International Journal of Oral Health Sciences

: 2015  |  Volume : 5  |  Issue : 2  |  Page : 80--86

The effect of cuspal inclination on stress distribution and implant displacement in different bone qualities for a single tooth implant: A finite element study

Subani Bedi1, Raison Thomas2, Rucha Shah2, Dhoom Singh Mehta2,  
1 Private Practitioner, New Delhi, India
2 Department of Periodontics, Bapuji Dental College and Hospital, Davangere, Karnataka, India

Correspondence Address:
Dr. Rucha Shah
Department of Periodontics, Bapuji Dental College and Hospital, Davangere - 577 004, Karnataka


Background: The aim of the present finite element study was to analyze effect of cuspal inclination on stress distribution and implant displacement in different bone densities for a single tooth implant. Materials and Methods: A three dimensional finite element model of mandibular molar section of the D1 bone (entirely cortical) and D4 bone (1 mm cortical shell with low density trabecular core) to receive an implant was constructed. Three ceramic crowns with cusp inclinations of 0 degree, 10 degree and 30 degree were modeled. A mechanical load of 202.23 N was applied at three different regions; the central fossa and 1- and 2-mm offsets horizontally from the center to the buccal side for the varying inclinations. The finite element analysis was performed and stress levels using von Mises stresses and maximum displacement (in mm) were calculated. Results: The maximum stress concentration in cortical bone was seen around the neck of the implant. There was favorable distribution of stresses during loading at the central fossa with maximum stress being 15.10 Mpa for 0 degree, which increased to 54.09 Mpa for 10 degree and 86.19 Mpa for 30 degree inclination at 2 mm offset. Higher stresses were generated in D4 than D1 bone density under all loading conditions. Conclusion: The occlusal topography plays an important role in stress distribution and may be helpful in preventing crestal bone loss. This phenomenon is more pronounced in poor quality bone. Therefore, proper occlusal morphology becomes a critical issue in poor quality bone for implant longevity.

How to cite this article:
Bedi S, Thomas R, Shah R, Mehta DS. The effect of cuspal inclination on stress distribution and implant displacement in different bone qualities for a single tooth implant: A finite element study.Int J Oral Health Sci 2015;5:80-86

How to cite this URL:
Bedi S, Thomas R, Shah R, Mehta DS. The effect of cuspal inclination on stress distribution and implant displacement in different bone qualities for a single tooth implant: A finite element study. Int J Oral Health Sci [serial online] 2015 [cited 2023 Mar 26 ];5:80-86
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A new era in oral rehabilitation began with the introduction of osseointegrated dental implants. High success rates and long term follow up of patients treated with osseointegrated dental implants have been reported for more than 20 years. Despite the high success rates reported to date, implant failures do occur. The biomechanical factors is considered as the most important cause of implant failure.[1]

Natural teeth are supported by periodontal ligament which help in buffering and absorption of the occlusal forces. Dental implants are more sensitive to occlusal loading, in which severe stress/strain directly leads to trauma or damage on the bony tissues.[2] On the other hand, inadequate transfer of the mechanical loading from the crown to the bone may reduce bone engagement, and thus lead to disuse atrophy of bone.[2]

The crown and abutment designs supported by dental implants, crown structure in particular can largely determine the biomechanical functional characteristics of an implant. The existing implant design objectives are still evolving towards maximizing occlusal function, minimizing overloading on implants and providing long term stability of prosthesis and implants.[3]

Bone quality is another significant factor in determining implant selection, primary stability and loading time.[4] Clinical success of dental implants is influenced by both the volume and density of available bone. Bone quality and quantity varies from site to site and from patient to patient. A study found higher survival rates for implants placed in bone of good quality and quantity, such as that found in the anterior region of the mandible.[5] Higher risk of failure also exist for implants placed in compromised cortical and trabecular bone such as that present in maxillary posterior region or in patients with osteoporosis.[6] Therefore, an accurate evaluation of bone structure is essential requisite prior to implant placement. Though the correlation of poor bone quality to implant failure has been well established, the precise relationship between bone quality and stress distribution is not adequately understood.[7]

Hence the aim of this study was to evaluate the effect of cuspal inclination on stress distribution and implant displacement in D1 bone (entirely cortical) and D4 bone (1 mm cortical shell with low density trabecular core) by means of finite element analysis.

 Materials and Methods

3-D model design

A 3-dimensional finite element model of a mandibular section of the bone with a tapered, threaded implant to receive a crown structure in relation to first molar area was constructed by using cone beam computed tomography scanner. Two different bone densities, D1 bone (entirely cortical) and D4 bone (1 mm cortical shell with low density trabecular core) were constructed as previously described by Misch.[8] The trabecular bone was assumed to be perfectly bonded with the cortical layer. The implant system used was based on a tapered Self-Thread Internal Hex Implant (EZ Hi-Tec, Israel) with the dimensions of 3.75 mm diameter and 10 mm length.

For the present study, three ceramic crowns with varying cusp inclinations were considered. Therefore, three models were created i.e. Model 1- with 30 degree cuspal inclination [Figure 1]a, Model 2- with 10 degree cuspal inclination [Figure 1]b, and Model 3- with 0 degree cuspal inclination [Figure 1]c.{Figure 1}

The three-dimensional finite element model corresponding to the geometric model was meshed by using Ansys Pre-processor (ANSYS version 14.0 software). The type of element suitable for this particular study was 10 noded tetrahedron element, which was assigned three degrees of freedom per node, namely translation in the x, y and z directions. The number of elements and nodes for each model are given in [Table 1].{Table 1}

Material properties

The cortical bone, cancellous bone and implant with abutment were presumed to be linearly elastic, homogenous and isotropic.[9] Although the cortical bone has anisotropic material characteristics and possesses regional stiffness variation, they were modelled isotropically due to the unavailability of sufficient data and difficulty in establishing the principal axis of anisotropy.[10] Two different bone densities were considered according to the classification by Misch.[11] These were Group 1 consisting of D1 Bone - entirely cortical (D1: >1250 HU) and group 2 consisting of D4 Bone - 1 mm cortical shell with low density trabecular core. (D4: 150 to 350 HU). The mechanical properties of the all components were taken from previous literature and are summarized in [Table 2].[7],[12]{Table 2}

Constraint and loads

A mechanical load of 202.23 N [12] was applied to the top of the crown at three different regions; the central fossa (load 1) and 1- (load 2) and 2-mm (load 3) offset horizontally from the centre to the buccal side for the varying inclinations [Figure 1]d.[12] These loads were perpendicular to the crown surface with inclinations of 0, 10 or 30 degrees from the vertical axis. The finite element analysis was performed with ANSYS version 14.0 Software. Maximum displacement (µm) in the implant-abutment complex and von Misses stresses which indicated the distribution of stress around implant in color coded maps evaluated for each loading condition.


The maximum von Mises stress distribution in both D1 bone density and D4 bone density were concentrated around the neck of the implant. One third of the stresses were transferred from implant to cortical bone in both D1 and D4 bone.

In D1 bone density, for 30 degree inclination of cusp the stresses ranged from 15.76 MP at the central fossa to 86.19 MPa at 2 mm offset horizontally. The maximum displacement was 0.007 mm at the central fossa and increased to 0.06 mm at 2 mm offset horizontally. The stresses were comparatively reduced for 10 degree inclination of cusp ranging from 14.14 MPa at the central fossa to 54.09 MPa at 2 mm offset, and lowest for 0 degree inclination ranging from 15.10 MPa at the central fossa to 36.61 MPa at 2 mm offset. The maximum displacement was noted to be 0.006 mm at the central fossa and increased to 0.019 mm at 2 mm offset horizontally for 0 degree model which was reduced in 10 and 30 degree models [Table 3] and [Figure 2]a-h.{Table 3}{Figure 2}

The maximum von Mises stress distribution in D4 bone density was inconsistently distributed and comparatively higher in the cortical bone as compared with D1 bone density. The stress concentration was found to be highest in 30 degree inclination of cusp ranging from 30.09 at central fossa to 112.67 MPa at 2 mm offset. The maximum displacement was also increased from 0.014 at central fossa to 0.08 mm at 2 mm offset horizontally. On comparison with D1 bone density, both the stress distribution and displacement was found to be higher in D4 bone for all loading conditions [Table 4] and [Figure 3]a-h.{Table 4}{Figure 3}

However, the stress concentration in D4 bone density was more sensitive to reduction in the inclination of the cusps as the stresses reduced from 75.59 Mpa for 10 degree inclination 54.87 MPa for 0 degree inclination of cusp at 2 mm offset loading. The difference for loading at central fossa for all the inclination was not significant.


The predictability of implant treatment is supported by many clinical studies reporting success rates higher than 90% for many implant systems.[2],[13],[14] However, in cases where implant failures occur, the predominant causes are biomechanical in nature.[15] These factors include the mechanical stiffness of the implant and bone and the magnitude, direction, location of forces on the restored implant.[16] The direction of forces falling on the implant can be controlled to some extent by modifying the occlusion. Lindquist and co-workers and Weinberg and Kruger affirmed the role of occlusion in controlling the stress concentration on an implant-supported prosthesis.[17],[18] It has been observed that occlusal forces affect the surrounding bone of dental implants and can result in loss of marginal bone or loss of osseointegration.[19]

In the present study, the influence of three cuspal inclinations on the stress distribution in D1 and D4 bone densities and the interactive effects of horizontal offset and loading angle on stress/strain fields in the bone and implant were investigated. It was done in order to obtain an optimized design of implant.

When the loads were applied perpendicular to the cusp inclination to analyze the generation of eccentric flexural component when the load was not directed axially at the central fossa. This is similar to a study conducted by Barbier and co-workers who investigated the influence of axial and non-axial occlusal loads on the bone remodeling.[20] They noted a strong correlation between the calculated stress distributions in the surrounding bone tissue and the remodelling phenomena. They also emphasized the importance of avoiding non axial stresses.

The propensity of stress concentration around the implant neck at the cortical bone level was observed in all of the models. This finding was consistent with results obtained by Reiger and co-workers from finite element analysis of loaded implants which showed bone loss starting around the neck of the implant.[21] This can be explained by an engineering principle called the composite beam analysis, which states that when 2 materials of different elastic modulus are together with no intervening material and when one is loaded, a stress contour found to increase will be observed where the two materials first come in contact.[22] In an implant bone interface, these stress contours are seen in the crestal bone region, as the crest is the first region where the bone and implant first comes in contact.

Loading on the central fossa of all the models caused least amount of von Mises stresses when compared with the 1 mm and 2 mm buccal offset loading on the occlusal surface. This is in agreement with several studies which recommended that the optimal transfer of vertical occlusal load through an implant is along the implant's long-axis, to decrease bending moments created within the implant.[18],[23]

The maximum stresses in the cortical bone were generated in Model 1 (30 degree cusp inclination) especially when the offset loads were applied. This is in conjunction with the study conducted by Weinberg and Kruger, who mathematically proved that cusp inclination is one of the most important factors in producing bending moments, and that for every 10 degree increase in cusp inclination, there was approximately a 30% increase in loading to the implant/prosthesis.[18]

The results obtained for trabecular bone revealed low-stress concentrations at the apex of the implant in both D1 and D4 bone. Similar results have been described in a study be Clelland and co-workers in which trabecular bone displayed low stress concentrations at the implant apex.[24] This is substantiated to the low elastic modulus of the trabecular bone which allows it to absorb transferred loads.[25] Skalak and co-workrrs have reported that while the maximum stress concentrations in cortical bone are located in the area of contact with the implant, the maximum stress concentrations in trabecular bone occur around the apex of the implant.[15]

The displacement was maximum when the cusp inclination was increased from 0° to 30° and load in the horizontal offset 2 mm where as it was least when load was at the central fossa with 0 degrees of cuspal inclination. This is in accordance with the results obtained by Benzing and co-workers. It can be explained by loading of an implant fixed with an abutment inducing a certain amount of deformation (force × length) into the system and causing bending of the abutment. This bending of abutment increased with increasing distance of the loading point from the central fossa. Because of the continuum of abutment and implant, the abutment bending causes displacement of the implant. The displacement of implant depends on the magnitude of abutment bending and the resistance to bending of all components of the complete system including the bone, implant and abutment.[26]

The maximum von Mises stresses and displacement were found to be consistently greater in D4 bone than in D1 bone. This is in accordance with other studies conducted by Holmes and Loftus, who examined the influence of bone quality on the transmission of occlusal forces for endosseous implants.[27] They concluded that the placement of implants in D1 bone quality resulted in less micromotion and reduced stress concentration.

It is clear from the results of the study that, cuspal inclination plays an important role in transferring stresses to the bone and an increase in inclination increases the bending movement leading to increase in stress concentration in the cortical bone near the neck of the implant. Also, less steep cusps result in more uniformly distributed forces when compared with more steep cusps. This phenomenon is more pronounced in poor quality bone. Therefore, minimum possible cuspal inclination should be considered when placing implants in poor quality bone.

This study may have a few limitations as several assumptions have been made for the present finite element analysis. The interface between the implant and the cortical bone and cancellous bone was assumed to be homogenously bonded, whereas in clinical situation it is not always so. The cortical and cancellous bone were assumed to be linearly elastic, whereas a nonlinear assumption is more accurate clinically. The structure of each bone layer was simplified, even though the actual shape of jaw bone and its detailed architecture, would have provided better information on stress/strain fields. Also, the properties of abutment and crown were kept constant in the models, so that the analysis could particularly be focused on the specific factors being assessed i.e. stress concentration and displacement in study. However, for the present study, these assumptions are considered reasonable keeping in mind that these models reflect the actual clinical situation.

The findings of our study raise a design optimization issue, specifically to minimize bone damage and increase stability of implant supported prosthesis. Future finite element, in vitro and in vivo experimental and clinical studies should focus on optimizing the implant design to withstand various functional stresses in the oral cavity for prevention of bone loss.


Cuspal inclination plays an important role in directing the forces axially for better distribution of occlusal stress over the surrounding bone and therefore, reduction in the cuspal inclination may be helpful in preventing crestal bone loss around the implant in patients with poor bone quality or patients having any para-functional habits like bruxism. Therefore, meticulous care should be taken while planning the occlusion for implant-supported prosthesis. Occlusal contacts that distribute stress axially should be incorporated in the prosthesis. During eccentric movements, the implant-supported prosthesis should allow only minimal functional contact to avoid forces from non-axial direction.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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