Finite Element Analysis of effect of cusp inclination and occlusal contacts in PFM and PEEK implant-supported crowns on resultant stresses

Abstract

Background

Effect of prosthesis design on occlusal overload and long-term implant stability cannot be overstated. In Porcelain Fused to Metal (PFM) crowns, low cusp inclination and occlusal contacts limited to central fossa ensure axially directed forces on an implant but often pose esthetic and functional challenges. It is theorized that resilient Polyetheretherketone (PEEK) crowns have shock absorption capacity for favorable stress distribution. This study compared two implant crown materials and evaluated the effect of cusp inclination and occlusal contact distribution on resultant stresses.

Methods

Thirty 3D finite element models of implant-supported PFM and PEEK crowns, generated using Solidedge 3D CAD solid modeling software (v19, Siemens PLM Software Inc.,US), were used to study the effect of 3 cups inclinations (0°, 15°, 30°) under five load conditions, with 300N force distributed over one, two, or three contact areas and exported to ANSYS (v18.1, ANSYS Inc. Pennsylvania, US) for stress analysis.

Results

Maximum stress in both PFM and PEEK models was at the neck of the implant under Load 3(300N distributed over three contact areas: central fossa, buccal cusp tip, marginal ridge). Minimum stress in all models was under Load 1(300N applied at one contact area in central fossa). Maximum stresses were recorded for 30° cusp inclination in PFM models.

Conclusion

In both PFM and PEEK crown models, contact areas placed away from the implant axis generated greater implant and peri-implant stresses and had more effect on resultant stresses than that of increase in cusp inclination. The effect of cusp inclination on the resultant stresses was dependent on the crown material.

Introduction

Long-term implant stability is a major determinant in the success of implant prosthesis. While primary implant stability is a mechanical phenomenon determined by local bone parameters, implant characteristics, and placement technique, secondary stability is a far more complex biological phenomenon, which is an outcome of a steady sequence of events involving the bone formation and remodeling at the bone-implant interface.¹ Magnitude, frequency, and duration of load play a vital role in this bone response.² The load causing structural and biological damage is classified as overload,³ and interdependence of overload and inflammation has been long debated to establish the primary cause in peri-implant bone loss.4, 5, 6 Occlusal overload is also an important cause of mechanical complications like screw loosening and fracture of implant prostheses⁷ and poses a greater challenge to a dental implant than the natural tooth due to the absence of a periodontal ligament. During bending movement, the implant lacks an initial adaptive phase of movement seen in the natural tooth with absorption of forces at the implant-bone interface, leading to stress concentration at the crestal bone and subsequent bone loss.⁸

Apart from poor quality of bone and para-functional habits that cause implant overload, Misch et al.⁹ recognized the role of various elements of implant prosthesis design like cusp inclination, occlusal contact distribution, crown contour, crown material, cantilevers, and interferences and proposed the implant-protected occlusion (IPO).

Weinberg et al.¹⁰ also reported that an increase in cusp inclination by 10° in implant restoration increased the bending moment by 30%. To prevent shear forces on the implant restoration and stress concentration in the crestal bone, IPO advocates low cusp inclination of posterior implant crown, with occlusal contact ideally on a flat surface in the central groove, widened to 2–3 mm. Although this ensures axially directed forces, the shallow morphology of the clinical crown often poses esthetic and functional challenges. Further, recent studies^11,12 reported that cusp angulation has no effect on peri-implant stress if occlusal contacts are well distributed, and low cusp inclination might actually compromise bone engagement and long-term implant stability. It was also suggested that implant overload can be avoided by the distribution of forces through multiple contacts on multiple posterior teeth instead of a single contact.^6,8 However, multiple contacts placed away from the center of the implant can cause a cantilever effect. It should be noted that all these observations were made in porcelain fused to metal (PFM) or full metal implant crowns.

Nonelastic crown materials like metal (E = 218Gpa) and porcelain (E = 82.8Gpa) can add to the damaging effect of overload on an implant, resulting in chipping and fracture of prostheses.¹³ Magne et al.¹⁴ stated that these mechanical complications and bone resorption caused by micro movements at the implant-abutment platform can be potentially minimized by using a resilient crown or abutment and its damping behavior. In this context, Polyetheretherketone (PEEK), a bioinert, thermoplastic polymer, with high mechanical performance, high shock absorption capacity, and low elastic modulus (4.1Gpa), comparable to that of bone, is a viable metal-free alternative to conventional implant restorations.^15,16

The present study compared PFM and PEEK crowns in the effect of different cusp inclinations and occlusal contact areas (CA) on the stresses generated in the implant-abutment complex and surrounding bone. As the understanding of overload in clinical studies is overshadowed by ethical concerns, as also by small sample size, high risk of bias and heterogeneity that prevents analysis of data,² a numerical method like Finite Element Analysis (FEA), that has found application in dentistry for the past 4 decades to study the effect of complex implant-bone geometry, prosthetic design, and material properties, on stress distribution,^17,18 was used.

Material and methods

Computerized 3D FEA models of an implant-supported crown, generated using Solid Edge 3D CAD solid modeling software (v19, Siemens PLM Software Inc.,US), was used in the study. Models of bone level titanium implant, abutment, and screw were digitally created using a 4.3 × 10 mm Nobel Replace, regular platform, conical connection implant (Nobel Biocare AB, Goteborg, Sweden), and 7 mm long Snappy abutment (Nobel Biocare AB, Goteborg, Sweden) design. The implant model, with abutment and screw, was embedded in a 30 mm high, 20 mm wide bone block, with 13 mm cancellous bone and 2 mm thick cortical bone, buccolingually, to simulate complete osseointegration of the implant in type 2 mandibular bone of first molar region. A mandibular molar crown was created on the implant model, with variation in crown material (PFM and PEEK) and cusp inclination (0°, 15°, and 30°). The PFM crowns had porcelain with a maximum thickness of 1.5 mm over a 0.5 mm metal substructure, and the PEEK crowns had a maximum thickness of 2 mm. They were 9 mm, 11 mm, and 10.5 mm in occlusogingival, mesiodistal, and maximum buccolingual dimension and 5.5 mm between the buccal cusp tips (Wheeler’s dimensions). The luting cement thickness was ignored (Fig. 1a and b). The fine 3D tetrahedral mesh of the models was created in HyperMesh (v11.0, Altair Hyperworks, Huntsville, AL). The completed FEA model had approximately 605,000 elements and 855,000 nodes (Fig. 1c). Due to the complexity of the geometry, 10-noded tetrahedral elements were used for meshing. Compared to the 4-noded tetra (lower order element), 10-noded tetra (higher order) gave better results. Much better brick elements could not be used due to meshing and higher approximation difficulties resulting from an irregular shape of threads in the models. The elements were also represented by quadratic displacement behavior with three degrees of freedom at each node. This made the application of translational loads at the required nodes possible. The mesh size adopted was around 0.2 mm. The nodes in the medial and distal end of the bone were constrained in all directions, and complete contact between the members was assumed for better load transfer. All the materials in the model were considered to be homogenous, isotropic, and linearly elastic, and the material properties used were obtained from previous studies19, 20, 21 (Table 1). The FEA models were exported to ANSYS (v18.1, ANSYS Inc., Pennsylvania, US) for stress analysis.

Fig. 1.

3D Implant models used in the study with (a) PFM crown and (b) PEEK crown (c) Elements and nodes in Implant models for different cusp inclinations. Meshed models showing (d) 0°(e) 15° (f) 30° cusp inclination and (g) 0.5 mm occlusal contact areas on central fossa, distobuccal cusp incline, distobuccal cusp tip, and distal marginal ridge.

Table 1.

Elastic modulus and Poisson’s ratio of materials used in the study.

Component	Material	Elastic modulus (MPa)	Poisson’s ratio
Implant	Commercially pure Titanium (Grade4)	105,000a	0.34a
Abutment	Commercially pure Titanium (Grade4)	104,000a	0.34a
Screw	Titanium alloy	113,000a	0.342a
Cortical bone		13,700a	0.3a
Cancellous bone		1370a	0.3a
Crown	Porcelain fused to metal	Porcelain – 82,800b	0.35b
		Metal – 218,000b	0.33b
	Polyetheretherketone	4100c	0.4c

^aPark JM et al.¹⁹

^bEskitascioglu G.²⁰

^cTekin S.²¹

To evaluate the effect of cusp inclination, distribution of occlusal contact areas and crown material, of an implant crown on the resultant stresses, the implant models with PFM crowns and PEEK crowns having 0°, 15°, and 30° cusp inclination (Fig. 1d,e,f), were subjected to 5 different load conditions. The von Mises stresses in the abutment, screw, implant, cortical bone, and cancellous bone were analyzed. Load 1 to 5 were predefined combinations of magnitude of load and contact areas, where a maximum vertical load of 300N was applied, divided among one to three occlusal contact areas (Table 2). The contact areas (CA) chosen were mid of the central fossa, distobuccal cusp tip, mid of the distobuccal cusp incline, and mid of the distal marginal ridge of the implant crown model (Fig. 1g). Contact points were designed as circular areas with 0.5 mm diameter because the application of load at a point implies applying finite force over an infinitely small area. This creates infinite stress at the point and represents the load distribution into the structure inappropriately. Hence the load was applied over an area, preventing the emergence of a singular point with unrealistically high stresses.

Table 2.

Number and location of occlusal contact areas for 5 different load conditions.

Load Condition	Force applied (N)	Occlusal contact area (CA)
		Number	Location
Load 1	300	1	Mid of the central fossa
Load 2	150 + 150	2	Mid of the central fossa and distobuccal cusp tip
Load 3	100 + 100 + 100	3	Mid of the central fossa, Distobuccal cusp tip and mid of the distal marginal ridge
Load 4	150 + 150	2	Mid of the central fossa and mid of the distobuccal cusp incline
Load 5	100 + 100 +100	3	Mid of the central fossa, Mid of the distobuccal cusp incline and mid of the distal marginal ridge

Results

The von Mises stresses and maximum displacement (DMX) values under different loading conditions and cusp inclinations of PFM and PEEK crown implant models were recorded and plotted as bar and line graphs.

Abutment and screw

Maximum von Mises stresses and DMX values in the model were recorded in the abutment. In PFM models, maximum stress in abutment was in Load 3 (191.26 Mpa for 0°, 191.18 Mpa for 15°, 191.14 Mpa for 30°) and minimal stress in Load 1 (99.79 Mpa for 0°, 99.78 Mpa for 15°, 99.58 Mpa for 30°). Maximum DMX values were in Load 3 (0.0143 mm) and minimum in load 1 (0.0068 mm). In PEEK models, maximum stress was in Load 3 (284.45 Mpa for 0°, 185.30 Mpa for 15°, and 278.72 Mpa for 30°) and minimum stress in load 2 (216.92 Mpa) for 0°, Load 1 (95.85 Mpa) for 15°, and load 4 (172.98 Mpa) for 30° cusp inclination. Maximum DMX values were in Load 3 (0.028 mm) and minimum in load 1 (0.01 mm) (Fig. 2).

Fig. 2.

(a) von Mises stress contours in abutment; comparison of (b) von Mises stress and (c) maximum displacement in abutment under 5 load conditions and 3 cusp inclinations in PFM and PEEK models.

In the screw, maximum and minimum stresses and DMX values observed were 43.15 MPa, 22.05Mpa, and 0.006 mm, 0.004 mm, respectively (Fig. 3).

Fig. 3.

(a) Stress distribution in Implant screw; comparison of (b) von Mises stress and (c) maximum displacement in Implant screw under 5 load conditions and 3 cusp inclinations in PFM and PEEK models.

Implant

The stresses in an implant were more, compared to cortical bone, and stress concentration was located at the neck of the implant (Fig. 5). In PFM models, maximum stress was in Load 3 (118.65 MPa for 0°, 118.64 MPa for 15°, 117.81 MPa for 30°) and minimum in Load 1 (53.61 Mpa for 0°, 53.53 MPa for 15°, 53.47 MPa for 30°). Maximum DMX values were in Load 3 (0.0062 mm) and minimum in Load 1 (0.0044 mm). PEEK models recorded maximum stress in Load 3 (109.54 MPa for 0°, 116.89 MPa for 15°, 109.58 MPa for 30°) and minimum in Load 1 (49.37 Mpa for 0°, 52.51 MPa for 15°, 49.44 MPa for 30°). Maximum DMX values were in Load 3 (0.0062 mm) and minimum in Load 1 (0.0044 mm) (Fig. 4).

Fig. 5.

(a) Stress distribution in cortical bone; comparison of (b) von Mises stress and (c) maximum displacement in the cortical bone under 5 load conditions for 3 cusp inclinations in PFM and PEEK models.

Fig. 4.

(a) Maximum stress concentration at the neck of implant model; comparison of (b) von Mises stress and (c) maximum displacement in implant under 5 load conditions for 3 cusp inclinations in PFM and PEEK models.

Cortical and cancellous bone

The stresses recorded in the cortical bone were greater compared to those in the cancellous bone. In PFM models, maximum stresses in cortical bone were in Load 3 for 0° (80.3 MPa) and Load 5 for 15°(77.79 MPa), and 30°(80.99 MPa). Minimum stresses were in load 1 (41.53 MPa at 0°, 41.52 at 15°, and 41.49 at 30°). Maximum DMX values were in Load 3 (0.0064 mm) and minimum in Load 1 (0.0045 mm). In PEEK models, maximum stresses in cortical bone were in Load 5 for 0°(78.94 MPa) and Load 3 for 15°(79.85 MPa), and 30°(82.04 MPa). Least stresses were in Load 1 for 0°(43.75 MPa), 15°(41.34 MPa), and 30°(43.78 MPa). Maximum DMX values were in Load 3 (0.0063 mm) and minimum in Load 1 (0.0044 mm) (Fig. 5).

Maximum stresses recorded in cancellous bone in PFM models were in Load 3 for 0° (19.11 MPa) and Load 2 for 15°(19.54 MPa) and 30°(19.61 MPa). Minimum stress recorded (17.04 MPa) was in Load 1 for all 3 cusp inclinations. Maximum DMX values were in Load 3 and Load 5 (0.0047 mm) and minimum in Load 1 (0.003 mm for 0°, 15°). PEEK models recorded maximum stresses in Load 2 for all cusp inclinations (19.39 in 0°, 19.53 9 in 15° and 19.48 in 30°) and minimum stresses in Load 1 for 0° (16.89 MPa), 15°(17.04 MPa), and 30°(16.89 MPa). Maximum DMX values were in Load 3 (0.0047 mm for 15° and 30°) and minimum in Load 1 (0.003 mm for 0°) (Fig. 6).

Fig. 6.

(a) FEA model of cancellous bone; comparison of (b) von Mises stress and (c) maximum displacement in the cancellous bone under 5 load conditions for 3 cusp inclinations in PFM and PEEK models.

In all components of PFM models, maximum stress and DMX values in Load 1, 2 and 3, were comparable for all cusp inclinations, whereas, in Load 4 and 5, maximum values were for 30° and minimum for 0°cusp inclination. PEEK models showed a varied association between the cusp inclination and resultant stresses.

Discussion

In the present study, although a constant overall vertical load of 300N was applied in each of the 30 FEA models, the von Mises stresses generated in different parts of these implant-bone models varied, based on the number and distribution of CA along which the force was applied. In all components of PFM and PEEK crown implant models, maximum von Mises stresses were seen under Load 3 followed by Load 5. This increase in the magnitude of von Mises stress when a load was applied on off-centric CA s like the distobuccal cusp tip, distobuccal cusp slope, or distal marginal ridge can be explained by the offset loading created. Park et al.¹⁹ made a similar observation that, under vertical load, peri-implant stresses increased with an increase in lingual offset distance, and under oblique load, maximum stress initially decreased but subsequently increased with offset distance. The authors suggested that the distance between the central axis of the implant and the vertical load created a clockwise bending moment, with resultant compressive and tensile stresses that increased in magnitude as offset distance increased. The initial decrease in stress under oblique load was due to the canceling of clockwise and counterclockwise bending moments generated simultaneously by the vertical and horizontal components of the oblique load. Similarly, maximum DMX values observed in the present study, in all components of FEA models subjected to Load 3 and 5, suggested increased deflection or bending at the nodes when the load applied was off-centered. Also, with the same number of contacts areas (2 CA in Load 2 and 4 and 3 CA in Load 3 and 5), the stress generated under Load 2 and 3 was greater than that generated under Load 4 and 5, respectively, because of the increased offset distance of CA at the distobuccal cusp tip in Load 2 and 3. This is in agreement with Bedi et al.²² who stated that load applied at the buccal offset of 2 mm, generated more stress and nodal displacement in the FEA model when compared to load applied at the central fossa in 0°–30°cusp inclination.

The importance of the number of contacts and their distribution in the intensity of stress was stressed in previous studies.^20,23,11 Eskitascioglu et al.²⁰ stated that vertical loading at 1 location generates more stress in the cortical bone and implant when compared to loading at 2 or 3 locations. This is contrary to the observations in the present study where least stresses were recorded in all models subjected to load at a single CA in the central fossa (Load 1) and can be explained by the fact that load applied by Eskitascioglu et al.²⁰ was at the buccal cusp tip and hence, an offset load. Rand et al.²³ also suggested that single contacts on internal cusp slopes create nonaxial forces to the implant and should be avoided. However, load distributed over multiple contact areas can also generate increased stress at the bone-implant interface if the contact distribution is nonuniform. This was demonstrated by Brune et al.¹¹ in an FEA, where the loading at 5 CA, uniformly distributed on buccal and lingual slopes, not only reduced the stress generated but also eliminated the effect of cusp angulation on peri-implant stresses, when compared to a nonuniform 3 CA distribution restricted to only the buccal slopes. In the present study, although load was distributed over 2 and 3 CA (Load 2,4 and Load 3,5), the absence of CA on the buccal slopes of the lingual cusps to counter the nonaxially directed forces could be the reason why offset distance stood out as a major factor in the resultant stresses. Further studies, with different combinations of CA distribution, might help us arrive at an unambiguous understanding of the subject.

Although marginal, PFM crown models subjected to Load 4 and 5 in this study showed an increase in DMX and von Mises stress values, as the cusp inclination increased from 0° to 30°. This is in agreement with various studies,^{10,12,22,24,25} which suggest that lateral force transmission, caused by the horizontal component of the vertical load applied on the cusp inclines, increases with an increase in cusp inclination and results in greater deflection and stresses. However, in models with PEEK crown, although stress and displacement values varied with a change in cusp inclination, no meaningful correlation was observed. As in previous studies,²⁶ higher stresses were observed in cortical bone (80.99 MPa) in all models, when compared to cancellous bone (19.6 Mpa), due to stress concentration in the area of the first contact, which in this case is the cortical bone at the implant-bone interface. Also, cortical bone has a higher modulus of elasticity compared to the cancellous bone resulting in greater resistance to deformation and higher stress concentration.²⁷ Minimal increase of von Mises stresses in cortical bone with cusp inclination (PFM – 44.77 MPa in Load 4, 0° to 51.89 MPa in Load 4, 30°; PEEK – 44.99 MPa in Load 4, 0° to 48.02 MPa in Load 4, 30°) compared to a large increase in the resultant stresses with a change in occlusal contact position and number (PFM – 51.89 MPa in Load 4, 30° to 80.99 MPa in Load 5, 30°; PEEK – 48.02 MPa in Load 4, 30° to 79.12 MPa in Load 5, 30°) demonstrates that even with a reasonable increase in cusp inclination, favorable peri-implant stress distribution can be achieved by optimal position of occlusal contact areas, in both PFM and PEEK crowns.

Contrary to the assumption that PEEK restorations generate lesser stresses in the underlying implant and bone, owing to their shock absorption capacity, the present study showed comparable stresses in FEA models with PEEK and PFM crowns. Nonetheless, greater stress that was well within the yield strength was seen in the abutment of PEEK crown models (284.45 MPa) compared to PFM crown models (191.26 MPa) for Load 3, 30°. The previous studies^15,21,28 that compared PEEK crowns and abutments to metal-ceramic crowns or zirconia abutments also demonstrated no difference in stress distribution in bone or implant, but reduced stress in superstructure with PEEK crowns. Wang et al.²⁹ explained this by demonstrating that various restorative materials showed different amounts of displacement, but the energy transfer to the implant-bone interface was comparable. Nevertheless, with PEEK increasingly becoming the material of clinical choice,³⁰ its dynamic response to load^13,14 that allows dental implants to manifest damping behavior seen in natural teeth is worth further study.

In the present study, certain assumptions were made in designing the 3D FEA models to reach an analytical solution. The component materials were considered isotropic, homogeneous, linearly elastic, and the implant was considered to be completely osseointegrated. However, discretization of the problem domain was carefully considered, and the load was applied over contact areas, instead of points, to eliminate singularity in the model. A static load was used to evaluate the stress distribution in a single implant-supported restoration modeled in a mandibular bone block with defined density. Under dynamic loading in-situ, with varying bone density, mandibular flexure, and friction with the dental antagonist, PEEK restorative material might exhibit different stress patterns.

Conclusion

Within the limitations of this 3D FEA, the following conclusions were drawn.

• 1.The stresses generated in the implant and peri-implant area in PEEK and PFM models were comparable. PEEK crowns generated greater stresses in the abutment.
• 2.Contact areas placed away from the implant axis generated greater implant and peri-implant stresses in models with PFM and PEEK crowns, irrespective of the number of contact areas that were loaded.
• 3.Effect of cusp inclination on the resultant stresses was dependent on the crown material used.

Optimal position and distribution of occlusal contact areas can be used for favorable peri-implant stress distribution when a reasonable increase in cusp inclination is warranted for esthetics and function in PFM or PEEK crowns.

Disclosure of competing interest

Thel authors have none to declare.