Comparative Evaluation of Implant Designs: Influence of Diameter, Length, and Taper on Stress and Strain in the Mandibular Segment-A Three-Dimensional Finite Element Analysis.

INTRODUCTION: Success or failure of dental implants depends on the amount of stress transferred to the surrounding bone. Increased amount of loading to the bone through implant cause failure, whereas decrease in the amount of loading to the bone causes improved success rate of implants. Biomechanical interaction between implant and bone decides the long-term function or prognosis of dental implant system. AIM AND
OBJECTIVES: The aims of this study were to evaluate the influence of implant length and diameter on stress distribution, to understand the stress distribution around bone-implant interface, and to understand the response of bone under axial and non-axial loading conditions.
MATERIALS AND METHODS: Finite element three-dimensional mandibular model was made using cone beam computed tomography of patient with completely edentulous mandible, and in that model five posterior bone segments were selected. NobelReplace Select Tapered implants with diameters and lengths 3.5 × 10 mm, 4.3 × 10 mm, 3.5 × 11.5 mm, and 4.3 × 11.5 mm, respectively were selected and three dimensionally modeled using Creo 2.0 Parametric Pro/E software. Bone and implant models were assembled as 20 models and finite element analysis was performed using ANSYS Workbench v17.0 under axial and non-axial loads. RESULT: Under axial and non-axial loads, 3.5 × 10 mm implant showed maximum von Mises stress and strain in both cortical and cancellous bone whereas implant with diameter and length 4.3 × 11.5 mm showed minimum von Mises stress and strain in both cortical and cancellous bone.
CONCLUSION: In axial and non-axial loads, amount of stress distribution around implant-bone interface is influenced by diameter and length of implant in cortical and cancellous bone, respectively. Increased diameter of the implant produces the minimum stress in cortical bone. Increased length of the implant produces the minimum stress in cancellous bone.

INTRODUCTION

A key factor for the success or failure of a dental implant is the manner in which stresses are transferred to the surrounding bone. Load transfer from implants to surrounding bone depends on the type of loading, the bone–implant interface, the length and diameter of the implants, the shape and characteristics of the implant surface, the prosthesis type, and the quantity and quality of the surrounding bone.[12] The finite element analysis (FEA) is an upcoming and significant research tool for biomechanical analyses in biological research. It is an ultimate method for modeling complex structures and analyzing their mechanical properties. FEA has now become widely accepted as a noninvasive and excellent tool for studying the biomechanics and the influence of mechanical forces on the biological systems. The finite element method (FEM) is basically a numerical method to analyze stresses and deformations in the structures of any given geometry.[3] The structure is discretized into the so-called “finite elements” connected through nodes.[45] The type, arrangement, and total number of elements impact the accuracy of the results. FEA allows researchers to predict stress distribution in the contact area of the implants with cortical bone and around the apex of the implants in trabecular bone. The biomechanical load management is dependent on the nature of the applied force and the functional surface area over which the load is dissipated. The principal factors that influence the load transfer at the bone–implant interface include implant geometry, which includes diameter and length; thread pitch; shape; depth in the case of threaded implants; the type and magnitude of loading; implant material properties; quality and quantity of the surrounding bone; type of loading in prosthesis; surface structure; surgical procedures; and the nature of the bone–implant interface.[67] FEA is capable of providing detailed quantitative data at any location within the mathematical model. Thus, FEA has become a valuable analytical tool in implant dentistry.[8] Stress analysis of dental implant is very necessary for the investigation of bone turnover and maximum anchorage success. Incorrect loading or overloading may lead to distributed bone turnover and consequent implant loss. Previous literature have shown that the cortical bone–implant interface has a higher concentration of stress, and implant having greater diameter produces minimum stress.[910] Bone quality also influences the long-term success of implant treatment; poor bone quality reduces the success rates. Load transfer to bone–implant interface depends on number, position, design, geometry of the implant, abutment connection, and quality and quantity of surrounding bone. Because clinical determination of stress and strain distribution in bone is not possible, an alternative technique should be used. So here FEA, which is a reliable method, is used to determine the information about stress and strain in implant–bone structure.[11]

Aim

The aims of this study were to evaluate the influence of variable length and diameter of implant on stress distribution in cortical and cancellous bone, to understand the pattern of stress and strain distribution around implant surface with variable length and diameter under axial and non-axial loading conditions, and to understand the response of cortical and cancellous bone, under axial and non-axial loading conditions.

MATERIALS AND METHODS

NobelReplace Select Tapered implants with sizes 3.5 × 10 mm, 4.3 × 10 mm, 3.5 × 11.5 mm, and 4.3 × 11.5 mm, and posterior mandibular segment (five regions) were selected using cone beam computed tomography (CBCT) scan. Cortical bone, cancellous bone, and implants were modeled using Creo 2.0. Twenty model assemblies were analyzed under FEM using ANSYS Workbench 17.0. Mechanical properties are shown in Table 1, contact types between the models are given in Table 2, and the forces applied in the abutment are given in Table 3. The models were subjected to axial (load 1) 100 N, non-axial buccolingual (load 2) 50 N, and non-axial mesiodistal (load 3) 50 N. From these loads, von Mises stress and strain values were evaluated. For statistical analyses, the four implants were grouped as G1, G2, G3, and G4, respectively. analysis of variance was used as statistical test.

Table 1

Mechanical properties of different materials used in the model

Material	Young’s modulus (ε) (MPa)	Poisson’s ratio (δ)	Reference
Cortical bone	13,000	0.30	[919]
Cancellous bone	690	0.30	[919]
Implant (titanium)	102,000	0.35	[919]

Table 2

Contact type between the three-dimensional models

Materials	Cortical bone	Cancellous bone	Implant
Cortical bone	—	Bonded	Frictional
Cancellous bone	Bonded	—	Frictional
Implant	Frictional	Frictional	—

Table 3

Load (force) and magnitude

Load	Magnitude
Axial	100 N
Non-axial (Buccolingual)	50 N
Non-axial (Mesiodistal)	50 N

The material properties applied to the cortical bone model, cancellous bone model, and implant model stress distribution pattern in cortical and cancellous bone. the strain formation in cortical and cancellous bone. strain formation in implant.

The material properties applied to the cortical bone model, cancellous bone model, and implant model

Stress distribution pattern in cortical and cancellous bone

Strain formation in cortical and cancellous bone

Strain formation in implant

RESULTS

Under load 1 axial (100 N) at cortical bone, the significant difference in the mean values of stress and strain was found among the groups G1, G2, G3, and G4, and their P value was greater than 0.05. In cortical bone, stress and strain distribution was influenced by diameter of the implant than the length and taper, so diameter factor was mainly taken into consideration. It was found from the analysis that G1 is having greater stress and strain than G2, and G2 is having lesser stress and strain than G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G2 and G4 are having same diameter, there is lesser significant difference in stress and strain between G2 and G4. G3 shows greater stress and strain than G4; hence, it is concluded that G2 and G4 are most effective than G1 and G3, because of greater diameter of G4 comparing to G1 and G3. Mean stress value in cortical bone was shown in Table 4. In coronal part, significant difference in the mean stress and strain among the four groups was found as their P value was less than 0.05. In cancellous bone, stress and strain distribution was influenced by diameter, length, and taper of implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length. G2 shows greater stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G2 are having same length, there is a lesser significant difference in stress and strain between G1 and G2. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3, because of greater diameter and lesser length of G4 comparing to G1 and G3. In cancellous bone, apical part shows more stress and strain than coronal and middle part. Mean stress and strain distribution under this was pictorially represented in Graph 1, respectively. In coronal part, significant difference in the mean stress and strain among the four groups was found as their P value is less than 0.05. Similarly, significant difference in the mean stress and strain was found among the groups G1, G2, G3, and G4 as their P value is less than 0.05 at middle part as well as in apical part of implant. In implant surface, stress and strain distribution was influenced by diameter in coronal part, length, and taper in the middle and apical part of the implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length. G2 shows lesser stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3, because of greater diameter and greater length of G4 comparing to G1 and G3. In implant surface, coronal part, apical part, and middle part show uniform distribution of stress and strain. Mean stress and strain distribution under this was pictorially represented in Graphs 2 and 3, respectively.

Table 4

Mean von Mises value stress value in cortical bone

Group	Mean load 1	Mean load 2	Mean load 3
G1	4.342	5.889	2.404
G2	3.330	4.782	1.458
G3	4.090	5.8	2.484
G4	2.812	4.266	0.926

Graph 1

Mean stress values in cortical bone—load 1 axial (100 N)

Graph 2

Mean stress values in cancellous bone—load 1 axial (100 N)

Graph 3

Mean stress values in implant—load 1 axial (100 N)

Under load-2 non-axial buccolingual (50 N) at cortical bone, the significant difference in the mean values of stress and strain was found among the groups G1, G2, G3, and G4 and their P value was greater than 0.05. In cortical bone, stress and strain distribution was influenced by diameter of implant than length and taper, so diameter factor was mainly taken into consideration. It was found from the analysis that G1 is having greater stress and strain than G2, and G2 is having lesser stress and strain than G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G2 and G4 are having same diameter, there is lesser significant difference in stress and strain between G2 and G4. G3 shows greater stress and strain than G4; hence, it is concluded that G2 and G4 are most effective than G1 and G3, because of greater diameter of G4 comparing to G1 and G3. Mean stress and strain distribution under this was pictorially represented in Graph 4, respectively. In the coronal part, significant difference in the mean stress and strain among the four groups was found as their P value is less than 0.05. Mean stress value was pictorially represented in Graph 3. In cancellous bone, stress and strain distribution was influenced by diameter, length, and taper of implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length. G2 shows greater stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G2 are having same length, there is a lesser significant difference in stress and strain between G1 and G2. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3, because of greater diameter and greater length of G4 comparing to G1 and G3. Mean stress value of cancellous bone was shown in Table 5. In cancellous bone, apical part shows more stress and strain than coronal and middle part. Mean stress and strain distribution under this load was pictorially represented in Graph 5, respectively. In coronal part, significant difference in the mean stress and strain among the four groups was found as their P value was less than 0.05. Similarly, significant difference in the mean stress and strain was found among the groups G1, G2, G3, and G4 as their P value was less than 0.05 at middle part as well as in apical part of implant. In implant surface, stress and strain distribution was influenced by diameter in coronal part, length, and taper in middle and apical part of implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length. G2 shows lesser stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3, because of greater diameter and greater length of G4 comparing to G1 and G3. In the implant surface, coronal part shows more stress and strain than middle and apical part. Mean stress and strain distribution under this was pictorially represented in Graph 3, respectively. In cortical bone, stress and strain distribution was influenced by diameter of implant than length and taper, so diameter factor was mainly taken is taken into consideration. It was found from the analysis that G1 is having greater stress and strain than G2, and G2 is having lesser stress and strain than G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G2 and G4 are having same diameter, there is lesser significant difference in stress and strain between G2 and G4. G3 shows greater stress and strain than G4; hence, it is concluded that G2 and G4 are more effective than G1 and G3 because of greater diameter of G4 comparing to G1 and G3. In coronal part, significant difference in the mean stress and strain among the four groups was found as their P value was less than 0.05. In cancellous bone, stress and strain distribution was influenced by diameter, length, and taper of implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length, G2 shows greater stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G2 are having same length, there is a lesser significant difference in stress and strain between G1 and G2. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3 because of greater diameter and greater length of G4 comparing to G1 and G3. In cancellous bone, apical part shows more stress and strain than coronal and middle part. Mean stress and strain distribution under this load was pictorially represented in Graph 4, respectively. In coronal part, significant difference in the mean stress and strain among the four groups was found as their P value was less than 0.05. Similarly significant difference in the mean stress and strain was found among the groups G1, G2, G3, and G4 as their P value was less than 0.05 at middle part as well as in apical part of implant. In implant surface, stress and strain distribution was influenced by diameter in coronal part, and length and taper in middle and apical part of the implant. It was found from the analysis that G1 is having greater stress and strain than G2 because of lesser diameter of G1 than G2 but same length. G2 shows lesser stress and strain than G3 because of lesser length of G2 comparing to G3. As G1 and G3 are having same diameter, there is a lesser significant difference in stress and strain between G1 and G3. As G3 and G4 are having same length, there is lesser significant difference in stress and strain between G3 and G4. G2 shows greater stress and strain than G4 because of lesser length of G2 comparing to G4; hence, it was concluded that G4 is most effective than G1, G2, and G3 because of greater diameter and greater length of G4 comparing to G1 and G3. In the implant surface, coronal part shows more stress and strain than middle and apical part.

Graph 4

Mean stress values in cancellous bone—load 2 buccolingual (50 N)

Table 5

Mean von Mises value stress value in cancellous bone and implant

	Groups	Cancellous bone			Implant surface
		Mean load 1	Mean load 2	Mean load 3	Mean load 1	Mean load 2	Mean load 3
Coronal part	G1	0.634	0.786	1.234	8.670	24.582	30.224
	G2	0.402	0.346	0.516	6.466	11.218	19.912
	G3	0.438	0.776	1.156	8.57	19.71	32.554
	G4	0.354	0.244	0.45	5.24	12.916	18.726
Middle part	G1	1.474	0.808	1.712	9.778	16.018	24.666
	G2	0.94	0.680	1.45	6.08	5.98	13.05
	G3	0.836	0.630	1.128	10.008	16.354	23.9
	G4	0.976	0.388	0.886	6.296	6.572	14.494
Apical part	G1	6.406	1.062	3.418	9.368	3.536	5.034
	G2	4.338	0.958	2.138	6.468	2.514	2.272
	G3	5.974	1.276	1.532	9.502	2.998	3.32
	G4	4.294	0.630	1.762	6.36	1.85	2.39

Graph 5

Mean stress values in implant—load 3 mesiodistal (50 N)

DISCUSSION

Clinical study reports that the predictable success rate of endosseous implants in many systems was greater than 90%.[12] Success or failure of implant and prosthesis is due to various biomechanical factors such as implant geometry, which includes diameter, length, and taper; surface topography such as thread pitch, type, and number; and magnitude and direction of masticatory force to implant through abutment and prosthesis. Para-functional force also plays a vital role in failure of implant treatment. Rangert et al.[13] also reported that patients with fractured implants were diagnosed to have para-functional activities. Petrie and Williams and Meijer et al.[14] observed that the length of implant had less influence on the amount of stress levels than diameter did. Apart from the geometrical factors of implant, other factors such as surface coating like hydroxyapatite and plasma spray also induce the healing period and osseointegration of bone–implant interface. FEM is used to analyze the complicated geometries under static and dynamic load conditions with certain limitations under various simulated environment types. Clinical measurement of stress and strain in bone and implant using strain gauge is impossible because of ethical reasons. Vertical force with certain magnitude from mastication induces axial forces and bending moments that result in stress gradients in the implant as well as bone.[291516] FEM is used to predict and measure the amount of stress and strain in contact area between the bone and implant and also in apical part of implant. In this study, three-dimensional FEA was performed rather than two-dimensional to visualize the stress/strain distribution in all axes. In finite element modeling, the structures modeled are simplified and simulated that reflects the reality. In this study, the segment of mandible and implant are modeled in a three-dimensional way.[17] The mandibular bone segments are simulated by taking CBCT and the scanned image segments are converted to three-dimensional models with particular dimensions. The segments of modeled cortical and cancellous bones are around 10–15 mm. In this study, the cortical bone, cancellous bone, and implant with abutment were assumed to be linearly elastic, homogenous, and isotropic. O’Mahony et al.[8] reported about the anisotropic properties of cancellous bone. However, the cortical and cancellous bones have anisotropic characteristics and regional stiffness variation; they are modeled isotropically because of nonavailability of sufficient scientific data to perform the analysis and difficulty in establishing principle axis geometry. For this analysis, the constraints at the end of the bone segment and the application of force on the top of the abutment are within the physiological limit. These simplifications result from limitations of the modeling procedure and thus give only a general insight into the tendencies of stress/strain variations under average conditions, without attempting to simulate individual clinical situations. Although this simplification could be expected to bring about quantitative changes in the results, it was not expected to influence them qualitatively. Therefore, it is advisable to focus on qualitative comparison rather than quantitative data from these analyses. Richter[1218] quantifies the vertical forces applied to dental implants during oral functions. Implants in the molar position that were fixed to a premolar with a prosthesis withstood maximum vertical forces of 60–120 N during chewing. Single molars and premolars carried maximum vertical forces of 120–150 N. Clenching in centric occlusion caused a load level of approximately 50 N for both natural and artificial abutments.[15] So in this study, 100-N force was applied as axial load and 50-N force was applied as buccolingual and mesiodistal load. This analysis shows that the stress/strain concentration is more at the coronal part of the implant and on the cortical bone; these results coincide with the previous studies and also with in vivo and in vitro clinical studies. The stress concentration is more in cortical bone because of higher modulus of elasticity ε = 13,000 MPa, which provides more rigidity and thus more capability to withstand higher stress. On axial loading, stress generated in G4 was comparatively less than that of G1, G2, and G3. This is due to greater diameter of G4 than G1 and G3. More the osseointegrated surface area better will be the stress distribution in the surrounding bone. Minimum amount of stress was developed during axial loading as compared to loading in non-axial direction. Baggi et al.[13] reported about the influence of implant diameter in stress distribution in cortical bone–implant interface. The probable reason could be that as the load is applied parallel to the long axis of the implant, the ability of the implant and cortical and cancellous bone to withstand stress increases. On buccolingual and mesiodistal loading conditions, less stress was shown by G4 than G1, G2, and G3; in cortical bone, this was due to lesser diameter of G4 than G1 and G3. The non-axial force is perpendicular to the long axis of implant; it will deform more when compared to a solid implant of greater diameter, thus causing generation of more stress in the cortical bone. The same reason is true for increased stress component in G1. There is a decrease in stress magnitude during axial loading in G4 due to increase diameter more stress was distributed among the implant and the cortical bone and thus, minimizes the load on cancellous bone, which is more susceptible to fracture because of its low modulus of elasticity. During non-axial loads, stress was found to be more in G1 on the lingual and distal sides. The reason is due to the direction of force perpendicular to the long axis of implant. Because of low modulus of elasticity of cancellous bone, the load-bearing capacity decreases while elasticity increases. Thus, more strain can be seen especially during horizontal loading. Von Mises strain value of cancellous bone during axial loading is less compared to the value obtained during horizontal loading even with the doubled the load, i.e., 100 N. This is because during axial loading, the stress was distributed to all sides of the cancellous bone, whereas in non-axial loading, stress concentration was distributed in one side of the cancellous bone, which is opposite to the direction of force. Irrespective of the direction and magnitude of loading, implant with abutment withstand maximum amount of stress compared to any other component of the model. The probable reason could be its high elastic modulus ε = 120,000 MPa, which is nearly nine times the elastic modulus of cortical bone ε = 13,000 Pa and nearly 173 times the elastic modulus of cancellous bone ε = 690 MPa. During axial loading, stress generated within the implant was least as compared to the stress generated during buccolingual and mesiodistal loading. The reason was that the direction of load along the long axis of the implant provides maximum cross-sectional area to withstand the stress. Loading of an implant fixed with an abutment in a horizontal direction induces a certain amount of deformation in the system and causes bending of the abutment. This bending of abutment decreases with increasing distance from the loading point. The displacement of the implant depends on the magnitude of bending of all components of the complete system including the bone, implant, and abutment. In mesiodistal loading, the resistance offered by the supporting bone was less than of buccolingual loading, so greater stress is seen the mesiodistal side. By this study, it is clear that implant with lesser diameter and length shows greater stress around the bone and implant. So diameter of the implant should be considered as an important factor for implant longevity.[4192021] Non-axial loading causes more stress around the implant and bone than axial loading, so it will lead to reduction of longevity or even failure of the implant-supported prosthesis. So planning of occlusion is an important criterion to improve the success rate by directing the axial loading during centric movements. Very minimal loading should be transferred to the implant and bone during eccentric movements by establishing minimal functional contact to avoid forces from non-axial direction. Even though FEM is the accurate and precise method for analyzing structures, this study had certain limitations. First, no movement was allowed between the implant and the bone during loading from different directions. The implant was also assumed 100% osseointegrated, which is never found in a clinical situation. This would alter forces transmitted to the supporting structures. Next the cortical bone, cancellous bone, and the implant were considered to be isotropic, and finally the static loads that are applied differed from the dynamic loading encountered during function.[22] Frictional coefficient factor is applied in the contact region between bone and implant, so the mathematical solver in workbench solves by assuming it as threaded implant in bone. FEA is based on mathematical calculations while living tissues are beyond the confines of set parameters and values because biology is not a computable entity. Therefore, FEA should not be considered as a sole means of understanding the behavior of a geometrical structure in a given environment.[21] Actual experimental techniques and clinical trials should follow FEA to establish the true nature of the biological system.

SUMMARY AND CONCLUSION

This study was carried out to determine the distribution of stress/strain around the implant, cortical bone, and cancellous bone. A three-dimensional FEM was used in this study. A geometric model of posterior mandibular region was generated using a computed tomography scan data. Four implants of different diameters and lengths 3.5 × 10 mm, 4.3 × 10 mm, 3.5 × 11.5 mm, and 4.3 × 11.5 mm were modeled and embedded in the section of bone, and material properties and boundary conditions were applied. Vertical load of 100 N and a horizontal load of 50 N from buccolingual and mesiodistal directions were applied on the abutment. The results were analyzed using von Mises and strain criteria. Despite the limitations of the methodology, the conclusions are as follows: By increasing the diameter of the implant, the stress distribution in the cortical bone can be decreased, which reduces the bone loss around the implant and optimal stress improves the lifetime of the implant. Increased length of the implant produces the minimum stress in the cancellous bone, which reduces the resorption of cancellous bone. In axial and non-axial loads, amount of stress distribution around the implant–bone interface is influenced by diameter and length of implant in cortical and cancellous bone, respectively. Increased diameter of the implant produces the minimum stress in cortical bone. In cancellous bone, stress distribution was more in coronal region irrespective of direction of force. Favorable distribution of stress and strain pattern occurs in axial loading condition. It was also concluded that axial loading of an implant appeared to be the favorable direction of loading and improved the longevity of implant-supported prosthesis.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.