Influence of Bone and Dental Implant Parameters on Stress Distribution in the Mandible: A Finite Element Study

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1 Influence of Bone and Dental Parameters on Stress Distribution in the Mandible: A Finite Element Study Hong Guan, PhD 1 /Rudi van Staden, BEng 2 /Yew-Chaye Loo, PhD 3 / Newell Johnson, PhD 4 /Saso Ivanovski, PhD /Neil Meredith, PhD 6 Purpose: The complicated relationships between mandibular components and dental implants have attracted the attention of structural mechanics researchers as well as dental practitioners. Using the finite element method, the present study evaluated various and implant parameters for their influence on the distribution of von Mises stresses within the mandible. Materials and Methods: Various parameters were considered, including Young s modulus of cancellous, which varies from 1 to 4 GPa, and that of cortical, which is between 7 and 2 GPa. length (7, 9, 11, 13, and 1 mm), implant diameter (3., 4., 4., and. mm), and cortical thickness (.3 to 2.1 mm) were also considered as parameters. Assumptions made in the analysis were: modeling of the complex material and geometric properties of the and implant using two-dimensional triangular and quadrilateral plane strain elements, % osseointegration between and implant, and linear relationships between the stress value and Young s modulus of both cancellous and cortical at any specific point. Results: An increase in Young s modulus and a decrease in the cortical thickness resulted in elevated stresses within both cancellous and cortical. Increases in the implant length led to greater surface contact between the and implant, thereby reducing the magnitude of stress. Conclusions: The applied masticatory force was demonstrated to be the most influential, in terms of differences between minimum and maximum stress values, versus all other parameters. Therefore loading should be considered of vital importance when planning implant placement. INT J ORAL MAXILLOFAC IMPLANTS 29;24: Key words: cancellous, cortical, dental implants, finite element technique, stress distribution characteristics Development of an ideal substitute for missing teeth has been a major aim of dental practitioners for millennia. 1 Dental implants are biocompatible 1 Associate Professor in Structural Engineering and Mechanics, Griffith School of Engineering, Griffith University Gold Coast Campus, Queensland, Australia. 2 PhD Student, Griffith School of Engineering, Griffith University Gold Coast Campus, Queensland, Australia. 3 Professor and Foundation Chair of Civil Engineering, Director of Internationalisation, and Professional Liaison, Science, Environment, Engineering and Technology Group, Griffith University Gold Coast Campus, Queensland, Australia. 4 Professor of Dental Research and Foundation Dean, School of Dentistry and Oral Health, Griffith University Gold Coast Campus, Queensland, Australia. Listerine Chair Professor of Periodontology, School of Dentistry and Oral Health, Griffith University Gold Coast Campus, Queensland, Australia. 6 Chief Executive Officer, Neoss Ltd, Harrogate, United Kingdom. Correspondence to: Associate Professor Hong Guan, Griffith School of Engineering, Griffith University, Gold Coast Campus, Queensland 4222, Australia. Fax: +61-() [email protected] screwlike titanium objects that are surgically placed into the mandible or maxilla to replace missing teeth. The mechanism by which an implant is biomechanically accepted by the jaw is called osseointegration. 2,3 Stimulus of the through applied stresses has been well documented to influence the success or failure of an implant. 4, Furthermore, primary stability is especially critical because the is still in a state of repair and necessitates applied stresses that promote growth. Himmlova et al, 6 Iplikçioglu and Akça, 7 and Pierrisnard et al 8 recognized the fact that the dimensions of an implant influence the magnitude and profile of stresses within the. It is commonly understood that increasing the implant length and/or diameter reduces the stresses within the. Furthermore, based on clinical experience, practitioners are aware that if the is weak, then a larger-diameter implant is required. However, these decisions are based primarily on clinical judgment rather than being supported by any theoretical data. It is critical for the practitioner to fully grasp the relationship 866 Volume 24, Number, BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

2 Tcor M F H Loading condition Tcor/2 F v L Fixed constraint Dental implant.2 mm VV Taper D Cortical Fig 1 Finite element model of the mandible and dental implant. (Left) Cross section in distal direction. (Right) Locations for stress reporting. D = implant diameter; L = implant length; F H = horizontal load; F V = vertical load; M = moment; Tcor = cortical thickness; Ecor = Young s modulus of cortical ; Ecan = Young s modulus of cancellous ; VV = length in cancellous used to determine von Mises stresses; = length in cortical used to measure von Mises stresses. Ranges of values used are reported in the text. between various combinations of and implant parameters and the resulting stresses on the from a wide range of masticatory forces. Finite element analysis (FEA) is becoming a common method to advance dental technologies. 9,1 Areas of application in implant dentistry include studies of jaw and implant properties as well as the implant interface In the past, extensive research has been undertaken on the characteristics of stress distribution in surrounding implants However, no published work appears to have investigated the stress distribution in the when various and implant parameters are considered. Ultimately the outcome of this study will help dental practitioners to identify the stimulus state of the ; hence, clinicians would be able to predict success or failure for all combinations of implant lengths and diameters with a given cortical thickness, as well as the material properties of cancellous and cortical, under a range of masticatory forces. METHODS Model Construction A two-dimensional (2D) representation of the and implant was analyzed using the Strand7 FEA system. 22 This is considered to be equally accurate and more efficient in terms of computation time, as compared to a three-dimensional (3D) equivalent. Data for the dimensions were based on computerized tomographic scans. The different types of, ie, cancellous and cortical, were distinguished and the boundaries were identified to assign different material properties within the finite element model. Figure 1a shows a mandible section and implant with the loading and restraint conditions. Also shown are the detailed parameters considered in this study. The modeled implant was conical with 2 degrees of taper and a helical thread. For a particular finite element model with dimension (D) = 4. mm, length (L) = 11 mm, and cortical thickness (Tcor) =, the total numbers of plane strain elements were 2,87 for the implant,,96 for cancellous, and 1,94 for cortical. The total number of nodal points in the entire model was 9,969. As indicated in Fig 1b, the von Mises stresses along the lines VV for cancellous and for cortical were measured for all possible parameter combinations. The relative locations of these lines are considered by clinicians to be critical for examining the stress levels and helping to understand the stimulus response of. Both lines VV and were chosen on the buccal side of the implant, where the stress level is higher than on the lingual because of the loading characteristics. The stress contour plots will be presented for the buccal side of the model only. The lengths of VV and were dependent on the implant dimensions and Tcor. Because of the irregularity of the mesh, a straight line (VV) of nodes used for measuring The International Journal of Oral & Maxillofacial s BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

3 Apparent density (g/cm 3 ) Carter et al 27 Lotz et al 26.2 Ciarelli et al 28 Ciarelli et al 28 Proposed, Eq (1) Ecan (GPa) Apparent density (g/cm 3 ) Abendschein and Hyatt 24 Lotz et al 26. Lotz et al 2 Proposed, Eq (2) Ecor (GPa) Fig 2 Relationship between Young s modulus and density in the mandible. (Left). (Right) Cortical. stress was only approximated.the distance of VV away from the thread tip was not a varying parameter affected by the implant diameter; it was fixed at.2 mm (see Fig 1b) in an attempt to capture the stresses at the most critical location. 23 Bone and Parameters An extensive literature review by van Staden et al 18 indicated that the commonly assumed Young s modulus for cancellous ranges from.8 to 7.93 GPa. Cortical is normally assumed to vary from.7 to 22.8 GPa. The present study adopted a range of Young s modulus for cancellous (Ecan) from 1 to 14 GPa and for cortical (Ecor) from 7 to 2 GPa, both at 1-GPa intervals (see Fig 1a). The selection of such a range was based on the understanding that in some exceptional cases Young s modulus of cancellous can reach 14 GPa when that of cortical is also at a high range. With such a large range of material parameters to be considered, the corresponding densities of cancellous and cortical needed to be determined. Figures 2a and 2b show the relationships between Young s modulus and the density of cancellous ( can ) and cortical ( cor ), respectively, as per published clinical data of several authors Note in Fig 2a that Ciarelli et al 28 suggested two different relationships for the cancellous in different regions. Based on these data, the following equations are proposed to determine the mean relationships between Young s modulus and the density of cancellous and cortical, respectively. can = (3.4 Ecan) +.16 (Equation 1) cor = (.2 Ecor) (Equation 2) 3 Tcor is another parameter to be evaluated. Mellal et al 29 assumed a thickness of 1 mm, whereas Natali et al 3 assumed.8 and 1.9 mm. For the present study, a more extensive range of Tcor (.3,.6,.9, 1.2, 1., 1.8, and 2.1 mm) was selected (Fig 1a). The Poisson s ratios ( ) for the implant (grade 4 commercially pure titanium), cancellous, and cortical were.3,.3, and.3, respectively. Note that the cortical was constrained along the lingual and buccal faces of the cross section in the distal direction (see Fig 1a), thus representing a realistic function of the mandible surrounding an implant. Various dimensions based on the Neoss 31 implant system were employed: lengths of 7, 9, 11, 13, and 1 mm and diameters of 3., 4., 4., and. mm. Loading Conditions The present study focused only on the stresses within cancellous and cortical ; therefore, the implant system was simplified, and such components as the abutment, abutment screw, and crown were not included. In reality, masticatory forces act on the top of the crown. Neglect of the implant components means that the masticatory force is transferred to the head of the implant. This requires the introduction of a moment (M) around the z-axis, together with the forces acting in the horizontal (x-axis) (F H ) and vertical (y-axis) (F V ) directions. Note that M was applied around the negative z-axis and is based on the horizontal load laterally transferred at a distance (crown height) of 6. mm. The range of loading was considered as F H = 2 to 2 N, F V = to N, and M = 162. to 1,62 Nmm. Based on a theoretical study by Choi et al, 32 these loading conditions are regarded as comprehensive. The present study included an extensive range of loading magnitudes to analyze the effect of traumatic 868 Volume 24, Number, BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

4 loading. Because of the linearly elastic behavior of the implant- system, only the maximum forces were applied in the analysis. The results upon application of the minimum and half maximum forces can be readily calculated. Assumption Strategies In addition to the assumption of a 2D representation of the and implant, other assumptions made in the model were: (1) % osseointegration between the and implant, and (2) linear relationships between the stress value and Young s modulus of both cancellous and cortical at any specific point. Bone- Interface. The interface surrounding the implant includes both blood and fragments. This interface is considered clinically ideal for osseointegration, although it is mechanically unfavorable. The stage after insertion and before full osseointegration is critical for the surrounding because it exhibits the most distinct stress concentrations. In the postosseointegration stage, however, the lamina dura has been formed and the implant stability drastically increases. Previous finite element studies 1,29,33,34 assumed that immediately loaded implants are in direct contact with cancellous, without a blood interface. Borchers and Reichart 3 suggested two typical stages of lamina dura interface formation: (1) immediately after implantation the cancellous is in direct contact with the implant, and (2) a layer of the lamina dura (cortical like) of approximately 1. mm in thickness forms. In a study by Natali et al, 3 the two formation stages of the lamina dura were modeled with Young s moduli of.3 GPa and 1. GPa, respectively. The formation of lamina dura improves the stress distribution and represents a clinically favorable course of healing. A study by Berglundh et al 36 provided an overview of the various phases of blood and hard () tissue formation during the healing stages at the implant interface, sampled 2 hours after implant placement.the blood interface extended.13 mm into the thread chamber. Based on these findings, the present study assumed % osseointegration between the and the implant. The voids between the and implant were modeled as blood (Fig 3). Young s modulus and the Poisson s ratio of the blood were taken as. and.3, respectively. Linear Relationship Between Stress and Young s Modulus. The total number of parameter combinations was 27,44, based on implant lengths, 4 implant diameters, 7 cortical thicknesses, and 14 Young s moduli each for cancellous and cortical, respectively. Because the completion of such a huge Hard tissue (cancellous ) Blood Fig 3 Proposed modeling of blood and hard tissue. number of simulations would be unviable, further assumptions were made to reduce the number of simulations to a manageable level. The feasibility of a linear relationship for the stress variation for all combinations of Ecan and Ecor was exploited. For the purpose of validation, an FEA was carried out to obtain the actual von Mises stress values for D = 4. mm, L =, and Tcor =. Varying Ecan from 1 to 14 GPa for every possible value of Ecor resulted in little variation from linearity. An example of this is shown in Figs 4a and 4b, where the actual stress at the midpoint of line VV is measured for all combinations of Ecan and Ecor and compared to the respective linear prediction. For Figs 4a and 4b, Ecan = and Ecor =, respectively. For Ecan and Ecor, the predicted stresses varied from the actual ones by an average of.7% and 4.3%, respectively. Note that the stresses recorded at the midpoint of line produced a similar percentage error (4.9% and 6.% for Ecan and Ecor, respectively) for VV. With linear relationships between the stress and Ecan or Ecor assumed, only the minimum and maximum values of Young s modulus were considered for each type of instead of the initial data set of 14. This reduced the total number of analyses to 6. RESULTS.13 mm To demonstrate the overall behavior of the implant system, the stresses measured along the lines VV and were presented for three load levels: minimum, half maximum, and maximum. The International Journal of Oral & Maxillofacial s BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

5 Predicted Actual Linear prediciton Fig 4 Actual and predicted stresses at the midpoint of line VV. (Top). (Bottom) Cortical Ecan (GPa) Predicted Actual Linear prediciton Ecor (GPa) Influence of Varying Diameter Figure presents the von Mises stresses measured along the lines VV and for all possible implant diameters. The other parameters were set to their average values (L =, Tcor =, Ecan = 7 GPa, Ecor = ). When D increased, the stress along the line VV oscillated more significantly, following the thread profile (Fig a). The increased oscillation was a result of reduced distance (IC) between the implant thread and cortical and the subsequent reduced volume of cancellous (Fig b). This reduced the capacity of cancellous to distribute the stress more evenly. The stresses along the line exhibited a reduction when D was increased (Fig c). This reduction was caused by the larger-diameter implant supporting an increased portion of the load; hence, less stress was induced in the cortical. Generally, higher stresses were found at the implant neck for all diameters. When D =. mm, stress was concentrated at H 1 because of the different shape of the implant head as compared to other implant diameters (Fig d). The stress levels along the lines VV and increased as F H,F V, and M increased, which is evident in Fig and subsequent figures. Influence of Varying Length The von Mises stresses measured along the lines VV and, for all possible implant lengths, are shown in Fig 6. Average values were assigned for all other parameters (D = 4. mm, Tcor =, Ecan =, Ecor = ). The stresses decreased within both cancellous and cortical (Figs 6a and 6c, respectively) as L increased. This is because the surface area contact between the and implant also increased, leading to the implant absorbing more of the load. Figures 6b and 6d show that, for all implant lengths, stress was concentrated at the implant neck within the cancellous and cortical. 87 Volume 24, Number, BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

6 mm 4. mm 4. mm. mm 4. mm 4. mm F H = 2 N, F V = N, M = 1,62 Nmm D = 3. mm IC VV D =. mm IC VV (mm) Cortical mm 4. mm 4. mm. mm 4. mm 4. mm F H = 2 N, F V = N, M = 1,62 Nmm D = 3. mm D =. mm Cortical H 1 (mm) Fig Stress profiles with varying D. (Top). (Bottom) Cortical. Influence of Varying Cortical Bone Thickness Figure 7 presents the von Mises stresses measured along the lines VV and for all possible values of Tcor. Average values were used for all other parameters (D = 4. mm, L =, Ecan =, Ecor = 13 GPa). As Tcor decreased, the ability of the cortical to support the load also decreased, leading to a slight increase in the magnitude of stresses along the line VV (Fig 7a). A nondistinctive trend was found for the stress profiles along the line (Fig 7c). Figures 7b and 7d, respectively, show that, for all cortical thicknesses, stresswas concentrated at the implant neck within the cancellous and cortical. Influence of Varying Young s Modulus for Bone In Fig 8 all other parameters were set to average values (D = 4. mm, L =, Tcor =, Ecor = 13 GPa). As shown in Fig 8a, as Ecan increased, the stress magnitude increased as a result of the cancellous s ability to support a greater portion of the load. The stress within the cortical (Fig 8b) increased as Ecan decreased. This was because the cancellous was supporting less load and therefore an increased portion of the load was supported by the cortical. The International Journal of Oral & Maxillofacial s BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

7 mm 9 mm 13 mm 1 mm F H = 2 N, F V = N, M = 1,62 Nmm L = 7 mm VV L = 1 mm 1 1 VV (mm) Cortical mm 9 mm 13 mm 1 mm F H = 2 N, F V = N, M = 1,62 Nmm L = 7 mm L = 1 mm Cortical (mm) Fig 6 Stress profiles with varying L. (Top). (Bottom) Cortical. Influence of Varying Young s Modulus for Cortical Bone In Fig 9 all other parameters were set to average values (D = 4. mm, L =, Tcor =, Ecan = 7 GPa). Figure 9a indicates that as Ecor decreased, the stress magnitude increased slightly in cancellous a result of the cancellous having to support an increased portion of the load. However, the stress within the cortical (Fig 9b) increased as Ecor increased.this is the result of the increased resistance of the cortical to the applied load. DISCUSSION FEA has been used extensively to predict the biomechanical performance of jaw surrounding a dental implant. Previous research investigated the stresses in the surrounding, which were influenced by both the implant dimensions 7,8,37 43 and the biomechanical bond formed between the and the implant. 23 However, to date no research has been conducted to evaluate the stress characteristics influenced by all combinations of the various and implant parameters. 872 Volume 24, Number, BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

8 mm.6 mm.9 mm 1. mm 1.8 mm 2.1 mm F H = 2 N, F V = N, M = 1,62 Nmm Tcor =.3 mm VV Tcor = 2.1 mm Cortical 1 1 VV (mm) mm.6 mm.9 mm 1. mm 1.8 mm 2.1 mm F H = 2 N, F V = N, M = 1,62 Nmm Tcor =.3 mm Tcor = 2.1 mm Cortical (mm) Fig 7 Stress profiles with varying Tcor. (Top). (Bottom) Cortical. The present analysis considered various combinations of, implant, and loading parameters, including D, L,Tcor, Ecan, Ecor, F H,F V, and M. In general, good agreement was found with previous research 7,8,37 41 in that an increase in implant length and diameter was associated with reductions in stress within the cancellous. However, this study also demonstrated that when D increased, the stress along the line VV oscillated more significantly, following the thread profile (Fig a). Himmlova et al 6 and Tawil et al 4 indicated that implant diameter was more important for improved stress distribution than implant length. However, this study shows that an increase in implant length reduces stress within both cancellous and cortical for a wider range of parameters. This is more obvious than the influence of varying diameter. The finding is also in contrast with that of Pierrisnard et al, 8 who concluded that the stress within the was virtually constant, independent of implant length and bicortical anchorage. The International Journal of Oral & Maxillofacial s BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

9 GPa 14 GPa F H = 2 N, F V = N, M = 1,62 Nmm GPa 14 GPa F H = 2 N, F V = N, M = 1,62 Nmm VV (mm) (mm) Fig 8 Stress profiles with varying Ecan. (Left). (Right) Cortical GPa F H = 2 N, F V = N, M = 1,62 Nmm GPa F H = 2 N, F V = N, M = 1,62 Nmm VV (mm) (mm) Fig 9 Stress profiles with varying Ecor. (Left). (Right) Cortical. No research to date has considered the influence of the cortical thickness on the stresses in cancellous and cortical. The present study concluded that decreased Tcor led to cortical supporting less load, which in turn caused a slight increase in the magnitude of stress in cancellous. Generally, as the strength of either cancellous or cortical increased, their ability to carry the load increased. When Ecan increased, the stress magnitude increased because the cancellous was able to support a greater load. When Ecor decreased, the stress magnitude increased within the cancellous because the cancellous had to support a greater portion of the load. On the other hand, the stress within the cortical increased as Ecor increased, because the cortical offered more resistance to the load. It was consistently found in the present study that elevated stress levels were located at the implant neck for all combinations of the different parameters. This phenomenon is supported by Meijer et al, 13 who concluded that the regions of exposed to maximum stresses are located around the implant neck. 874 Volume 24, Number, BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE

10 CONCLUSION This research is a pilot study aimed at offering an initial understanding of the complicated stress distribution characteristics in the resulting from variations in and implant parameters. Realistic geometries, material properties, loading, and support conditions for the jaw and implant were considered in the present study. Modeling assumptions were validated and a vast range of parameters was studied. The majority of stress characteristics correlated well with previous research, with some new findings. In general, it was found that the implant length had a noteworthy characteristic relationship with the stress in the. length was more influential than implant diameter in terms of the stress variation in cancellous. However, implant diameter was more influential in the stress variation in cortical. Overall, in both cancellous and cortical, the applied load and moment were the most influential and should therefore be given priority when planning implant placement. Evaluating the influence of other parameters that affect the stresses governing osseointegration and growth can constitute future work. These parameters include implant taper, pitch and thread design, implant neck offset, different percentages of osseointegration, and implant orientation within the. ACKNOWLEDGMENTS Special thanks go to John Divitini and Fredrik Engman from Neoss Limited for their technical advice. REFERENCES 1. Irish JD. A,-year-old artificial human tooth from Egypt: A historical note. Int J Oral Maxillofac s 24;19: Brånemark PI, Adell R, Breine U, Hansson BO, Lindstrom J, Ohlsson A. Intra-osseous anchorage of dental prostheses. I. Experimental studies. Scand J Plast Reconstr Surg 1969;3: Brånemark PI, Hansson BO, Adell R, et al. Osseointegrated implants in the treatment of the edentulous jaw. Experience from a 1-year period. Scand J Plast Reconstr Surg 1977;16: Mellal A, Wiskott HW, Botsis J, Scherrer SS, Belser UC. 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