multiple dental loss

Journal of the Mechanical Behavior of Biomedical Materials 94 (2019) 249–258

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Periprosthetic biomechanical response towards dental implants, with functional gradation, for single/multiple dental loss Subhomoy Chatterjeea,b,1,2, Sulagna Sarkara,c,1, Surya R. Kalidindia,d, Bikramjit Basua,b,e,

T ⁎

a

Materials Research Centre, Indian Institute of Science, Bengaluru 560012, Karnataka, India Translational Center on Biomaterials for Orthopaedic and Dental Applications, Indian Institute of Science, Bengaluru 560012, Karnataka, India c Department of Metallurgical and Material Engineering, Jadavpur University, Kolkata 700032, West Bengal, India d George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, North Avenue, Atlanta, GA 30332, USA e Centre for BioSystems and Engineering, Indian Institute of Science, Bengaluru 560012, Karnataka, India b

A R T I C LE I N FO

A B S T R A C T

Keywords: Dental bridge Finite element Implant Stress/strain

The differences in shape and stiffness of the dental implants with respect to the natural teeth (especially, dental roots) cause a significant alteration of the periprosthetic biomechanical response, which typically leads to bone resorption and ultimately implant loosening. In order to avoid such clinical complications, the implant stiffness needs to be appropriately adapted. In this study, hollow channels were virtually introduced within the designed implant screws for reduction of the overall stiffness of the prototype. In particular, two opposing radial gradients of increasing hollow channel diameters, i.e., outside to inside (Channel 1) and inside to outside (Channel 2) were considered. Two clinical situations of edentulism were addressed in this finite element-based study, and these include a) loss of the first molar, and b) loss of all the three molars. Consequently, two implantation approaches were simulated for multiple teeth loss - individual implantation and implant supported dental bridge. The effects of implant length, approach and channel distribution on the biomechanical response were evaluated in terms of the von Mises stress within the interfacial periprosthetic bone, under normal masticatory loading. The results of our FE analysis clearly reveal significant variation in periprosthetic bone stress between the different implant designs and approaches. An implant screw length of 11 mm with the Channel 2 configuration was found to provide the best biomechanical response. This study also revealed that the implant supported dental bridge approach, which requires lower bone invasion, results in favorable biomechanical response in case of consecutive multiple dental loss.

1. Introduction Dental implantation is a routinely performed clinical treatment to address either partial or full edentulation, in order to recover natural mastication, speech, etc., as well as aesthetic appearance (Turkyilmaz et al., 2007). Many studies have reported the concept of using dental bridges supported by osseointegrated implants as a treatment modality in case of multiple dental loss (Pietrabissa et al., 2000; Li et al., 2004a, 2004b, 2005, 2006; Quinn et al., 2010; Fernandez‐Redondo et al., 1998; Shi and Fok, 2009). Because of their clinical success, the demand for these surgical prosthetic components is on a sharp rise (Turkyilmaz

and McGlumphy, 2008). The stable anchorage and performance of the dental implants is dependent on the osseointegration with the periprosthetic bone (Meyer et al., 2004). The difference in density and stiffness of the implant material with respect to the original tooth, especially at the region where it interfaces with the mandible (i.e., the root region) results in a difference in the stress/strain profile in the periprosthetic bone in comparison to the normal anatomical situation, on being physiologically loaded. It is known that the bone, being a smart living material, remodels itself in accordance to the changes in the external loading (Ruimerman et al., 2005). Natural bone densifies in the higher stressed regions, while it erodes in the areas experiencing

Abbreviations: CT, Computed tomography; E, Young’s Modulus; FE, Finite element; HU, Hounsfield Unit; IS, Implant screw; LS, Locking screw; εmax, Maximum value of von Mises strain over interfacial bone; ν, Poisson’s ratio; σmax, Maximum value of von Mises stress over IS ⁎ Correspondence to: Lab for Biomaterials, Materials Research Centre, Indian Institute of Science, CV Raman Rd, Bengaluru, Karnataka 560012, India. E-mail addresses: [email protected] (S. Chatterjee), [email protected] (S. Sarkar), [email protected] (S.R. Kalidindi), [email protected] (B. Basu). 1 Equal contribution. 2 Present Address: Department of Prosthetics & Orthotics, Schieffelin Institute of Health Research & Leprosy Centre, Karigiri – 632 106, Tamil Nadu, India. https://doi.org/10.1016/j.jmbbm.2019.03.001 Received 4 February 2019; Received in revised form 28 February 2019; Accepted 2 March 2019 Available online 02 March 2019 1751-6161/ © 2019 Elsevier Ltd. All rights reserved.

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topology optimization technique. They reported that the implant retains its biomechanical properties even if its volume is reduced up to 17.9%, with introduction of designed porosity. The reduction of implant volume makes space available for bone growth and, thus, imparts better primary stability. In another FE-based study, Roy et al. considered uniformly distributed spherical pores within the implant to reduce the stiffness (Roy et al., 2018, 2017). However, the manufacturing of such an implant with structured internal porosity can present significant challenges and is likely to demand highly sophisticated manufacturing process. Such sophisticated manufacturing environment is likely to add significantly to the cost of the product as well. Moreover, no gradient of porosity within the implant model was considered. It is important to study the clinical advantage of novel implant designs, which are easily manufacturable and considers porosity gradients, using biomechanical analysis. This is one of the main objectives of the present work. The importance of the present study lies in its focus on evaluating the effects of a graded channeled structure in the implant, together with the approach of implantation, on the biomechanics of the periprosthetic bone. More specifically, the effects of the design (porosity gradient), length and the implantation approach (single, multiple or bridged) on the von Mises stress profile of the periprosthetic bone have been studied. Several implant models were created with varying geometry and channel arrangements. The FE computed von Mises stresses at periprosthetic interfacial bone were considered in evaluating the multiple designs for their osseointegration.

stress shielding (i.e., lower stressed regions). Erosion of the periprosthetic bone is reported to lead to implant loosening and detachment, while periprosthetic bone densification would enhance osseointegration (Santiago et al., 2013). Thus, the implant stiffness is required to be adjusted (generally it is required to be reduced) in order to minimize stress shielding (Pérez Pozo et al., 2015; Sheikh, 2015; Asgharzadeh Shirazi et al., 2017; Lin et al., 2009a). Reduction of the implant stiffness can be hypothetically accomplished by using a limper material. But in real clinical situation, it is a challenge to achieve a material of required stiffness that would, in all respects, be suitable for use as the implant material. Alternatively, the effective stiffness of the implant as a whole may be altered by its structural alteration. In this process, apart from having a desired overall stiffness, we may also achieve differential stiffness like a functional gradation. In the current study, structural alteration of the implant screw (IS) was attempted through introduction of hollow channels that would reduce the overall stiffness. The IS was targeted for diminution of the effective stiffness because this is the component which gets embedded within the bone replacing the natural bone tissue and also, this component has the maximum interface with the periprosthetic bone. This will ultimately improve the implant anchorage. The main goal of this work is to employ a rigorous stress analysis in arriving at design choices for a dental implant that minimize stress shielding effects. A probable cause of implant failure can be attributed to improper design, resulting from inadequate simulation of the biomechanical environment in the maxillofacial region. Even a minimum bone loss may form a serious issue for a dental implant (Wiskott and Belser, 1999). Numerical approaches such as finite element (FE) analyses have been widely employed for studying these biomechanically complicated phenomena due to their capability to provide site-specific results, including stress/strain profiles in simulated maxillofacial environment, and storability (Turkyilmaz et al., 2007; Lin et al., 2008; Natali et al., 2010). For example, Toniollo et al. incorporated Morse taper into FE model of the dental implant to explore the biomechanical effects of different levels of implantation with such implants (Toniollo et al., 2012). They observed that slightly deeper placement of the implant is beneficial in terms of loss of the cortical bone at the cervical region of the implant. Pietrabissa et al. used FE analysis to evaluate the mechanical stresses at the bone-implant interface in case of various design misfits of dental bridge and reported that such method is capable of the estimation of the differences in the stress distributions (Pietrabissa et al., 2000). In a different study, Chen et al. adopted 3-D (three-dimensional) FE analysis to examine the mandibular biomechanics for three missing posterior teeth either individually implanted or implanted using two implants support fixed partial denture (Chen et al., 2012). Their study revealed an increased von Mises stress in the supporting bone in case of the fixed partial denture. The design features of the dental implant, such as the length, diameter, tilt, loading angle, thread type, etc., play significant roles in the post-implantation performance (Eazhil et al., 2016; Bevilacqua et al., 2008; Alvarez-Arenal et al., 2013). For example, hollow dental implants have been studied since the 1980s and their specific advantages include larger contact surface for osseointegration and formation of minimal surgical bone defect (Sutter et al., 1988; Buser et al., 1988). However, a few studies have reported multiple negative clincial outcomes for the hollow implants, which include increased bone loss (Buser et al., 1997; Merickske-Stern, 1990; Meijer et al., 2003; Versteegh et al., 1995; Merickse‐Stern et al., 2001), faster growth of pathogenic bacteria (Piattelli et al., 1999), higher tendency of fatigue fracture (MerickskeStern, 1990; Behneke et al., 2002; Levine et al., 1999; Hellem et al., 2001), etc. On the contrary, other studies have reported good clinical success rates with hollow implants (Ferrigno et al., 2002; Karoussis et al., 2004; Telleman et al., 2006; Chang et al., 2012). For example, Telleman et al. (2006) concluded that hollow implants provide a stable base for long-term support for a mandibular overdenture. Chang et al. (2012) explored optimal material distribution of the implant, through

2. Materials and methods The human mandible was modeled, based on CT scan data of a normal subject, taken in DICOM format (512 × 512 pixels per slice, pixel size of 0.6445 mm and slice thickness of 1 mm) (ten Broeke et al., 2014) [Fig. S1, Supplementary Section]. The three dimensional (3D) reconstruction was conducted using MIMICS (Materialise NV, Leuven, Belgium) (Bujtár et al., 2010; Karimi et al., 2014; Tang et al., 2012; Vatu et al., 2018; Zhang et al., 2018; Perez et al., 2018). Majority of the previous studies, where parts of the skeletal structure has been modeled, considered fixed mechanical properties for the cortical and the cancellous bone (Styranivska et al., 2017; Culhaoglu et al., 2013; Sabatini and Goswami, 2008; Abdullah et al., 2010). Though this simplification of bone properties has been practiced in recent past, it fails to consider the diversity of the bone properties over various regions. Thus the current study considers the voxel wise X-ray attenuation, which is expressed in Hounsfield Unit (HU), as the basis for assignment of bone properties in a site-specific manner, individually for each element, as done by our group in recent past (Chatterjee et al., 2018). Two clinical case studies of mandibular dental loss have been considered here. These are 1) single tooth loss (first molar) and 2) loss of all the three molars. Two implantation approaches have been adapted in the later case study: (i) the implant supported dental bridge configuration, and (ii) individual implantation of each molar [see Fig. 1]. The molar implant models of all of these situations and considering different lengths were prepared in Computer Aided Design (CAD) package, SolidWorks® 2012 (SolidWorks Corp., MA, U.S.) (Moraes et al., 2018; Calì et al., 2018; Ameddah and Mazouz, 2018). The FE package, ANSYS® 18 (ANSYS Inc., Pennsylvania, USA) (Calì et al., 2018; Hou et al., 2018; Cervino et al., 2018; Massoumi et al., 2018) was used for simulation of the mechanical environment. The implant models were virtually implanted, in computational environment, within the reconstructed model of the mandible in ANSYS® Workbench. The von Mises stress environment of the components and the periprosthetic bone has been simulated through FE analysis, for each implant design, to compare among the designs.

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Fig. 1. The dental implant models. The four components of a single implant model are illustrated separately. The dimensional details of an implant screw (IS) have been provided. In this study, the implant screw lengths taken are 9 mm, 10 mm, and 11 mm. The section through the width of the mandible illustrates the placement of each of the components. The implant supported dental bridge and individual dental implants, in case of loss of all the three molars, are also illustrated. Further, the Channel 1 and Channel 2 designs are shown with axial view with respect to the IS from above.

coupled with the IS by the LS. The implants for the dental bridge designs were considered to be of similar configuration of IS, abutment, and LS for the first and the third molars. But the three crowns were bridged by joining to each other. Consequently, the second crown was sustained by attachment with the adjacent crowns, to reduce bone invasion. Thus, the risk of bone fracture in between two successive molar implants, either during the process of implantation or due to physiological loading, post-implantation, has been avoided by the bridge configuration. A uniform taper angle was implemented throughout the implant screw. All the geometric characteristics of the implant are illustrated in Fig. 1.

2.1. Dental implant models A new design concept of 4-piece dental implant system is considered in this study. The components of each individual implant included the implant screw (IS), the abutment, the locking screw (LS), and the crown [see Fig. 1]. The abutment design employs a pentagonal anti-rotation feature, which being more asymmetric compared to the conventional hexagonal one, is expected to be more efficient to restrict relative movement between the abutment and the IS under physiological loading conditions. The crown was considered to be completely fixed with the abutment using synthetic glue, while the abutment was 251

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Table 1 The volume of the three designs of IS for all the three lengths and the percentage of volume reduction due to channeling in all Channeled cases. IS length

9 mm 10 mm 11 mm

Solid

Channel1

Channel2

Volume (mm3)

Volume (mm3)

Volume Reduction (%)

Volume (mm3)

Volume Reduction (%)

70.65 80.65 89.92

69.41 78.71 87.59

1.76 2.41 2.59

66.86 75.51 84.17

5.36 6.37 6.39

Fig. 2. The implanted region of the mandible was sectioned through approximately the middle portions of the screw holes and divided into lateral and medial sides for observation of the stress profile over the entire interfacial region. This figure shows the case of dental bridge having IS lengths of 10 mm. H1 and H2 denotes the site of implantation for the 1st and the 3rd molars respectively. Such sectioning has been done for all the cases of dental implants in this study for viewing the results.

Fig. 3. Distribution of bone density over the entire interfacial bone, splitting it into lateral and medial halves as illustrated in Fig. 2 for better observation, considering individual implantation for the loss of all three molars in case of IS length of 11 mm. The Red line indicates the termination point for IS of length 9 mm while the White line indicates the termination point for IS of length 10 mm.

Five longitudinal through hollow channels of uniform diameter, one in the center surrounded by four in the peripheral regions, were incorporated within the implant screw design for reducing the overall stiffness. Two types of channels were considered: Thick, i.e. 0.5 mm diameter, and Thin, i.e. 0.25 mm diameter. Two types of channel configurations were considered; central thick channel and peripheral thin channels (Channel 1 configuration) and central thin channel and peripheral thick channels (Channel 2 configuration). These selections reflect different types of gradients in the hollowness from inside to the outside. It should be noted that Shirazi et al. reported a radial functionally graded screw implant, analogous to Channel 2 of this study, wherein better biomechanical environment was generated within the surrounding bone leading to faster bone generation (Asgharzadeh Shirazi et al., 2017). Three different screw lengths (9 mm, 10 mm and 11 mm) were considered in the present case. For single dental loss, the solid IS was also considered as the conventional design for comparison. The volume of the IS for solid, Channel 1 and Channel 2 configurations for all the three lengths are shown in Table 1 along with the percentage of volume reduction for all Channeled cases.

Fig. 4. The finite element modeling of the mandible implanted with a single dental implant has been shown. The models have been meshed with ten-node tetrahedral elements. The element size considered in general was 3 mm while the region of interest, i.e. the region of the implantation, was meshed much finer with element size of 0.5 mm using the ‘sphere of influence’ option in ANSYS Workbench. Fixed constraints in all directions have been applied on the temporo-mandibular joint and a biting load of 100N was applied on the implant crown.

2.2. Finite element models The implant components were assumed to be composed of isotropic, linearly elastic, and homogeneous materials in accordance with earlier FE studies (Jonkers et al., 2008; Yamako et al., 2014; Sevimay et al., 2005; Papavasiliou et al., 1997; Eskitascioglu et al., 2004; Gallas et al., 2005; Abou-Emara et al., 2015; Schwitalla et al., 2015; Duan and Griggs, 2015; Rungsiyakull et al., 2015). The material properties of the bone, i.e., modulus of elasticity (E in MPa) and bone density (ρ in gm/ cc) were assigned element wise, based on voxel-wise attenuation of Xrays (indexed in terms of HU values), through empirical relations (Eq. (1)) (Roy et al., 2017; Lin et al., 2009b):

ρ = (0.000769 × HU ) + 1.028⎫ ⎬ E = 2349 × ρ2.15 ⎭

(1)

‘E ’ denotes the isotropic elastic modulus of heterogeneous bone and has been derived from ‘ ρ ’ which, in turn, was derived from the HU values. Each element in the FE model has been assigned material properties obtained as an average over all the voxels within its volume. As the region of interest of the mandible in this study is the interface 252

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Fig. 5. Variation of maximum von Mises stress (σmax) over the interfacial bone for the different types of implantation and of different lengths of the IS: (a) Single Implant (b) Dental bridge for multiple teeth loss (c) Individual Implants for multiple teeth loss. Fig. 6. Distribution of von Mises stress over the entire interfacial bone, splitting it into lateral and medial halves for observation, as shown in Fig. 2, considering all the three IS lengths for the case of implantation for single dental loss of first molar. The cases of solid as well as the channeled (Channel 1 and Channel 2) are shown.

with the implant, the distribution of ‘ ρ ’ over the interface has been shown. In order to visualize the whole interface the corresponding area of the right side of the mandible has been split through approximately the middle of the implant broach holes, into medial and lateral sides [Fig. 2]. The distribution of ‘ ρ ’ on these interfacial regions has been shown in Fig. 3. It has been found that the value of ‘ ρ ’ ranged from 0.5 g/cm3 to 2.4 g/cm3 and the corresponding value of E ranged from 0.59 GPa to 15.44 GPa at the interfaces. This high degree of inhomogeneity of the interfacial bone plays a role in the biomechanical outcome of the dental implant as the grip of the implant depends on the location of denser bone around it. This location varies according the length of the implant and the position where implantation is done. The abutments, IS, and LS were considered to be made of titanium alloy (Ti-6Al-4V) (E = 110 GPa, ν = 0.33) and the crowns were considered to be made of porcelain (E = 68.9 GPa, ν = 0.28) (Lin et al., 2009b, 2012; Schwitalla et al., 2015; Abou-Emara et al., 2015; Okamoto et al., 2008). For virtual implantation, the edentulous model of the mandible was reconstructed. The reference model was

reconstructed with the right side molars taken into consideration. Virtual implantations were performed on the edentulous models, where the reference models were used for locating the exact position and orientation of the implants on the mandible. The implant positions were obtained by superimposing them over the respective original tooth position of the reference model. Then they were virtually implanted within the edentulous model, by Boolean operation, maintaining the obtained position. Ten-node tetrahedral elements (SOLID187) (ten Broeke et al., 2014; Chatterjee et al., 2013) were used to mesh the bone and the implant components. While the general element size was targeted as 3 mm, the implants and the surrounding bone were meshed with a finer element size of 0.5 mm in order to capture accurately the changes in the values of the von Mises stress over the zone of interest 253

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Fig. 7. von Mises stress profile over the interfacial bone, splitting it into lateral and medial halves for observation, as shown in Fig. 2, in case of the dental bridge supported by channeled implants (Channel 1 and Channel 2), for the loss of all three molars, considering three IS lengths.

(9 mm, 10 mm and 11 mm). Variances of σmax in the periprosthetic bone among different types for a particular architecture or a particular IS length were analyzed; variances of these stresses among different IS lengths for a particular architecture were also analyzed.

[see Fig. 4]. The temporomandibular joint was assumed to be constrained in all directions for all the cases (Menicucci et al., 1998; Wagner et al., 2002). A normal compressive load of 100N was applied on each modeled crown to simulate the masticatory loading (El-Anwar and El-Zawahry, 2011). The coefficient of friction (µ) between the abutment, IS, and LS has been assumed to be 0.5, while µ between the bone and the interfacing components was assumed to be 0.4 (Zhang et al., 2016). The crown and the abutment were considered to be fully bonded (Zhang et al., 2016). The variation of the von Mises stress profile within the interfacial bone with respect to variation in length and design of the implant were critically assessed. Accordingly, variations of the maximum values of von Mises stress (σmax) in the periprosthetic bone with the variation of implant length were also evaluated and reported in this study.

3. Results and discussion Mechanically, larger stress concentration within a material component would lead to its failure. But bone, being a living material, behaves differently and remodels in the presence of an external mechanical stimuli. During such remodeling process, bone densifies at higher stressed zones and rarefies at the zones of stress-shielding. (Ghosh and Gupta, 2014; Ghosh et al., 2013; Ruben et al., 2012; Huiskes and van Rietbergen, 1995; Van Rietbergen et al., 1993; Weinans et al., 1993). Generally, in case of metallic or ceramic implantation, the stress values in the periprosthetic bone gets reduced as the implant, being stiffer, takes up the major share of the physiological load, relieving the bone from load bearing. This portion of the bone suffers from stress shielding, leading to erosion and damage. Thus, in this study, increment of stress in the periprosthetic bone is a criteria for selection of the design of IS. For this reason, the von Mises stress profile over the interfacial bone of the mandible were studied, considering various types of implantation and also for various implant lengths. The overall pattern of the stress distribution in the surrounding bone,

2.3. Statistical analysis Variance of von Mises stress in the periprosthetic bone, among the various parameters, has been estimated through the analysis of variance (one way ANOVA), together with tukey analysis for the Post hoc tests. The statistical analysis was performed using the IBM SPSS Statistics 20 software. The three parameters of the implant were taken as: a) type (single, individual implants for multiple loss, and dental bridge), b) porosity architecture (Channel 1 and Channel 2) and c) length of IS 254

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Fig. 8. Profile of von Mises stress over the periprosthetic bone, splitting it into lateral and medial halves for observation, as shown in Fig. 2, in the case of individual implantation (Channel 1 and Channel 2), for the loss of all three molars, considering three IS lengths.

may be seen that, though the σmax value generally increases with increase in IS length, increase of σmax was not observed as IS length increased from 9 mm to 10 mm, except the case of Channel 2 in dental bridge configuration. Rather a shallow decline of σmax has been observed in almost all cases. It was also observed that the Channel 2 designs, which are limper due to higher material excavation away from the center of the implant, produced higher bone stress and, thus, higher σmax. The higher resiliency allows it to have more strain and deformation pressing through the bone, resulting in higher interfacial bone stress. Additionally, it was observed that the bone stress values were much higher for the case of implantation of single tooth loss than for the cases of loss of multiple teeth.

obtained in this study, are in qualitative agreement with those reported in prior literature (Culhaoglu et al., 2013; Bhat et al., 2014; Djebbar et al., 2010; Omori et al., 2015; Hussein, 2013; Baggi et al., 2008). It has been reported in previous studies that limper and functionally graded dental implants produced better results in terms of reduced stress-shielding since the stiffness of the component, in such cases, matched closer to that of the surrounding bone (Pérez Pozo et al., 2015; Sheikh, 2015; Asgharzadeh Shirazi et al., 2017; Lin et al., 2009a). As already mentioned, the main motivation of this study was mechanically evaluating the IS with reduced overall stiffness (through channeling). The solid IS was treated as the control for the single implantation case. It has been found that the limper (Channeled) implants produced higher value of σmax compared to the solid design [see Fig. 5(a)]. For the boneimplant interfacial region, the superior portion shows highest values of von Mises stress since this region contains stiffer cortical bone [see Figs. 6–8]. This is in agreement with earlier research works (Pierrisnard et al., 2003). A small region of higher stress was also observed at the inferior tip of the interface, since the implant presses down the bone through its flat end in this region. Prior to this terminal portion, the interfacial stress diminished distally. Thus, this stress reaches further lower values in case of longer IS. But such diminution in stress did not affect the value of σmax present at the cortical surface. For all the IS designs, it was observed that the von Mises stress in the interfacial bone increased with IS length of 11 mm [see Figs. 6–8]. This is also reflected in the value of σmax in the bone interface [see Fig. 5]. It

3.1. Implantation for single tooth loss In this case, the value of σmax in the interfacial bone is almost same for Channel 1 and Channel 2 when the IS lengths are 9 mm or 10 mm. But in case of IS length of 11 mm, reasonably higher value of σmax was exhibited using Channel 2 than Channel 1 [Fig. 5(a)]. This is likely a consequence of both the stiffness reduction in Channel 2 design and the anchoring of the 11 mm implant in the more dense bone at the inferior end.

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Table 2 Statistical significance of variance of σmax in the periprosthetic bone (Bone Stress) among the various implant parameters (p ≤ 0.05). The cases which are statistically significant, are indicated by ‘*’. Variance among implant types of a particular porosity architecture The porosity architecture Significance for Bone Stress (through One way ANOVA) Channel1

0.000*

Channel2

0.000*

Variance among implant types of a particular IS Length The IS length Significance for Bone Stress (through One way ANOVA) *

Length 9 mm

0.000

Length10mm

0.003*

Length11mm

0.003*

Variance among IS lengths of a particular porosity architecture The porosity architecture Significance for Bone Stress (through One way ANOVA) Channel1

0.974

Channel2

0.945

Post hoc (tukey) Pairs of implant typesa 1&2 2&3 1&3 1&2 2&3 1&3

Significance For Bone Stress 0.000* 0.671 0.000* 0.000* 0.755 0.000*

Post hoc (tukey) Pairs of implant typesa 1&2 2&3 1&3 1&2 2&3 1&3 1&2 2&3 1&3

Significance For Bone Stress 0.001* 0.971 0.001* 0.004* 0.819 0.004* 0.004* 0.977 0.004*

Post hoc (tukey) Pairs of implant lengths 9 mm & 10 mm 10 mm & 11 mm 9 mm & 11 mm 9 mm & 10 mm 10 mm & 11 mm 9 mm & 11 mm

Significance For Bone Stress 0.999 0.975 0.983 0.999 0.961 0.948

* Statistically significant variance. a 1: Single Implantation, 2: Dental Bridge, 3: Individual implantation for multiple dental loss.

the interfacial bone for each IS length. Here also, the post hoc study on bone stress shows significant variance between any two pair of implantation types, except between individual implantation of multiple dental loss and dental bridge, in case of any IS length. The statistical study could not predict any significant variance of bone stress among IS lengths for each porosity architecture. Here, post hoc results also show insignificant variance of von Mises stress in all cases. At the closure, the clinical implication of the present study can be emphasized. For the case of loss of consecutive multiple molars, individual implantation is considered as a surgically invasive process. Moreover, since the bone mass in between two consecutive implants is quite thin, there is a potential risk of bone failure in case of some angular physiological load on the crown. The implant supported dental bridge configuration is an alternative process, which is comparatively lower invasive. The current study suggests that the biomechanical response of the interfacial bone, in the case of dental bridge configuration for the loss of the three molars, may not be detrimental in comparison to the former process. Thus, such an alternate approach may be preferred for the case of consecutive dental loss. This study has few limitations. Only mandibular molars have been considered. Moreover, non-consecutive dental loss has not been considered. However, this study provides a comprehensive idea regarding the biomechanical response of the process of implant supported dental bridges, which is otherwise considered as a minimally invasive surgical process of dental reconstruction. Another limitation is that bone ingrowth at the implant interface has not been studied. To this conjuncture, it may be mentioned that the osteoblastic / osteoclastic activities within the bone take place in accordance to the biomechanical environment as a result of the externally applied load stimulus. Bone tissue tends to be eroded at the regions of stress-shielding. This study proposes the IS designs in order to establish such biomechanical environment in the periprosthetic bone that prevents stress-shielding and maintains the interfacial bone properties. The novelty of this study is that a new abutment design having pentagonal anti-rotation feature has

3.2. Implantation for the loss of all the three molars As already reported by Yokoyama et al., higher interfacial stresses were observed with the mesial implant (Yokoyama et al., 2004) [Figs. 7 and 8]. Each implant screw, considered here, was a channeled design. There is significant variation of σmax over IS and the interfacial bone with different IS lengths [Fig. 5(b,c)]. 3.2.1. Implant supported dental bridge for loss of multiple teeth The line graph for σmax over the periprosthetic bone for various IS lengths follow curved paths [Fig. 5(b)]. Here, opposite nature of curves of σmax was obtained between Channel 1 and Channel 2. 3.2.2. Individual dental implants for multiple teeth loss Here also the values of von Mises stress are highest for 11 mm IS length, as analogues to the case of dental bridge approach [see Fig. 8]. This is also reflected in the nature of the curves for σmax of the interfacial bone [see Fig. 5(c)]. In contrary to the case of single dental loss, here the value of σmax in the interfacial bone is almost same for Channel 1 and Channel 2 when the IS length is 11 mm. But in cases of IS length of 9 mm and 10 mm, reasonably higher value of σmax was exhibited using Channel 2 than Channel 1 [Fig. 5(c)]. 3.3. Statistical analysis The results of statistical analysis show significant variance of the von Misses stress in the interfacial bone among various implant parameters (p ≤ 0.05) (Table 2). There was significant variance of bone stress among the different implantation types for each porosity architecture. The post hoc studies show significant variance of σmax values at the interfacial bone in between any two pair of implantation types, except between individual implantation of multiple dental loss and dental bridge, in case of either of the porosity architectures. The implantation types also exhibit significant variance of von Misses stress in 256

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been considered and radially distributed through longitudinal channels with different diameters have been incorporated within the IS for achieving functional gradation of stiffness reduction. In future, this study can be extended to multiple loss of non-consecutive teeth and may include teeth other than only the molars. The maxiliary denture may also be included. In addition, different bone conditions, loads considering different masticatory situations, pre-tapping force and interfacial bone ingrowth would also serve as meaningful additions in future endeavors.

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4. Conclusions Higher stress in the interfacial bone is desirable for minimization of the effect of stress shielding for having better bone remodeling. Based on the extensive FE analyses together with statistical analysis, the following key conclusions emerge, a) This study shows that the functionally graded implant screw with core to periphery radial gradient of increasing hollow porosity, generally provides higher interfacial bone stress. b) Considering the core to periphery radial gradient of increasing hollow porosity configuration, the implant screw length of 11 mm show the highest value of interfacial bone stress in all cases. c) For the case of loss of all the molars, dental bridge approach provides nearly similar periprosthetic bone stress as compared to individual implantation for each tooth. d) According to the results of the FE analyses of the current study, the dental bridge configuration with screw length of 11 mm and core to periphery radial gradient of increasing hollow porosity configuration presents the most favorable implant option for multiple edentulation due to its lower surgical invasiveness without compromising biomechanical response. Acknowledgements The authors thank “Translational Center on Biomaterials for orthopaedic and dental applications” sponsored by Department of Biotechnology (DBT), Govt. of India. (Grant No. DBTO0455), and Department of Science and Technology, Centre for Mathematical Biology (Grant No. DSTO1303), Govt. of India, for providing financial support towards this work. They had no role in the collection, analysis and interpretation of data in this study. The authors also acknowledge Prof. Amit RoyChowdhury, Indian Institute of Engineering Science and Technology, Shibpur, Mr. Srimanta Barui and Mr. Anupam Purwar for their suggestions and useful comments. One of the authors, Prof. Surya R. Kalidindi, acknowledges the support from the DST-SERB funded Vajra scheme. Declaration of interest disclosure None. Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmbbm.2019.03.001. References Abdullah, A.H., MohdAsri, M., Alias, M.S., Tardan, G., 2010. Finite element analysis of cemented Hip arthroplasty: influence of stem tapers, in: Proceedings of the international Multi Conference of Engineering and Computer Scientists, Citeseer. Abou-Emara, M., Schwitalla, A., Spintig, T., Lackmann, J., Müller, W., 2015. 194 basic research: biomechanical effects of elastic-modulus-graded PEEK implants. Clin. Oral Implants Res. 26 (S12) (26-26). Alvarez-Arenal, A., Segura-Mori, L., Gonzalez-Gonzalez, I., Gago, A., 2013. Stress distribution in the abutment and retention screw of a single implant supporting a

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