Summer Workshop of Applied Mechanics. Influence of implant length and diameter on stress distribution

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1 Summer Workshop of Applied Mechanics June 2002 Department of Mechanics Faculty of Mechanical Engineering Czech Technical University in Prague Influence of implant length and diameter on stress distribution Lucie Himmlová, MD, PhD 1, Taťjana Dostálová, MD, PhD 1, Alois Kácovský, Dipl. Ing. 2, and Svatava Konvičková, Dipl. Ing., PhD 2 1 Institute of Dental Research 1. MF GMH Prague Vinohradská Prague 2 Czech Republic 2 Czech Technical University in Prague Faculty of Mechanical Engineering Laboratory of Biomechanics of Man Technická Prague 6 Czech Republic vuspraha@mbox.vol.cz Klíčová slova: dental implants, length diameter, stress distribution, Finite Element Analysis Abstract Statement of problem. The chewing force acting on dental implants causes mechanical stress of the bone surrounding the implants. In some cases, this stress can be inadequate and in consequence, causes bone defects and the failure of implants. Purpose. Mathematical simulation of stress distribution around the implants was used to find the ideal length and diameter of implants. Material and methods. Computations were made by the finite-element method using 3D models of implants over a range of diameters and lengths. 52

2 Results Maximum stress area was located around the implant neck. The implant diameter was the most critical factor influencing the stress values. Stress decrease was the greatest between diameters of 3.6 mm and 4.2 mm (almost 40%). The implant length also had a certain effect; it was not, however, as pronounced as for the diameter. Conclusions Within the limitations of this study, the implant diameter positively influenced the distribution of chewing force and decreased the maximum stress as a result of favorable distribution of this force. Clinical implications. Mathematical analysis indicates that implant diameter is more of a diagnostic risk factor for overloading than implant length, therefore, wider implants should be used where allowed by anatomy. Implants with 4.2 mm diameter have a certain advantage compared with 3.6 mm ones. The presented method, used in combination with Carter s hypothesis, may help clinicians to improve their planning of an implant treatment. Introduction In clinical practice, two periods of an implant failure can be distinguished. The first occurs within a short time post insertion of an enosseal part, the second takes place after an osseointegrated implant is loaded by forces during chewing. The failure in the first period mainly occurs due to an inflammation; while failure in the second period is predominantly caused by unequal resorption and redeposition during physiologic bone turnover, and leads to the loss of the bone in the neck area. 1 It has been suggested that this could be caused by the long-lasting loading of an implant and surrounding bone by an inappropriate magnitude and/or direction of the acting chewing force. 1,2,3,4 The implant size (as well as shape and surface modification) influences the area of possible retention in the bone. Several factors such as occlusion, chewing force, implant geometry, number of implants and their position within the prosthesis, etc., affect forces acting on the bone adjacent to implants. 2 Healing of tooth extraction wounds, the long-lasting wear of removable dentures, both those accompanied by reduction of alveolar bone and some anatomical structures (e.g. fossa canina, anthrum, nasal cavity or mandible canal), may force the placement of implants into unfavorable positions. These factors limit the size of implants that are used, and may cause their length and/or diameter to be inadequate for effective distribution of the chewing force. Applied mechanical force deforms the structural arrangement of the bone. The force divided by unit area is defined as stress. The ratio between the length of an object under stress and its original dimension is the strain. 1 The response of the bone to the mechanical stress was first defined by Wolff in Carter 3 described a hypothesis that the remodeling of cortical bone is the response to mechanical loading. In 53

3 this hypothesis, high strain rates (around 3000 microstrains) initiate a hypertrophic response; low rates (under 2000 microstrains) lead to calcium loss and bone atrophy, and rates above 4000 microstrains cause site-specific microdamage exceeding the mechanical threshold of bone in as few as 5000 chewing cycles. 1 Bone with dental implants has a greater turnover rate compared to the normal setting with teeth. This may be due to a repair stimuli caused by compressive and tensile loading damage in tissues adjacent to the implants. 5,1 Isidor 6 claimed that excessive force acting on the implant causes bone decrease in the surrounding area, followed by fibrointegration and the possible release of the implant from the bone socket. From clinical practice it is known, that loaded implants lose from 0.5 to 1.0 mm of alveolar bone margin in the first year after loading and subsequently approximately 0.1 mm per year. 7,1 Sometimes, implants are lost within a few years. These findings are in accordance with recent 3D mathematical models of dental implants under nonaxisymmetric loading, which indicates maximum stress around the implant cervix. 8,9,4 This study was performed with the objective to compare the influence of the diameter and the length of an implant on the stress distribution around the implant. For this purpose, situations where single cylindrical dental implants of various diameters and lengths are optimally inserted into the molar part of mandibles were modeled using 3D graphics. The distribution of the stress (the force divided by a unit of area) on the interface between the implant and the bone socket after loading by averaged chewing force was computed by the finite-element method (FEM). The influence of implant length with a diameter of 3.6 mm was calculated for lengths of 8,10,12,14, 16,17, and 18 mm. To model the influence of the diameter, the stress was calculated for a 12 mm-long implant with diameters of 2.9 mm, 3.6 mm, 4.2 mm, 5.0 mm, 5.5 mm, 6.0 mm and 6.5 mm. The reference (100 %) implant for comparison was 12 mm long and 3.6 mm in diameter. These dimensions were selected as the most frequently used in practice. 1 Material and methods 1.1 Method The finite-element method was used to analyze stress around cylindrical dental implants inserted in the molar part of the mandible. This method is an analytical tool that is widely used for mathematical modeling of real bodies. The computations were performed for the implant diameter and length variations mentioned above. To generate this 3D model, the new pre- and post-processor ABAQUS CAE 1.0 was used. This processor enables a parametric definition of the geometry and the system. It is a part of the FEM software of ABAQUS (HKS Inc., USA), which enable one to describe a group of properties characterizing modeled implants. The parameter is used to investigate other subject properties and behaviors as its function. The pre- and 54

Figure 1: Simplified 3D model of implant inserted into the bone with mesh generated in ABAQUS CAE 1.0. Arrows represent the forces of 17.1 N, 114.6 N and 23.

4 Figure 1: Simplified 3D model of implant inserted into the bone with mesh generated in ABAQUS CAE 1.0. Arrows represent the forces of 17.1 N, N and 23.4 N, in a vestibulo-oral direction, an axial direction and a disto-mesial direction, respectively, acting on the center of the upper surface of the abutment at a distance of 4.5 mm from the upper margin of the bone in the 3D non-axisymmetric loading scheme. post-processing and computations were carried out on the Silicon Graphics Indigo II work station of the Faculty of Mechanical Engineering Czech Technical University (CTU) using SGI Power Challenge L and IBM SP at the Center for Intensive Computation of CTU. The computation time demand for each single size implant variety was approximately 12 hours. 1.2 Models Geometrical 3D models of the implant and part of the mandible, as well as material properties of the bone, were simplified. Simplifications used to reduce the computer time and memory did not affect the accuracy of the computation of the proposed parametric study. 10 3D models of commonly available submerged titanium solid cylindrical dental implants without threads (IMZ implants, similar to ITI Bonefit, etc.) were simplified to a cylinder without any anti-rotation elements. These simulated implants were inserted into the model of the bone in a vertical position (Fig. 1). The models were made for the following sizes: diameter of 3.6 mm - lengths of 8,10,12,14,16,17 and 18 mm; length 12 mm - diameters of 2.9, 3.6, 4.2, 5.0, 5.5 and 6.5 mm. The implant surface was modeled with a bioactive coating providing an immovable junction between the implant and the bone. For this reason the TIED contact in ABAQUS software was chosen, i.e., firm connection between contact bodies (implant and bone socket surfaces). The molar part of mandible was simplified to a prism with a quadrangular base and irregular octagonal walls (Fig. 1). The mesial and distal borders of the model were constrained so that the displacement of nodes in all directions was equal to 0. The bone was considered a homogeneous, isotropic material with the character of cortical bone in the whole volume. 55

(A) (B) Figure 2: Distribution of Von Mises stress around implants with different diameters computed by FEM. The view is from the inside of the bone socket.

The area of maximum stress is wider in the case of an implant 2.9 mm in diameter. The values of maximum stress given by scales are also higher for B).

5 (A) (B) Figure 2: Distribution of Von Mises stress around implants with different diameters computed by FEM. The view is from the inside of the bone socket. The red-colored area represents the region of maximum stress - around the neck of the implant. A) model computed for an implant 2.9 mm in diameter. B) model computed for an implant 6.5 mm in diameter. The area of maximum stress is wider in the case of an implant 2.9 mm in diameter. The values of maximum stress given by scales are also higher for B). The implant and bone were modeled as consisting of elements, depending on the implant size. 1.3 Loading All models were loaded with forces of 17.1 N, N and 23.4 N, in a vestibulo-oral direction, an axial direction and a disto-mesial direction, respectively (Fig. 1). This 3D loading acted on the center of the upper surface of the abutment at a distance of 4.5 mm from the upper margin of the bone. The force magnitudes, as well as the acting point, were chosen with respect to the measurement of Mericske-Stern Computation The reduced von Mises stress was computed and values for the three most stressed elements for each alternative of the implant diameter and length were averaged. These averaged values were compared with those of the reference implant with a diameter of 3.6 mm and a length of 12 mm. The obtained relative stress data were used to determine its dependence on both the diameter and the length of the implant. 2 Results The results of the FEM computation depend on many individual factors (material properties, boundary conditions, interface definition, etc.) and also on the overall ap- 56

(A) (B) Figure 3: Distribution of Von Mises stress around implants of different length, A) model computed by FEM for an implant 8 mm in length and 3.6 mm in diameter.

The red-colored area represents the locality where the maximum stress acts. There is only a small difference in the area affected by the maximum stress for the short A) and long B) implant.

6 (A) (B) Figure 3: Distribution of Von Mises stress around implants of different length, A) model computed by FEM for an implant 8 mm in length and 3.6 mm in diameter. B) model computed for an implant 17 mm in length and 3.6 mm in diameter. The same view as Fig. 2 - from inside of the bone socket. The red-colored area represents the locality where the maximum stress acts. There is only a small difference in the area affected by the maximum stress for the short A) and long B) implant. Note that values are in a similar range. proach to the model. It is apparent that the presented model is only an approximation of reality, with, however, required degree of accuracy. 2.1 Stress distribution The analysis showed an uneven stress distribution inside the socket around the loaded implants (Fig. 2 A,B, 3 A,B). The elements exposed to maximum stress were located around the neck of the implant on the mesio-lingual rim of the bone socket (area indicated by red color in Fig. 2 and 3). This location was the same for all implant sizes. 2.2 Implant diameter A comparison of the areas with maximum stress for implants of the same length but different diameter showed surprisingly dramatic differences. As shown in the example of the 2.9 mm diameter implant (Fig. 2A) and the 6.5 mm diameter implant (Fig. 2B), the area of maximum stress is not only reduced, but the actual values computed for the same loading are smaller (note the scale in the figures). The plotting of averaged (from the three most stressed elements) related von Misses stress values for implant diameter varying from 2.9 mm to 6.5 mm showed an exponential regression curve, indicating dramatic influence of the implant diameter on stress in the bone (Fig. 4). It is interesting that the relative stress acting in the bone around the implant 4.2 mm in diameter was smaller by almost 40% than for the reference implant (diameter 3.6 mm). Further stress reduction for the 5.0 mm 57

7 Figure 4: The relations between the relative values of stress and the implant diameter. The stress decrease is the greatest between diameters of 3.6 mm and 4.2 mm (almost 40%). Further stress reduction for the 5.0 mm implant is only about 10%. implant was only an additional 10% and continued to decrease for larger diameters. Using a 6.5 mm diameter implant enables the maximum values of stress to be reduced by almost 70%. 3 Implant length The computer model of stress distribution around implants of the same diameter (3.6 mm) but of different length showed a substantially milder effect of the length. As exemplified by the case of implants 8 mm and 17 mm in length (Fig 3A and B, respectively), there is only a small difference in the area affected by maximum stress, and the values are almost in a similar range. The relation between averaged (from the three most stressed elements) related von Misses stress values and the implant length showed, as expected, a similar curve as in the case of variable diameters, but surprisingly, there is a visibly smaller effect of the implant length on stress in the bone indicated by a less steep curve (Fig. 5). The relative stress acting in the bone around the implant 17 mm in length was smaller of only 30% than for the reference implant (length 12 mm). As shown in the example of the 8 and 17 mm long implants, there is a difference of only 40% (Fig 3A and B, respectively). 4 Discussion The finite element method is one of the most frequently-used methods in stress analysis in many branches of industry and science. In experimental medicine, it is used for the analysing hip joints, knee prostheses, dental implants 8,9,4, stents in angiosurgery, 58

8 Figure 5: The relations between the relative values of stress and the implant length. The exponential regression curve is less steep than for the implant diameter shown in Fig. 4. The difference between values for 8 and 17 mm long implants is only about 40%. etc. The application of a 3D model with the non-symmetric loading by the chewing force on a dental implant resulted in a more satisfactory modeling of the real state than that achieved with 2D models used in other studies. The parametric model used in this study enable us to compare implants of various sizes. However, the absolute values of stress can not be related to results computed under different conditions. The simplification of the model, e.g., the implant in the shape of a cylinder rather than a screw or other shapes commonly used in clinical practice and the simplification of material properties enabled the required computer time to be reduced without affecting the purpose of this study to establish relative importance of the implant length and diameter. The results of this study complement the already-published facts that stress distribution in the bone around the implant depends on the shape and the size of the enosseal part. 2,4 However, the implant diameter was found to be more important than its length, probably due to the distribution of the chewing force over a wider area in the case of implants with a bigger diameter. It is known from clinical experience that it is not always possible to insert the implants into a place that is favorable from the loading point of view. Carter s hypothesis 3 claims the bone strain above 3000 microstrains to be inconvenient for the bone, and, above 4000 microstrains to cause local overloading followed by bone loss in the locations of the acting force. The values obtained by computer-assisted simulation in this parametric study for size variations of cylindrical dental implants cannot be directly compared with those of Carter s hypothesis due to the simplicity of our model. However, the location of zones with higher stress around the implant neck may indicate a danger of overloading in this area, as all size variations found here display maximum values of stress. The elements exposed to maximum stress were located at places to which most of non-axial chewing force was transferred (i.e., forces 59

9 acting in vestibulo-oral and disto-mesial directions which work during grinding movements - in comparison with axial loading during chopping movements). This situation corresponds to non-parametric computerized models of loaded dental implants, where the utmost strain (and according to Carter s hypothesis this is where bone overloading occurs) acts in the surroundings of the implant neck. 4,8 Our findings support the recommendation for keeping a long-lasting stable bond between the implant and the bone bed in order to provide optimal axial loading, which does not overload the bone locally, in particular its alveolar margin. Generally, the assessment of the dental implants from physical, biological, and technological viewpoints enabled the time prognosis of implants in the oral cavity to be improved. These findings can help to increase the percentage of long-lasting successful implants. 5 Conclusion This simulation study showed that implant diameter positively influenced the distribution of chewing force and decreased the stress around the implant neck. The highest reduction of stress in comparison with the reference implant (100%, diameter 3.6 mm) was obtained for the diameter of 4.2 mm (a 40% decrease). From a biomechanical perspective, the optimum choice is an implant with the maximum possible diameter allowed by the anatomy. In this study, the impact of implant length was less notable. Acknowledgements This study was supported by the GACR grant No. 304/00/P048 and by Grant Agency Min. of Education of the CR grant No Bibliography [1] Wiskott HWA, Belser UC. Lack of integration of smooth titanium surfaces: a working hypothesis based on strains generated in the surrounding bone. Clin Oral Impl Res, 1999(10: [2] Akpinar I, Demirel F, Parnas L, Sahin S. A comparison of stress and strain distribution characteristics of two different rigid implant designs for distalextension fixed prostheses. Quintessence Int., 1996(27:

10 [3] Carter DR, van der Meulen MCH, Beaupré GS. Mechanical factors in bone growth and development. Bone, Supplement, 1996(18(1):5S-10S. [4] Meijer HJA, Starmans FJM, Steen WHA, Bosman F. Loading conditions of endosseous implants in an edentulous human mandible: a three-dimensional, finite-element study. J Oral rehab, 1996(23: [5] Roberts WE, Turley PK, Brezniak N, Felder PJ. Bone physiology and metabolism. J Calif Dent Assoc 1987(15(10): [6] Isidor F. Loss of osseointegration caused by occlusal load of oral implants. A clinical and radiographic study in monkeys. Clin Oral Impl Res, 1996(7: [7] Malevez CH, Hermans M, Daelemans PH. Marginal bone levels at Branemark system implants used for single tooth restoration. The influence of implant design and anatomical region. Clin Oral Impl Res, 1996(7: [8] Lai H, Zhang F, Zhang B, Yang C, Xue M. Influence of percentage of osseointegration on stress distribution around dental implants. Chin J Dent Res, 1998(Dec; 1(3):7-11. [9] Holmes DC, Loftus JT. Influence of bone quality on stress distribution for endosseous implants. J Oral Implantol, 1997(23(3): [10] Teixeira ER, Sato Y, Akagawa Y, Shindoi N. A comparative evaluation of mandibular finite element models with different lengths and elements for implants biomechanics. J Oral Rehabil, 1998(Apr;25(4): [11] Mericske-Stern R, Piotti M, Sirtes G. 3-D in vivo force measurements on mandibular implants supporting overdentures. Clin Oral Impl Res 1996; 7:

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ISSN 2395-1621 Effect of Screw Profile on Stress Distribution Pattern of Dental Implants by FEA #1 RaiphaleGovind, #2 Shinde B.M. 1 govindaraiphale@gmail.com*1 2bharat.shinde@zealeducation.com 1 (M.E Student