Mechanical Evaluation of Implant-Assisted Removable Partial Dentures in Kennedy Class I Patients: Finite Element Design Considerations

applied sciences Article Mechanical Evaluation of Implant-Assisted Removable Partial Dentures in Kennedy Class I Patients: Finite Element Design Considerations Ana Messias 1, Maria A. Neto 2,* , Ana M. Amaro 2, Vítor M. Lopes 3and Pedro Nicolau 1   Citation: Messias, A.; Neto, M.A.; Amaro, A.M.; Lopes, V.M.; Nicolau, P. Mechanical Evaluation of Implant-Assisted Removable Partial Dentures in Kennedy Class I Patients: Finite Element Design Considerations. Appl. Sci. 2021,11, 659. https:// doi.org/10.3390/app11020659 Received: 21 December 2020 Accepted: 8 January 2021 Published: 12 January 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Department of Dentistry, Center for Mechanical Engineering, Materials and Processes (CEMMPRE), University of Coimbra, 3030-788 Coimbra, Portugal; [email protected] (A.M.); [email protected] (P.N.) 2Department of Mechanical Engineering, Center for Mechanical Engineering, Materials and Processes (CEMMPRE), University of Coimbra, 3030-788 Coimbra, Portugal; ana.amar[email protected] 3Department of Mechanical Engineering, University of Coimbra, 3030-788 Coimbra, Portugal; [email protected] *Correspondence: [email protected]; Tel.: +351-239790700 Abstract: The main purpose of this work was to construct a clinically valid numerical model of a mandibular Kennedy class I patient rehabilitated with a conventional removable partial denture and another two with implant-assisted removable partial dentures at two different implant locations. The selected patient was classified as ASA I and its mandible geometry reconstruction was performed by the conversion of the Cone-Beam computed Tomography (CBCT) scan raw medical data into a 3D model and subsequent conversion to a CAD file by reverse engineering methods. The soft tissue and removable denture geometries were also included in the CAD model as well as implants, ball attachments and matrix. Moreover, periodontal ligament was modelled by offsetting the mesh of the root surface of each tooth. The finite element results showed that the installation of a dental implant in each of the bilateral edentulous regions helps providing support and retention to the extension bases of the Removable Partial Denture (RPD) and significantly reduces the vertical and anterior-posterior displacements, regardless of its position. Keywords: implant; removable partial dentures; finite element method; Mandibular Kennedy Class I 1. Introduction The use of clasp-retained removable partial dentures has been a popular option among patients and clinicians to rehabilitate patients with partial edentulism due to the noninvasive nature of the treatment and fair cost-efficiency relationship on the short-term [ 1 , 2 ]. However, on the long-term, this cost-efficiency relationship is disturbed by the limitations of a removable partial denture, which inevitably leads to patient dissatisfaction and a drop of the usage rate, particularly, in the case of mandibular distal extension dentures [3–5]. To reduce some of these limitations, the adjunctive use of dental implants with or without retentive elements have been proposed by several authors [ 6 – 10 ] and are called implant-assisted removable partial dentures. The typical indications for implant-assisted removable partial dentures are situations of Kennedy Class I and II edentulism, particularly with long edentulous spans, and Kennedy class IV situations, or situations of patient refusal to wear dentures with complete palatal coverage or visible clasp assemblies and insufficient retention in the existing removable partial dentures. In these cases, the type of implant to use and the position within the edentulous sites, as well as the type of retentive elements, is a decision of the clinician, often based on surgical, aesthetic or economic criteria [11]. The clinical guidelines and principles for the design of implant-assisted removable partial dentures proposed by Grossmann et al. [ 12 ] in patient situations of Kennedy Class I edentulism indicate that per edentulous area, one implant should be inserted as distally as Appl. Sci. 2021,11, 659. https://doi.org/10.3390/app11020659 https://www.mdpi.com/journal/applsci Appl. Sci. 2021,11, 659 2 of 18 possible to provide maximal support and stability, particularly in the mandible. However, they also admit the possibility of placing the implants in a mesial position adjacent to the abutment teeth (natural teeth supporting and retaining a removable partial denture), whenever these are poor to provide support or to avoid unesthetic clasps in maxillary rehabilitations. Only two non-clinical studies considered in the work of Grossmann et al. comprised the biomechanical evaluation of the use of dental implants in mandibular Kennedy Class I situations, that is the study of movement and deformation of the biological structures (abutment teeth, bone, mucosa, etc.) under forces applied over the prosthesis and implants. One of those studies, performed by Ohkubo et al. [ 13 ], used an experimental setup to measure the pressure under a conventional or an implant-assisted removable partial denture with the implants placed distally. The results indicated that the implant support contributed to the reduction of displacement at the distal extension of the removable partial dentures and decreased the pressure on soft tissues. The other study [ 14 ] also considered in the above-mentioned revision, evaluated the biomechanical efficacy of placing implants underneath the denture base to obtain stable occlusal support, using an in-silico bi-dimensional model. The authors considered the possibility of implant support in the distal (second molar), mesial (first premolar) or intermediate position (second premolar). Compared to the conventional removable partial denture option, the least stress was obtained at the temporomandibular joint using the implant in the distal position, followed by the intermediate and mesial positions. The study of Maeda et al. was the first to use the finite element method (FEM) to evaluate the biomechanical effect of the implant support in the structures involved, namely denture, mandibular bone and temporomandibular joint. In the time following that study, several researchers have been using the finite element method to evaluate the stress distribution over the mandibular bone due to the screwed overdenture positioned on dental implants [ 15 – 20 ]. In this study, three-dimensional finite element analysis is also used to clarify the criteria for implant positioning within the edentulous span in prosthetic treatments with IARPD (implant assisted removable partial dentures). The primary aim is achieved by evaluating the different patterns of stress in the prosthetic structure for variations of the implant positioning in the edentulous area. 2. Materials and Methods 2.1. Geometrical Models Three-dimensional finite element models of IARPDs with two different implant locations and one conventional RPD, that is, a tooth assisted RPD, were constructed based on the reconstruction of the CBCT Kennedy Class I patient. The three finite element models were identified as: the conventional RPD; the IARPD PREMOLARS (IARPD PM), presenting the implants at the premolar regions; the IARPD MOLARS (IARPD MO), with the implants placed in the molar’s region. The selected patient showed no signs of relevant systemic or oral diseases, including severe periodontal disease, and presented mandibular bilateral posterior edentulism missing three teeth per edentulous site and moderate resorption of the residual ridges. The geometries of the compact and trabecular bones of the mandible were created by the conversion of the CBCT scan raw medical data into 3D models and subsequent conversion to a CAD file by reverse engineering methods. Similarly, to the process of segmentation of the mandible bones, teeth segmentation allowed separating abutment teeth (34, 33, 43, 44) from the remaining teeth, while periodontal ligaments were modelled by offsetting the mesh of the root surface of each tooth (34, 33, 43, 44) by 0.25 to 0.3 mm. The 3D geometrical model of the acrylic portion of the RPD was obtained from the scanning of a conventional denture, which had been created over the plaster mode of the patient, using the inEOS ® X5 laboratory scanner (Sirona Dental Systems Inc., Long Island City, NY, USA). The 3D model of the metal framework of the RPD was created over the scanned plaster model using the 3Shape Dental System ™ software and, posteriorly, assembled with the acrylics of the 3rd and 4th quadrants. Moreover, the external surface of the mandibular Appl. Sci. 2021,11, 659 3 of 18 plaster model of the patient was also scanned to create a 3D model of the coronal portion of the remaining teeth and soft tissue of the edentulous areas. The implants were created using s CAD tools (Solidworks ® 2014, Dassault Systèmes Pte. Ltd., Singapore) after feature extraction of the specific geometrical dimensions from official images of Straumann Standard Plus implants (Ø 4.1 mm) with regular platform and 10 mm long provided by the manufacturer (Institut Straumann AG, Basel, Switzerland). A ball attachment (patrix) and corresponding matrix were also created to establish the connection between prosthesis and the implant. In the assemblage of IARPD models the implants were placed as parallel as possible to the abutment teeth in the regions of the second premolar (Model IARPD PM) and of the extremity of metallic framework (Model IARPD MO), which corresponded to the virtual position of the first molar. To model the implant-bone contact, the implants were then trimmed from the cortical and cancellous bone bodies using Boolean operations. The same operation was performed on the soft tissue body to create the space required to the transmucosal portion of the implant. The matrices were aligned with the ball attachments of the implants and housed within the framework. The acrylic portions of the prostheses were also modified to accommodate the implants, ball attachments and matrices. A single plate was created to apply the prescribed load uniformly over the acrylic teeth of the removable partial denture. The plate was sketched in the horizontal plane of the mandible (parallel to the occlusal plane) and vertically extruded to obtain a final thickness of 10 mm. Additionally, a 10 mm diameter circle was included in the geometric centre of the sketch and extruded 25 mm for force application. After the assembly of all components of the models with implant-assisted removable partial dentures, the solid bodies were exported in the format of single Parasolid binary files. 2.2. Numerical Models Each one of the three model files was imported into the ADINA system for linear and nonlinear finite element analysis (ADINA AUI version 9.3.1, ADINA R&D Inc., Watertown, WA, USA) including the following bodies: cortical bone and non-abutment teeth; individualized abutment teeth (34, 33, 43, 44); individualized periodontal ligaments of the abutment teeth (34, 33, 43, 44); cancellous bone; soft tissue (3rd and 4th quadrants); metal framework of the removable partial denture (including 2 matrices in the case of the Models IARPD PM and IARPD MO); acrylic denture bases with the missing teeth (3rd and 4th quadrants); implants and ball attachments (Models IARPD PM and IARPD MO); loading plate. In both numerical models of the IARPDs the implants were assumed bonded with cancellous and cortical bones, simulating complete osseointegration. Moreover, the glue mesh option was also used to model the attachment of other pairs of components to remain perfectly bonded together, such as the inner surfaces of the cortical bone and the outer surfaces of the cancellous bone or the inner and outer surfaces of the periodontal ligament and the teeth and bone, respectively. Nevertheless, the Lagrange multiplier technique was used to impose contact constraint conditions, assuring the possibility of relative motion between the surfaces of the following contact pairs: implant/soft-tissue; soft-tissue/acrylic; soft-tissue/framework; framework/teeth; teeth-premolar/teeth-canine; teeth/cortical; and acrylic/implant. Assignment of the mesh density to the solid bodies of each model was made by promoting equally spaced subdivisions of the bodies using the desired element edge length. In some cases, the subdivision of specific faces was recalculated with smaller lengths to promote a more refined mesh in areas requiring higher precision of the results. Table 1 presents the mesh density attributed to each body and the refinement areas. Discretization of the domains was assured by the Delaunay free-form meshing algorithm to generate 8-node hexahedral (brick) elements with mixed interpolation formulation (displacement and pressure-based), considering a constant pressure (1 degree of freedom). For elements with linear elastic material properties, additional displacement degrees of freedom were Appl. Sci. 2021,11, 659 4 of 18 allowed by selecting the incompatible modes option. The total number of nodes and elements of each model are detailed in Table 2. Table 1. Description of the length of element edge attributed to each body and the refinement areas. Body Length (mm) Refinement Zone (mm) Cortical bone 1 Implants region (0.5) Alveolus region (0.25) Cancellous bone 1 Implants region (0.5) Teeth 0.5 Root length (0.25) Loading Plate 1 Acrylic contact region (0.5) Soft tissue 0.5 - Implants 0.5 - Acrylic 0.5 - Framework 0.5 - Periodontal Ligament 0.25 - Table 2. Description of the total number of elements and nodes per model. Conventional IARPD PM IARPD MO Elements 871,851 889,884 857,671 Nodes 506,375 472,936 478,075 2.3. Numerical Models This study assumed isotropic linear elastic properties for the cortical and cancellous bones, teeth, framework, acrylic, implants, ball attachments and loading plate but not for the oral soft tissues. These, i.e., oral mucosa and periodontal ligament, were modelled considering non-linear hyperelastic properties. Several models have been proposed to model the hyperelastic effects of biological soft tissues [ 21 ]. Nevertheless, the approximation proposed by Ogden [ 22 , 23 ] provides the closest matching to experimental data and was herein considered for the modelling of both the oral mucosa and the periodontal ligament. The mechanical properties of the materials displaying a linear force-displacement relationship as implied in Hooke’s law are presented in Table 3. Table 3. Mechanical properties of the isotropic linear elastic materials. Material Young’s Modulus (GPa) Poisson’ Ratio Cortical Bone 20.0 [24–26] 0.30 Cancellous bone 1.37 [24,27] 0.30 Teeth (dentin) 13.0 [28] 0.37 Chromium-cobalt 211 [29] 0.30 Acrylic 2.20 [29] 0.31 Titanium grade 4 110 0.32 Stainless steel 180 0.30 The nonlinear constitutive models of the oral mucosa and of periodontal ligaments were derived from a strain energy density function (SEDF), W, which is defined per unit of reference volume (ADINA R&D 2012). This model is based directly on principal stretches instead of invariants to determine the deviatoric strain energy function (WD) and accounts for volumetric compressibility by the inclusion of a term for the volumetric strain energy density (ADINA R&D 2012). In the case of the oral mucosa, the strain energy density function was set based on the fitting of a uniaxial stress–strain curve from experimental data reported by Kishi et al. in 1972 cited in Chen et al. [ 30 ], using a Ogden 9th Appl. Sci. 2021,11, 659 5 of 18 order approximation obtained by the method of singular value decomposition. Similarly, the periodontal ligament material properties were obtained from the data of porcine periodontal ligaments subjected to uniaxial tensile tests that were performed along the fibber direction, as reported by Natali et al. [ 31 ] and Nishihira et al. [ 32 ]. The curve fitting procedure for the Ogden function was also obtained by singular value decomposition and 9th order approximation. 2.4. Loading and Boundary Conditions Boundary conditions were applied in the condyles of the mandible and in the insertion areas of the mastication muscles. Thus, as shown in Figure 1, all three nodal degrees of freedom were fixed in the insertion of the masseter muscle in the lower border of the mandible and in the insertion of the medial pterygoid, the middle temporalis, and the lateral pterygoid muscles in the coronoid process. Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 The nonlinear constitutive models of the oral mucosa and of periodontal ligaments were derived from a strain energy density function (SEDF), W, which is defined per unit of reference volume (ADINA R&D 2012). This model is based directly on principal stretches instead of invariants to determine the deviatoric strain energy function (WD) and accounts for volumetric compressibility by the inclusion of a term for the volumetric strain energy density (ADINA R&D 2012). In the case of the oral mucosa, the strain energy density function was set based on the fitting of a uniaxial stress–strain curve from experimental data reported by Kishi et al. in 1972 cited in Chen et al. [30], using a Ogden 9th order approximation obtained by the method of singular value decomposition. Similarly, the periodontal ligament material properties were obtained from the data of porcine periodontal ligaments subjected to uniaxial tensile tests that were performed along the fibber direction, as reported by Natali et al. [31] and Nishihira et al. [32]. The curve fitting procedure for the Ogden function was also obtained by singular value decomposition and 9th order approximation. 2.4. Loading and Boundary Conditions Boundary conditions were applied in the condyles of the mandible and in the insertion areas of the mastication muscles. Thus, as shown in Figure 1, all three nodal degrees of freedom were fixed in the insertion of the masseter muscle in the lower border of the mandible and in the insertion of the medial pterygoid, the middle temporalis, and the lateral pterygoid muscles in the coronoid process. Figure 1. Boundary conditions applied to the model as all degrees of freedom fixity of the nodes located at the theoretical insertion of the mastication muscles masseter, middle temporalis and medial pterygoid, as well as complete fixity of the condyles. The load was applied on a 78.5 mm 2 circle in the geometric center of the loading plate as a homogenously distributed pressure corresponding to a 240 N load in the Z direction, as shown in Figure 2. The loads were applied gradually to avoid dynamic effects and convergence problems. The automatic time stepping procedure was used for the model CONVENTIONAL RPD to improve the convergence rate. Figure 1. Boundary conditions applied to the model as all degrees of freedom fixity of the nodes located at the theoretical insertion of the mastication muscles masseter, middle temporalis and medial pterygoid, as well as complete fixity of the condyles. The load was applied on a 78.5 mm 2 circle in the geometric center of the loading plate as a homogenously distributed pressure corresponding to a 240 N load in the Z direction, as shown in Figure 2. The loads were applied gradually to avoid dynamic effects and convergence problems. The automatic time stepping procedure was used for the model CONVENTIONAL RPD to improve the convergence rate. Appl. Sci. 2021,11, 659 6 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 Figure 2. Loading conditions applied to all three models as a uniform pressure equivalent to a 240 N force along the Z direction (purely vertical), applied to a 78.5 mm 2 circle in the geometric center of the loading plate, designed by CAD for perfect fitting to the occlusal surfaces of the acrylic teeth. 3. Results Simulations of both models of IARPD successfully completed all time steps of the computation, whereas the simulation of the CONVENTIONAL RPD stopped at the incremental 66-step, due to excessive deformation of the tissue. Hence, the step 50, corresponding to a 120 N load, was the basis for comparisons among models. These comparisons were based on the qualitative interpretation of the band plots and quantitative analysis of the values of displacement, strain and stress of different element groups at the same load step. The distribution of values of the three models was statistically analysed using the one-way ANOVA test of the Statistical Package for Social Sciences (SPSS) version 23.0. Post-hoc comparisons were made using the t-test for independent samples with Bonferroni correction. The significance level was set at 0.05. 3.1. Overal Displacements The CONVENTIONAL RPD model revealed significant displacement in the sagittal plane, particularly noticed on the bottom of the acrylic where the highest absolute values were identified. All displacement occurred in the posterior–anterior direction (towards the natural teeth) and showed the least value in the occlusal surfaces of the acrylic teeth and on the occlusal rests that seat on the premolars Figure 3, with a mean value of −190 ± 36 μm. The same pattern was identified in the IARPD PM model. Nevertheless, comparison of the values registered for the two homologous bands reveals that the displacements in the IARPD PM occur at a scale of hundred times smaller. The mean displacement in the sagittal plane for the IARPD PM model was −6.30 ± 2.33 μm. In the IARPD MO model, displacements were registered from posterior to anterior with approximation to the remaining teeth (negative values), but also from anterior to posterior, however, most elements showed no displacement (as represented in light green). The highest movement of approximation to the remaining teeth was observed in the clasps and occlusal rests whereas the opposite movement was detected in the portion of the lower border of the acrylic between the abutment tooth and the implant. Figure 2. Loading conditions applied to all three models as a uniform pressure equivalent to a 240 N force along the Z direction (purely vertical), applied to a 78.5 mm 2 circle in the geometric center of the loading plate, designed by CAD for perfect fitting to the occlusal surfaces of the acrylic teeth. 3. Results Simulations of both models of IARPD successfully completed all time steps of the computation, whereas the simulation of the CONVENTIONAL RPD stopped at the incremental 66-step, due to excessive deformation of the tissue. Hence, the step 50, corresponding to a 120 N load, was the basis for comparisons among models. These comparisons were based on the qualitative interpretation of the band plots and quantitative analysis of the values of displacement, strain and stress of different element groups at the same load step. The distribution of values of the three models was statistically analysed using the one-way ANOVA test of the Statistical Package for Social Sciences (SPSS) version 23.0. Post-hoc comparisons were made using the t-test for independent samples with Bonferroni correction. The significance level was set at 0.05. 3.1. Overal Displacements The CONVENTIONAL RPD model revealed significant displacement in the sagittal plane, particularly noticed on the bottom of the acrylic where the highest absolute values were identified. All displacement occurred in the posterior–anterior direction (towards the natural teeth) and showed the least value in the occlusal surfaces of the acrylic teeth and on the occlusal rests that seat on the premolars Figure 3, with a mean value of −190 ±36 µm . The same pattern was identified in the IARPD PM model. Nevertheless, comparison of the values registered for the two homologous bands reveals that the displacements in the IARPD PM occur at a scale of hundred times smaller. The mean displacement in the sagittal plane for the IARPD PM model was −6.30 ±2.33 µm. In the IARPD MO model, displacements were registered from posterior to anterior with approximation to the remaining teeth (negative values), but also from anterior to posterior, however, most elements showed no displacement (as represented in light green). The highest movement of approximation to the remaining teeth was observed in the clasps and occlusal rests whereas the opposite movement was detected in the portion of the lower border of the acrylic between the abutment tooth and the implant. Appl. Sci. 2021,11, 659 7 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18 Figure 3. Band plot of the displacement in the Y direction for the three models analysed: CONVENTIONAL Removable partial denture (RPD) (left), implant-assisted removable partial denture) IARPD PM (center), IARPD MO (right). Nonmatching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Displacement in the Z direction was mainly responsible for the displacement magnitude of the RPDs, accompanying the direction of the applied force, i.e., downwards, in the direction of the underlying soft tissues. For CONVENTIONAL and IARPD PM models there was a noticeable trend of sinking of the acrylic portion of the RPD with displacements increasing with the increase of the distance to the supports (teeth or implant). Despite the similar pattern of vertical displacement of these two models, the tissue ward movement was higher in the CONVENTIONAL RPD model and the difference between models reduced from being 250 times higher in the most anterior portion of the framework and acrylic to 40 times in the distal extreme of the two prostheses. In the IARPD MO model, on the contrary, the least vertical displacement was registered in the region of the implants and the largest displacements in the apical direction were associated with the anterior region, where the framework contacts the abutment teeth. Mean values for the three models were, respectively, −710 ± 84 μm, −14 ± 6.4 μm and −4 ± 0.81 μm. The corresponding maximum values were −900, −28.4 and −5.5 μm. The magnitude of displacements is plotted in Figure 4. In conformity with the reported magnitudes for the horizontal and vertical displacements, the CONVENTIONAL and IARPD PM models presented similar distributions. Overall, these distributions were symmetrical and f the highest displacement taking place in the acrylic portions, increasing from mesial to the distal free end of the acrylic flange. Though also symmetrical, the IARPD MO model revealed the highest displacements in the most proximal portion of the acrylic and in the clasp assembly and indirect retainer. The lowest displacements were found in the vicinity of the implant attachment. Figure 4. Distribution of the global displacements of the elements in each of the three models: CONVENTIONAL RPD (left), IARPD PREMOLARS (center), IARPD MOLARS (right). Nonmatching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Figure 3. Band plot of the displacement in the Y direction for the three models analysed: CONVENTIONAL Removable partial denture (RPD) ( left ), implant-assisted removable partial denture) IARPD PM ( center ), IARPD MO ( right ). Nonmatching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Displacement in the Z direction was mainly responsible for the displacement magnitude of the RPDs, accompanying the direction of the applied force, i.e., downwards, in the direction of the underlying soft tissues. For CONVENTIONAL and IARPD PM models there was a noticeable trend of sinking of the acrylic portion of the RPD with displacements increasing with the increase of the distance to the supports (teeth or implant). Despite the similar pattern of vertical displacement of these two models, the tissue ward movement was higher in the CONVENTIONAL RPD model and the difference between models reduced from being 250 times higher in the most anterior portion of the framework and acrylic to 40 times in the distal extreme of the two prostheses. In the IARPD MO model, on the contrary, the least vertical displacement was registered in the region of the implants and the largest displacements in the apical direction were associated with the anterior region, where the framework contacts the abutment teeth. Mean values for the three models were, respectively, − 710 ± 84 µ m, − 14 ± 6.4 µ m and − 4 ± 0.81 µ m. The corresponding maximum values were −900, −28.4 and −5.5 µm. The magnitude of displacements is plotted in Figure 4. In conformity with the reported magnitudes for the horizontal and vertical displacements, the CONVENTIONAL and IARPD PM models presented similar distributions. Overall, these distributions were symmetrical and f the highest displacement taking place in the acrylic portions, increasing from mesial to the distal free end of the acrylic flange. Though also symmetrical, the IARPD MO model revealed the highest displacements in the most proximal portion of the acrylic and in the clasp assembly and indirect retainer. The lowest displacements were found in the vicinity of the implant attachment. Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18 Figure 3. Band plot of the displacement in the Y direction for the three models analysed: CONVENTIONAL Removable partial denture (RPD) (left), implant-assisted removable partial denture) IARPD PM (center), IARPD MO (right). Nonmatching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Displacement in the Z direction was mainly responsible for the displacement magnitude of the RPDs, accompanying the direction of the applied force, i.e., downwards, in the direction of the underlying soft tissues. For CONVENTIONAL and IARPD PM models there was a noticeable trend of sinking of the acrylic portion of the RPD with displacements increasing with the increase of the distance to the supports (teeth or implant). Despite the similar pattern of vertical displacement of these two models, the tissue ward movement was higher in the CONVENTIONAL RPD model and the difference between models reduced from being 250 times higher in the most anterior portion of the framework and acrylic to 40 times in the distal extreme of the two prostheses. In the IARPD MO model, on the contrary, the least vertical displacement was registered in the region of the implants and the largest displacements in the apical direction were associated with the anterior region, where the framework contacts the abutment teeth. Mean values for the three models were, respectively, −710 ± 84 μm, −14 ± 6.4 μm and −4 ± 0.81 μm. The corresponding maximum values were −900, −28.4 and −5.5 μm. The magnitude of displacements is plotted in Figure 4. In conformity with the reported magnitudes for the horizontal and vertical displacements, the CONVENTIONAL and IARPD PM models presented similar distributions. Overall, these distributions were symmetrical and f the highest displacement taking place in the acrylic portions, increasing from mesial to the distal free end of the acrylic flange. Though also symmetrical, the IARPD MO model revealed the highest displacements in the most proximal portion of the acrylic and in the clasp assembly and indirect retainer. The lowest displacements were found in the vicinity of the implant attachment. Figure 4. Distribution of the global displacements of the elements in each of the three models: CONVENTIONAL RPD (left), IARPD PREMOLARS (center), IARPD MOLARS (right). Nonmatching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Figure 4. Distribution of the global displacements of the elements in each of the three models: CONVENTIONAL RPD ( left ), IARPD PREMOLARS ( center ), IARPD MOLARS ( right ). Non-matching colour scales. Homologous bands of the CONVENTIONAL RPD and IARPD PM models have 100 times discrepancy in values. Appl. Sci. 2021,11, 659 8 of 18 Statistically significant differences were found between the mean values of displacement of the three groups (p< 0.001), Table 4. Mean values of displacement of the IARPD MO were 4 ± 0.8 µ m, ranging from 2 to 6 µ ms and were significantly lower than any other model. Despite the similarities in distribution of displacements in the CONVENTIONAL and the IARPD PM models, the values of those groups were also statistically different, with means of 730 ± 80 µ m and 20 ± 6 µ m respectively. Pairwise comparisons of the three models are detailed in Table 5. Table 4. Mean values and range of the magnitude of displacement of each model. Statistical analysis with one-way ANOVA. SDstandard deviation; minminimum; maxmaximum. Model Mean ±SD (µm) Range (Min-Max) ANOVA Conventional RPD 730.0 ±80 530–910 F(2, 320686) = 7825410, p< 0.001 IARPD PM 20.0 ±6.0 3–30 IARPD MO 4.0 ±0.8 2–6 Table 5. Mean differences in the magnitude of displacement of the prosthesis (framework and acrylic) between pairs of models. Statistical analysis with two sample t-tests, assuming unequal variances and Bonferroni correction. 95% CI−95% confidence interval for the difference. Pair Mean Difference (µm) 95% CI pValue Conventional RPD/IARPD PM 718 (717,718) <0.001 Conventional RPD/IARPD MO 730 (729–731) <0.001 IARPD PM/IARPD MO 12 (11–13) <0.001 Loading of the acrylic portion of the prosthesis induced displacement of the abutment teeth by means of the contact with the framework, through the occlusal and cingulum rests. For the two implant-assisted models the largest component of the displacement was vertical and in the direction of the load, whereas for the CONVENTIONAL RPD model, the largest displacements were consistently distributed between vertical and anterior-posterior, as can be seen in Table 6. In this case, the abutment teeth not only move in the direction of the load but also present tipping towards the edentulous span. Table 6. Displacements of the abutment teeth in all three directions, X, Y and Z, corresponding to lingual–buccal, posterior–anterior and vertical, respectively, and the corresponding magnitude. Mean ±SD (Min–Max) (µm). Model Ling.-Buc. Post.-Ant. Vertical Magnitude Conventional RPD 2.2 ±9.0 (−33.6 to 39.7) −14.4 ±16.9 (−104.4 to 24.0) 12.0 ±5.2 (−40.2 to −1.0) 22.4 ±15.7 (6.5 to 110.0) IARPD PM 0.4 ±0.1 (0.08 to 0.7) −4.4 ±1.2 (−7.8 to −1.5) −9.8 ±0.8 (−12 to −7.9) 10.9 ±0.9 (9.1 to 13.8) IARPD MO 0.1 ±0.5 (−1.0 to 1.6) −0.5 ±0.05 (−2.2 to 0.5) −2.2 ±0.4 (−3.2 to −1.3) 2.3 ±0.4 (1.3 to 3.3) The addition of the implants to the rehabilitation have significantly reduced the magnitude of displacements of the abutment teeth and the lowest displacements were registered in the IARPD MO model. 3.2. Overall Stresses The stress distribution in the frameworks was different for all three models. The CONVENTIONAL RPD model presented the highest values of effective stress, showing extensive areas with values superior to 10 MPa, as presented in Figure 5a. The mean von Mises stress was 11.3 ± 14 MPa, ranging from 0.8 MPa to 200 MPa. Critical areas were at the Appl. Sci. 2021,11, 659 9 of 18 direct retainers, namely the rigid portion of the retentive clasp and the minor connectors, as well as the major connector, where the maximum principal stresses are of tensile type, as can be seen in Figure 5b. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 18 the direct retainers, namely the rigid portion of the retentive clasp and the minor connectors, as well as the major connector, where the maximum principal stresses are of tensile type, as can be seen in Figure 5b. (a) (b) Figure 5. Smoothed stresses distribution on the framework of the CONVENTIONAL RPD model: (a) von Mises stress, bottom view on the left, top view on the right; (b) principal stresses in the direct retainer, with all non-purple colors representing tensile stresses and the areas in pink with values superior to 100 MPa. In the case of the IARPD PM and IARPD MO models, there was no high stress accumulation in the direct retainers or major connector. The highest stress accumulation was in the interior portion of the matrix and surrounding material, as observed in Figure 6, and, generally, was lower than in the CONVENTIONAL RPD model. For the IARPD PM model, the mean von Mises stress value was 3.04 ± 4.96 MPa, ranging from 462 Pa to 68 MPa, while in the IARPD MO model the von Mises stress value was of 1.81 ± 2.37 MPa, ranging from 651 Pa to 43 MPa. The values distribution of the three models are shown in the box plot graphic presented at Figure 7. One-way ANOVA detected significant differences between models, F(2, 77087) = 8740, p < 0.001. All three models were found to be different in the pairwise comparisons presented at Table 7. Figure 5. Smoothed stresses distribution on the framework of the CONVENTIONAL RPD model: ( a ) von Mises stress, bottom view on the left, top view on the right; ( b ) principal stresses in the direct retainer, with all non-purple colors representing tensile stresses and the areas in pink with values superior to 100 MPa. In the case of the IARPD PM and IARPD MO models, there was no high stress accumulation in the direct retainers or major connector. The highest stress accumulation was in the interior portion of the matrix and surrounding material, as observed in Figure 6 , and, generally, was lower than in the CONVENTIONAL RPD model. For the IARPD PM model, the mean von Mises stress value was 3.04 ± 4.96 MPa, ranging from 462 Pa to 68 MPa, while in the IARPD MO model the von Mises stress value was of 1.81 ±2.37 MPa , ranging from 651 Pa to 43 MPa. The values distribution of the three models are shown in the box plot graphic presented at Figure 7. One-way ANOVA detected significant differences between models, F(2, 77087) = 8740, p< 0.001. All three models were found to be different in the pairwise comparisons presented at Table 7. Appl. Sci. 2021,11, 659 16 of 18 risk of failure, which should be considered in the case of extensive edentulism, namely when 4 teeth are missing per edentulous span. Limitations of the present work are mainly related to the nature of the study and possibility of transposition to the clinical setting. For instance, in this study the behavior of RPDs in the oral cavity was simulated assuming that the framework and abutment teeth were not rigidly bonded, allowing sliding, whereas the ball attachment and the matrix incorporated in the framework were rigidly attached, ensuring a total transmission of loads from the contactor to the target surfaces. This was a technical option to improve convergence of results and approximation accuracy but limited the possibility of free rotation around the ball attachment which is clinically observed [ 52 – 54 ] when the acrylic teeth are loaded. Future research should address other parameters that might change the magnitude of all effects emphasized in this work, namely the type of attachment system, the height of the corresponding abutment [ 55 – 57 ] and the type of implant (one or two-piece). Notwithstanding this, it is very clear that the addition of one implant to the denture bearing areas, regardless of the position, is paramount for the reduction of the displacements of the prosthesis and, consequently, of the abutment teeth mobility. 5. Conclusions Within the limitations of a static finite element analysis, it is possible to conclude that the loading of conventional Kennedy class I RPDs leads to significant vertical displacement of the extension bases towards the underlying soft tissues, like a cantilever beam under flexion. The installation of a dental implant in each of the bilateral edentulous regions to provide support and retention to the extension bases of the RPD significantly reduces the vertical and anterior-posterior displacements, regardless of the position. However, implant-assisted removable partial dentures (IARPDs) with the implant placed in the most mesial/anterior position, adjacent to the abutment teeth retain a pattern of displacements comparable to that of the conventional RPDs. In the conventional RPDs the areas of the highest effective stress of the frameworks spread through the direct retainers, auxiliary rests and major connector. In the IARPDs the highest stress accumulation is shifted to the interior portion of the matrix and surrounding material, regardless of the implant position. The lowest effective stress of the framework is obtained with the implant in the most distal/posterior position. The findings of this work might be used for helping the design of implant assisted removable partial dentures (IARPDs). Author Contributions: Conceptualization, P.N.; methodology, P.N. and M.A.N.; software, A.M., V.M.L. and M.A.N.; validation, A.M., M.A.N. and A.M.A.; writing—original draft preparation, A.M.; writing—review and editing, M.A.N., P.N. and A.M.A. All authors have read and agreed to the published version of the manuscript. Funding: This research was sponsored by FEDER funds through the program COMPETE–Programa Operacional Factores de Competitividade–and by national funds through FCT–Fundação para a Ciência e a Tecnologia, under the project UIDB/00285/2020 and under a PhD fellowship from the Portuguese awarded to Ana Messias (SFRH/BD/82442/2011). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest. References 1. Wostmann, B.; Budtz-Jorgensen, E.; Jepson, N.; Mushimoto, E.; Palmqvist, S.; Sofou, A.; Öwall, B. Indications for removable partial dentures: A literature review. J. Prosthet. Dent. 2006,95, 70. [CrossRef] 2. Rehmann, P.; Orbach, K.; Ferger, P.; Wöstmann, B. Treatment Outcomes with Removable Partial Dentures: A Retrospective Analysis. Int. J. 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