1 Volume 22 2023 e238152 Original Article Braz J Oral Sci. 2023;22:e238152http://dx.doi.org/10.20396/bjos.v22i00.8668152 1 PhD Student, Department of Prosthodontics and Periodontology, University of Campinas - Piracicaba Dental School, Piracicaba, SP, Brazil. 2 Professor, Department of Prosthodontics, Faculty of Technology and Sciences (UniFTC), Salvador, BA, Brazil. 3 Professor, Department of Prosthodontics and Periodontology, University of Campinas - Piracicaba Dental School, Piracicaba, SP, Brazil. 4 Postdoctoral Research Fellow, Department of Prosthodontics and Periodontology, University of Campinas - Piracicaba Dental School, Piracicaba, SP, Brazil. Corresponding author: Dra. Raissa Micaella Marcello-Machado Department of Prosthodontics and Periodontology Piracicaba Dental School, University of Campinas Limeira Avenue, 901 Piracicaba, SP, Brazil. Phone: +55 (019) 21065211 E-mail: raissammm@gmail.com Editor: Valentim A. R. Barão Received: November 30, 2021 Accepted: February 5, 2022 Influence of diameter in the stress distribution of extra-short dental implants under axial and oblique load: a finite element analysis Vanessa Felipe Vargas-Moreno1 , Rafael Soares Gomes2 , Michele Costa de Oliveira Ribeiro1 , Mariana Itaborai Moreira Freitas1 , Altair Antoninha Del Bel Cury3 , Raissa Micaella Marcello-Machado4* Aim: This study evaluated the influence of a wide diameter on extra-short dental implant stress distribution as a retainer for single implant-supported crowns in the atrophic mandible posterior region under axial and oblique load. Methods: Four 3D digital casts of an atrophic mandible, with a single implant-retained crown with a 3:1 crown-to-implant ratio, were created for finite element analysis. The implant diameter used was either 4 mm (regular) or 6 mm (wide), both with 5 mm length. A 200 N axial or 30º oblique load was applied to the mandibular right first molar occlusal surface. The equivalent von Mises stress was recorded for the abutment and implant, minimum principal stress, and maximum shear stress for cortical and cancellous bone. Results: Oblique load increased the stress in all components when compared to axial load. Wide diameter implants showed a decrease of von Mises stress around 40% in both load directions at the implant, and an increase of at least 3.6% at the abutment. Wide diameter implants exhibited better results for cancellous bone in both angulations. However, in the cortical bone, the minimum principal stress was at least 66% greater for wide than regular diameter implants, and the maximum shear stress was more than 100% greater. Conclusion: Extra-short dental implants with wide diameter result in better biomechanical behavior for the implant, but the implications of a potential risk of overloading the cortical bone and bone loss over time, mainly under oblique load, should be investigated. Keywords: Jaw, edentulous, partially. Dental implants. Dental prosthesis, implant-supported. Finite element analysis. https://orcid.org/0000-0003-3334-6297 https://orcid.org/0000-0002-7989-0098 https://orcid.org/0000-0001-7679-0502 https://orcid.org/0000-0001-7729-8536 https://orcid.org/0000-0002-4329-0437 https://orcid.org/0000-0001-7661-703X 2 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 Introduction Implant-supported rehabilitation of the mandibular posterior region is challenging when severe mandibular bone resorption is present. The poor bone availability above the mandibular canal difficult the insertion of regular length implants1,2. There are dif- ferent treatments for this clinical situation, including short dental implants (SDI), >6 to <10 mm in length, extra-short dental implants (ESDI), ≤6 mm in length3, or surgeries for vertical bone augmentation2,4. A recent systematic review showed at 1-year fol- low-up that SDIs have less morbidity, rehabilitation cost, and better survival rate (97%) than regular implants (92.6%) installed in a grafted bone area5. Besides, in this same study, the proportion of patients with biological and mechanical complications was lower for SDIs, with an incidence of 6%, while 39% of complications were reported for regular implants in grafted areas5. Meanwhile, over a 5-year follow-up period, it was shown that there was no statistically significant difference in implant survival and suc- cess rates between SDIs and regular implants in the grafted area4. Also, ESDIs com- pared to regular implants have similar survival rates, 96.2%, and 99%, respectively, as well as the technical complications incidence, 14.14%, and 18.36%, respectively, after 3-years of follow-up6. In addition, a study that evaluated the long-term effectiveness of ESDI reported a sur- vival rate of 94.1% at a five-year follow-up1. This slightly lower survival rate, when com- pared to regular implants, can be explained by its unfavorable biomechanics7, due to an increased crown-to-implant ratio (C:I) that creates a more significant vertical lever arm and a disadvantageous stress distribution2. These implants have a smaller bone/ implant contact surface, which leads to increased stresses at the bone and prosthetic components8. Therefore, SDI and ESDI generally have a wide diameter (WD) compen- sating the limitation in high, increasing the surface and its bulk, which improves the stress dissipation9, leading to better biomechanical behavior10. The treatment plan also requires checking the patients’ occlusion and the antag- onistic type affecting the implant success10. In a physiological occlusion predomi- nantly occur axial loads (AL), in the mandibular posterior region, transmitted by the long implant axis to the bone, resulting in an adequate stress dissipation11,12. How- ever, when a non-physiological occlusion is present, the resultant occlusal force is an oblique load (OL), creating an unbalanced stress distribution8. Therefore, when the high C:I anchored by ESDI is used, the incidence of OL increases the bending moment of the vertical lever arm, causing a non-homogeneous force dissipation, leading to poor prognosis, which may contribute to peri-implant bone loss8,12. Clinical and in vitro studies showed that the increased C:I only negatively influences the stress distribu- tion when an OL is present8,13. Previous systematic reviews focused on C:I evaluation have shown no significant differences in biological complications and peri-implant health results14,15, being 2.36:1 the higher C:I evaluated15. Meanwhile, a recent four-year retrospective clin- ical trial concluded that the higher the C:I ratio (0.47 to 3.01), the less the mar- ginal bone loss16. However, the biomechanical behavior of a challenging scenario where a 3:1 C:I crown supported by an ESDI, with 5 mm in length, at the severe 3 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 reabsorbed mandibular posterior region, in the presence of OL, has not yet been investigated. That is critical since it can make the long-term success of this type of rehabilitation uncertain. Besides, the benefits of using WD in ESDI have not reached a consensus in the litera- ture since clinical and laboratory studies have not found differences in survival rates when assessing different diameters and lengths2,17. This fact contradicts the prerog- ative of better biomechanics due to its larger contact surface10. Therefore, there is a need for further studies to evaluate the rehabilitation mechanical behavior12 before future prospective clinical studies. Thus, by using finite element analysis (FEA), the present study evaluated the influence of WD on the stress distribution of ESDI as support for single implant-supported crowns in the posterior region of the atrophic mandible, with a 3:1 C:I ratio, under AL or OL. For then, to verify if the WD is relevant enough to justify the insertion of an implant that will wear out more bone. The tested null hypothesis stated that WD would have no difference from the RD regarding the stress distribution. Materials and Methods Through the computer-aided design (CAD) software (SolidWorks; Dassault-Syste- mes SolidWorks Corp; Waltham, Massachusetts, USA) were created the 3D virtual models of a single crown, cement layer, cortical and cancellous bone. Also, CAD models of a universal abutment (4.5 x 2 x 6 mm) and two morse-taper implants of 4 x 5 mm (28.274 mm3, bone/implant contact surface: 101.39 mm2) and 6 x 5 mm (75.75 mm3, bone/implant contact surface: 155.36 mm2) were assessed virtually, and were left 2 mm submerged into the bone, which were obtained by the manu- facturer (S.I.N Implant System, São Paulo, SP, Brazil). Two study factors were evalu- ated: I) implant diameter: 4 mm (RD: regular diameter, being this the control group) or 6 mm (WD) (Fig. 1); II) load angulation: AL or OL (30° off-axis) being applied at the mesiobuccal cusp (Fig. 2)18. The bone model had a 12.94 mm height and 16.11 mm of thickness, and a 2 mm layer of cortical bone surrounding the cancellous bone (Fig. 1)19. The crown of a mandibular right first molar, 13 mm in height with a 3:1 C:I15 (Fig. 1), was virtually cemented on the abutment (70-μm layer), and four groups were created: RDAL (regular diameter implant under AL); WDAL (wide diameter implant under AL); RDOL (regular diameter implant under OL); WDOL (wide diameter implant under OL). The FEA models validation20 was performed by past literature for the location of force application and bone layers dimensions and by past in vivo study for crown and C:I. 4 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 13.47 mm 12.80 mm 13 mm A B Figure 1. Sagittal view: (A) regular implant diameter, 4mm; (B) wide implant diameter, 6 mm. Dimensions of bone and crown (red) used are equal in all groups. Axial Load Oblique Load Figure 2. Load angulation applied at the mesiobuccal cusp for different groups, axial load and 30º oblique load. After assembly, the virtual models were exported to finite element software (ANSYS Workbench 15.0; ANSYS Inc; Canonsburg, Pennsylvania, USA) for a mathematical solution. A tetrahedral mesh was generated with an element size of 0.6 mm after convergence analysis with 5% tolerance. The Young modulus (GPa) and Poisson ratio (δ) of each material were set in the software according to table 1. The number of elements and nodes of each element is described on table 2. All components were considered homogenous, isotropic, and linearly elastic. Also, the contact conditions between implant/abutment were assumed as no separation, and the contacts crown/ abutment and implant/bone were assumed as bonded. 5 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 Table 1. Mechanical properties of materials. Material Young Modulus (GPa) Poisson ratio (d) Titanium Grade IV21,22 110 0.33 Co-Cr alloy23 220 0.3 Cortical bone24 13.7 0.3 Cancellous bone24 1.370 0.3 Resin cement 25 18.3 0.33 Table 2. Numbers of nodes and elements of each component. Components Nodes Elements Crown 16769 9940 Abutment 11121 6327 Cement layer 7862 3966 Cortical bone (RD) 30221 17527 Cortical bone (WD) 30757 17910 Cancellous bone (RD) 28762 17244 Cancellous bone (WD) 30325 18004 Implant (RD) 106384 61350 Implant (WD) 142268 82199 RD, regular diameter groups; WD, wide diameter groups. Then, the models were fixed in two lateral portions of the bone segment and were submit- ted to a 200N load on the occlusal surface of the mandibular right first molar (Fig. 2)8. The equivalent von Mises stress (σvM) was used for the implant and the abutment8,10. Minimum principal stress (σmin), and maximum shear stress (τmax)8,26, were used for both cortical and cancellous bone. A qualitative analysis was performed for the implants, abutment, and bone, using the colors of the resulting FEA images. The colors varied from warmer (red) to cooler (blue) tones, with the peak stress represented by the warmest tone. Results Results for the FEA assessment are presented in table 3. Regardless of diameter, there was a significant increase in stress in all components, over 200%, under OL compared to AL results. Also, the stress was greater on the abutment and cortical bone and less on the cancellous bone and implant for WD groups. A substantial increase in stress was observed in cortical bone for WD groups compared to RD groups, being higher 66.3% for σmin and 99.8% for τmax under AL and higher 125.7% for σmin and 201.7% for τmax under OL (Table 3). For the AL groups, the peak stress concentration was in the area in contact with the apical region of the implant, being the maximum values found at σmin of 72.34 MPa (WDAL) (Fig. 3) and τmax of 42.02 MPa (WDAL) (Fig. 4). Meanwhile, in the OL groups, the highest stress concentration was in the cervical third of the bone, and the maximum val- ues were at σmin 266.7 MPa (WDOL) (Fig. 3) and τmax 130.88 MPa (WDOL) (Fig. 4). The analysis of σmin and τmax showed decrease stress in the cancellous bone for WD groups, about 44.9% for σmin and 55.9% for τmax under AL and 73.2% for σmin and 6 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 71.9% for τmax under OL (Table 3). Also, the images showed a peak stress concentra- tion in the cervical third of the bone in all groups, and the minimum value of the σmin was 9.79 MPa (WDAL) and of the τmax 7.32 MPa (WDAL) (Fig. 5 and Fig. 6). Besides, the σVm evaluation images showed that in all groups, the peak stress area was at the abutment collar level (Fig.7) and in the corresponding region of the implant (Fig. 8). The analysis demonstrated that with the WD, a low increase occurred in the abutment stress of 3.6% under AL (WDAL: 202.94 MPa) and 12.7% under OL (WDOL: 1157.4 MPa) (Table 3). However, a decrease in the implant of 38.7% was observed under AL (WDAL: 185.98 MPa) and 38.2% under OL (WDOL: 873 MPa) (Table 3). Table 3. Von-Mises criteria (MPa) for implants and abutment, minimum principal stress and shear stress for cortical and cancellous bone (MPa), and the differences between the groups and direction of the load. Axial load Oblique load of 30º Axial load x Oblique load of 30º RDAL WDAL % stress RDOL WDOL % stress % RDAL/ RDOL % WDAL/ WDOL Abutment (σvM) 200.97 202.94 *3.6% 1026.9 1157.4 *12.7% *511.0% *570.3% Implant (σvM) 303.48 185.98 #38.7% 1414.4 873.4 #38.2% *466.1% *469.6% Cortical bone (τmax) 21.02 42.02 *99.8% 43.37 130.88 *201.7% *206.3% *311.5% Cortical bone (σmin) 43.53 72.34 *66.3% 118.19 266.7 *125.7% *271.5% *368.7% Cancellous bone (τmax) 16.62 7.324 #55.9% 73.5 20.66 #71.9% *442.2% *282.1% Cancellous bone (σmin) 17.78 9.795 #44.9% 94.19 25.23 #73.2% *529.8% *257.6% RDAL, regular diameter implant under axial load; WDAL, wide diameter implant under axial load; RDOL, regular diameter implant under oblique load; WDOL, wide diameter implant under oblique load; *, increased stress; #, stress decreased. RDAL 20,119 Max -43,535 Min RDAL -72,342 Min WDAL -118,19 Min RDOL -266,7 Min WDOL WDAL RDOL WDOL Figure 3. Minimum principal stress peak concentration for cortical bone (MPa) for all groups. Blue to red color represents stress values from higher to lower, respectively. 7 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 RDAL 130,88 Max WDOL 21,024 Max RDAL 42,016 Max WDAL RDOL 43,374 Max 0,13952 Min WDAL RDOL WDOL Figure 4. Maximum shear stress peak concentration for cortical bone (MPa) for all groups. Blue to red color represents stress values from lower to higher, respectively. RDAL -25,228 Min WDOL -17,778 Min RDAL -9,7946 Min WDAL -94,192 Min RDOL 29,32 Max WDAL RDOL WDOL Figure 5. Minimum principal stress peak concentration for cancellous bone (MPa). Blue to red color represents stress values from higher to lower, respectively. 8 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 RDAL WDOL 20,658 Max 16,622 Max RDAL 7,324 Max WDAL 73,503 Max RDOL 0,0094777 Min WDAL RDOL WDOL Figure 6. Maximum shear stress peak concentration for cancellous bone (MPa). Blue to red color represents stress values from lower to higher, respectively. RDAL WDAL RDOL WDOL 1157,4 Max WDOL RDAL 200,97 Max 202,94 Max WDAL 1026,9 Max RDOL 0,34574 Min Figure 7. Von-Mises stress peak concentration (MPa) in abutment. Blue to red color represents stress values from lower to higher, respectively. 9 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 RDAL WDAL RDOL WDOL 873,4 Max WDOL RDAL 303,48 Max 185,98 Max WDAL 1414,4 Max RDOL 0,45843 Min Figure 8. Von-Mises stress peak concentration (MPa) in implant. Blue to red color represents stress values from lower to higher, respectively. Discussion There is no consensus in the literature about the benefits of using WD in ESDI in the treatment of severe mandibular bone resorption in the posterior region12. Also, recent studies showed that a high C:I ratio only increases the stress concentration when OL is present8,27, being traumatic occlusion the primary cause of biomechanical compli- cations8,13,27. Thus, by FEA, the present study evaluated the influence of WD on ESDIs stress distribution as support for single implant-supported crowns in the posterior region of the atrophic mandible, under AL and OL. The hypothesis that WD would have no difference from the RD regarding the stress distribution, had to be rejected. It was observed that WD in ESDI, under both load directions, showed a decrease of stress at the implant and the cancellous bone (WDAL: τmax=7.324 MPa, σmin=9.795; WDOL: τmax=20.66 MPa, σmin=25.23 MPa), a relevant increase in the cortical bone, and a possible slight increase in the abutment. Besides, when submitted to OL, there was an increase in stress in all components and groups by more than 200%, corroborating with previous studies8,13,27. In this study, the stress distribution on the peri-implant bone was different when a WD was used. A relevant increase (up to 66%) in the stress can be observed in the cortical bone when τmax and σmin were evaluated independently of load angulation. This is important since some studies have reported, without a consensus, a critical threshold of compressive (ranging from 50 MPa to 170 MPa) and tensile stress (ranging from 34.72 MPa to 100 MPa) of the bone28-31, and in the WDAL, RDOL, and 10 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 WDOL these values were overtaken. What shows the need for more studies and other methods of evaluation of bone impact when WD is used. Also, the figures in WD groups shows a stress peak in the cervical third of the bone of at least 311.5% under OL higher than the findings of the AL groups, which could be explained by the use of the WD implant providing a 34.73% higher bone/implant contact and wear on the cortical bone. These results corroborate with Elias et al.27, which evaluated the influence of the prosthetic crown height in SDI and found a higher stress concentra- tion in the OL groups. Meanwhile, in the WD groups, a decrease in the stress was observed in the can- cellous bone, bringing the MPa values found within the limits of compressive and tensile stress at WDOL28-31. This may be related to its Young modulus, since its value is lower than that of the cortical bone. The greater the Young modulus the stiffer the material, the greater the stress accumulation10, and more resistance to defor- mation32. In the present study, when the WD implant was evaluated the contact between the implant and cortical bone was increased, leading to higher stress on the cortical bone and a reduction on the cancellous bone, which can explain the results10. This enhanced contact with the cortical bone may negatively influence the bone remodeling around the implants since the cortical bone is less vascularized than the cancellous bone, which leads to interference of blood supply that directly affects the bone resorption response33. According to the results of this study, this would only be a problem in the presence of oblique load. Considering that in the pos- terior region the pattern of forces is axial, perhaps it would not be a clinical problem, as long as the patient has a favorable occlusal pattern. The consequences of higher stress concentration on the cortical bone associated with its decrease on the cancellous bone remain uncertain since low-stress values around the implant resulting in a bone loss due to disuse atrophy, while high-stress cause microfracture at the bone resulting either in bone loss or fatigue failure of the implant32,33. Also, since WD in ESDI increases the stress at the implant/cortical bone interface, being MPa values over the compressive and tensile limits of the bone28-31, it represents a potential biological risk for marginal bone loss that might be even higher under OL. Besides, the mechanical loading conditions regulate the morphology of the bone34, and it is still unknown how much bone/implant contact is necessary for the success of ESDIs27. The results of von Mises stress showed, in all groups, a higher stress concentra- tion at the surface of the abutment collar level and at the implant platform where it touches the abutment collar. In both loads, the WD showed an increase of 12.7% in stress at the abutment and a reduction of at least 38.2% in the implant. Despite this percentage difference, the color pattern exhibits a great similarity in the stress distribution in general for the abutment, and under axial load for the implant. This substantial stress reduction at WD implants might be explained by its structure 62% bulkier than RD implants. Since the stress increased over 400% at implant and abut- ment at the OL groups, clinically, would increase the risk of the implant, and abut- ment failure once was exceeded the limits of tensile yield strength 0.2% (483 MPa) and ultimate tensile strength (550 MPa) of the titanium grade IV35. Suggesting that 11 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 should be avoided the use of ESDI when it is impossible to eliminate OL during man- dibular excursive movements, for example, in a parafunction scenario. Another important point to be highlighted is that a WD implant might reduce the bone mechanical resistance, since the remaining bone around it is reduced when compared to a RD implant. There is a literature gap regarding the effects gener- ated by an overload on the cortical bone, when a mandibular implant-retained crown is evaluated under different load directions. Also, the maximum stress values of FEA studies strongly depend on the size of the mesh used. So, even with this study results being encouraging, showing that the WD ESDI can be a reliable option as shown in the AL groups, it also shows the necessity to perform further studies on this behalf. Clinically the masticatory forces are not acting in just one way, and it is impossible to isolate the force direction. So, it is essential to perform in silico studies, which allow the researcher to evaluate and study every direction of occlusal forces like was performed in this study. Besides, the present study is a numerical theoreti- cal analysis, and its results should be validated with an in vitro study assessing implant failure mode in the same conditions of this study. In addition, other simu- lations could be performed to estimate possible statistical differences, for exam- ple, by using different prostheses, abutments, and materials with different elastic modulus since they could reach a different result because of its dampers chewing loads10. Finally, a reliable way to effectively assess the influence on the bone would be performing randomized controlled trials. These studies must include patients with severe bone atrophy in the posterior region of the mandible with different types of occlusal patterns and a minimum of 1 mm cortical bone wall to surround the implant. Therefore, extra-short implants with wide diameter result in better biomechani- cal behavior for the implant, but the implications of a potential risk of overload- ing the cortical bone and bone loss over time, mainly under oblique load, should be investigated. Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The authors thank S.I.N. Implant System for their support with the CADs used in this study. Data availability Datasets related to this article will be available upon request to the corresponding author. Conflicts of interest None. 12 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 Author Contribution Vanessa Felipe Vargas-Moreno: Design of the work; Acquisition and interpretation of data for the work; Drafting the work; Revising it critically for important intellectual con- tente; Final approval of the version to be published; Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Rafael Soares Gomes: Drafting the work; Interpretation of data for the work; Revis- ing it critically for important intellectual contente; Final approval of the version to be published. Michele Costa de Oliveira Ribeiro: Drafting the work; Interpretation of data for the work; Revising it critically for important intellectual contente; Final approval of the version to be published. Mariana Itaborai Moreira Freitas: Drafting the work; Revising it critically for important intellectual contente; Final approval of the version to be published. Altair Antoninha Del Bel Cury: Drafting the work; Revising it critically for important intellectual contente; Final approval of the version to be published. Raissa Micaella Marcello-Machado: Design of the work; Drafting the work; Revis- ing it critically for important intellectual contente; Final approval of the version to be published; Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. References 1. Ravidà A, Barootchi S, Askar H, Suárez-López Del Amo F, Tavelli L, Wang HL. Long-Term Effectiveness of Extra-Short (≤ 6 mm) Dental Implants: A Systematic Review. Int J Oral Maxillofac Implants. 2019 Jan/Feb;34(1):68-84. doi: 10.11607/jomi.6893. 2. Bordin D, Bergamo ETP, Bonfante EA, Fardin VP, Coelho PG. Influence of platform diameter in the reliability and failure mode of extra-short dental implants. J Mech Behav Biomed Mater. 2018 Jan;77:470-4. doi: 10.1016/j.jmbbm.2017.09.020. 3. Al-Johany SS, Al Amri MD, Alsaeed S, Alalola B. Dental implant length and diameter: a proposed classification scheme. J Prosthodont. 2017 Apr;26(3):252-60. doi: 10.1111/jopr.12517. 4. Lee SA, Lee CT, Fu MM, Elmisalati W, Chuang SK. Systematic review and meta-analysis of randomized controlled trials for the management of limited vertical height in the posterior region: short implants (5 to 8 mm) vs longer implants (> 8 mm) in vertically augmented sites. Int J Oral Maxillofac Implants. 2014 Sep-Oct;29(5):1085-97. doi: 10.11607/jomi.3504. 5. de N Dias FJ, Pecorari VGA, Martins CB, Del Fabbro M, Casati MZ. Short implants versus bone augmentation in combination with standard-length implants in posterior atrophic partially edentulous mandibles: systematic review and meta-analysis with the Bayesian approach. Int J Oral Maxillofac Surg. 2019 Jan;48(1):90-6. doi: 10.1016/j.ijom.2018.05.009. 6. Zadeh HH, Guljé F, Palmer PJ, Abrahamsson I, Chen S, Mahallati R, et al. Marginal bone level and survival of short and standard-length implants after 3 years: An Open Multi-Center Randomized Controlled Clinical Trial. Clin Oral Implants Res. 2018 Aug;29(8):894-906. doi: 10.1111/clr.13341. 13 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 7. 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 Mar-Apr;21(2):275-82. 8. Sotto-Maior BS, Senna PM, da Silva WJ, Rocha EP, Del Bel Cury AA. Influence of crown-to-implant ratio, retention system, restorative material, and occlusal loading on stress concentrations in single short implants. Int J Oral Maxillofac Implants. 2012 May-Jun;27(3):e13-8. 9. Brink J, Meraw SJ, Sarment DP. Influence of implant diameter on surrounding bone. Clin Oral Implants Res. 2007 Oct;18(5):563-8. doi: 10.1111/j.1600-0501.2007.01283.x. 10. Arinc H. Effects of prosthetic material and framework design on stress distribution in dental implants and peripheral bone: a three-dimensional finite element analysis. Med Sci Monit. 2018 Jun;24:4279-87. doi: 10.12659/MSM.908208. 11. Verma M, Nanda A, Sood A. Principles of occlusion in implant dentistry. Interview. J Int Clin Dent Res Organ. 2015 May;7(3):S27-33. doi: 10.4103/2231-0754.172924. 12. Reddy MS, Sundram R, Eid Abdemagyd HA. Application of finite element model in implant dentistry: a systematic review. J Pharm Bioallied Sci. 2019 May;11(Suppl 2):S85-S91. doi: 10.4103/JPBS.JPBS_296_18. 13. Sütpideler M, Eckert SE, Zobitz M, An KN. Finite element analysis of effect of prosthesis height, angle of force application, and implant offset on supporting bone. Int J Oral Maxillofac Implants. 2004 Nov-Dec;19(6):819-25. 14. Meijer HJA, Boven C, Delli K, Raghoebar GM. Is there an effect of crown-to-implant ratio on implant treatment outcomes? A systematic review. Clin Oral Implants Res. 2018 Oct;29 Suppl 18(Suppl 18):243-52. doi: 10.1111/clr.13338. 15. Garaicoa-Pazmiño C, Suárez-López del Amo F, Monje A, Catena A, Ortega-Oller I, Galindo-Moreno P, et al. Influence of crown/implant ratio on marginal bone loss: a systematic review. J Periodontol. 2014 Sep;85(9):1214-21. doi: 10.1902/jop.2014.130615. 16. Tang Y, Yu H, Wang J, Gao M, Qiu L. Influence of crown-to-implant ratio and different prosthetic designs on the clinical conditions of short implants in posterior regions: A 4-year retrospective clinical and radiographic study. Clin Implant Dent Relat Res. 2020 Feb;22(1):119-27. doi: 10.1111/cid.12881. 17. Monje A, Fu J-H, Chan H-L, Suarez F, Galindo-Moreno P, Catena A, et al. Do implant length and width matter for short dental implants (<10 mm)? A meta-analysis of prospective studies. J Periodontol. 2013 Dec;84(12):1783-91. doi: 10.1902/jop.2013.120745. 18. Silva NR, Bonfante E, Rafferty BT, Zavanelli RA, Martins LL, Rekow ED, et al. Conventional and modified veneered zirconia vs. metalloceramic: fatigue and finite element analysis. J Prosthodont. 2012 Aug;21(6):433-9. doi: 10.1111/j.1532-849X.2012.00861.x. 19. Sotto-Maior BS, Mercuri EG, Senna PM, Assis NM, Francischone CE, Del Bel Cury AA. Evaluation of bone remodeling around single dental implants of different lengths: a mechanobiological numerical simulation and validation using clinical data. Comput Methods Biomech Biomed Engin. 2016;19(7):699-706. doi: 10.1080/10255842.2015.1052418. 20. Chang Y, Tambe AA, Maeda Y, Wada M, Gonda T. Finite element analysis of dental implants with validation: to what extent can we expect the model to predict biological phenomena? A literature review and proposal for classification of a validation process. Int J Implant Dent. 2018 Mar;4(1):7. doi: 10.1186/s40729-018-0119-5. 21. Bordin D, Bergamo ETP, Fardin VP, Coelho PG, Bonfante EA. Fracture strength and probability of survival of narrow and extra-narrow dental implants after fatigue testing: In vitro and in silico analysis. J Mech Behav Biomed Mater. 2017 Jul;71:244-9. doi: 10.1016/j.jmbbm.2017.03.022. 14 Vargas-Moreno et al. Braz J Oral Sci. 2023;22:e238152 22. Cruz M, Wassall T, Toledo EM. Finite element stress analysis of dental prostheses supported by straight and angled implants. J Prosthet Dent. 2009 Nov;104(5):346. doi: 10.1016/S0022-3913(10)60154-0. 23. Erkmen E, Meriç G, Kurt A, Tunç Y, Eser A. Biomechanical comparison of implant retained fixed partial dentures with fiber reinforced composite versus conventional metal frameworks: a 3D FEA study. J Mech Behav Biomed Mater. 2011 Jan;4(1):107-16. doi: 10.1016/j.jmbbm.2010.09.011. 24. Arinc H. Effects of prosthetic material and framework design on stress distribution in dental implants and peripheral bone: a three-dimensional finite element analysis. Med Sci Monit. 2018 Jun;24:4279-87. doi: 10.12659/MSM.908208. 25. Li LL, Wang ZY, Bai ZC, Mao Y, Gao B, Xin HT, et al. Three-dimensional finite element analysis of weakened roots restored with different cements in combination with titanium alloy posts. Chin Med J (Engl). 2006 Feb;119(4):305-11. 26. Amaral CF, Gomes RS, Rodrigues Garcia RCM, Del Bel Cury AA. Stress distribution of single-implant- retained overdenture reinforced with a framework: A finite element analysis study. J Prosthet Dent. 2018 May;119(5):791-6. doi: 10.1016/j.prosdent.2017.07.016. 27. Elias DM, Valerio CS, de Oliveira DD, Manzi FR, Zenóbio EG, Seraidarian PI. Evaluation of Different Heights of Prosthetic Crowns Supported by an Ultra-Short Implant Using Three-Dimensional Finite Element Analysis. Int J Prosthodont. 2020 Jan/Feb;33(1):81-90. doi: 10.11607/ijp.6247. 28. Pattin CA, Caler WE, Carter DR. Cyclic mechanical property degradation during fatigue loading of cortical bone. J Biomech. 1996 Jan;29(1):69-79. doi: 10.1016/0021-9290(94)00156-1. 29. Sugiura T, Horiuchi K, Sugimura M, Tsutsumi S. Evaluation of threshold stress for bone resorption around screws based on in vivo strain measurement of miniplate. J Musculoskelet Neuronal Interact. 2000 Dec;1(2):165-70. 30. Papavasiliou G, Kamposiora P, Bayne SC, Felton DA. 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 Dec;76(6):633-40. doi: 10.1016/s0022-3913(96)90442-4. 31. Bozkaya D, Muftu S, Muftu A. Evaluation of load transfer characteristics of five different implants in compact bone at different load levels by finite elements analysis. J Prosthet Dent. 2004 Dec;92(6):523-30. doi: 10.1016/j.prosdent.2004.07.024. 32. Chen LJ, He H, Li YM, Li T, Guo XP, Wang RF. Finite element analysis of stress at implant– bone interface of dental implants with different structures. Trans Nonferrous Met Soc China. 2011;21(7):1602-10. doi: 10.1016/S1003-6326(11)60903-5. 33. Pilliar RM, Deporter DA, Watson PA, Valiquette N. Dental implant design--effect on bone remodeling. J Biomed Mater Res. 1991 Apr;25(4):467-83. doi: 10.1002/jbm.820250405. 34. Frost HM. A 2003 update of bone physiology and Wolff’s Law for clinicians. Angle Orthod. 2004 Feb;74(1):3-15. doi: 10.1043/0003-3219(2004)074<0003:AUOBPA>2.0.CO;2. 35. Breme H, Biehl V, Reger N, Gawalt ES. Metallic biomaterials: titanium and titanium alloys. In: Murphy W, Black J, Hastings G. Handbook of biomaterial properties. New York, NY: Springer New York; 2016. Chapter 1c. p.167-89.