Comparative finite element analysis of 3-unit implant-supported bridges restorated with different prosthetic materials in posterior mandible

Abstract

Background

The aim of this study was to investigate the mechanical behaviour and stress distribution characteristics of different prosthetic materials (Co-Cr/porcelain; Zirconia/porcelain; Fibre- reinforced composite/Composite) used in mandibular posterior implant-supported fixed prostheses using finite element analysis (FEA), with particular emphasis on the influence of material stiffness under different loading conditions.

Methods

Three-dimensional finite element models of a mandibular first premolar and first molar were constructed. Implant-supported fixed prosthetic restorations were simulated using three different restorative materials: metal-supported porcelain (MP), zirconia-supported ceramic (ZP), and fibre-reinforced composite (Trinia-composite, TC). Vertical and oblique occlusal loads were applied to the models. Maximum principal stress, minimum principal stress, and Von Mises stress values were calculated to evaluate stress distribution within the restorative materials and supporting structures.

Results

Across all models, oblique loading resulted in higher stress concentrations compared with axial loading. The first premolar models exhibited higher stress levels than the first molar models under identical loading conditions. The mechanical behaviour and stress distribution in the fixed prostheses were influenced by the prosthetic material used. Restorations fabricated with MP and ZP demonstrated higher stress values than those restored with TC. The fibre-reinforced composite material showed a more homogeneous stress distribution, indicating a more favourable load-transfer behaviour.

Conclusions

All tested materials generated stress values within physiological limits. The fibre-reinforced polymer-based restoration exhibited improved stress redistribution, most likely due to its elastic compatibility peri-implant structures. These findings suggest that fibre-reinforced composites may offer biomechanical advantages in posterior implant-supported restorations.

Background

The loss of a tooth is an irreversible condition that affects an individual’s quality of life, not only causing functional loss but also impacting physical, emotional, and social well-being [1]. Implant-supported fixed prostheses can be used for oral rehabilitation in partially edentulous patients [2].

Although both types of prostheses are established and successful treatment options, their outcomes can vary depending on the prosthetic approach [2]. The biomechanical behaviour of dental implants under functional forces differs from that of natural teeth. The periodontal ligament, absent in peri-implant tissue, acts as a mechano-receptive interface that absorbs incoming forces [3].

The elastic modulus of restorative materials affects stress distribution in the tooth, implant, and peri-implant bone [4]. Materials with a high elastic modulus tend to accumulate stress within themselves, whereas materials with a lower modulus transfer stress to adjacent, stiffer structures. Therefore, the selection of prosthetic materials is crucial for mechanical performance, aesthetic outcomes, biomechanical behaviour, and the preservation of peri-implant tissue health [5].

According to Wolff’s law, bone tissue responds to mechanical stress depending on the direction and magnitude of forces, implant material, and implant design [6, 7]. The choice of prosthetic material has received increasing attention because it can improve stress distribution throughout the implant system and reduce stress on the surrounding bone [8]. Appropriate material selection is therefore critical for long-term stability and load distribution in supportive tissues [9].

Metals, ceramics, resins and polymers are commonly used in implant-supported fixed prostheses. Cobalt-chrome (Co-Cr) alloys are frequently used because they are compatible with ceramics, corrosion-resistant, and biocompatible [1]. Zirconia is preferred for its superior mechanical and biological properties, low plaque accumulation, and favourable optical characteristics [10]. As a rigid material, zirconia has a higher elastic modulus than hybrid ceramics or polymer-based materials.

Trinia™ (BICON, Boston, MA, USA) is a fibre-reinforced polymer with an elastic modulus and tensile strength similar to dentin. Compared to zirconia and polyetheretherketone(PEEK), Trinia exhibits better fracture resistance.11 Resins are often chosen over metal-ceramic restorations due to their aesthetic advantages, biomechanical performance, and ease of modification. However, the polymer matrix in resin-based materials has been shown to generate excessive stresses in the implant–prosthesis system [12].

Finite element analysis (FEA) is a research method that allows simulation of complex structures to evaluate correlations between internal stresses and force-displacement behaviour. FEA can model irregular and heterogeneous structures such as bone, implants, and prostheses. In addition to being repeatable, reliable, and cost-effective, FEA provides quantitative data for comprehensive biomechanical evaluation [13, 14].

Despite the extensive use of FEA, clear guidance on which prosthetic material provides the most reliable performance in implant-supported restorations is lacking. Therefore, the aim of this study was to evaluate the biomechanical behaviour of implant-supported prostheses restored with different materials using FEA. The null hypothesis was that the prosthetic material does not influence stress distribution in the restoration or supporting tissues under vertical and oblique forces.

Methods

Creation of geometric models

To develop the mandibular geometric model, tomographic images were obtained from a fully edentulous adult patient. The mandible was scanned using cone-beam computed tomography (ILUMA, Orthocad, CBCT, 3 M Imtec, Oklahoma, USA), yielding 601 slices at 120 kVp, 380 mA, with a scanning time of 40 s. Volumetric data were reconstructed with a slice thicknessof 0.2 mm. The reconstructed slices were imported into 3D-Doctor software (Able Software Corp., MA, USA) for segmentation (Fig. 1a) Bone tissues were separated using the interactive segmentation method, and 3D models were generated using the 3D Complex Render technique, completing the bone tissue modeling process [6].

Fig. 1.

a Interactive segmentation in mandibular and maxillary bone b Titanium implant, abutment and screw c Contact points of the functional tubercles of the teeth, d Functional tubercle peaks, e Forces were applied at an angle of 45° in the bucco-lingual direction

For three-unit fixed dental prostheses (FDPs), teeth numbers 44 and 46 were selected. For implant-supported FDPs, the model included a titanium implant (4.1 mm diameter, 10 mm length, Bone Level, Rapid Implant, MODE, Istanbul, Turkey) with a 4.8 mm abutment exit profile and titanium abutment and screw [10] (Fig. 1b).

Material properties and boundary conditions

To create mathematical models passing to the geometric modelling stage, anatomic 3D models were produced using Blender software (Blender foundation, the Netherlands). After creating the geometric models, they were uploaded to the Fusion 360 program (One Market, USA) for single piece analysis to be performed.

All models were assumed to be linear, homogeneous, and isotropic. Full contact was assumed between components, and implants were considered 100% osseointegrated with the surrounding bone [9]. At the stage of creating a mesh, tetrahedral elements were used, and the mesh density was increased in critical areas such as the implant-abutment connection. Implant-supported models with different prosthetic framework designs were positioned in the 44–46 region of the mandibular posterior segment, as summarized in Table 1.

Table 1.

Properties of the experiment materials

	Elastic modulus (GPa)	Poisson ratio	Mesh size
Cortical bone	13.7	0.30	0.2 mm
Cancellous bone	1.37	0.30
Titanium implant(Mode: Rapid implant)	110	0.35
Co-Cr substructure	218	0.33
Zirconia substructure	210	0.33
Trinia substructure	18.5	0.3
Feldspathic porcelain	82.8	0.35
Composite (Ceramage By Shofu)	10.7	0.3

Cobalt-chrome(M), zirconia (Z), and Trinia (T) were used as prosthetic framework materials. The elastic modulus and Poisson’s ratio of all materials are listed in Table 1. In the Fusion software, solid meshing was made with the properties listed in Table 1. All the models were accepted as linear, homogeneous, and isotropic materials. The elements contained in the scenarios and node numbers are given in Table 2. Co-Cr and zirconia frameworks were designed with a thickness of 0.7 mm and a connector area of 9 mm², whereas the Trinia polymer framework had a thickness of 0.7 mm and a 7 mm² connector area [11, 12]. Feldspathic porcelain was used for the veneer material of Co-Cr and zirconia frameworks, while Ceramage composite (Shofu, Japan) was applied for the Trinia veneer.

Table 2.

Numbers of nodes and elements

	Material	Model number	Numbers of nodes and elements
Implant supported fixed prothesis	MP	Model 1 and 4	Number of nodes: 371,960 Number of elements:1,895,178
	ZP	Model 2 and 5	Number of nodes: 342,984 Number of elements:1,757,540
	TC	Model 3 and 6	Number of nodes: 371,960 Number of elements:1,895,178

For the meshing, the convergence test was based on the number of nodes (350,628) and elements (185,842) obtained with 10% of relevance. The element used in the mesh division was the tetrahedral with 10 nodes (Tet-10). The mesh quality parameters were element quality defined as 0.72 ± 0.12, aspect ratio of 1.93 ± 0.84, average maximum corner angle of 96.43° and skewness average of 0.24 ± 0.15. The inflation option was defined as a smooth transition between the geometries. The rigid body behavior has been standardized as dimensionally reduced.

Vertical occlusal forces were applied to the teeth with a total load of 500 N, distributed across three points on the buccal tubercles: 100 N on the first premolar, 150 N on the second premolar, and 250 N on the first molar [13].

Contact points were determined based on the tubercle- fossa relationship (Fig. 1c). Oblique forces were applied at a 45° angle in the buccolingual direction, simulating dynamic occlusion, with the same force distribution (Fig. 1d, e).

Stress analysis was performed using Von Mises stress (σVM) for ductile materials, and maximum (σMax) and minimum principal stress (σMin) for non-ductile materials. Total system deformation was also evaluated.

Results

The Von Mises and principal stress values obtained in the study are presented in Figs. 2, 3, 4, 5, 6 and 7; Table 3. FEA results demonstrated that under occlusal loading, stress was transmitted continuously from the prosthetic structure to the peri-implant bone. Stress concentration was primarily observed in the material transition zones, particularly at the implant–abutment interface and cervical cortical bone region.

Fig. 2.

Von Mises stress distribution of the prosthetic materials: a MP-vertical occlusal forces, b MP-oblique occlusal forces, c ZP vertical occlusal forces, d ZP-oblique occlusal forces e TC-vertical occlusal forces, f TC-oblique occlusal forces

Fig. 3.

Maximum and minimum principal stress in the cortical bone: a,b MP-vertical occlusal forces, c,d MP-oblique occlusal forces, e,f ZP-vertical occlusal forces, g,h ZP-oblique occlusal forces, i,j TC-vertical occlusal forces, k,l TC-oblique occlusal forces

Fig. 4.

Von Mises stress distribution of the implant bodies; a,b MP-vertical occlusal forces, c,d MP-oblique occlusal forces, e,f ZP-vertical occlusal forces, g,h ZP-oblique occlusal forces, i,j TC-vertical occlusal forces, k,l TC-oblique occlusal forces

Fig. 5.

Von Mises stress distribution of the implant bodies; a,b MP-vertical occlusal forces, c,d MP-oblique occlusal forces, e,f ZP-vertical occlusal forces, g,h ZP-oblique occlusal forces, i,j TC-vertical occlusal forces, k,l TC-oblique occlusal forces

Fig. 6.

Maximum and minimum principal stress in the cortical bone: a,b MP-vertical occlusal forces, c,d MP-oblique occlusal forces, e,f ZP-vertical occlusal forces, g,h ZP-oblique occlusal forces, i,j TC-vertical occlusal forces, k,l TC-oblique occlusal forces

Fig. 7.

Maximum and minimum principal stress in the spongios bone: a,b MP-vertical occlusal forces, c,d MP-oblique occlusal forces, e,f ZP-vertical occlusal forces, g,h ZP-oblique occlusal forces, i,j TC-vertical occlusal forces, k,l TC-oblique occlusal forces

Table 3.

Von Mises stress values under axial and oblique forces

	Group MP (MPa)		Group ZP (MPa)		Group TC (MPa)
	Axial	Oblique	Axial	Oblique	Axial	Oblique
Prothesis	12.33	12.51	14.09	14.96	7.38	11.47
Abutment	136.14	372.28	212.98	230.60	179.14	188.75
Abutment screw	85.39	189.17	106.73	325.63	130.23	209.08
Implant body	79.30	172.59	90.66	170.94	78.19	119.48
Cortical bone max principal stress	16.88	21.42	16.92	21.60	18.01	18.23
Cortical bone minimum principal stress	-39.12	-74.30	-39.95	-74.33	-32.55	-62.06
Cancellous bone max principal stress	7.94	8.96	7.94	8.98	7.24	9.04
Cancellous bone minimum principal stress	-16.93	-9.55	-16.92	-9.55	-15.11	-8.04

Von mises stress in prosthesis

Stress distribution within the prosthetic restoration is shown in Fig. 2a-f. The red colours represent higher tensile stresses and the blue colours represent lower tensile stresses. Under vertical force, Group ZP was exposed to the highest stress (14 MPa). Oblique forces (Fig.b, d,f) generated higher stress values than axial forces(Fig. 2a, c,e) In the MP models of the prostheses, stress was most pronounced in the connector region (Fig. 2a, b). Stress was concentrated in the posterior connector under oblique force for Groups MP and TC (Fig. 2b, f) and in the anterior connector for Group ZP (Fig. 2c). In the ZP and TC groups, stress was concentrated in the cusp tips.(Fig. 2c, d,e, f).

Von mises stress in implant abutments

In implant abutments, stress was concentrated at the step regions (Fig. 3a-l). Under oblique loading, the first premolar experienced the highest stress, with Von Mises values recorded as MP (372 MPa) > ZP (230 MPa) > TC (188 MPa).(Fig. 3c, g,k).

Von mises stress in abutment screws

Stress distribution within the prosthetic superstructures is shown in Fig. 4a-l. Stress evaluation of the abutment screws revealed that the first premolar experienced the highest stress, with values in descending order: ZP (325 MPa) > TC (209 MPa) > MP (189 MPa).(Fig. 4g, i,k) Visual inspection indicated that in the ZP model under vertical loading, stress was concentrated immediately below the screw head. Overall, the highest screw stress was observed in the ZP model.

Von mises stress in implant bodies

Stress values occurring in the implant bodies are shown in Fig. 5a–l. When the superstructure options were compared, the highest stress value was obtained in the MP models subjected to oblique loading (172 MPa). In all models, stresses were observed to be more concentrated in the cervical (neck) region of the implants, whereas the lowest stress values occurred in the apical region. In contrast, TC models exhibited lower stress values compared with the other materials (57 MPa).

Principal stress in cortical and trabecular bone

The stress distribution is shown in Figs. 6 and 7. The stress distribution in cortical and spongious (trabecular) bone changed according to the loading conditions. The stress values formed in spongious bone were found to be relatively lower under both vertical and oblique loading (7–9 MPa) and this reduced the risk of resorption or stability loss.

The stress values in cortical bone were seen to be higher, ranging between 16 and 21 MPa under vertical and oblique loads. Under both loading conditions, stress was concentrated in the bone-implant connection in cortical bone, on the lingual side of the distal implant in spongious bone, and in the fixture-bone connection in the buccal section of the implant body in the mesial.

Discussion

Examination of the biomechanical performance of prosthetic materials includes what kind of response is given to various factors such as the bone surrounding the implant, abutment and screw in implant-supported restorations. This can be achieved with the simulation and determination of potential strengths and weaknesses in clinical scenarios using the finite element analysis (FEA) method. In this FEA study, the effects on stress distribution were evaluated of different implant-supported fixed prosthetic restorations under vertical and oblique forces. The null hypothesis of the study that the prosthetic materials would show no difference in the stress formed on the supporting tissues was rejected.

Implants and natural teeth respond in different ways to chewing forces [14]. These differences are associated with the presence or absence of periodontal ligaments, which function as an elastic buffer [15]. Analysis of the biomechanical responses of these structures is extremely difficult because of the tooth anatomy and complexity of microstructural details [16]. Finite element analysis (FEA), allowing the standardisation of parameters, is an appropriate analytical method for the evaluation of biomechanical behaviour in complex geometry.

FEA models can be formed as two-dimensional (2D) or three-dimensional (3D). In 2D models, deformations outside the plane, strains and stresses are ignored, and artificial constraints cause more errors in the analysis. Therefore, compared to 2D models, the use of 3D models in the analysis of biological or biocompatible structures enables more realistic results to be obtained [17].

When applying FEA to dental implants, it is important to take oblique occlusal forces into consideration, because the stresses formed in structures in these conditions reflect clinical reality better than results obtained using only vertical occlusal force [18]. Similar to the results of the current study, it has been previously shown that oblique loading forces cause the highest maximum stress values in prosthetic infrastructures and these loads can increase the stress values by as much as 10-fold [19].

The greater stress forming in the body of an implant with anterior placement in implant-supported prostheses can be explained by the difference in resilience in region of the mandible [20, 21]. The findings of the current study demonstrated that stress was concentrated in the upper segment of screws and the neck regions of abutments and implants. In respect of the abutment screw, the highest stress values were determined in the neck section of the screw and the upper part of the thread. These findings suggest that the collar of the abutment screw and the level of the thread region could be the areas where fracture is most frequently seen. From a mechanical perspective, abutments serve as the first tool for occlusal load transfer [22]. Based on these results, materials with a high Young’s modulus show superior load transfer capability.

The findings of this study may be of help to clinicians in predicting the biomechanical behaviour of different prosthetic materials used in implant-supported prostheses. The type of restoration is important in the success of dental implants. Zirconia, which is used as an alternative to metal-supported porcelain restorations, can be used in the posterior region where occlusal loading is greater [23]. However, when the end resistance limit of zirconia (900-1200 MPa) is considered, the use of zirconia substructure under oblique forces may be a cause for concern. Compared to other prosthetic materials, oblique forces on zirconia can cause the formation of more intense stress in prosthetic materials and the implant screw. This can be attributed to the high elastic modulus of zirconia. Although the findings obtained in this study remained within physiological limits, it must not be forgotten that oblique forces will increase with a change in placement and angulation of the implant, and this can have destructive effects [19].

The lower stress values observed in the Trinia restorations may be related to the lower elastic modulus of this material compared with Co-Cr and zirconia. Materials with a lower elastic modulus can undergo greater elastic deformation under loading, which may help distribute occlusal forces more evenly and reduce peak stress concentrations within the restoration. In contrast, due to greater rigidity, Co-Cr and zirconia exhibited higher stress concentrations in the prosthetic structure. While previous studies have suggested that materials with a high Young’s modulus contribute to greater overall stiffness and stability of the implant–abutment complex, the findings of the current study indicate that less rigid materials such as Trinia may provide a more favourable stress distribution within the restoration by reducing localized stress concentrations [24].

Various studies have evaluated the effects of different prosthesis materials on the stress distribution on implants and the surrounding bone tissue, and it has been reported that a change in prosthetic material does not lead to significant differences in stress patterns or have only a limited effect [25, 26]. Although Wang et al. reported that restorative crowns produced from different materials could show displacement at different amounts, the total energy transferred to the implant-bone interface was similar [25].

The stress formed as a result of chewing forces in implant-supported prostheses is transmitted to the bone tissue supporting the implant via the prosthetic material and the abutment. It has been determined that deformations occurring in the cortical bone are affected by the prosthesis material at a negligible level, whereas a change of approximately 30% is seen under oblique loading compared to vertical loading [27]. This finding suggests that the load energy is dampened by being distributed within the model components and therefore the effect reaching the cortical bone remains limited.

In this study, similar biomechanical responses for cortical and cancellous bone were observed. Although resin matrix ceramics have been recommended as shock-absorbing materials [13–28], no significant reduction was observed in the stress concentrations in implants and the surrounding bone. The structures and various layers including the substructure material used for restoration, veneer material [29], cement layer, inner screw, and abutment, play a role in transmitting chewing forces to implants and surrounding bone. The total energy transferred to the implant-bone interface first passes from the abutment-implant interface [24]. It is thought that part of this transmitted energy is absorbed into these interfaces. This may explain the similar biomechanical responses observed in the implants in which different prosthetic substructure materials were used.

The connector dimensions were selected according to the manufacturer-recommended and clinically accepted minimum cross-sectional areas for each restorative material. Consequently, the observed differences may reflect the combined influence of material properties and framework design requirements, rather than material composition alone. In the distribution of stress formed by occlusal loading, oblique forces cause a concentration of stress in connector regions. This is a common finding in FEA studies of implant-supported prostheses [30]. The same stress pattern was observed for different framework materials in a previous FEA study [21]. This finding was confirmed in an in-vitro study that evaluated the resistance of a zirconia three-unit fixed prosthesis, which reported that fracture occurred most often in the connector region [11].

Some FEA studies have not confirmed the effect of restoration materials on stress distribution [31, 32]. However, this could be due to limitations of the finite element models. Although loading conditions are usually defined with the assumption of static and linear deformation, it is accepted that materials with different elasticity modulus are perfectly connected without any freedom of movement [31]. It has been shown in previous in-vitro studies that the shock absorption capacity of implant restorations depends on the damping behaviour of different dental materials under cyclical loading [32]. The viscoelastic properties of polymeric materials have been reported to increase damping behaviour [12, 31]. These changes occurring in restorative layers can be determined with FEA models. When the damping effect of platform switch design is taken into consideration, the similar effect of elastic prosthetic components is thought to be increased.

The Von Mises stress value should not exceed 550 MPa as the flow resistance in a titanium implant, otherwise there may be irreversible failures [34]. No stress value > 550 MPa was obtained in any of the implant models in the current study. In the MP frameworks, the Von Mises stress value of 372.28 MPa was obtained under oblique loading on the abutment.

An increase in the rigidity of fixed dental prosthesis material decreases deformation, and prosthetic framework materials such as metal and zirconia are known to have the properties of high mechanical strength and fracture resistance. However, there is insufficient evidence related to the efficacy of these materials in decreasing tensile distribution in the implant system and the underlying bone tissue. Kasem et al. supported this with a report stating that when the rigidity of the material used in a fixed prosthesis is increased, both deformation and catastrophic failures of the material decrease depending on the stress, and correspondingly stresses are transferred more to the underlying and supportive structures [33]. The Von Mises stress values obtained in the current study implant-supported prostheses were found to be lower in the polymer-based TC group. When this was evaluated in terms of the force transmission of shock-absorbing materials, it is a valuable finding in respect of being able to reduce unwanted complications such as abutment and screw fracture.

Trinia, which is a fibre-reinforced polymer, was evaluated in respect of the stress formed in peri-implant cancellous and cortical bone, and that the stress findings were caused by micro-stresses forming on these materials is supported by a previous study that reported no significant effect on stress values in the marginal bone surrounding supporting tissues [23]. When it is considered that all the chewing forces in prostheses supported by a limited number of implants are borne by a limited number of implants, peri-implant bone should be preserved in a way to minimise resorption.

There were some limitations to this study, inherent to the design [35]. In other studies of evaluations made with FEA, there have been seen to be various limitations such as not considering the internal structural model defects, not including technical sensitivities specific to clinical application, and no modelling of patient-related factors. Therefore, although the findings obtained are supportive of clinical application, they should be interpreted through careful evaluation together with other studies.

The vertical and oblique loading conditions were defined to be fixed from certain points. Variables such as parafunctional forces, age, gender, temperature, pH, loading direction, and fatigue were not taken into consideration. The materials undergoing simulation were accepted as isotropic and it was assumed that flawed populations were not included. Vertical incompatibility of the prostheses, early contact, and operator-related errors were not simulated. Although the use of linear contact between the screw and polymeric materials may not fully represent the most accurate stress status during loading, the models were standardised to allow comparisons. Nevertheless, to prevent any misunderstanding and better explain clinical behaviour, there is a need for further clinical studies to confirm the differences in mechanical behaviour, especially related to shock absorption properties, between Trinia and other prosthetic materials.

Conclusion

From the findings of this study, the following conclusions can be made;

1. Implant-supported fixed prosthetic restorations are influenced by the prosthetic materials used for the rehabilitation.

2. All the stress values for all the materials were within physiological limits.

3. The physical properties of materials affect stress distribution in fixed partial prostheses. Materials with a high elasticity modulus, such as Co-Cr and zirconia, cause the formation of intense stress, compared to ductile materials such as Trinia.

There is a need for further clinical research of all these materials that are used in implant-supported prostheses, and the support of in-vitro studies.

Abbreviations

Co-Cr

Cobalt Chrome

FEA

Finite Element Analysis

PEEK

Poly Ether Ether Ketone

FDP

Fixed Dental Prothesis

3D

3 dimensional

N

Newton

MPa

Mega Pascal

Authors’ contributions

S.S.G. and A.G.S. performed the finite element analysis.  The authorscontributed to data interpretation.  A.G.S. conceived and designed the study. A.G.S. drafted the manuscript. All authors read and approved the final manuscript.

Funding

This study was financially supported by the Scientific Research Projects Unit of Sivas Cumhuriyet University (Project No. DIS-2024-330).

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study was approved by the Non-Interventional Ethics Committee of Sivas Cumhuriyet University on 21.03.2024 ((Approval Number:2024-03/13). The study was conducted in accordance with the Declaration of Helsinki. The requirement for informed consent was waived by the Ethics Committee due to the retrospective and anonymized nature of the computed tomography data used in the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.