) assigned to different material compounds of the finite element model were determined from the literature to study stress distribution.8,20
681
to simulate cortical bone; the final external dimensions were 71.0 3 18.0 3 8.0 mm. It was not necessary to build a model of the entire mandible. By doing so, one has the advantage of reducing the modeling and calculation time.8,9 A second beam 71.0 mm long, 4.0 mm high, and 6.0 mm wide was added in connection to the abutments to simulate the Co-Cr framework. The attachment of the second beam to the abutments is considered to be rigid. The length of this beam was modified as per the cantilever segment to be studied. The length of the cantilever segment was considered as 10, 15, and 20 mm from the distal part of the terminal implant to the terminal point of the Co-Cr superstructure (Fig. 1A). Six cylindrical implants were modeled, 11.5 mm long. The implant diameter in the incisor region (2 implants) was 3.5 mm, and the implant diameter in the canine (2 implants) and bicuspid region (2 implants) was 4.0 mm. The implants were positioned at a distance of 3.0 mm from each other. Abutments were also modeled with diameter equal to that of the corresponding implant. All the abutments were modeled with an equal height of 4.0 mm. The abutments were screwed and considered as rigidly fixed to the implant body. The FEA model assumed a state of optimal osseointegration, which means that the cortical and trabecular bones are assumed to be 100% osseointegrated with the implant surface for refinement of the mesh.18 An average occlusal force of 150 N was determined from the literature.8,9,18 The ends were constrained, and the load was applied along the distal portion of the cantilever to assess stress distribution. The final meshed model comprised 167,188 elements and 31,359 nodes (Fig. 1, B and C). The constraints at the end of the bone segment and force application on top of the Co-Cr framework roughly approximate the complex balance between masticatory forces and their reactions (Fig. 1D). All materials were presumed linear elastic, homogeneous, and isotropic.17,18 The cortical and cancellous bones were modeled as having elastic properties of a D2-type bone.19 The corresponding elastic properties such as Young’s modulus (E) and Poisson ratio (m) were
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
682
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
IN
BONE
AND IMPLANTS
Fig. 2. A, Von Mises stress distribution pattern on application of load at the distal-most point on cantilever. B, Stress distribution along implants. C, Stress distribution along the Co-Cr framework. D, Stress distribution along the cortical bone. E, Stress distribution along the cancellous bone. F, Compressive forces seen acting along the distal implants, tensile forces along the anterior implants.
determined from (Table 1).8,20
the
literature
RESULTS All the parameters required to load the model and produce stress patterns
were fed to the computer program. On application of forces along the distal terminal point of the model, Von Mises stress patterns were obtained as contour lines (Fig. 2A). Stress concentration in all the configurations was seen at the distolingual
PADHYE
ET AL
aspect of the distal-most implants. Stresses were more of the compressive type along the distolingual region, while the buccal, mesial, and distal sides demonstrated more tensile stresses (Fig. 2B). Stresses decreased for implants away from the point of application of the load. There was a generalized increase in the amount of stresses experienced by the implants as the length of the cantilever arm increased (Fig. 3A). The prosthetic framework was bearing the maximum amount of stress. The stresses were concentrated at the point attachment of framework to the distal abutment (Fig. 2C). The Von Mises stress values increased linearly as the length of the framework increased beyond the support of distal implant (Fig. 3B). In the cortical bone, stresses were concentrated at the crest along the crestal module of the implants (Fig. 2D), whereas in the cancellous bone section, stresses were distributed along the whole length of the implant body along the distolingual region (Fig. 2E). An increasing trend in the amount of stresses experienced by the cortical and cancellous bones was evident when the length of the cantilever arm was increased (Fig. 3, C and D). The implants closest to the cantilever showed compressive stresses, whereas the implants in the incisor region showed tensile stresses opposite to the direction of load application (Fig. 2F).
DISCUSSION
Fig. 3. Von Mises stress distribution around (A) implants, (B) Co-Cr framework, (C) cortical bone, and (D) cancellous bone.
The distribution of loads applied to implant-supported prostheses depends on the number, arrangement, placement, design, and stiffness of the implants used, as well as on the shape and stiffness of the prosthesis and type of bone.13,20–22 In this study, the effect of cantilever length on stress distribution around the periimplant bone was studied by the application of occlusal loads on the distal-most point of the cantilever arm at 10, 15, and 20 mm on a computer model. The results suggest that at every 5-mm increment of cantilever length, there was a generalized increase in the amount of stresses on all structures (prosthesis, bone: cortical and cancellous, and implant). The maximum
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
ET AL
stresses were borne by the Co-Cr framework and then by the implants, cortical bone, and cancellous bone in descending order, respectively. For all configurations studied, which can be compared with a class 1 lever, the maximum concentration of stresses around implants was seen near the distolingual region, which was a common finding.12,14,23,24 Tensile stresses were seen in the buccal and mesial regions and were similar to results published in a study of tilted distal implants with a 5 mm cantilever arm.9,24 There was an increase in the amount of stress by 41.03% when the length of the cantilever arm was extended from 10 to 15 mm and a 29.17% additional increase on further increasing the cantilever to 20 mm. There was a 68.16% total increase in the amount of stress levels when the cantilever arm is extended from 10 to 20 mm. This implies that the stresses on implants increase with increase in the length of the lever arm, which was evident from this study and a previous similar study.8 The most distal implant acts as the fulcrum of a class 1 lever, and therefore it is subjected to greater compression forces while the intermediary implants suffer tension.23 It is recommended that the arches of free-end prosthesis with implants within the interforaminal region be connected in a rigid manner, so that the implants on one side may help balance tensions generated on the other.25,26 Contrary to this, if implant placement in mandible is beyond the interforaminal region, the framework should be segmented to allow for flexure movement of the mandibular arch.5,27 In the prosthetic framework, the maximum stress concentration was seen at the position where it connects the distal-most implant. The framework stresses increased considerably by 49.58% at 15 mm; then, there was an additional 33.37% stress increase when the cantilever was increased by 5 mm. The total percentage stress increase when the cantilever arm extended from 10 to 20 mm was 79.66%. The use of an alloy with high modulus of elasticity transmits less stress to the surrounding bone, itself bearing the maximum amount of stresses.28 Co-Cr framework allowed for more even distribution of
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015 load with decreased bulk and reduced cost when cantilevers are present, compared with gold alloy or silverpalladium framework, which demonstrate accurate fitting framework and ease in casting but with less flexure strength.8,14,28–30 In this study, Co-Cr framework demonstrated compression along the length of the cantilever arm and tensile stresses from a point mesial to the implant in canine region with maximum tensile stress evident at the buccal surface of crest module of incisor implants, cortical bone, and cancellous bone. The tensile stresses were well within the failure stress limits of the bone; this implies that the material of the framework plays a decisive role in determining the length of the cantilever.31,32 Biomechanics of an osseointegrated system suggest that forces applied to an implant are modified by the specific implant geometry, material, or design affecting the interfacial load transferred to the surrounding bone.29 Also, the density of the available bone in an edentulous site is a determining factor in treatment planning, implant design selection, surgical approach, healing time, and initial progressive bone loading during prosthetic reconstruction. In this study, a D-2 bone block was used to simulate a mandible because it is the most common variant in the anterior mandible.19 It was assumed that the models were homogeneous and isotropic.17,18 Cylindrical flat implants without abutment housing and prosthetic screws were considered for study.24 Moreover, ideal conditions were established, such as single-point loading on framework, 100% contact between bone and implant, and perfect fit of the implants, abutments, and prosthetic bars (absence of gap or frictional coefficient), as the main intent of the study was to study the cantilever length of the framework and its effect on bone. As this study was comparative in nature, such assumptions would not interfere in the aims because they were present in all models. Simplifications are present and are common in any study of implant dentistry that uses FEA.28,31,33–36 The area of bone around the distalmost implant bores the maximum amount of stresses; the amount decreased
683
while traveling to the symphyseal region. In every situation, the stresses tended to be concentrated at the crest of the cortical bone along the distolingual aspect of the implant closest to the point of application of the load. There was a 35.25% increase in cortical bone stress levels when increasing the length of the cantilever arm from 10 to 15 mm and an additional 26.08% increase when the arm was further extended to 20 mm. Stresses increased by 59.96% when the cantilever arm increased in length from 10 to 20 mm. Also, the magnitude of stresses in the cortical bone was approximately 10 times greater than that seen in the cancellous bone, which can be explained by the higher modulus of elasticity of cortical bone, which therefore bears more stress.13,14 The stresses would be underestimated in the study, as the implants were modeled as flat cylinders; to counter this, the bone margins were not modeled physiologically.9,33 It has been reported that overloading of implants resulted in increased bone resorption around the implant crestal module and a decreased percentage of mineralized bone tissue in the cortex.37 The modeled mandible and framework connected to each other by implants displayed a composite beam structure, with a multitude of difference in physical properties between both structures (Table 1). The mandible being a biological structure tends to alter its physical properties depending on the stresses exerted on it; contrary to this, the Co-Cr framework does not display any change in its physical properties. The implant-abutment assembly, which acts as connector between the 2 beams, gains significance in the given situation as it transfers the stresses from framework to bone. Optimum design and number of implants that would dissipate the forces to the bone become key factors in considering the length of the cantilever arm.23 Excessive cantilever length has shown to produce greater stresses, which may decrease the bone density around the implant crestal module and lead to crater-like defects.38,39
CONCLUSION Under the conditions of this study, the following conclusions were drawn:
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
684
FINITE ELEMENT STUDY
OF
STRESS DISTRIBUTION
1. The stress location and distribution pattern were very similar in the 3 models with variable cantilever lengths. 2. Regardless of the length of the cantilever arm, the greatest amount of stress in the prosthesis was seen around the distal-most implant, and the value decreased as the measurements traveled along the length of the mandible towards anterior symphysis. 3. The Co-Cr framework absorbed the maximum amount of stresses followed by the titanium implants, cortical bone, and cancellous bone bearing the least. 4. Extension of the cantilever beyond 15 mm could lead to greater stresses in the periimplant region, which could jeopardize the integrity of the implant-bone interface. The cantilever arm of an implantsupported prosthesis framework is easily controlled by the dentist; to keep the length of the cantilever arm to a minimum in the prescription to the dental technician is a procedure that should not be neglected.
DISCLOSURE The authors claim to have no financial interest, either directly or indirectly, in the products or information listed in the article.
REFERENCES 1. Humphris GM, Healey T, Howell RA, et al. The psychological impact of implantretained mandibular prosthesis. Int J Oral Maxillofac Implants. 1995;10:437–444. 2. Wright P, Glantz P, Randow K, et al. The effects of fixed and removable implant-stabilized prostheses on posterior mandibular residual ridge resorption. Clin Oral Implants Res. 2002;13:169–174. 3. Goodacre CJ, Bernal G, Rungcharassaeng K, et al. Clinical complications with implant and implant prostheses. J Prosthet Dent. 2003;90:121–132. 4. Adell R, Lekholm U, Rockler B, et al. A 15-year study of osseointegrated implants in the treatment of the edentulous jaws. Int J Oral Surg. 1981;10:387–416. 5. Misch CE. The completely edentulous mandible: Treatment plans for fixed restorations. In: Misch CE, ed. Contemporary
IN
BONE
AND IMPLANTS
Implant Dentistry. 3rd ed. St. Louis, MO: C.V. Mosby; 2008:314–326. 6. Rodriguez AM, Aquilino SA, Lund PS. Cantilever and implant biomechanics: A review of the literature, Part 2. J Prosthodont. 1994;3:114–118. 7. Haroldson T, Carlsson GE. Bite force and oral function in patients with osseointegrated oral implants. Scand J Dent Res. 1977;85:200. 8. Rubo JH, Souza EA. Finite element analysis of stress in bone adjacent to dental implants. J Oral Implantol. 2008;34:248–255. 9. Bellini CM, Romeo D, Galbusera F, et al. Comparison of tilted versus non-tilted implant-supported prosthetic designs for the restoration of the edentulous mandible: A biomechanical study. Int J Oral Maxillofac Implants. 2009;24:511–517. 10. English CE. Critical A-P spread. Implant Soc. 1990;1:2–3. 11. Falk H, Laurell L, Lundgren D. Occlusal interferences and cantilever joint stress in implant-supported prosthesis occluding with complete dentures. Int J Oral Maxillofac Implants. 1990;5:70–77. 12. Rangert B, Jemt T, Jörneus L. Forces and moments on Brånemark implants. Int J Oral Maxillofac Implants. 1989;4:241–247. 13. Skalak R. Biomechanical considerations in osseointegrated prostheses. J Prosthet Dent. 1983;49:843–848. 14. Jacques LB, Moura MS, Suedam V, et al. Effects of cantilever length and framework alloy on the stress distribution of mandibular-cantilevered implant-supported prostheses. Clin Oral Implants Res. 2009;20:737–741. 15. English CE. The mandibular overdenture supported by implants in the anterior symphysis: A prescription for implant placement and bar prosthesis design. Dent Implantol Update. 1993;4:1–3. 16. English CE. Prosthodontic prescriptions for mandibular implant overdentures. Dent Implantol Update. 1996;7:1–4. 17. Bellini CM, Romeo D, Galbusera F, et al. A finite element analysis of tilted versus non-tilted implant configuration in the edentulous maxilla. Int J Prosthodont. 2009;22:155–157. 18. Bevilacqua M, Tealdo T, Pera F, et al. Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths. Int J Prosthodont. 2008;21:539–542. 19. Misch CE. Density of bone: Effect on treatment plans, surgical approach, healing and progressive loading. Int J Oral Implantol. 1990;6:23–31. 20. Greco GD, Jansen WC, Landre J, et al. Stress analysis on the free-end distal extension of an implant-supported mandibular complete denture. Braz Oral Res. 2009;23:175–181.
PADHYE
ET AL
21. Bidez MW, Misch CE. Force transfer in implant dentistry: Basic concepts and principles. J Oral Implantol. 1992;18: 264–274. 22. Bidez MW, Misch CE. Issues in bone mechanics related to oral implants. Implant Dent. 1992;1:289–294. 23. Misch CE. Clinical biomechanics in implant dentistry. Misch CE, ed. Dental Implant Prosthetics. 1st ed. St. Louis, MO: C.V. Mosby; 2005:309–321. 24. Fazi G, Tellini S, Vangi D, et al. Three-dimensional finite element analysis of different implant configurations for a mandibular fixed prosthesis. Int J Oral Maxillofac Implants. 2011;26:752–759. 25. Jemt T. Failures and complications in 391 consecutively inserted fixed prostheses supported by Brånemark implants in edentulous jaw: A study of treatment from the time of prosthesis placement to the first annual checkup. Int J Oral Maxillofac Implants. 1991;6:270–276. 26. Skalak R. Aspects of biomechanical considerations. In: Brånemark PI, Zarb GA, Albreksson T, eds. Tissue-Integrated ProsthesesdOsseointegration in Clinical Dentistry. Chicago, IL: Quintessence; 1985:117–128. 27. Omar R, Wise MD. Mandibular flexure associated with muscle force applied in retruded axis position. J Oral Rehabil. 1981;8:209–221. 28. Sertgoz A. Finite element analysis study of the effect of superstructure material on stress distribution in an implant-supported fixed prosthesis. Int J Prosthodont. 1997;10:19–27. 29. Cibirka RM, Razzoog ME, Lang BR, et al. Determining the force absorption quotient for restorative materials used in implant occlusal surfaces. J Prosthet Dent. 1992;67:361–364. 30. Silva GC, Mendonça JA, Lopes LR, et al. Stress patterns on implants in prostheses supported by four or six implants: A three-dimensional finite element analysis. Int J Oral Maxillofac Implants. 2010;25:239–246. 31. Geng JP, Tan KBC, Liu GR. Application of finite element analysis in implant dentistry: A review of the literature. J Prosthet Dent. 2001;85:585–598. 32. Van Oosterwyjck H, Duyck J, Vander Sloten J, et al. The influence of bone mechanical properties and implant fixation upon bone loading around oral implants. Clin Oral Implants Res. 1998;9: 407–418. 33. Zampelis A, Rangert B, Heijl L. Tilting of splinted implants for improved prosthodontic support: A two-dimensional finite element analysis. J Prosthet Dent. 2007;97:35–43. lar A, Aydin C, Ozen J, et al. 34. Cag Effects of mesiodistal inclination of implants
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
PADHYE
ET AL
on stress distribution in implant-supported fixed prostheses. Int J Oral Maxillofac Implants. 2006;21:36–44. lu H, Akça K. Comparative 35. Iplikçiog evaluation of the effect of diameter, length and number of implants supporting threeunit fixed partial prostheses on stress distribution in the bone. J Dent. 2002;30:41–46. 36. Van Staden RC, Guan H, Loo YC. Application of finite element method in
IMPLANT DENTISTRY / VOLUME 24, NUMBER 6 2015 dental research. Comput Methods Biomech Biomed Engin. 2006;9:257–270. 37. Hoshaw SJ, Brunski JB, Cochran GVB. Mechanical loading of Brånemark implants affects interfacial bone modeling and remodeling. Int J Oral Maxillofac Implants. 1994;9:345–360. 38. Suedam V, Capello Souza EA, Jacques LB, et al. Effect of abutment’s height and framework alloy on the load
685
distribution of mandibular cantilevered implant-supported prosthesis. Clin Oral Implants Res. 2009;20:196–200. 39. Papavasiliou G, Kamposiora P, Bayne SC, et al. Three-dimensional finite element analysis of stress-distribution around single tooth implants as a function of bony support, prosthesis type, and loading during function. J Prosthet Dent. 1996;76:633–640.
Copyright © 2015 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.
