Biomechanical evaluation of three full-arch immediate loading protocols in the mandible via finite element analysis: All-on-4, Trefoil, and Five-implant design

Abstract

Background

Immediate-loading full-arch concepts such as All-on-4, Trefoil, and Five-Implant protocols are widely used for mandibular rehabilitation, yet their comparative biomechanical behavior remains insufficiently defined.

This study aimed to biomechanically compare three immediate loading full-arch rehabilitation protocols—Trefoil, All-on-4, and 5-Implant designs—in the edentulous mandible using three-dimensional (3D) finite element analysis (FEA), focusing on stress distribution, strain accumulation, and deformation patterns under functional loading.

Materials and Methods

A digital edentulous mandible model was constructed, incorporating cortical and cancellous bone layers, and standardized prosthetic designs for each configuration. Three implant-supported protocols were simulated: Trefoil (three axial implants with a prefabricated bar), All-on-4 (two axial anterior and two posterior tilted implants), and a Five-Implant design (midline, canine, and second premolar implants). The implant–bone interface, simulating immediate loading without full osseointegration, was assigned a coefficient of 0.30. Axial and 45° oblique loads of 100 N were applied to the first molar. Von Mises stress, principal stresses, equivalent strain, and total deformation were analyzed.

Results

The Five-Implant model exhibited the most favorable biomechanical outcomes, demonstrating the lowest stress and strain values across prosthesis, implant components, and cortical bone. The Trefoil system showed the highest prosthetic stress (156.48 MPa axial; 119.32 MPa oblique) and abutment screw deformation, attributed to its reduced implant support and increased cantilever length. All-on-4 generated elevated cortical bone strain under oblique loading (4180 με), surpassing the pathological overload threshold (>4000 με), whereas, the Five-Implant model maintained cortical strain within the physiological remodeling range.

Conclusion

Implant number and distribution significantly affect biomechanical behavior in immediate full-arch rehabilitation. The Five-Implant design offers biomechanical superiority in stress mitigation and bone-strain control, while Trefoil and All-on-4 configurations present design-dependent biomechanical challenges. Treatment planning considering anatomical limitations and functional loading conditions is essential to optimize clinical outcomes.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12903-025-07404-1.

Introduction

Edentulism, particularly in the mandibular arch, continues to present significant functional and biomechanical challenges due to the progressive alveolar bone resorption and the limited stability of conventional complete dentures [1]. Implant-supported full-arch fixed restorations have therefore become the gold standard for mandibular rehabilitation, offering improved masticatory efficiency, patient comfort, and long-term predictability, particularly in immediate loading protocols [2].

Among the most widely accepted immediate loading treatment strategies is the All-on-4 concept, which places two anterior axial implants and two posterior tilted implants to increase the anteroposterior spread and circumvent anatomical limitations such as the mandibular canal or mental foramen [3]. Numerous finite element analysis (FEA) studies have shown that tilting distal implants reduces the cantilever length and optimizes the stress distribution within both peri-implant bone and prosthetic structures (4, 5).

Another innovative approach is the Trefoil system, which utilizes three axially placed implants in the interforaminal region (midline and bilateral first premolars) along with a prefabricated bar that incorporates adaptive joints. This system aims to reduce surgical time and laboratory procedures while providing immediate fixed rehabilitation for the edentulous mandible [4]. The Trefoil system represents an evolution of the earlier Brånemark Novum protocol, which also employed three axial implants and a prefabricated metallic bar. Although the Novum system showed initial promise, it required strict surgical precision and offered limited tolerance for intraoperative deviations, which restricted its widespread clinical adoption. The Trefoil design addresses these challenges through guided templates and adaptive components that enhance passive fit and prosthetic predictability [5–8].

In contrast, the five-implant-supported fixed prostheses— typically involving implants placed at the midline, canines, and second premolars—offers improved biomechanical support and minimized cantilever forces but requires more bone volume and surgical complexity [9]. Although biomechanically favorable, this approach may not be feasible in cases of severe mandibular resorption or financial limitations. Recent evidence suggests that adding a fifth implant (All-on-5) can substantially improve stress distribution; a 2025 FEA study by Sevinç Gül et al. demonstrated reductions of up to 16.9% in cortical bone stress and 46% in implant stress in V-shaped mandibles compared with the All-on-4 configuration [10].

FEA has emerged as a powerful tool in implant biomechanics, enabling detailed, noninvasive assessment of stress, strain, and deformation patterns under controlled functional conditions [11–16]. A substantial body of FEA research has shown that implant number, inclination, cantilever length, and mandibular morphology are critical determinants of the mechanical behavior of full-arch prostheses [17–19]. For instance, Sun et al. reported that five-implant configurations generate lower cortical bone stresses than All-on-4 designs in V-shaped mandibles [18], whereas Sultanoğlu et al. emphasized that increased cortical bone thickness can reduce peak stresses in Trefoil-supported prostheses [19]. In addition, Correa et al. showed that three-implant frameworks, especially with cantilevers of 15 mm or more, tend to surpass biomechanical safety thresholds, recommending the use of at least four implants and cantilever lengths of ≤ 10 mm to preserve structural integrity [20].

Implant loss has been shown to substantially increase stress on the remaining implants and surrounding bone, particularly in reduced support configurations such as the Trefoil system [21]. Implant angulation, as used in the All-on-4 concept, has been reported to improve load transfer mechanics compared with parallel implant placement by redirecting forces along more favorable axes [17]. Consistent with this, Fazi et al. demonstrated that increasing posterior angulation (e.g., 34° vs. 17°) reduces stress at the bone-implant interface and within the prosthetic framework [22]. Furthermore, increasing the number of supporting implants also provides biomechanical advantages; All-on-6 models show lower stress magnitudes than All-on-4 [23], and tilted narrow-diameter implants exhibit distinct stress patterns under oblique loads, underscoring the influence of implant geometry on force distribution [24].

Despite extensive research, the existing evidence remains fragmented due to variations in implant dimensions, loading protocols, modeling assumptions, and bone geometry. Consequently, the comparative biomechanical of Trefoil, All-on-4, and Five-Implant concepts has not been clearly established. To date, no study has performed a direct, standardized evaluation of these three immediate loading strategies using identical FEA conditions and under both axial and oblique functional loading.

Therefore, the present study aims to provide the first unified and clinically relevant three-dimensional FEA comparison of Trefoil, All-on-4, and Five-Implant immediate loading protocols in the edentulous mandible. By maintaining identical model geometry, material properties, boundary conditions, and loading assumptions across all configurations, the analysis isolates the biomechanical effects attributable solely to implant number and distribution. The primary objective is to evaluate and compare stress distribution, cortical bone strain, and prosthetic deformation among the three designs, with the null hypothesis stating that no significant differences in biomechanical behavior exist between them.

Materials and methods

This study aimed to compare the biomechanical performance of three immediate-loading protocols for mandibular full-arch rehabilitation—Trefoil, All-on-4, and a five-implant configuration—using 3D FEA.

Finite element mandible model design

A 3D digital model of a fully edentulous mandible was created on the basis of a Frasaco acrylic phantom jaw (Frasaco GmbH, Tettnang, Germany). The model incorporated anatomically accurate representations of cortical bone (2 mm thickness), cancellous bone, and a 3 mm layer of soft tissue, reflecting the morphology of a moderately resorbed mandibular arch. Dimensional parameters—approximately 98 mm intergonial width, 16 mm vertical height in the interforaminal region, and 7 mm midline ridge width—were consistent with Modified Cawood and Howell Class V resorption, characterized by a rounded, flattened ridge contour [25]. To ensure geometric symmetry and standardization, the mandible was mirrored across the midline and refined in CAD software to produce a proportionally accurate and uniform edentulous model.

Implant systems and prosthetic components

All implants and components were sourced from Nobel Biocare (Gothenburg, Sweden). To ensure standardization across the models, implants with identical dimensions (5.0 mm diameter × 11.5 mm length) were selected. The All-on-4 and Five-Implant models incorporated NobelParallel Conical Connection RP implants, whereas the Trefoil protocol employed system-specific Trefoil implants characterized by a Conical Connection and a 4.5 mm Tissue Collar design. Although Trefoil rehabilitation typically requires implant lengths of 11.5 mm and 13 mm to accommodate the prefabricated bar [26], identical implant dimensions were adopted for all groups to eliminate confounding influences related to implant size.

Implant positions were assigned according to each treatment protocol. The Five-Implant model included axial implants at the midline, canine, and second premolar regions. In the All-on-4 configuration, anterior implants were placed axially in the lateral incisor sites, while posterior implants were tilted 30° distally and positioned at the second premolars. The Trefoil system incorporated three axial implants at the midline and first premolar sites.

Prostheses were designed using semi-anatomical artificial teeth (SR Orthotyp DCL, Ivoclar Vivadent) and acrylic resin to replicate immediate loading conditions. A standardized occlusal plane was used for all models, and each prosthesis included 12 teeth with gingival contours adapted to compensate for cervical tissue loss. Multi-unit abutments with 3 mm transmucosal height were employed in the All-on-4 and Five-Implant groups, whereas the Trefoil model utilized its prefabricated titanium bar and dedicated system components(Fig. 1) .

Fig. 1.

Schematic representation of the models showing implant positions in the mandible, separated components, and the assembled configuration

Material properties

Material properties were assigned according to values reported in the literature. Implants, implant components, and acrylic prostheses were assumed to be linearly elastic, homogeneous, and isotropic materials, whereas cortical and cancellous bone were defined as anisotropic to reflect their directional mechanical behavior [27]. Titanium grade 4 was used for the implants, whereas titanium grade 5 was used for the abutments and screws [24]. The mechanical properties applied in the simulations, obtained from previous studies [28–30] are summarized in Table 1.

Table 1.

Material properties (Young’s modulus and poisson’s ratio) used in the finite element models

Materials	Young’s modulus (GPa)	Poisson’s ratio
Cortical bone	Ex 12.600	νxy 0.30
	Ey 12.600	νyz 0.39
	Ez 19.400	νxz 0.39
Cancellous bone	Ex 1.150	νxy 0.01
	Ey 2.100	νyz 0.32
	Ez 1.150	νxz 0.05
Implant fixture (Titanyum grade 4)	110	0.35
Implant component (Titanyum grade 5)	117	0.30
Prosthesis and Teeth (Acrylic resin)	2.4	0.40

Meshing and contact conditions

3D modeling and preprocessing were performed in SolidWorks (Dassault Systèmes), and the finite element analyses were conducted using ANSYS Workbench (ANSYS Inc., USA). Mesh refinement followed a 5% convergence criterion based on maximum von Mises stress, resulting in a final element size of 0.3 mm. The models were discretized with tetrahedral elements, yielding approximately 1.1–1.2 million elements and nearly 2 million nodes depending on the implant configuration.

Contact interactions were defined using frictional coefficients derived from previous literature. The implant–bone interface, representing immediate loading without full osseointegration, was assigned a coefficient of 0.30 [31, 32]. Titanium–titanium interfaces between implants and components were assigned a coefficient of 0.16 [32, 33]. The interface between the prosthesis and multi-unit abutment copings was modelled as fully bonded.

Loading and boundary conditions

Two unilateral loading scenarios were simulated. In the first scenario, an axial load of 100 N was applied to the central fossa of the first molar (approximately 1.5 mm² contact area). In the second scenario, an oblique load of 100 N was applied at a 45° angle relative to the x, y, and z axes on the same contact point. These loads were selected to represent physiologically relevant functional masticatory forces.

To enable a controlled and comparable biomechanical evaluation of the Trefoil, All-on-4, and Five-Implant configurations, identical loading conditions were applied across all models. Standardizing load magnitude is essential in comparative FEA studies because it isolates the influence of implant distribution and geometry while eliminating confounding variations caused by differences in force application. Using consistent axial and oblique loads therefore allows direct comparison of stress distribution, cortical bone strain, and prosthetic deformation among the three treatment strategies.

Boundary conditions were defined by fully constraining the mandibular base in all degrees of freedom.

Output parameters and analysis

The biomechanical assessment focused on four primary outcome measures: von Mises stress, principal stresses, equivalent strain, and total deformation. Von Mises stress was analyzed in the prosthesis, abutments, abutment screws, implants, and cortical bone to characterize overall mechanical response under loading. Maximum and minimum principal stresses were evaluated in the cortical bone to capture tensile and compressive behavior relevant to overload-induced bone resorption. Equivalent strain was included due to its established correlation with bone remodeling thresholds according to Frost’s mechanostat theory, and total deformation was used to quantify structural displacement within prosthetic and implant components.

To reduce the influence of localized peak artifacts and numerical singularities, stress results were evaluated using the average of the top ten nodal values for each region of interest. Stress and strain distributions were visualized through color-coded contour maps generated in ANSYS, and all values were reported in megapascals (MPa). Because finite element analysis is a deterministic technique, no statistical testing was applied; instead, biomechanical behavior was interpreted directly from stress magnitudes, patterns, and comparative trends across the three configurations.

Results

FEA revealed notable differences in stress distribution and deformation among models under axial and oblique loading conditions [Simulation videos are available as Supplementary Material.]. Across all the models and loading scenarios, the highest von Mises stress, principal stress, equivalent strain, and total deformation values were predominantly concentrated in the regions adjacent to the site of load application. This pattern was consistently observed under both axial and oblique loading conditions, emphasizing that regions directly subjected to occlusal forces bear the greatest mechanical burden .

The numerical values for stress, strain, and deformation are summarized in Tables 2, 3, 4 and 5; Figs. 2, 4 and 6, and 8, while their distribution patterns are illustrated in Figs. 3, 5 and 7, and 9. Specifically, Table 2; Fig. 2 present the average von Mises stress values (MPa) for the prosthesis, abutment, abutment screw, and implant under axial and oblique loading in the Trefoil, All-on-4, and 5-implant models, with the corresponding distributions shown in Fig. 3. Table 3; Fig. 4 display the average von Mises and principal stresses (maximum tensile and minimum compressive, MPa) in cortical bone, and Fig. 5 depicts their spatial distributions, highlighting stress concentrations near the crestal region. The average equivalent strain values are reported in Table 4; Fig. 6, with their distributions shown in Fig. 7. Finally, Table 5 lists the total deformation magnitudes, which are illustrated graphically in Fig. 8 and spatially in Fig. 9.

Table 2.

Average von mises stress values (MPa) in prosthesis, abutment, abutment screw, and implant under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Models	Prosthesis		Abutment		Abutment Screw		Implant
	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading
Trefoil	156.48	119.32	115.77	79.09	92.44	123.62	105.17	126.45
All-on-4	80.40	76.57	265.61	216.01	56.00	57.59	214.54	187.82
5-Implant	64.00	58.91	103.72	180.75	45.27	76.29	606.42	158.99

Table 3.

Average von mises stress and principal stresses (maximum tensile and minimum compressive) in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Models	Cortical Bone
	Von Mises Stress (MPa)		Maximum Principal Stress (MPa)		Minimum Principal Stress (MPa)
	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading
Trefoil	34.32	38.12	22.88	31.90	54.23	48.52
All-on-4	29.46	52.07	29.81	35.08	18.24	43.74
5-Implant	14.80	19.32	13.30	15.02	11.83	17.95

Table 4.

Average equivalent von mises strain values (µε) in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Models	Cortical Bone equivalent Von Mises strain value (µε)
	Axial Loading	Oblique Loading
Trefoil	2830	2930
All-on-4	2420	4180
5-Implant	1110	1490

Table 5.

Total deformation values (mm) in prosthesis, abutment, abutment screw, and implant under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Models	Prosthesis		Abutment		Abutment Screw		Implant
	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading	Axial Loading	Oblique Loading
Trefoil	0.125	0.122	0.020	0.029	0.044	0.040	0.017	0.025
All-on-4	0.087	0.136	0.015	0.030	0.019	0.040	0.011	0.014
5-Implant	0.073	0.111	0.011	0.026	0.014	0.034	0.008	0.013

Fig. 2.

Bar charts of von Mises stress values (MPa) in the prosthesis and implant components under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 4.

Bar charts of von Mises and principal stresses (maximum tensile and minimum compressive, MPa) in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 6.

Bar charts of equivalent von Mises strain values (µε) in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 8.

Bar charts of total deformation values (mm) in the prosthesis, abutment, abutment screw, and implant under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 3.

ANSYS-derived distribution maps of von Mises stress in the prosthesis and implant components under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 5.

ANSYS-derived distribution maps of von Mises and principal stresses (maximum tensile and minimum compressive) in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 7.

ANSYS-derived distribution maps of equivalent von Mises strain in cortical bone under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Fig. 9.

ANSYS-derived distribution maps of total deformation in the prosthesis, abutment, abutment screw, and implant under axial and oblique loading in the Trefoil, All-on-4, and 5-Implant models

Stress distribution

Prostheses

Under axial loading conditions, the Trefoil prosthesis exhibited the highest von Mises stress value (156.48 MPa), which was nearly double that of the All-on-4 prosthesis (80.40 MPa) and approximately 2.45 times higher than the Five-Implant prosthesis (64.00 MPa). A similar distribution trend was observed under oblique loading, with stress values of 119.32 MPa, 76.57 MPa, and 58.91 MPa for the Trefoil, All-on-4, and 5-Implant prostheses, respectively.

Implant

The Five-Implant model demonstrated the highest implant-level von Mises stress under axial loading (606.42 MPa), which was significantly greater than All-on-4 (214.54 MPa) and Trefoil (105.17 MPa) configurations. However, under oblique loading, the All-on-4 implants exhibited elevated stress (187.82 MPa), surpassing those of the Five-Implant (158.99 MPa) and Trefoil (126.45 MPa) models.

Abutment

Among the abutments, the All-on-4 model experienced the highest stress concentrations, with von Mises values of 265.61 MPa under axial loading and 216.01 MPa under oblique loading. The Trefoil abutment followed with 115.77 MPa (axial) and 79.09 MPa (oblique), whereas the Five-Implant abutment demonstrated lower stress magnitudes (103.72 MPa axial; 180.75 MPa oblique).

Abutment screw

In the abutment screw regions, Trefoil screws exhibited the highest von Mises stresses under axial (92.44 MPa) and oblique (123.62 MPa) loading. The All-on-4 model presented moderate stress values (56.00 MPa axial; 57.59 MPa oblique), while the Five-Implant abutment screws showed the lowest stress levels under axial loading (45.27 MPa) but exhibited an increase under oblique loading (76.29 MPa).

Cortical bone

In terms of the cortical bone von Mises stress distribution, the Trefoil model demonstrated the highest von Mises stress under axial loading (34.32 MPa), followed by theAll-on-4 (29.46 MPa) and Five-Implant (14.80 MPa) configurations. However, under oblique loading, the stress magnitudes increased across all the models, with All-on-4 exhibiting the highest cortical bone stress (52.07 MPa), followed by Trefoil (38.12 MPa) and Five-Implant (19.32 MPa).

Under axial loading conditions, the All-on-4 model generated the highest maximum principal stress in the cortical bone (29.81 MPa), followed by the Trefoil (22.88 MPa) and Five-Implant (13.30 MPa) configurations. With respect to the minimum principal stress values, the Trefoil model exhibited the highest compressive stress magnitude (54.23 MPa), while the All-on-4 (18.24 MPa) and Five-Implant (11.83 MPa) models demonstrated considerably lower compressive stress levels.

When subjected to oblique loading, the All-on-4 configuration again demonstrated the highest maximum principal stress in cortical bone (35.08 MPa), surpassing the Trefoil (31.90 MPa) and Five-Implant (15.02 MPa) designs. In terms of the minimum principal stress, the Trefoil model exhibited the most pronounced compressive stress (− 48.52 MPa), followed by All-on-4 (− 43.74 MPa) and Five-Implant (− 17.95 MPa) models.

Overall, while the All-on-4 design induced higher tensile stresses in the cortical bone under both loading scenarios, the Trefoil configuration resulted in elevated compressive stress concentrations, particularly under axial loading. The Five-Implant model consistently demonstrated the lowest principal stress magnitudes across both the maximum (tensile) and minimum (compressive) stress parameters.

Equivalent strain distribution in cortical bone

Under axial loading conditions, the Trefoil model showed the highest equivalent strain in the cortical bone (2830 µε), followed by the All-on-4 (2420 µε) and Five-Implant (1110 µε) configurations. These findings indicate that the Trefoil protocol induces more pronounced strain concentrations in the surrounding bone tissue under vertical masticatory forces.

When subjected to oblique loading, a marked increase in cortical strain values was observed across all configurations. The All-on-4 model demonstrated the highest equivalent strain (4180 µε), significantly exceeding the values recorded for the Trefoil (2930 µε) and Five-Implant (1490 µε) models.

Overall, while the Trefoil model generated the greatest cortical strain under axial loading, the All-on-4 configuration was associated with the most critical strain accumulation under oblique functional loads. The Five-Implant model consistently exhibited the lowest strain magnitudes under both loading scenarios, indicating more favorable biomechanical behavior in terms of the bone strain distribution.

Total deformation

Prosthesis

Under axial loading conditions, the Trefoil prosthesis exhibited the greatest total deformation (0.125 mm), followed by the All-on-4 (0.087 mm) and Five-Implant (0.073 mm) configurations. However, under oblique loading, the deformation magnitudes shifted; the All-on-4 prosthesis demonstrated the highest deformation (0.136 mm), exceeding that of Trefoil (0.122 mm) and Five-Implant (0.111 mm) models. These findings indicate that while the Trefoil design is more susceptible to deformation under axial forces, the All-on-4 configuration exhibits increased flexibility under oblique functional loads.

Implant

Implant deformation values were highest in the Trefoil model, with total deformations of 0.017 mm (axial) and 0.025 mm (oblique). The All-on-4 configuration demonstrated moderate deformation (0.011 mm axial; 0.014 mm oblique), while the Five-Implant model exhibited the least amount of implant deformation, with values of 0.008 mm under axial loading and 0.013 mm under oblique loading.

Abutment

At the abutment level, the Trefoil model again recorded the highest deformation magnitudes, with 0.020 mm under axial loading and 0.029 mm under oblique loading. The All-on-4 abutments followed with deformation values of 0.015 mm (axial) and 0.030 mm (oblique). The Five-Implant abutments demonstrated the least deformation, with values of 0.011 mm (axial) and 0.026 mm (oblique).

Abutment screw

For the abutment screws, the Trefoil model displayed the highest total deformation under both loading scenarios (0.044 mm axial; 0.040 mm oblique). Interestingly, under oblique loading, both the All-on-4 and Trefoil models exhibited identical abutment screw deformation (0.040 mm), whereas the Five-Implant model showed slightly lower values (0.014 mm axial; 0.034 mm oblique).

Discussion

The present finite element analysis demonstrated distinct biomechanical differences among the Trefoil, All-on-4, and Five-Implant immediate loading protocols in the edentulous mandible. These differences were reflected in stress distribution, cortical strain, and deformation patterns, thereby disproving the null hypothesis of equivalent biomechanical behavior across the three configurations.

The Five-Implant model consistently demonstrated the most favorable biomechanical behavior, with the lowest von Mises stress, strain, and deformation across the prosthesis, implant, and cortical bone. These findings corroborate previous studies demonstrating that increasing the number of supporting implants improves load distribution and reduces cantilever-induced bending forces [18, 23]. The additional anchorage at the midline and second premolars in this design effectively minimizes bending moments, resulting in more uniform transfer of occlusal loads. Although this configuration exhibited the highest implant-level stress (606.42 MPa) under axial loading, this peak remained below the yield strength of Ti-6Al-4 V, indicating that the system operated within safe mechanical limits (830 MPa) [34]. Overall, the Five-Implant model demonstrated biomechanical superiority by providing lower prosthetic and component stresses and substantially more favorable cortical bone strain patterns.

Conversely, the Trefoil system exhibited the highest stress concentrations and deformation magnitudes, particularly under axial loading. These findings are consistent with the reduced implant support and longer cantilever inherent to this design, both of which increase bending moments on the framework and concentrate stresses in unsupported regions. Correa et al. similarly reported that three-implant prostheses with cantilevers greater than 10 mm are prone to biomechanical compromise [20]. Although the prefabricated bar in the Trefoil system enhances structural rigidity, it can also channel a substantial portion of occlusal forces into the bar itself, leading to elevated internal stresses. In contrast, the Five-Implant model offers a broader and more evenly distributed support base, effectively limiting cantilever-related load amplification and resulting in lower prosthetic stress values.

Although the prefabricated bar in the Trefoil configuration enhances the structural rigidity and optimizes the load distribution, its limited flexural capacity may contribute to greater localized deformation under axial loading. Under oblique loading, however, this rigidity can be advantageous by constraining lateral displacement. The adaptive joint mechanism and prefabricated workflow of the Trefoil system provide meaningful clinical benefits by simplifying surgery and reducing chairside time [5]. These advantages must nonetheless be weighed against biomechanical drawbacks, including higher prosthetic stresses and abutment screw deformation. Clinically, minimizing cantilever length, reinforcing the prosthetic framework, and avoiding use in patients with high occlusal forces or parafunctional habits may help mitigate these risks. Importantly, clinical data have shown that using the system-specific 5.0 mm diameter implants with lengths of 13 and 11.5 mm, 85% and 86% of patients, respectively, were eligible for treatment with the standardized Trefoil prosthesis [26]. This evidence supports the feasibility of the implant dimensions adopted in this biomechanical analysis.

The All-on-4 configuration displayed a distinct biomechanical pattern. Although prosthetic deformation was lower than in the Trefoil design, this configuration produced higher cortical bone stress and strain, particularly under oblique loading. This outcome is likely related to the posteriorly tilted implants, which enhance prosthetic support but modify load-transfer pathways to the bone. Fazi et al. reported that increasing implant angulation can improve load direction and reduce interface stresses [22]; however, when tilt becomes excessive, stress concentrations may shift unfavorably to the surrounding cortical bone, as observed in the present analysis. This may help explain the marginal bone loss patterns frequently reported in clinical All-on-4 studies [12, 35].

Prosthetic deformation patterns differed among the configurations. The Trefoil design demonstrated the greatest deformation under axial loading, whereas the All-on-4 system showed higher deformation under oblique forces. These trends reflect the influence of implant number, cantilever length, and support geometry on framework flexibility, with Trefoil being more vulnerable to axial displacement and All-on-4 exhibiting increased deformation under lateral loading.

Interestingly, the Trefoil configuration demonstrated lower implant-level stresses than both the All-on-4 and Five-Implant models. This behavior may be attributed to the system’s tissue-collar implant design, which positions the implant–abutment interface coronally and promotes supracrestal load transfer. Such a stress-shifting mechanism reduces the concentration of forces at the crestal bone and within the implant body, consistent with FEA studies demonstrating the biomechanical advantages of tissue-level platforms [36]. Additionally, the conical connection of Trefoil implants enhances interface stability and may contribute to the more favorable stress dissipation observed compared with bone-level implants used in the other configurations.

The abutment screws in the Trefoil configuration exhibited the highest deformation, raising concerns about a potential increased risk for mechanical complications such as screw loosening or fracture. This behavior may be related to the longer screw design required to combine the abutment connection and occlusal fixation functions, effectively increasing the moment arm and bending forces applied to the screw. Similar findings have been reported in studies showing that reduced implant-supported frameworks place greater mechanical demand on the abutment complex [4, 37].

Additionally, the Trefoil model exhibited elevated compressive stresses in cortical bone under axial loading, approaching levels associated with overload-induced bone resorption. This behavior is consistent with reports indicating that three-implant prostheses with extended cantilevers may exceed biomechanical tolerance limits and compromise long-term bone stability [1]. In contrast, the Five-Implant design maintained cortical stress and strain levels within physiological ranges, reinforcing its biomechanical superiority.

According to Frost’s mechanostat theory and corroborated by clinical FEA reviews, physiological cortical‑bone remodeling is typically triggered by strain values between approximately 2000 and 4000 µε, whereas strain exceeding ~ 4000 µε is considered to enter a pathological overload zone potentially leading to microdamage or resorption [38, 39]. Based on these thresholds, the equivalent strain values observed in cortical bone under both axial and oblique loading conditions revealed distinct biomechanical behaviors among the evaluated configurations. In the present analysis, Trefoil and All-on-4 configurations produced axial strain values within the upper physiological range, while the Five-Implant design generated substantially lower strains, reflecting a more favorable biomechanical environment. Under oblique loading, the All-on-4 system slightly exceeded the overload threshold, suggesting a potential risk for cortical microdamage during functional loading. In comparison, Trefoil remained within the adaptive zone and Five-Implant consistently demonstrated the lowest strain magnitudes. These findings indicate that although Trefoil and All-on-4 can support physiological adaptation under axial forces, the All-on-4 configuration may predispose cortical bone to overload under oblique loading, whereas the Five-Implant model maintains cortical strain within biologically safe limits across both conditions.

Although the Five-Implant configuration demonstrated the most favorable biomechanical profile, its clinical applicability depends on adequate bone volume and may be limited in patients with advanced ridge resorption. In such cases, less invasive protocols such as All-on-4 or Trefoil remain viable alternatives, despite their comparatively higher mechanical demands. These findings underscore the need to balance biomechanical optimization with anatomical feasibility and patient-specific factors, reinforcing the importance of individualized treatment planning in full-arch rehabilitation.

This study has several limitations. First, static loading conditions and idealized material properties were assumed, which may not fully replicate the dynamic and heterogeneous nature of in vivo masticatory forces and biological tissues. Second, the immediate loading scenario was simulated through frictional contacts without accounting for the progressive osseointegration process. Third, screw pretension was not incorporated, potentially influencing local stress predictions at the abutment–implant interface. In addition, the deterministic nature of FEA precludes statistical variability; however, reliability was strengthened through top-node averaging and by confirming consistency with trends reported in previous FEA studies. Future research incorporating dynamic fatigue loading, patient-specific anatomical modeling, and clinical outcome validation is needed to better characterize the long-term biomechanical performance of these full-arch protocols.

Clinical implications

The biomechanical superiority of the Five-Implant configuration—characterized by reduced prosthetic stress, lower component deformation, and minimal cortical strain—supports its use whenever anatomical conditions and patient resources allow. By providing broader support and minimizing cantilever effects, this design offers a favorable long-term prognosis.

In contrast, the Trefoil system, although advantageous in reducing surgical time and simplifying laboratory procedures, demonstrated higher stress concentrations in prosthetic structures and abutment screws. Its use should therefore be approached with caution in patients presenting high occlusal forces, parafunctional habits, or limited bone quality. Controlling cantilever length and reinforcing the prosthetic framework may help mitigate mechanical risks.

The All-on-4 configuration exhibited increased cortical bone strain under oblique loading, emphasizing the need for careful implant angulation and prosthetic design optimization. Regular follow-up to monitor bone adaptation is advisable in these cases.

Overall, these findings highlight the importance of integrating patient-specific anatomical and functional factors into implant selection. While simplified protocols such as Trefoil and All-on-4 remain valuable options in compromised clinical situations, their biomechanical trade-offs must be balanced against long-term prosthetic durability and patient expectations.

Conclusion

Within the limitations of this finite element analysis, implant number and distribution were shown to have a decisive influence on the biomechanical performance of immediate-loading full-arch rehabilitations in the edentulous mandible. The Five-Implant configuration consistently demonstrated the most favorable mechanical behavior—characterized by lower prosthetic stress, reduced component deformation, and cortical strain levels within physiological limits—supporting its use whenever adequate bone volume is available.

The Trefoil and All-on-4 systems remain valuable options in anatomically or financially constrained situations; however, Trefoil exhibited higher prosthetic and screw stresses, and All-on-4 produced cortical strain that exceeded overload thresholds under oblique loading. These findings highlight the importance of minimizing cantilevers, optimizing implant angulation, and selecting the treatment protocol according to patient-specific anatomical and functional demands.

Overall, the results emphasize that strategic implant distribution and cantilever control are critical to reducing biomechanical overload and enhancing long-term stability in mandibular full-arch rehabilitation.

Abbreviations

FEA

Finite element analysis

3D

Three-dimensional

MPa

Megapascal

N

Newton

Authors’ contributions

Conception – M.T., N.B., G.Y.A.; Design – M.T., N.B., G.Y.A.; Supervision – G.Y.A., M.T.; Fundings – Inonu University Scientific Research Projects Unit; Materials – M.T., N.B.; Data Collection and/or Processing – M.T.; Analysis and/or Interpretation – M.T., G.Y.A.; Literature Review – M.T., G.Y.A.; Writing – M.T., N.B., G.Y.A.; Critical Review – M.T.; All authors reviewed the manuscript.

Funding

This study was supported by grant No. TDH-2020-2271 from the Inonu University Scientific Research Projects Unit, Malatya, Türkiye.

Data availability

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

Declarations

Ethics approval and consent to participate

This study is an in vitro 3D finite element stress analysis study. Ethical approval is not needed.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.