Posterior implant angulation without cantilever reduction in mandibular All-on-4: a controlled finite element analysis of stress transfer and implant macrodesign effects

Abstract

Background

Posterior implant angulation is widely used in mandibular All-on-4 rehabilitation, but its proposed biomechanical benefit is often confounded by concurrent cantilever reduction and/or increased distal support. This finite element analysis isolated the effect of posterior angulation under standardized prosthetic geometry and assessed whether implant macrodesign modified stress transfer under healed, bonded-interface assumptions.

Methods

Four three-dimensional finite element models of an edentulous mandible were created: axial posterior implants (VERT4) and 30° distally tilted posterior implants (ALL4). Each configuration was simulated with two implant macrodesigns (NobelActive and Straumann BL). A 12-unit screw-retained prosthesis extending to the first molars was modeled with identical emergence profile, distal extension, and cantilever length across all models, without angulation-dependent distal implant-length gain. A healed condition was simulated using bonded bone-implant interfaces, and linear static analyses were performed. Two unilateral vertical load cases (300 N) were applied via a rigid food bolus over the left canine or left first-molar region. Principal stresses were extracted for cortical and trabecular bone, and von Mises stresses for implants, multiunit abutments, and the framework and veneering complex. Ranking stability was tested by ± 10% load variation.

Results

When posterior angulation was applied without cantilever reduction or increased distal support, tilted models showed higher peak stresses than axial models. Under first-molar loading, ALL4-N produced the highest cortical stresses (Pmax 100.44 MPa; Pmin − 95.30 MPa) and posterior implant von Mises stress (925.82 MPa). Under canine loading, ALL4-N also showed the highest posterior implant stress (546.94 MPa). The highest anterior multiunit abutment stress occurred in ALL4-S under first-molar loading (287.27 MPa). Across matched configurations, NobelActive models showed higher implant and connection stresses than Straumann BL models. Relative rankings were unchanged in sensitivity analyses.

Conclusions

Within this linear-elastic, healed-interface model, posterior implant angulation did not provide a biomechanical advantage when used without cantilever reduction or increased distal support. It was associated with increased mechanical demand in peri-implant bone and implant-prosthetic components under unilateral loading. Findings should be interpreted as comparative trends within this model, not direct predictions of clinical failure or generalized inferiority of tilted implants in other scenarios. Implant macrodesign also influenced stress transfer.

Introduction

Mandibular edentulism is commonly associated with greater alveolar bone resorption in posterior regions than in the interforaminal area, and implant placement may be constrained by the proximity of the inferior alveolar nerve [1, 2]. When posterior support is required, augmentation procedures such as guided bone regeneration, block grafting, or nerve lateralization may be considered; however, these interventions increase surgical complexity, morbidity, cost, and treatment time [2–4].

To reduce surgical morbidity, mandibular full-arch rehabilitation protocols frequently prioritize implant placement within the interforaminal region [5] and have demonstrated high long-term survival in clinical cohorts, albeit with persistent mechanical complication rates [6]. Within this framework, the All-on-4 concept described by Malo et al. [7] combines two anterior axial implants with two posteriorly tilted implants, primarily to reduce cantilever length and/or increase distal support. However, posterior angulation may also be used without cantilever reduction, distal support gain, or longer posterior implants; under these conditions, its independent biomechanical effect remains uncertain [8]. Consistent with this concern, computational evidence suggests that posterior tilting is not inherently advantageous unless accompanied by cantilever reduction and/or increased distal support [9, 10].

Implant macrodesign is an additional determinant of load transfer in full-arch reconstructions [11, 12]. Implants with more aggressive cutting/thread features are frequently selected to enhance primary stability, particularly in immediate-loading protocols, whereas less aggressive macrogeometries may exhibit different stress-transfer behavior under healed loading [11, 13]. Despite the extensive finite element literature on full-arch rehabilitation, studies that isolate posterior angulation while holding prosthetic support geometry constant remain limited, and direct macrodesign comparisons under standardized geometry and loading conditions are scarce.

Accordingly, this three-dimensional finite element analysis isolated the biomechanical effect of posterior implant angulation by standardizing prosthetic geometry, emergence profile, and cantilever length while using clinically comparable implant sizes. Two implant macrodesigns (NobelActive and Straumann BL) were evaluated in four configurations: axial posterior placement (VERT4-N and VERT4-S) and posteriorly tilted placement (ALL4-N and ALL4-S; 30° distal angulation of posterior implants). Stress was assessed in peri-implant bone and implant-prosthetic components under healed-interface assumptions, and ranking robustness was tested via ± 10% load perturbations.

The null hypotheses were that: (1) posterior implant angulation, when applied without cantilever reduction or increased distal support, would not reduce stress concentrations relative to axial placement; and (2) implant macrodesign would not materially influence stress distribution under healed loading conditions.

Materials and methods

Study design

A controlled three-dimensional finite element analysis (FEA) was performed to isolate the biomechanical effect of posterior implant angulation in mandibular full-arch rehabilitation by standardizing prosthetic support geometry (emergence profile, distal extension, and cantilever length).

Implant systems and prosthetic reconstruction

Two commercially available implant systems were evaluated: NobelActive (Nobel Biocare, Zurich, Switzerland) and Straumann Bone Level (BL; Institut Straumann AG, Basel, Switzerland). Implant and prosthetic component geometries (implants, multiunit abutments, and prosthetic components) were digitized using an optical 3D scanner (Activity 880; Smart Optics Sensortechnik GmbH, Bochum, Germany), exported as STL files, and assembled in Rhinoceros 4.0 (Robert McNeel & Associates, Seattle, WA, USA). Because optical scanning does not fully capture internal connection details, these were reconstructed in CAD using manufacturer reference information.

To enable controlled comparisons across systems, prosthetic geometry—including emergence profile, distal extension, and cantilever length—was identical in all models. Because commercially available implant dimensions differ between systems, clinically comparable sizes were selected (Straumann BL 4.1 × 12 mm; NobelActive 4.3 × 11.5 mm). Implant platform level and apico-coronal positioning were adjusted to preserve identical emergence profile and prosthetic distal extension across configurations, thereby standardizing bending geometry despite minor dimensional differences between systems. Posterior angulation was not used to achieve any additional distal implant length advantage.

A standardized mandibular 12-unit screw-retained full-arch prosthesis extending to the first molars was modeled for all configurations. The framework was modeled as a cobalt-chromium (Co-Cr) alloy veneered with acrylic resin. Tooth morphology, occlusal alignment, and prosthetic thickness were kept constant across models.

Finite element model configurations

Four mandibular full-arch configurations were constructed (Fig. 1):

Fig. 1.

Finite element models evaluated in the study: ALL4-S (Straumann BL, posterior implants tilted 30°), ALL4-N (NobelActive, posterior implants tilted 30°), VERT4-S (Straumann BL, all implants axially placed), and VERT4-N (NobelActive, all implants axially placed)

• VERT4-S: Straumann BL, all implants axially placed.

• VERT4-N: NobelActive, all implants axially placed.

• ALL4-S: Straumann BL, posterior implants tilted 30° distally.

• ALL4-N: NobelActive, posterior implants tilted 30° distally.

To isolate the effect of angulation, tilted configurations were created without cantilever reduction, increased distal support, or distal implant-length gain, while preserving identical emergence profiles, distal extension, and cantilever length across models. Within each implant system, axial and tilted models were aligned to preserve equivalent prosthetic support geometry, so that angulation remained the principal design variable, independent of distal extension, cantilever change, or distal implant-length gain. A 30° distal angulation was selected because it is commonly used in All-on-4 protocols and allows direct comparison with axial placement under identical support geometry.

Anatomical modeling

Mandibular geometry was constructed as a generic virtual edentulous mandible. A fully anonymized archival CBCT dataset was used only to approximate the general external contour envelope and global spatial orientation. After initial contour extraction in 3D-Doctor (Able Software Corp., Lexington, MA, USA), the geometry was extensively re-parameterized and standardized. All anatomical features—including cortical thickness, trabecular compartment definition, crestal width, mandibular canal-crest distance, interforaminal height, mental foramen position and diameter, and mucosal thickness—were reassigned to predefined uniform values.

The standardized model consisted of trabecular bone surrounded by a uniform 2.0-mm cortical shell, an 8-mm crestal width, a 6-mm canal-to-crest distance, and a 14-mm interforaminal height. Mental foramina were positioned symmetrically 25 mm from the midline (interforaminal distance: 50 mm), with 7 mm and 4 mm distances to the inferior and superior borders, respectively, and a diameter of 3 mm. A 3-mm mucosal layer was included. Components were transferred to Rhinoceros while preserving the coordinate system. A single generic geometry was used to eliminate anatomical variability and enable a controlled comparison across configurations. In cantilever models, a 20-mm extension was defined distal to the terminal implant.

Mesh generation, element type, solver, and numerical verification

Preprocessing and solution were performed using a commercial finite element solver (ALGOR FEMPRO; ALGOR Inc., Pittsburgh, PA, USA) under linear static assumptions. The most recent stable release available to the authors at the time of analysis (ALGOR FEMPRO 2014) was used under an active license. STL geometries were converted to solid bodies and discretized using three-dimensional tetrahedral solid elements, with local refinement at the crestal cortical bone, implant neck, and implant-abutment connection.

For each configuration and load case, the solver-generated mesh statistics were as follows:

• VERT4-S, canine loading: 336,783 nodes; 1,734,229 elements

• VERT4-S, first-molar loading: 336,760 nodes; 1,734,596 elements

• ALL4-S, canine loading: 378,729 nodes; 1,831,659 elements

• ALL4-S, first-molar loading: 378,706 nodes; 1,832,026 elements

• ALL4-N, canine loading: 673,113 nodes; 3,310,705 elements

• ALL4-N, first-molar loading: 673,090 nodes; 3,311,072 elements

• VERT4-N, canine loading: 678,363 nodes; 3,585,307 elements

• VERT4-N, first-molar loading: 678,340 nodes; 3,585,674 elements

Mesh convergence was evaluated by additional local refinement in peri-implant and connection regions (~ 20% reduction in local element size). Under unilateral first-molar loading, two high-gradient metrics were used: peak von Mises stress at the posterior implant neck and maximum principal stress in crestal cortical bone. Variations in these metrics were < 5% relative to baseline meshes, supporting the numerical stability of the comparative trends. First-molar loading was selected for convergence verification because it generated the highest mechanical demand in the distal implant-prosthetic region and therefore represented the more stringent condition for numerical checking.

Material properties

All materials were modeled as homogeneous, isotropic, and linearly elastic. Elastic moduli (E) and Poisson’s ratios (ν) were assigned as follows:

• Cortical bone: E = 13,700 MPa; ν = 0.30

• Trabecular bone: E = 1,370 MPa; ν = 0.30

• Titanium alloy: E = 100,000 MPa; ν = 0.30

• Co-Cr framework: E = 218,000 MPa; ν = 0.33

• Acrylic resin: E = 3,000 MPa; ν = 0.35

Contact and interface assumptions

A healed-condition assumption was applied. Bone-implant interfaces were modeled as perfectly bonded to represent complete osseointegration. For controlled comparative evaluation focused on angulation and macrodesign, implant-abutment and abutment-framework interfaces were also modeled as bonded (tied contact), without simulation of preload, microgap formation, or interface sliding. Accordingly, results are interpreted as relative mechanical demand under the specified assumptions rather than absolute predictors of clinical failure. This bonded approach was used to isolate comparative effects under healed loading conditions; partially bonded or frictional interfaces could produce different local stress magnitudes and distributions, particularly at the implant-abutment and multiunit connection levels.

The bolus-occlusal interface was modeled as frictionless surface-to-surface contact to minimize shear artifacts and emphasize vertical load transfer.

Boundary conditions

To prevent rigid body motion, the inferior border of the mandibular body and the inferior portions of both rami were constrained with zero displacement in all translational degrees of freedom. Boundary conditions were identical across models.

Loading protocol

Two unilateral load cases were analyzed (Fig. 2) by positioning a rigid spherical food bolus (12 mm diameter) over:

Fig. 2.

Loading conditions used in the finite element models. A vertical load of 300 N was applied separately through a rigid spherical bolus positioned over the left canine or left first-molar region

1. the left canine region (unilateral canine loading), and

2. the left first-molar region (unilateral first-molar loading).

For each load case, a total vertical load of 300 N was applied to the bolus. Load transfer was distributed through the bolus-occlusal contact region rather than applied to a single node to reduce stress singularities. Unilateral loading was selected to represent a controlled asymmetrical loading condition and to facilitate direct comparison of stress-transfer patterns among configurations. The spherical bolus provided a standardized and reproducible contact geometry independent of maxillary tooth anatomy or intercuspation.

Sensitivity analysis

To test the robustness of comparative rankings, load magnitude was perturbed by ± 10% (270 N and 330 N) for both load cases. The relative ranking of configurations across outcomes remained unchanged.

Outcome measures and reporting

For bone, maximum principal stress (Pmax) and minimum principal stress (Pmin) were extracted separately for cortical and trabecular compartments. For ductile components (implants, multiunit abutments, and the Co-Cr framework), von Mises stress was evaluated. All stresses were reported in MPa.

For implants and multiunit abutments, peak von Mises stresses were reported separately for anterior and posterior component sets, defined as the maximum value within the two anterior or two posterior components for each model and load case. Stress maps were generated using consistent visualization settings within each outcome category to facilitate direct comparisons across configurations. Principal stresses were used for bone, and von Mises stresses were used for metallic components, according to material behavior. For each component category, peak values were recorded at each occurrence; under the tested unilateral loading conditions, these maxima localized predominantly on the loaded side.

Because FEA yields deterministic outputs under fixed inputs, no inferential statistical testing was applied; comparisons relied on spatial stress distributions and peak stress values.

Results

Reporting convention

For implants and multiunit abutments, values are reported separately for posterior and anterior components. “Posterior” refers to the two posterior implants/abutments and “anterior” to the two anterior implants/abutments. For each model and loading condition, the reported value represents the maximum von Mises stress among the two corresponding components. Under unilateral loading, these peak values occurred predominantly on the loaded side. All stresses are reported in MPa.

Two unilateral load cases were analyzed: (i) a rigid bolus positioned over the left canine region with a 300 N vertical load, and (ii) a rigid bolus positioned over the left first-molar region with a 300 N vertical load.

Principal stresses in peri-implant bone

(Pmax indicates peak tensile principal stress; Pmin indicates peak compressive principal stress.)

Cortical bone

Pmax

Canine loading: cortical Pmax was highest in ALL4-N (30.85 MPa) and lowest in ALL4-S (18.50 MPa); VERT4-N (18.57 MPa) and VERT4-S (18.60 MPa) were comparable (Table 1; Fig. 3).

Table 1.

Maximum principal stresses (Pmax, MPa) in cortical and trabecular bone under unilateral canine and first-molar loading (300 N)

Loading condition	Model	Cortical Pmax	Trabecular Pmax
Canine loading	VERT4-N	18.57	2.63
Canine loading	VERT4-S	18.60	1.01
Canine loading	ALL4-N	30.85	11.72
Canine loading	ALL4-S	18.50	2.72
First-molar loading	VERT4-N	18.58	2.64
First-molar loading	VERT4-S	10.28	3.34
First-molar loading	ALL4-N	100.44	17.15
First-molar loading	ALL4-S	14.60	3.67

Values represent peak tensile principal stress within each bone compartment for the corresponding model and loading condition. ALL4-S: Straumann BL, posterior implants tilted 30°; ALL4-N: NobelActive, posterior implants tilted 30°; VERT4-S: Straumann BL, all implants axially placed; VERT4-N: NobelActive, all implants axially placed

Fig. 3.

Maximum principal stress (Pmax, MPa) distribution in cortical and trabecular bone under unilateral canine loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

First-molar loading: cortical Pmax was highest in ALL4-N (100.44 MPa) and lowest in VERT4-S (10.28 MPa), with intermediate values in ALL4-S (14.60 MPa) and VERT4-N (18.58 MPa) (Table 1; Fig. 4).

Fig. 4.

Maximum principal stress (Pmax, MPa) distribution in cortical and trabecular bone under unilateral first-molar loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Pmin

Canine loading: cortical Pmin was most compressive in ALL4-N (-63.09 MPa) and least compressive in VERT4-S (-14.33 MPa) (Table 2; Fig. 5).

Table 2.

Minimum principal stresses (Pmin, MPa) in cortical and trabecular bone under unilateral canine and first-molar loading (300 N)

Loading condition	Model	Cortical Pmin	Trabecular Pmin
Canine loading	VERT4-N	-17.23	-6.01
Canine loading	VERT4-S	-14.33	-1.08
Canine loading	ALL4-N	-63.09	-9.70
Canine loading	ALL4-S	-15.77	-3.00
First-molar loading	VERT4-N	-17.24	-9.22
First-molar loading	VERT4-S	-19.71	-3.02
First-molar loading	ALL4-N	-95.30	-31.41
First-molar loading	ALL4-S	-35.22	-2.63

Negative values indicate compressive principal stress. Values represent peak compressive stress within each bone compartment for the corresponding model and loading condition. ALL4-S: Straumann BL, posterior implants tilted 30°; ALL4-N: NobelActive, posterior implants tilted 30°; VERT4-S: Straumann BL, all implants axially placed; VERT4-N: NobelActive, all implants axially placed

Fig. 5.

Minimum principal stress (Pmin, MPa) distribution in cortical and trabecular bone under unilateral canine loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

First-molar loading: cortical Pmin was again most compressive in ALL4-N (-95.30 MPa) and least compressive in VERT4-N (-17.24 MPa) (Table 2; Fig. 6).

Fig. 6.

Minimum principal stress (Pmin, MPa) distribution in cortical and trabecular bone under unilateral first-molar loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Trabecular bone

Pmax

Canine loading: trabecular Pmax was highest in ALL4-N (11.72 MPa) and lowest in VERT4-S (1.01 MPa) (Table 1; Fig. 3).

First-molar loading: trabecular Pmax was highest in ALL4-N (17.15 MPa) and lowest in VERT4-N (2.64 MPa) (Table 1; Fig. 4).

Pmin

Canine loading: trabecular Pmin was most compressive in ALL4-N (-9.70 MPa) and least compressive in VERT4-S (-1.08 MPa) (Table 2; Fig. 5).

First-molar loading: trabecular Pmin was again most compressive in ALL4-N (-31.41 MPa) and least compressive in ALL4-S (-2.63 MPa) (Table 2; Fig. 6).

Von Mises stresses in implant-prosthetic components

Implants

Canine loading: posterior implant stress was highest in ALL4-N (546.94 MPa) and lowest in VERT4-S (47.76 MPa); anterior implant stress was highest in ALL4-N (288.43 MPa) and lowest in ALL4-S (25.44 MPa) (Table 3; Fig. 7).

Table 3.

Von Mises stresses (MPa) in implants and multiunit abutments under unilateral canine and first-molar loading (300 N)

Loading condition	Model	Posterior implant	Anterior implant	Posterior multiunit	Anterior multiunit
Canine loading	VERT4-N	71.38	40.12	42.33	30.60
Canine loading	VERT4-S	47.76	28.25	45.17	31.29
Canine loading	ALL4-N	546.94	288.43	238.67	226.18
Canine loading	ALL4-S	67.95	25.44	212.89	226.55
First-molar loading	VERT4-N	176.37	102.17	138.64	81.51
First-molar loading	VERT4-S	145.90	76.90	144.94	83.92
First-molar loading	ALL4-N	925.82	190.96	186.06	280.20
First-molar loading	ALL4-S	112.66	29.91	85.85	287.27

Posterior and anterior values represent the peak von Mises stress among the two posterior or two anterior components, respectively. ALL4-S: Straumann BL, posterior implants tilted 30°; ALL4-N: NobelActive, posterior implants tilted 30°; VERT4-S: Straumann BL, all implants axially placed; VERT4-N: NobelActive, all implants axially placed

Fig. 7.

Von Mises stress distribution (MPa) in implants under unilateral canine loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

First-molar loading: posterior implant stress was highest in ALL4-N (925.82 MPa) and lowest in ALL4-S (112.66 MPa); anterior implant stress was highest in ALL4-N (190.96 MPa) and lowest in ALL4-S (29.91 MPa) (Table 3; Fig. 8). These values are presented as comparative peak stresses within this linear-elastic model and are not interpreted here as direct clinical failure thresholds.

Fig. 8.

Von Mises stress distribution (MPa) in implants under unilateral first-molar loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Multiunit abutments

Canine loading: posterior multiunit stress was highest in ALL4-N (238.67 MPa) and lowest in VERT4-N (42.33 MPa); anterior multiunit stress was highest in ALL4-S (226.55 MPa) and lowest in VERT4-N (30.60 MPa) (Table 3; Fig. 9).

Fig. 9.

Von Mises stress distribution (MPa) in multiunit abutments under unilateral canine loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

First-molar loading: posterior multiunit stress was highest in ALL4-N (186.06 MPa) and lowest in ALL4-S (85.85 MPa); anterior multiunit stress was highest in ALL4-S (287.27 MPa) and lowest in VERT4-N (81.51 MPa) (Table 3; Fig. 10).

Fig. 10.

Von Mises stress distribution (MPa) in multiunit abutments under unilateral first-molar loading (300 N). Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Prosthetic framework (Co-Cr substructure)

Canine loading: framework stress was highest in ALL4-N (144.33 MPa) and lowest in VERT4-N (87.04 MPa) (Table 4; Fig. 11).

Table 4.

Von Mises stresses (MPa) in the prosthetic framework and acrylic superstructure under unilateral canine and first-molar loading (300 N)

Loading condition	Model	Framework (Co-Cr)	Acrylic superstructure
Canine loading	VERT4-N	87.04	13.12
Canine loading	VERT4-S	87.15	13.13
Canine loading	ALL4-N	144.33	12.03
Canine loading	ALL4-S	106.49	12.02
First-molar loading	VERT4-N	169.07	5.39
First-molar loading	VERT4-S	175.03	5.39
First-molar loading	ALL4-N	156.13	5.41
First-molar loading	ALL4-S	53.58	5.41

Framework stresses refer to the cobalt-chromium (Co-Cr) substructure, and superstructure stresses refer to the acrylic resin veneering. Values represent peak von Mises stress. ALL4-S: Straumann BL, posterior implants tilted 30°; ALL4-N: NobelActive, posterior implants tilted 30°; VERT4-S: Straumann BL, all implants axially placed; VERT4-N: NobelActive, all implants axially placed

Fig. 11.

Von Mises stress distribution (MPa) in the prosthetic framework under unilateral canine loading (300 N), shown from occlusal and inferior views. Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

First-molar loading: framework stress was highest in VERT4-S (175.03 MPa) and lowest in ALL4-S (53.58 MPa) (Table 4; Fig. 12).

Fig. 12.

Von Mises stress distribution (MPa) in the prosthetic framework under unilateral first-molar loading (300 N), shown from occlusal and inferior views. Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Prosthetic superstructure (acrylic resin)

Acrylic resin stresses were low and clustered across configurations. Under canine loading, the highest value occurred in VERT4-S (13.13 MPa) and the lowest in ALL4-S (12.02 MPa) (Table 4; Fig. 13). Under first-molar loading, values were nearly identical (5.39–5.41 MPa), with minima in VERT4-N and VERT4-S (5.39 MPa) and maxima in ALL4-N and ALL4-S (5.41 MPa) (Table 4; Fig. 14).

Fig. 13.

Von Mises stress distribution (MPa) in the acrylic superstructure under unilateral canine loading (300 N), shown from occlusal and inferior views. Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Fig. 14.

Von Mises stress distribution (MPa) in the acrylic superstructure under unilateral first-molar loading (300 N), shown from occlusal and inferior views. Group comparisons are shown for VERT4-N, VERT4-S, ALL4-N, and ALL4-S

Sensitivity analysis (± 10% load perturbation)

A ± 10% variation in load magnitude produced proportional changes in stress magnitudes without altering the relative ranking of configurations across outcomes.

Summary of stress patterns

Across both unilateral loading conditions, ALL4-N consistently produced the highest stresses in cortical and trabecular bone and the highest posterior implant von Mises stresses. Peak values were generally higher in the posterior than in the anterior components. Under first-molar loading, the highest anterior multiunit abutment stress occurred in ALL4-S. Overall, when posterior angulation was applied without cantilever reduction or increased distal support, tilted configurations did not show lower peak mechanical demand than axial configurations.

Discussion

This three-dimensional finite element analysis compared axial (VERT4) and posteriorly tilted (ALL4) mandibular full-arch configurations using two implant macrodesigns (NobelActive and Straumann BL). Unlike conventional All-on-4 planning, in which tilt is typically coupled with cantilever reduction and/or increased distal support, prosthetic support geometry was standardized to isolate posterior angulation as a geometric variable while using clinically comparable implant sizes. Implant macrodesign was evaluated as a secondary modifier under healed, bonded-interface assumptions. Thus, the main contribution of this study is the controlled isolation of posterior angulation without cantilever reduction, distal support gain, or angulation-enabled distal implant-length gain.

The primary null hypothesis was that posterior angulation, when applied without cantilever reduction or increased distal support, would not reduce stress concentrations relative to axial placement. The secondary null hypothesis was that implant macrodesign would not materially influence stress distribution under healed loading conditions. A ± 10% load perturbation changed stress magnitudes proportionally without altering configuration rankings, supporting robustness to modest load variation [14–17].

Under these controlled conditions, posterior angulation increased rather than reduced stress peaks. The tilted NobelActive configuration (ALL4-N) produced the highest cortical principal stresses, reaching Pmax = 100.44 MPa and Pmin = − 95.30 MPa under unilateral first-molar loading. This pattern is consistent with increased bending demand at the crestal cortex when angulation is introduced without the design features that usually reduce bending moments in All-on-4 treatment—most notably cantilever shortening and/or increased distal support [17, 18]. Accordingly, the frequently cited biomechanical advantage of posterior tilt appears more attributable to accompanying changes in support geometry than to angulation alone. These findings should therefore not be generalized to tilted posterior implants used together with cantilever reduction or increased distal support.

This interpretation is consistent with evidence indicating that angulation alone can increase peri-implant stress, whereas cantilever reduction can mitigate it [9, 10, 17]. Clinical studies showing comparable short- to mid-term survival and marginal bone loss between axial and tilted implants do not exclude higher localized mechanical demand under specific loading scenarios. In this context, CBCT-based analyses identifying implant tilting and cantilever length as independent risk factors for marginal bone loss support the view that stress concentration is a contributory factor rather than a direct surrogate for early failure [19, 20]. Likewise, finite element studies indicate that connection geometry and angle-correction strategy can materially influence deformation patterns and von Mises stress concentrations under posterior loading [21, 22].

A configuration-dependent macrodesign effect was also observed. In ALL4-N, posterior implant von Mises stress increased from 546.94 MPa under canine loading to 925.82 MPa under first-molar loading, indicating pronounced concentration at the implant-abutment region during unilateral posterior loading. Because this peak exceeds the approximate yield strength often reported for Grade 5 titanium alloy, it should not be interpreted as a direct prediction of clinical yielding or fracture. In linear-elastic bonded FEA, highly localized peak stresses may occur at geometric concentration sites, especially near the implant-abutment connection, and may overestimate absolute mechanical risk if interpreted outside the model assumptions. Accordingly, this value is interpreted as a localized comparative hotspot within the model rather than as direct evidence of inevitable material failure under clinical conditions. The implant stress results are therefore better interpreted comparatively, as indicators of greater relative mechanical demand rather than as stand-alone failure thresholds. Across matched configurations and load cases, Straumann BL models generally showed lower localized implant and connection stresses than NobelActive models, consistent with the influence of taper and thread geometry on load transfer [13, 23, 24]. Given the non-negligible rate of mechanical complications in long-term mandibular All-on-4 cohorts [6], these findings support considering post-osseointegration stress-transfer behavior alongside primary stability and insertion mechanics when selecting implant systems for full-arch rehabilitation [13, 24].

An additional strength of this study is that stresses were assessed not only in peri-implant bone and implant bodies but also in prosthetic components. This is clinically relevant because technical complications—particularly screw loosening and veneering fractures—remain common in full-arch rehabilitation [5, 25, 26]. In the present models, tilted configurations increased mechanical demand at the prosthetic connection, with prominent peaks at the multiunit abutment level. Mechanistically, posterior tilting is expected to be advantageous mainly when it enables cantilever reduction and/or increased distal support [7, 9, 17]. When these compensatory mechanisms are absent, as in the present design, angulation can increase bending demand transmitted through the implant-abutment-framework complex, with greater stress concentration at the crestal bone and connection levels [13, 17]. This is directionally consistent with finite element evidence that abutment-level angle correction can increase deformation and von Mises stress concentration compared with implant-level correction under posterior loading [22]. Notably, the highest anterior multiunit abutment stress under unilateral first-molar loading occurred in ALL4-S (287.27 MPa), while posterior multiunit stresses peaked in ALL4-N, supporting the implant-abutment-framework complex as a locus of elevated demand under unilateral posterior loading [13, 17, 25]. Collectively, these findings suggest that, under standardized prosthetic geometry, posterior angulation may increase connection-level demand rather than reduce it [10, 13, 17].

Framework behavior was not uniformly increased by posterior tilting and depended on the loading site and implant system. Prior finite element work indicates that framework stiffness can redistribute demand toward the implant-abutment connection and peri-implant bone; framework peak stress alone should therefore not be used as a surrogate for overall mechanical risk [27]. In this study, the highest framework stress occurred in ALL4-N under canine loading, whereas under first-molar loading, it occurred in VERT4-S. Thus, lower framework stress does not necessarily indicate lower technical vulnerability when connection-level stresses are elevated.

Overall, posterior tilting, when introduced without cantilever reduction or increased distal support, did not confer a biomechanical advantage in this model and could increase stress concentrations in peri-implant bone and/or implant-prosthetic components. This supports an indication-driven use of posterior angulation based on case-specific anatomical and prosthetic constraints, rather than assuming that tilt is beneficial as an isolated maneuver. Available computational literature is directionally consistent: stress reduction is mainly observed when tilt enables cantilever shortening and/or increased distal support, whereas increasing distal implant angulation under standardized support geometry can elevate peri-implant and component stresses [9, 10, 28, 29]. The present results, therefore, apply specifically to posterior angulation without cantilever reduction or distal support gain, not to all full-arch tilted-implant scenarios.

The results also suggest that implant macrogeometry remains relevant after osseointegration. Although aggressive designs such as NobelActive are often selected to enhance primary stability in immediate-loading protocols [13, 17, 30], the healed-condition analyses here indicate that macrodesign can modulate localized stress transfer during definitive function. Across matched configurations and unilateral loading conditions, NobelActive models exhibited higher localized implant and connection stresses than Straumann BL models, with the contrast most pronounced in tilted posterior configurations [11, 13, 30].

Several limitations should be acknowledged. Interfaces were idealized as perfectly bonded, and screw preload, microgap behavior, and frictional contact nonlinearity were not simulated; stresses should therefore be interpreted as indicators of relative mechanical demand rather than direct predictors of specific technical failure modes. Materials were modeled as homogeneous, isotropic, and linearly elastic, which does not capture bone heterogeneity or anisotropy [14, 16]. A single mandibular geometry was used, so patient-specific variability in cortical thickness, trabecular architecture, arch form, and bone quality was not represented. Accordingly, absolute stress magnitudes may differ in models with different cortical thickness, bone quality, or arch form, even if the comparative trends observed here remain directionally informative. Loading was modeled as a quasi-static vertical force without oblique components or time dependence; thus, bilateral simultaneous loading, lateral force components, and fatigue accumulation were outside the scope of this analysis [14]. Soft-tissue damping was not modeled, which may affect absolute magnitudes. In addition, ALGOR FEMPRO is a discontinued commercial solver; although analyses were performed using its final stable release (2014) under an active license, this may limit direct reproducibility in currently supported platforms. For this reason, the present results should be interpreted primarily as internally consistent comparative outputs rather than solver-independent absolute predictions. No separate simulation of screw mechanics, preload relaxation, or partial osseointegration was performed; therefore, local connection-level stresses, particularly at the implant-abutment and multiunit interfaces, may differ from those obtained in nonlinear contact models. Despite these simplifications, strict standardization of prosthetic emergence profile and cantilever length strengthens internal validity for isolating the effects of angulation and macrodesign.

Future work should incorporate cyclic loading, fatigue-focused modeling of the prosthetic connection, and experimental validation to determine whether the relative mechanical trends observed here translate into biological and technical outcomes. Cross-verification using a currently supported solver and sensitivity analyses across multiple mandibular geometries or cortical thickness values would further strengthen generalizability. Longitudinal clinical data will be required to determine whether configuration- and macrodesign-related differences in localized stress concentration correspond to distinct complication profiles during definitive function.

Conclusion

Within the limits of this linear-elastic, healed-interface model, posterior implant angulation did not provide a biomechanical advantage over axial placement when used without cantilever reduction or increased distal support. Instead, tilted configurations showed higher mechanical demand in peri-implant bone and implant-prosthetic components, with the highest stresses observed in the tilted NobelActive model under unilateral first-molar loading. These findings, therefore, apply specifically to this condition set and should not be generalized to tilted configurations in which cantilever reduction or distal support gain is achieved.

Implant macrodesign also modified stress transfer under healed, bonded-interface assumptions. Across matched configurations and loading conditions, NobelActive models showed higher localized implant and connection stresses than Straumann BL models, particularly in tilted posterior configurations. Accordingly, the reported stress values should be interpreted as comparative mechanical indicators rather than direct predictors of clinical failure.

Clinically, posterior angulation should be reserved for situations in which it provides a clear prosthetic benefit, especially when it enables cantilever reduction and/or increased distal support. Further studies incorporating cyclic and fatigue-focused loading, connection preload behavior, cross-validation in currently supported FEA platforms, and patient-specific anatomical variability are needed to determine whether these relative mechanical trends translate into long-term biological and technical outcomes.

Abbreviations

FEA

Finite Element Analysis

ALL4

All-on-4 configuration with posterior tilted implants

VERT4

Full-arch configuration with axially placed implants

Co–Cr

Cobalt–Chromium

CBCT

Cone-Beam Computed Tomography

Pmax

Maximum principal stress

Pmin

Minimum principal stress

MPa

Megapascal

Authors’ contributions

Sercan KÜÇÜKKURT (Istanbul Aydın University): Conceptualization; Study design; Supervision; Data acquisition; Analysis and interpretation; Literature review; Drafting of the manuscript; Critical revision for important intellectual content; Final approval of the manuscript.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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

The study design was evaluated by the Ethics Committee of Istanbul Aydın University, Faculty of Dentistry. It was determined not to require formal ethical approval, as the use of fully anonymized archival CBCT data was solely to approximate general external mandibular contours for computational modeling. No human participation, intervention, identifiable information, or patient-specific anatomical replication was involved.

Accordingly, informed consent to participate was not required under national regulations governing non-interventional research using anonymized data.

Not required. The study did not involve human participants and does not contain identifiable individual data.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.