Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage

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1 JIOS /jp-journals RESEARCH ARTICLE Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage 1 PS Vijayalakshmi, 2 AS Veereshi, 3 Vijay P Jayade, 4 MR Dinesh, 5 Mukesh Kumar ABSTRACT Biomechanical influences on bone structure play an important role in the longevity of bone around an implant. The quantity and direction of applied force influence the implant and cause deformation of the bone. FEA was used to analyze the changes in the bone on loading the implant with orthodontic force in oblique and vertical directions and orthopedic force. The Mini-implants used in the present study efficiently resisted the oblique loading. But their use, for the purpose of orthopedic loading is questionable. FE models showed the area with the highest stress and strain to be around the neck of the implant and the surrounding bone at the cervical margin. Keywords: Finite element analysis, Mini-implant, Stress, Strain, Cortical bone, Trabecular bone. How to cite this article: Vijayalakshmi PS, Veereshi AS, Jayade VP, Dinesh MR, Kumar M. Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage. J Ind Orthod Soc 2012;46(4): INTRODUCTION Efficient attainment and control of anchorage is fundamental to successful orthodontic and dentofacial orthopedic treatment. Adequate anchorage to correct dental or skeletal malocclusions is often a critical consideration in treatment planning. Because of anchorage limitations, we may have to settle for a compromised treatment alternative, or more complicated treatment alternatives like extraoral traction devices (which heavily depend on patient s compliance) or orthognathic surgery. 1 Implants are an excellent alternative to traditional orthodontic anchorage methodologies, and they are a necessity when dental elements lack quantity or quality, when extraoral devices are impractical, or when noncompliance during treatment is likely. In the last few years, implants of smaller sizes have been specially designed for orthodontic anchorage. These miniimplants are small enough for placement at any surface of the 1 Reader, 2 Associate Professor, 3 Former Professor and Head, 4 Professor and Head, 5 Professor 1,4 Department of Orthodontics, DAPM RV Dental College, Bengaluru Karnataka, India 2,5 Department of Orthodontics, Rungta College of Dental Sciences Bhilai, Chhattisgarh, India 3 Department of Orthodontics, SDM College of Dental Sciences, Dharwad Karnataka, India Corresponding Author: PS Vijayalakshmi, Reader, Department of Orthodontics, DAPM RV Dental College, Bengaluru, Karnataka, India drvijaya_ps@yahoo.com Received on: 20/12/11 Accepted after Revision: 20/6/12 alveolar process, even in the interdental areas. They are relatively inexpensive, and techniques for their placement and retrieval are simple. 2 Several researchers have reported studies related to the use of implants for orthodontic anchorage When using any of the load bearing implants in the bone, the stress and strain distribution in the bone around the implant must be understood. Biomechanical influences on bone structure play an important role in the longevity of bone around an implant. The quantity and direction of applied force influence the implants, and cause deformation of the bone. Stress analyses of endosseous implants are necessary for the investigation of bone turnover and maximum anchorage possible. Incorrect loading or overloading may lead to disturbed bone turnover and consequent implant loss. 26 Since, clinical determination of stress and strain distribution in the bone is not possible, an alternative technique should be used. The finite element method (FEM), which has been successfully applied to the mechanical study of stresses and strains in the field of engineering, makes it practicable to elucidate stresses in the living structures caused by various internal and external forces. Finite element analysis (FEA) has become an increasingly useful tool for the prediction of the effects of stress on the implant and its surrounding bone. The key factor for the success or failure of dental implant is the manner in which the stresses are transferred to the surrounding bone. FEA allows predicting stress distribution in the contact area of the implant with the cortical bone, and around the apex of the implant in the trabecular bone. 27 Numerous investigations 28,29 have been conducted to assess the stress and strain distribution that occurs around larger/bulkier prosthodontic implants, but limited literature is available regarding the same about mini-implants used for The Journal of Indian Orthodontic Society, October-December 2012;46(4):

2 PS Vijayalakshmi et al orthodontic anchorage. Also, the nature of loading of prosthodontic implants would be different compared to those used for orthodontic purposes. Hence, it was felt that there is a need to explore the changes in the bone adjacent to the implant following orthodontic loading. Therefore, the present study was undertaken with the following aims and objectives: 1. To analyze, by applying the FEM the stress and strain distribution patterns in the bone surrounding a miniimplant. 2. To investigate the deformation of the bone around an implant in response to forces of different magnitudes and applied in different directions. 3. To derive clinical implications, which may aid in optimization of implant design and its usage. MATERIALS AND METHODS The study was done in two parts as follows: 1. Data collection 2. FEM analysis Data Collection Data collection involved four steps: a. In the first step, a case was selected for the placement of the mini-implants. A patient, who presented with severe bimaxillary dentoalveolar protrusion and had critical anchorage requirements (needing complete utilization of the extraction spaces for retraction) was selected- an ideal case indicated for placing mini-implants for anchorage. 29 The implants were fixed using the following surgical procedure (as recommended by the authors) 30 in the interdental region between the 2nd premolar and the 1st molar (Figs 1A and B) and the insertion site chosen was measured from a guide bar on the bite-wing X-ray. To avoid any damage to the roots, the screws were implanted at a 60 angle between the teeth to the occlusal plane. 29 At the same time, the implants maintained an angle of approximately 30 to 40 to the long axis of the maxillary teeth and 10 to 20 to the mandibular teeth, to ensure optimum retention by augmenting the area of contact between the implant and adjacent bone (Figs 1A and B). b. The second step of the study was to evaluate the implant to bone integration. After 3 weeks of healing period, before loading the implants, the Dentascan (Figs 2A and B) was taken to ascertain the implant to bone integration. The data was also used to measure the thickness and depth of the cortical and trabecular bone around the implant. c. The third step was to determine the dimensions of the implant, so that these measurements could be used for modeling the implant. The dimensions of the implant were measured directly using a micrometer (to measure the pitch of the screw) and Vernier calipers (to measure the vertical and horizontal dimensions) Using the micrometer (0.25 range), the diameter at the tip, diameter at the first pitch, and the diameter at the tip of the implant were measured. The Vernier calipers of 8" were used to measure the vertical and horizontal dimensions. Along with the micrometer, a threading pitch gauge was also used to measure the pitch of the screw. d. Finally, the thickness of the bone surrounding the implant was measured using the implant assessment algorithm provided in the resident Dentascan software. As per the Dentascan, cortical bone thickness was 2.6 mm and cancellous bone thickness was 2.4 mm. Figs 1A and B: Mini-implants placed in the interdental region between the second premolar and the first molar region in a patient having critical anchorage requirement 176 JAYPEE

3 JIOS Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage Figs 3A and B: Models of implant and implant-cortical-trabecular bone in hypermesh FE modeling package Assigning the material properties: In this study, the assumption was made that the materials were homogenous and linear and that they had elastic material behavior characterized by 2 material constants viz. Young s modulus and Poisson s ratio. Figs 2A and B: Dentascan of the same patient, which was used to evaluate the implant to bone integration and to measure the thickness of the cortical and trabecular bone Finite Element Analysis Software The initial modeling was done using hypermesh FE modeling package and AutoCAD mechanical. The finite element analysis was done using MSC Patran version 3 as the pre- and postprocessor and MSC Nastran solver for Windows XP professional. Modeling the Mini-implant and the Surrounding Bone The modeling was done using the software, Hypermesh FE modeling package. Once the dimensions of the bone and the implant were obtained, these values were fed as input in both X and Y dimensions into the modeling software. These points were joined by lines to create the 2D crossection of the implant and the bone. Then, this crossection was revolved 360 to get 3D model (Figs 3A and B). The completed 3D model was then converted into a MSC Nastran input file (dat format) and imported into MSC Patran. The final model had hexahedral elements and nodes. Boundary conditions: Since the implant was assumed to be rigidly anchored in the bone, the entire outer surface of the bone was restrained from translation along all three axes, and restrained from rotations around all three axes. The FE Model Two types of FE models of the implant bone complex were generated (Figs 3A and B) Type I: Implant being surrounding completely by cortical bone. Type II: Implant being surrounded 3/4th by cortical bone and the tip being embedded in the trabecular bone. Implant Loading The effects of 2 different static loading conditions were planned to be examined. These loads were to be applied to simulate the following clinical situations: Orthodontic loading: Intrusion and retraction/oblique Vertical force Orthopedic loading ( as in protraction of maxilla). Magnitudes of Force Following force values were applied: Orthodontic loading: Intrusion and retraction/oblique: 150, 200 and 250 gm. Vertical force: 45, 60, 75 and 90 gm Orthopedic loading (as in protraction of maxilla): 400, 500 and 600 gm. The displacements produced by each of the force sets, and the stresses generated in the implant and in the surrounding The Journal of Indian Orthodontic Society, October-December 2012;46(4):

4 PS Vijayalakshmi et al bone were studied. Maximum and minimum principal stresses produced in each of the said structures were tabulated. Along with these, the maximum and minimum principal strain was also tabulated. A current measure for small strain values is strain µeps, where a strain of 1 means a deformation of 100%. Thus, for example, a strain of 100 µeps coincides with a strain of or 0.001% ( = 10 6 ). These values obtained were then correlated with Frost s Mechanostat theory (1994) 30 given in the table below. The compressive stresses were greater than the tensile stresses. These compressive and tensile stresses gradually reduced toward the tip of the implant. b. Distribution of stresses in the bone: Bone experienced a similar pattern of stress distribution, tensile stresses on RESULTS Interpretation of Results The results obtained are discussed under three headings: 1. Distribution of maximum and minimum principal stresses in the implant and bone. 2. Displacement of the implant and bone 3. Distribution of maximum and minimum principal strain in the implant-bone junction and bone. These parameters are analyzed for both types I and II FE models, under 3 different loading conditions. Figures 6 to 9 are graphical representation of the results obtained. Fig. 5: Distribution of maximum principal (compressive) strain in the cortical bone, on application of an orthopedic load of 400 gm to the type I FE model OBLIQUE LOADING OF THE IMPLANT FOR INTRUSION AND RETRACTION Implant in Cortical Bone: Type I FE Model The oblique force, when applied to the implant, caused the following stress distribution pattern: a. Distribution of stresses in the implant: Compressive stresses were seen on the mesial surface of the implant, with the maximum compressive stress being concentrated at the neck of the implant (Fig. 4).The tensile stresses were distributed on the opposite side of force application, i.e. on the distal surface. The maximum tensile stresses were concentrated at the point of force application. Fig. 6: Maximum and minimum principal stresses at the implantcortical bone junction for both type I and type II FE models Fig. 4: Distribution of maximum principal stresses in the implant, on application of an oblique force of 250 gm to the type I FE model Fig. 7: Maximum and minimum principal stresses experienced by the implant for both type I and type II FE models 178 JAYPEE

5 JIOS Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage The maximum principal strain further increased as the magnitude of force was increased. These strain values were correlated with the Frost mechanostat theory (1994). 29 On comparison, it was found that the strain values at implant-bone interface were in the range required for physiologic bone maintenance. In the deeper layers of the bone, these strain values decreased significantly. Implant in Cortical and Trabecular Bone: Type II FE Model Fig. 8: Maximum and minimum principal strains at the implant-cortical bone junction for both type I and type II FE models Fig. 9: Maximum and minimum principal strains in the cortical bone for both type I and type II FE models the distal aspect and compressive stresses on the mesial surface. The cortical bone around the implant revealed that the cervical margin and the bone around the first thread of the implant were the most stressed areas. c. Distribution of stresses at the implant-bone interface: At the junction of the implant and bone, maximum compressive stresses were seen. The 1st thread of the implant had maximum compressive stress. The stresses gradually reduced from the 1st ring to the 5th ring. The pattern of stress distribution was similar for application of 150, 200 and 250 gm loads. Displacement of the Implant and the Bone On application of oblique force to the implant, the implant showed a very negligible amount of displacement. The implant tended to tip toward the direction of force applied. This displacement was in the range of to mm. Distribution of Strain On application of force on the implant, it created an area of maximum strain at the junction of the implant and the bone. On oblique loading, the implant in the type II model experienced the same magnitude of stress as the type I model. The concentration of the stresses was seen at the neck of the implant, with the maximum tensile stress at the point of force application. The cortical bone experienced lower compressive and tensile stresses as compared to the type I model. However, unlike in model I, there were no significant differences between the tensile and the compressive stresses in the bone. The trabecular bone experienced lower stresses when compared to the cortical bone. But in contrast to the cortical bone, compressive stresses were slightly greater than the tensile stresses. Within the trabecular bone, maximum stress concentration of both tensile and compressive stresses was seen at the corticotrabecular junction. Implant-cortical bone junction experienced greater stresses when compared to the implant-trabecular bone junction. At both the interfaces, tensile stresses were greater than the compressive stresses. The implant in the type II model experienced a greater displacement when compared to the type I model. The magnitude of displacement increased in all the areas with the increase in the load applied. On loading the implant, the maximum strain was found at the implant-cortical bone junction, near the point of force application. Overall, the bone experienced greater tensile strain than compressive strain, which reduced gradually to the last layer of bone to a negligible amount. These strain values were correlated with the Frost s mechanostat Table 1, similar to the type I model. The correlation revealed that the strain values at implant-cortical bone interface and in the cortical bone were well within the optimum range for bone maintenance. The strain values in the trabecular bone and the implant-trabecular bone interface were significantly lower. According to the Frost s theory, such low strain values are not conducive for bone maintenance. Factor Table 1: Frost s mechanostat values Mechanical Disuse atrophy <200 Bone maintenance 200 to 2500 Physiologic hypertrophy 2500 to 4000 Pathologic overload > micron ( ) = 10 6 Peak load in microstrain ( E) The Journal of Indian Orthodontic Society, October-December 2012;46(4):

6 PS Vijayalakshmi et al VERTICAL LOADING OF THE IMPLANT FOR INTRUSION Implant in Cortical Bone: Type I Model The vertical force, applied to the implant to cause intrusion, created areas of greater tensile stresses than compressive stresses. The implant, cortical bone and the junction between implant and bone experienced greater tensile than compressive stresses,unlike the oblique loading, where the implant experienced greater compressive stresses than tensile stresses. On application of vertical force to the implant, the implant showed a very negligible amount of displacement. This displacement was very minimal in the range of to mm. Vertical loading of the implant created an area of maximum strain at the junction of the implant and the bone, concentrating at the point of force application. The maximum principal strain further increased as the magnitude of force was increased. The strain values gradually decreased in the deeper layers of the bone (Table 1). Implant in Cortical and Trabecular Bone: Type II Model The implant experienced the same magnitude of stresses as the type I model. The concentration of the stresses was seen at the neck of the implant, with maximum tensile stress at the point of force application. At the junction of implant and cortical bone, the stresses were slightly lower than the type I model. The cortical bone experienced similar compressive and tensile stresses when compared to the type I model, with tensile stresses were greater than the compressive stresses. Highest tensile stresses were concentrated at the implantcortical bone junction. The trabecular bone experienced lower stresses when compared to the cortical bone. Both the tensile and the compressive stresses were in the same range. Greater concentration of both tensile and compressive stresses was seen at the corticotrabecular junction. The implant in the Type II model displaced to the same extent as the Type I model. The cortical bone showed displacement slightly greater than the Type I model in the range of to mm with maximum displacement at the implant-cortical junction.the trabecular bone displaced to a negligible amount in the range of to mm. On loading the implant, the maximum strain was found at the implant-cortical bone interface, similar to the type I model. Overall, the bone experienced greater tensile strain than compressive strain, which reduced gradually to the last layer of bone. ORTHOPEDIC LOADING OF THE IMPLANT Relatively heavy forces (400, 500 and 600 gm) were applied on the implant in a mesial (sagittal) direction simulating the orthopedic force in maxillary protraction. Implant in Cortical Bone: Type I FE Model On loading the implant with orthopedic forces (Fig. 5), the implant experienced greater tensile and compressive stresses when compared to the previous two orthodontic loadings. These stresses were concentrated at the point of force application. In contrast, the minimum principal compressive stresses were greater than the maximum principal tensile stresses. The bone experienced greater compressive and tensile stresses compared to the orthodontic loading. The maximum principal tensile stress was greater than the minimum principal compressive stress.the interface experienced greater stresses compared to the previous two orthodontic loadings. Here, the compressive stresses were greater than the tensile stresses in contrast to the overall stress distribution in the bone. Displacement of the implant: On application of orthopedic force to the implant, the implant showed a greater amount of displacement when compared to the previous two orthodontic loadings. This displacement was in the range of to mm. On application of orthopedic force to the implant, the bone experienced maximum compressive and tensile strain. The junction between the implant and the cortical bone experienced greater strain compared to the deeper layers of bone. Similar to all the previous loads, these strain values were compared with the Frost s mechanostat Table 1, which revealed that all the three orthopedic loads resulted in strain in the range of physiologic bone maintenance. Implant in Cortical and Trabecular Bone: Type II FE Model The implant experienced greater tensile and compressive stresses compared to the type I implant. i. The cortical bone also experienced greater tensile and compressive stresses when compared to the type I model. Similar to the previous model, the tensile stresses were greater than the compressive stresses. ii. The trabecular bone experienced lower stresses compared to the cortical bone. Implant-cortical bone junction experienced greater stresses when compared to the implant-trabecular bone junction. Displacement of the implant: The implant displaced to a greater extent than the type I implant. This displacement was in the range of to mm. The strain values were comparatively higher than the type I model. Similar to all the previous loads, the values obtained were compared with the Frost s mechanostat Table 1. Strain values in the cortical bone and implant-cortical bone interface were sufficient for bone maintenance, while the strain values in trabecular bone and implant-trabecular interface were significantly less, which would probably result in atrophy of bone according to Frost s mechanostat theory. 180 JAYPEE

7 JIOS Finite Element Analysis of Stress and Strain Distribution in the Bone around the Implants used for Orthodontic Anchorage DISCUSSION Biomechanical influences on bone structure play an important role in the longevity of bone around implants. 3 Bone tissue is known to remodel its structure in response to mechanical stress. Low stress levels around an implant may result in poor connection with bone or bone atrophy. On the other hand, abnormally high stress concentrations in the supporting tissues can result in pressure necrosis and subsequently in implant failure. 3 The present study was aimed at analyzing the deformation of bone surrounding a mini-implant in response to different force magnitudes. COMPARISON WITH OTHER STUDIES Melsen and Verna (2005) 21 evaluated the load transfer from the Aarhus miniscrew on the bone, and the influence of different cortical bone thicknesses and the underlying trabecular bone density, on applying a mesially directed force of 50 gm. The results obtained from our study matched with their study. The primary component of the load transfer was seen at the first revolution of the miniscrew thread within the cortex. Authors found that on decreasing the thickness of the cortical bone, the peak strain values reached the pathological overload window (Frost s mechanostat theory). But in our study, the thickness of the cortical bone was kept constant with the larger part of the implant being surrounded by the cortical bone. Hence, the cortical bone experienced greater strain values than the underlying trabecular bone. At this thickness of the cortical bone, the peak strain values were in the optimal range of bone maintenance. Chen, Esterle and Roberts (1999) 31 investigated the mechanical environment of cortical bone adjacent to retromolar endosseous implants used for orthodontic anchorage in a coordinated histomorphometric and finite element study. The authors studied the change in the stress pattern in the bone before and after placement of implants. They noticed a strong change in the stress pattern in the bone after implantation, wherein the stresses increased by 2 to 4 times on orthodontic loading. It was observed that on loading the implant by an anterior force, compressive stresses were found on the buccal and distal sides, and tensile stresses were found on the lingual and mesial sides. The results obtained in our study were similar to the above study. Their coordinated histomorphometric study revealed that the high areas of stress were associated with high remodeling activity of the bone. Our study also showed similar areas of high stresses distribution around the first few threads of implant. CLINICAL IMPLICATIONS From the results of the present study, following clinical implications could be derived: 1. The mini-implants would efficiently resist oblique loading, simulating anterior intrusion and retraction. The loads of 200 and 250 gm produced strain in the optimal range of bone maintenance. These devices would serve as a reliable means of absolute anchorage as per the initial stress pattern. 2. The use of these mini-implants for the purpose of orthopedic loading is questionable, since the stress values experienced by the implant are quite high. Even though the strain values experienced by the bone were in the range of optimal maintenance, the site of placement of the implants and the timing become crucial factors in deciding the usage of these implants for orthopedic loading. The ideal time for orthopedic protraction of maxilla is during the mixed dentition phase. The miniscrew can loosen, even after having been initially fixed, if an adjacent deciduous tooth is exfoliating. There can also be a risk of injuring the underlying permanent tooth bud. 3. In the implant, the most critical area is its neck, where there is maximum stress concentration, and the marginal bone (cervical margin) which surrounds it. Thus, this area should be preserved clinically in order to maintain the bone-implant interface structurally and functionally. 4. It was seen in our study that the implant tipped to a very negligible amount in the direction of the load applied, like a tooth tipping on application of load. But the displacement seen was very negligible and clinically insignificant. 5. Based on the experience from our study, the following suggestions can be made for optimization of the implant design: a. The neck of the implant must be long enough to project away from the soft tissues, so that any attachments placed on the implants do not impinge the mucosa. The inflammation of the overlying soft tissue and/or the marginal bone resorption can jeopardize the stability of the implant. b. The neck of the implant must be sturdy enough, since the maximum stress concentration occurs at the neck of the implant. If the implant is not strong in this region, it may affect the integrity of the implant. c. When using these mini-implants for orthodontic loading, it is advisable to take all the necessary precautions to place the implant as much in the cortical bone as possible. The reason is that the stress and strain values in the trabecular bone were very low, which would result in atrophy of the surrounding bone (as postulated in Frost s mechanostat principle). CONCLUSION From this study, it can be concluded that: 1. The mini-implants used in the present study efficiently resisted the oblique loading, which simulated intrusion and retraction of the anterior teeth. The loads of 200 and 250 gm produced strains in the optimal range of bone maintenance. The Journal of Indian Orthodontic Society, October-December 2012;46(4):

8 PS Vijayalakshmi et al 2. The use of these mini-implants for the purpose of orthopedic loading is questionable. 3. The implant tipped on loading in all the three clinical situations simulated in the present study. But this displacement was to a negligible amount and was clinically insignificant. 4. Both the types of FE models showed the area with the highest stress and strain to be around the neck of the implant and the surrounding bone at the cervical margin. This finding is clinically important in order to preserve the bone-implant interface functionally and structurally in this area. 5. To obtain an optimal biomechanical response, the implant should preferably be placed entirely in the cortical bone (however, this may not always be feasible clinically). The neck of the implant should be sturdy enough, and the head of the implant should not produce any kind of irritation to the overlying mucosa. REFERENCES 1. Roberts WE, Helm FR, Marshall KJ, Gongloff RK. 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