Comparison of biomechanical performance of custom implants with different designs under functional load: a finite element analysis

Abstract

Objective

Rehabilitation of severely atrophic edentulous maxillae is clinically challenging because of limited bone volume and the constraints of conventional implants. Recent advances in digital planning and additive manufacturing have increased interest in patient-specific titanium subperiosteal implants. This study aimed to compare the biomechanical performance of 6 titanium subperiosteal implant designs for fixed prosthetic rehabilitation.

Methods

A three-dimensional atrophic maxilla model was reconstructed from Visible Human Project tomography data. 6 subperiosteal implant designs, comprising three single-piece and three 2-piece configurations, were modeled using CAD software. Abutments were positioned at the 2nd, 4th, and 6th tooth regions. Vertical (150 N) and oblique (50 N at 30°) masticatory loads were applied. All materials were assumed to be homogeneous, isotropic, and linearly elastic. Maximum principal stress, minimum principal stress, and von Mises stress distributions were evaluated in the implant, abutment, prosthetic framework, and surrounding bone.

Results

Stress distribution patterns were comparable under vertical and oblique loading. Single-piece designs exhibited lower von Mises stress values within the implant, whereas 2-piece designs showed reduced stress transfer to the surrounding bone. Mesh-type designs generated the highest implant stresses but lower stresses in the abutment, prosthetic framework, and bone. Peak cortical bone stresses remained within physiologically acceptable limits and were mainly concentrated in the nasal buttress region.

Conclusion

Subperiosteal implant biomechanics are strongly influenced by design and configuration. Single-piece designs favor implant-level stress reduction, while 2-piece designs appear advantageous for minimizing bone stress.

Introduction

Edentulism is a significant global health issue, especially common among older adults. The partial or complete loss of natural teeth results in considerable functional impairments and social limitations affecting patients’ overall health. After tooth loss, alveolar bone resorption occurs due to the reduction or absence of normal mechanical forces on the jawbone, consistent with Wolff’s law. This process leads to progressive bone volume loss and deterioration of facial aesthetics [1]. In patients with severely atrophic, totally edentulous maxillae, conventional implant placement presents significant challenges due to insufficient volume and quality of maxillary bone, and the presence and pneumatization of the maxillary sinus. Traditional treatment for these cases involves augmenting bone horizontally and/or vertically with autogenous bone grafts such as iliac, ramus, and symphysis bone grafts, and sinus augmentation. While autografting is considered the “gold standard,” it has disadvantages such as requiring general anesthesia in some cases, a longer hospital stay, a high risk of infection, a high resorption rate (especially in iliac grafts), and donor site morbidity including pain, nerve damage, and gait disturbance [2, 3].

Faced with these challenges, subperiosteal implants, first described by Dahl in the 1940s, have re-emerged in modern implantology due to recent technological advancements [4–6]. Historically, subperiosteal implants (SIs) demonstrated variable long-term outcomes. Studies from the 1980s and 1990s reported 5-year success rates ranging from 90% to 100%; however, survival declined over extended follow-up periods. With the introduction of digital planning and additive manufacturing technologies, a new generation of subperiosteal implants has emerged, enabling improved anatomical adaptation and renewed clinical interest. Since then, subperiosteal implants have been increasingly used in the rehabilitation of patients with severe maxillary atrophy and post-resection defects [7–11]. Despite these advances, current finite element studies on subperiosteal implants remain limited in scope, typically focusing on comparisons between one or two design configurations. A comprehensive evaluation of how multiple design parameters—such as single-piece versus two-piece configurations, variations in wing geometry, mesh versus solid frameworks, and the presence of palatal connections—affect stress distribution has not been systematically performed. This lack of integrated analysis limits the ability to derive design-specific clinical recommendations for the rehabilitation of severely atrophic maxillae. Modern titanium subperiosteal implants provide stability by resting on a broad area of the bone surface without relying entirely on osseointegration, being fixed instead with osteosynthesis screws [3, 12]. This design allows occlusal forces to be distributed over a wide bone surface, minimizing localized overload [6, 13]. The success of implant systems depends directly on the distribution of occlusal forces on the implant and surrounding tissues [14–15]. Finite element analysis (FEA) is considered one of the most effective tools for evaluating the impact of implant design and material properties under masticatory loads by transforming complex biological structures into mathematical models. FEA simulations enable the prediction of potential mechanical failures before surgery and the optimization of implant geometry [3, 15].

This study aims to comparatively examine the biomechanical performance of 6 different titanium subperiosteal implant designs intended for fixed prosthetic rehabilitation of a maxilla with advanced atrophy. Loads applied to implants placed on an atrophic maxilla model through 6 abutment outlets positioned at the levels of teeth 2, 4, and 6 were analyzed. To simulate realistic masticatory loading, the system was subjected to vertical forces of 150 N and oblique forces of 50 N applied at a 30-degree angle across multiple abutment positions representing the maxillary arch.

Materials and methods

The bone model used in this study was obtained from data provided by the Visible Human Project (National Library of Medicine, Office of Communications and Public Liaison, Maryland, USA). Bone and tooth models were generated from tomography data using 3DSlicer software(https://www.slicer.org/). Additionally, the .stl model was created from the same tomography data using 3DSlicer. Reverse engineering and three-dimensional CAD processes were performed with Blender software, while the adaptation of solid models to the analysis environment and the creation of optimized meshes were conducted using ALTAIR HyperMesh software (Altair Engineering, Michigan, USA). The ALTAIR OptiStruct solver (ALTAIR, Troy, MI, USA) was employed to solve the generated finite element models.

Modeling of cortical and trabecular bone

To create the maxillary bone model used in this study, tomography data from the Visible Human Project was reconstructed with a slice thickness of 0.33 mm. The resulting tomography data were transferred to 3DSlicer software in DICOM (.dcm) format. The DICOM CT data were processed in 3DSlicer according to appropriate Hounsfield unit thresholds (Threshold Range: 426.50–3193.04). Unwanted regions and artifacts were removed using the ‘Erase’ and ‘Scissors’ tools. The most challenging aspect of processing the DICOM data was determining the appropriate threshold range and cleaning unwanted regions. The segmented data were converted into three-dimensional models through the segmentation process, and the models were exported in .stl format. These three-dimensional models were imported into Blender software (Blender Foundation), where a 1 mm thick cortical bone layer was created by applying a 1 mm inward offset to the maxillary bone model. The trabecular bone was then generated by referencing the inner surface of the three-dimensional maxillary cortical bone with the adjusted thickness. All prepared models were positioned at the correct coordinates in 3D space using Blender software, completing the modeling process.

Modeling and fabrication of functional models of subperiosteal implants, fixation screws, acrylic prostheses, prosthetic framework, abutments, and occlusal screws

6 distinct subperiosteal implant models were created using Blender software, each featuring the following characteristics:

The different implant designs were developed to represent clinically relevant variations in subperiosteal implant configuration. Specifically, the models were designed to compare single-piece and two-piece frameworks, variations in support geometry (block-type versus plate-type wings), and differences in load distribution strategies (localized versus distributed support, as in mesh-type designs). These variations reflect alternative surgical and prosthetic approaches used in the rehabilitation of severely atrophic maxillae, allowing a comparative evaluation of their biomechanical performance.

For structured comparison, the models were also grouped according to design characteristics and configuration: Group A (wing-type, block wings) included M1 (2-piece) and M3 (single-piece); Group B (wing-type, mini-plate width wings) included M2 (2-piece) and M4 (single-piece); and Group C (mesh-type designs) included M5 (2-piece) and M6 (single-piece).

Model 1(M1): The 2-piece subperiosteal implant is designed with 2 wings on each piece, each approximately 3–4 mm wide and block-shaped. One wing is positioned in the nasal buttress region, and the other in the zygomatic buttress region. Each wing is secured with three screws on the buccal side and 2 screws on the palatal side, with a thickness of 1.8 mm (Fig. 1).

Fig. 1.

Study Models: (a) M1: 2-piece, block-type Wings; (b) M2: 2-piece, plate-type Wings; (c) M3: single-piece (modified M1); (d) M4: single-piece (modified M2); (e) M5: 2-piece mesh-type design; (f) M6: single-piece mesh-type design

Model 2(M2): The 2-piece subperiosteal implant is designed with 2 wings on each piece, each wing having a width equal to that of the mini plate. One wing is positioned in the nasal buttress region, and the other in the zygomatic buttress region. Each wing is secured with three screws on the buccal side and 2 screws on the palatal side, with a thickness of 1.8 mm (Fig. 1).

Model 3(M3): This is a modified version of model 1. There are no screws in the palatal region. A bar is designed to cross the palate from right to left, extending between the premolar regions. This allows for a single-piece connection originating from the palatal region, fixed from the buccal region but not from the palatal region (Fig. 1).

Model 4(M4): This is a modified version of model 2. There are no screws in the palatal region. A bar is designed to cross the palate from right to left, extending between the premolar regions. This creates a subperiosteal implant design that provides a single-piece connection from the palatal region, is fixed from the buccal region but not from the palatal region and receives palatal support from both the bar and the palatal mucosa (Fig. 1).

Model 5(M5): This is a 2-piece model designed as a titanium mesh-like structure. Modeled similarly to the edges of a total prosthesis, it extends from the nasal edge to the tubercle region in the buccal area, approximately at the height of the tooth roots. It also has a surface that extends into the palatal region. Each piece includes 6 screw holes in the buccal region and 2 in the palatal region (Fig. 1).

Model 6(M6): This is a single piece subperiosteal implant model. Modeled similarly to the edges of a total prosthesis, it extends from one buccal tubercle to the opposite tubercle, approximately at the height of the tooth roots. It has a surface that extends into the palatal region. The model includes 6 screw holes in the buccal region and 2 in the palatal region (Fig. 1).

Fixation screws, measuring 2 × 7 mm, are placed in the designated locations. The abutment, occlusal screw, acrylic resin prosthesis, and prosthetic framework were modeled using Blender software, based on catalog data. The designs were completed with abutment exits in regions 2, 4, and 6. To ensure force transfer between the models, the mesh structures were matched using Altair HyperMesh software (Fig. 2).

Fig. 2.

Modeling of the abutment, occlusal screw, and prosthetic frame

Material definitions

All subperiosteal implants in the present study were modeled using Ti-6Al-4 V titanium alloy, which is widely accepted as the standard material in implant dentistry due to its high strength-to-weight ratio, corrosion resistance, and excellent biocompatibility. All materials were assumed to be homogeneous, isotropic, and linearly elastic. The elastic properties assigned to bone, titanium alloy and acrylic were adopted from previously published biomechanical and FEA studies [5, 16]. Linear material properties, characterized by a specified elastic modulus and Poisson’s ratio, were used in the analyses. The material properties used in the analysis sources are summarized in Table 1.

Table 1.

Mechanical properties of the materials

Structure	Modulus of elasticity (MPa)	Poisson’s ratio	References
Cortical bone	13,700	0.30	[5, 16]
Medullary bone	1370	0.30	[5, 16]
Titanium alloy (Ti-6Al-4 V)	110,000	0.35	[5, 16]
Acrylic	2700	0.35	[5, 16]

Finite element modeling and meshing

The geometric models were discretized into finite elements to enable numerical analysis. Following the completion of geometric modeling in Blender software, the models were imported into ALTAIR HyperMesh (Altair Engineering, MI, USA) for mesh generation and preprocessing.

Surface meshes were generated using triangular (tria) elements to accurately represent the complex anatomical contours of the maxilla and implant components. Subsequently, solid meshes were created using tetrahedral elements to ensure volumetric discretization of all structures. Triangular surface elements were selected due to their superior adaptability to irregular geometries, particularly in anatomically complex regions such as the screw–bone interface and abutment connections. During mesh generation, standard mesh quality criteria, including aspect ratio, skewness, and Jacobian measures, were evaluated to ensure that element quality remained within acceptable limits for reliable finite element computation. The finite element models were then transferred to the ALTAIR OptiStruct solver (Altair Engineering, MI, USA) for numerical analysis.

Maximum and minimum principal stresses were used to evaluate bone behavior, as bone is more sensitive to tensile and compressive stress states. Von Mises stress was used to assess the mechanical behavior of metallic components, as it is an appropriate criterion for evaluating yielding in ductile materials such as titanium.

Mesh convergence analysis

A mesh convergence (sensitivity) analysis was performed to verify mesh independence and ensure the numerical accuracy of the finite element results. Three progressively refined mesh densities were generated with element sizes of 0.25 mm (coarse), 0.15 mm (medium), and 0.10 mm (fine) under the most critical loading condition (150 N vertical load), while all other model parameters, including material properties, boundary conditions, and loading configurations, were kept constant.

Peak von Mises stress values in the implant and principal stress values in cortical bone were evaluated at consistent anatomical locations, particularly at the abutment connection regions and screw–bone interfaces. The difference in stress values between the medium and fine mesh configurations was found to be below 10%, indicating that further mesh refinement resulted in negligible changes in the computed results.

Based on these findings, the selected mesh density range was considered sufficient to ensure mesh-independent results while maintaining computational efficiency.

Loading scenarios and boundary conditions

The loading protocol was designed to simulate generalized masticatory forces distributed across the maxillary arch rather than exclusively posterior loading conditions. Forces were applied to abutments positioned in the 2nd, 4th, and 6th tooth regions to represent a full-arch loading scenario.

In all models:

• A vertical force of 150 N was applied to the central fossae of teeth 2, 4, and 6 (Fig. 3a) [17–19].

Fig. 3.

Loading Scenarios and Boundary Conditions (a) Application of vertical load (150 N) at the abutment sites (b) Application of oblique load (50 N at 30°) (c) Boundary conditions showing fixed constraints at the superior region of the maxilla

• An oblique force of 50 N, applied at a 30-degree angle, was exerted on the central fossae of teeth 2, 4, and 6(Fig. 3b) [17, 19, 20].

The forces were applied by distributing them across the circumferential nodal points, thereby preventing stress singularities in the loading zones. The models were constrained by restricting all degrees of freedom at the nodal points located in the superior region of the bone, preventing movement along all three axes (Fig. 3c). A total of twelve nonlinear static analyses were conducted under the specified force and boundary conditions.

Quantitative model information

Data on the number of nodes and elements for the 6 analysis models created are presented in Table 2.

Table 2.

Study models and number of nodes and elements

Models		Total of Nodes	Total of Elements
M1		403,846	1,554,044
M2		387,134	1,493,588
M3		391,840	1,514,570
M4		393,852	1,518,873
M5		449,038	1,739,918
M6		439,114	1,704,580

System integration and inter-component connection status

In the finite element analysis, contact definitions between model components were established to ensure appropriate load transfer and mechanical interaction within the system. A frictional contact with a coefficient of 0.3 was defined at the interface between the subperiosteal implant and the bone. In all analyses, a FREEZE-type contact definition was applied to other contacting components. This approach assumes that the parts move in full correlation during movement. This assumption was adopted to simulate rigid fixation between components, representing clinically stable screw-retained and prosthetic connections where relative micromotion is negligible under functional loading.

The nonlinear behavior in the present analyses originates exclusively from the frictional contact defined at the implant–bone interface, while all materials were modeled as linearly elastic. Geometric nonlinearity was not included, as the expected deformations under the applied loading conditions were considered negligible.A friction coefficient of 0.3 was assigned based on previously published finite element studies, where similar values have been used to represent the mechanical interaction between titanium implants and bone tissue. This assumption allows for a realistic simulation of load transfer in conditions where full osseointegration is not assumed.

Results

In this study, 6 subperiosteal implant designs with different configurations were evaluated under vertical (150 N) and oblique (50 N at 30°) loading conditions applied to an atrophic maxilla model. Stress distributions were assessed in the implant, abutment, prosthetic framework, and surrounding bone using maximum principal, minimum principal, and von Mises stress criteria (Fig. 4, 5, 6 and 7) and (Table 3).

Fig. 4.

Stress distribution under oblique loading (50 N at 30°) for M1–M3. (a) Maximum principal stress in cortical bone; (b) Minimum principal stress in cortical bone; (c) Von Mises stress in the subperiosteal implant; (d) Von Mises stress in the abutment; (e) Von Mises stress in the prosthetic framework

Fig. 5.

Stress distribution under oblique loading (50 N at 30°) for M4–M6. (a) Maximum principal stress in cortical bone; (b) Minimum principal stress in cortical bone; (c) Von Mises stress in the subperiosteal implant; (d) Von Mises stress in the abutment; (e) Von Mises stress in the prosthetic framework

Fig. 6.

Stress distribution under vertical loading (150 N) for M1–M3. (a) Maximum principal stress in cortical bone; (b) Minimum principal stress in cortical bone; (c) Von Mises stress in the subperiosteal implant; (d) Von Mises stress in the abutment; (e) Von Mises stress in the prosthetic framework

Table 3.

The highest maximum principal stress, minimum principal stress, and von Mises stress values in the study models

	Bone Maximum Principal Stress (MPa)	Bone Minimum Principal Stress (MPa)	Subperiosteal Implant Von Mises Stress (MPa)	Abutment Von Mises Stress (MPa)	Prosthetic Framework Von Mises Stress (MPa)
ObliqueForce
M1	7.3	-13.2	43.2	14.4	27.9
M2	5	-13	51.5	15.2	30.0
M3	8.2	-14.1	29	14.1	26.8
M4	6.4	-13.7	48.7	15.0	28.9
M5	5.9	-11.8	52.4	13.7	27.7
M6	5.5	-12.4	35.8	12.8	26.7
Vertical Force
M1	23.4	-39.8	114.6	43.1	46.2
M2	14.9	-36.9	152.6	49.6	48.5
M3	25.2	-42	87	41.2	45.8
M4	18.7	-37.9	151.3	48.8	46.2
M5	12.6	-32.8	153.6	34.6	37.8
M6	13.7	-32.9	96.1	34.0	36.5

The reported peak stress values correspond to specific anatomical locations detailed in the Results section. In bone, maximum and minimum principal stresses were predominantly localized in the nasal buttress and screw–bone interface regions. In the implant, peak von Mises stresses were mainly observed at the abutment connection sites

Fig. 7.

Stress distribution under vertical loading (150 N) for M4–M6. (a) Maximum principal stress in cortical bone; (b) Minimum principal stress in cortical bone; (c) Von Mises stress in the subperiosteal implant; (d) Von Mises stress in the abutment; (e) Von Mises stress in the prosthetic framework

Comparative overview

Clear design-dependent differences in stress distribution were observed. Overall, single-piece configurations demonstrated lower von Mises stress values within the implant structure, whereas two-piece designs were more effective in reducing stress transfer to the surrounding bone. In addition, designs with increased surface coverage exhibited more homogeneous stress distribution patterns.

Stress distribution in the subperiosteal implant

Under both vertical and oblique loading conditions, similar stress distribution trends were observed among the implant designs. Within comparable design groups, two-piece configurations (M1, M2, M5) consistently exhibited higher stress values than their single-piece counterparts (M3, M4, M6). Among all models, M5 demonstrated the highest implant-level stress values. Under vertical loading, the maximum von Mises stress values recorded in the implant were 114.6 MPa (M1), 152.6 MPa (M2), 87 MPa (M3), 151.3 MPa (M4), 153.6 MPa (M5), and 96.1 MPa (M6) (Table 3). Peak stresses were primarily localized at the abutment connection regions, particularly in the anterior and premolar zones. These trends were consistent under oblique loading conditions. The reduction in implant stress observed in single-piece designs can be attributed to improved structural continuity, allowing more efficient load redistribution across the implant framework. In contrast, mesh-type designs (M5 and M6) exhibited higher implant stress values due to reduced effective surface area and localized load concentration.

Stress distribution in cortical bone

The highest maximum principal stress values in cortical bone were primarily localized in the nasal buttress region, particularly around screw–bone interface areas. Under vertical loading, peak tensile stress values reached 25.2 MPa (M3), while lower values were observed in mesh-type designs (M5: 12.6 MPa, M6: 13.7 MPa) (Table 3).

Minimum principal stress values (compressive stress) followed a similar distribution pattern. The highest compressive stress was observed in M3 (-42 MPa), approaching the upper physiological threshold for cortical bone. In contrast, M5 and M6 demonstrated lower compressive stress values, indicating a more favorable stress environment for bone preservation. Under oblique loading, stress magnitudes were lower overall but maintained similar distribution patterns, with peak values consistently localized in the nasal buttress region.

Stress distribution in abutment and prosthetic framework

Stress patterns observed in the abutment and prosthetic framework closely followed those of the implant, indicating a direct mechanical coupling between these components. Under oblique loading, stress concentrations were primarily observed in the anterior region, whereas under vertical loading, stress was concentrated around the 2nd and 4th abutment regions. Mesh-type designs demonstrated lower stress values in the abutment and prosthetic framework compared to other configurations, suggesting that these designs may reduce load transmission to secondary components.

Overall trends

Three primary biomechanical patterns were identified across all models: (i) single-piece designs reduced implant-level stress, (ii) two-piece designs reduced stress transfer to cortical bone, and (iii) designs with increased surface area and distributed support provided more homogeneous stress distribution.

Across all models and loading conditions, stress values remained within physiologically acceptable limits for cortical bone and below the yield strength of titanium, indicating adequate mechanical safety of all evaluated implant designs (Table 4).

Table 4.

Summary of biomechanical trends across implant designs

Model	Configuration	Key Implant Finding	Key Bone Finding
M1	Two-piece	Moderate stress	Lower bone stress
M2	Two-piece	Higher stress	Lower bone stress
M3	Single-piece	Lowest stress	Higher bone stress
M4	Single-piece	Lower stress	Higher bone stress
M5	Two-piece mesh	Highest implant stress	Lowest bone stress
M6	Single-piece mesh	Moderate stress	Low bone stress

Discussion

Severe maxillary atrophy (Cawood and Howell Class V and VI) presents one of the most complex challenges in oral surgical rehabilitation, as it lacks sufficient vertical and horizontal bone volume for conventional dental implant placement [21]. Traditional approaches, such as iliac crest bone grafting and zygomatic implants, are associated with high surgical morbidity, prolonged treatment times, and risks of serious complications. In this context, advances in additive manufacturing (3D printing) and CAD/CAM technologies have renewed clinical interest in patient-specific titanium subperiosteal implants as a less invasive alternative that does not require grafting [22]. Given the growing clinical success of subperiosteal implants due to technological advancements, this study was designed to evaluate the biomechanical advantages and disadvantages of subperiosteal implants with various designs. The present FEA study evaluated the biomechanical behavior of 6 different titanium subperiosteal implants designed for use in the atrophic maxilla under chewing forces. Loads were applied through abutments positioned in the 2nd, 4th, and 6th tooth zones to more accurately simulate the clinical loading conditions encountered in the maxilla. Simultaneous analysis of maximum principal stress, minimum principal stress, and von Mises stress distributions enabled a comprehensive investigation of force transfer mechanisms between the implant-abutment complex and the surrounding bone tissue. The observed stress patterns in the prosthetic framework closely followed those in the abutment, indicating a direct mechanical coupling and efficient load transfer between these components. According to the literature, functional chewing forces range from approximately 100 to 300 N; these forces include off-axis components that can induce stress concentrations in the bone surrounding the implant [23, 24]. In this study, vertical forces of 150 N and oblique forces of 50 N applied at a 30° angle were selected to represent physiological masticatory loading conditions, thereby providing a comparative evaluation of subperiosteal implant behavior under axial and off-axis loads. Although posterior regions typically experience higher occlusal forces, the inclusion of anterior abutment positions reflects a full-arch prosthetic rehabilitation scenario, where load distribution occurs across the entire maxillary arch.

From a clinical perspective, the evaluated stress parameters have direct biological and mechanical implications. Maximum principal stress represents tensile forces, which are particularly relevant for assessing the risk of material fatigue and potential implant fracture under repeated loading. In contrast, minimum principal stress reflects compressive forces within bone tissue; excessive compressive stress, especially beyond physiological limits, has been associated with microdamage, bone resorption, and, in extreme cases, necrosis. In the present study, the stress values observed in cortical bone remained below commonly reported critical thresholds (approximately 50 MPa for compressive stress), suggesting a biomechanically favorable environment. Von Mises stress, which represents the combined effect of different stress components, is widely used to evaluate the overall mechanical loading of the implant structure and its susceptibility to structural failure. The observed distribution patterns indicate that, depending on the implant design, stress may be either concentrated within the implant or more evenly transferred to surrounding bone, which has direct implications for long-term implant stability and peri-implant bone preservation.

Material selection plays a critical role in the success of subperiosteal implants, influencing both mechanical strength and biomechanical interaction with the surrounding bone tissue. Historically, these implants were manufactured from cast metals such as Vitallium and tantalum; however, they exhibited high failure rates due to factors such as bone incompatibility and inadequate fixation [5]. Today, thanks to advances in additive manufacturing (AM) technologies, modern biomaterials such as titanium alloys and polyether ether ketone (PEEK) have become prominent. Altıparmak et al. reported that Cfr-PEEK implants reduced implant stress compared to titanium, whereas Keleş et al. found higher stress generation in the trabecular bone surrounding implants made from PEEK. Although titanium has demonstrated superior mechanical stability, PEEK increases cortical bone stress while reducing implant stress. This finding suggests a balance between mechanical performance and biological response [17, 25]. Titanium is regarded as the gold standard for subperiosteal implants because of its excellent corrosion resistance and high mechanical stability. The yield strength of titanium alloys typically ranges from 830 to 972 MPa, and finite element analysis (FEA) studies confirm that the stress values under chewing forces remain well below these limits [26]. Therefore, the risk of permanent deformation is low. In light of this information and considering its frequent use in clinical practice, titanium alloy was selected as the material for all 6 implant designs in the present study.

In subperiosteal implant surgery, the number of implant components—whether single-piece (monoblock) or 2-piece (dual) designs—and the number of abutments are critical parameters that directly influence biomechanical success, stress distribution, and the clinical lifespan of the system. There are varying biomechanical findings in the literature regarding whether subperiosteal implants should be designed as a single piece or as 2 separate segments (right and left). FEA studies by Ayhan et al. revealed that dual (2-piece) implant systems exhibit significantly lower Von Mises stress values (124–178 MPa versus 131–206 MPa) and less displacement compared to monoblock structures [20]. Similarly, Arı et al. reported that 2-piece subperiosteal implant designs provide the most balanced stress distribution between abutments [27]. This is attributed to the potential of dual designs to offer better local adaptation to bone and improve long-term survival rates. In some cases, it is argued that single-piece designs may be more effective in absorbing and distributing occlusal forces. Acar et al. found that a single-piece subperiosteal implant design achieved optimal stress distribution particularly under oblique loading conditions simulating off-axis masticatory forces [28]. Roshdy et al. demonstrated that one-piece designs resulted in lower stress values within the implant framework itself (i.e., the subperiosteal structure), which may reduce the risk of mechanical fatigue and long-term structural failure [29]. The present study was conducted using a total of 6 subperiosteal implant designs: three single-piece and three 2-piece. For clearer interpretation, the models were conceptually grouped as follows: Group A (M1–M3), Group B (M2–M4), and Group C (M5–M6), pairing corresponding 2-piece and single-piece configurations within each design category. M1 is a 2-piece implant, while M3 is a single-piece version of M1 connected by a bar on the palatal side. Similarly, M2 is a 2-piece implant, with M4 as its single-piece counterpart connected by a bar on the palatal side. M5 is also a 2-piece implant, and M6 is the single-piece version of M5, connected on the palatal side. M3 showed lower Von Mises stress values ​​than M1, M4 than M2, and M6 than M5 implants under both oblique and vertical forces. Regarding the maximum and minimum principal stresses on the bone under both oblique and vertical forces, the single-piece M3 and M4 implants exhibited higher values than the 2-piece M1 and M2 implants. This situation can be explained by the fact that in implant designs where the load is collected and absorbed within the implant itself—resulting in higher stress values experienced by the implant—there is a corresponding reduction in the stress transmitted to the abutment, prosthetic framework, and bone tissue. Consequently, the stress in these surrounding structures is decreased. The high maximum principal stress (tensile stress) values observed in the nasal buttress region in the M1, M2, and M3 models under vertical loading confirm the critical role of this anatomical area in load transfer. This preferential stress concentration in the nasal buttress region can be explained by its anatomical position and role in load transmission. The nasal buttress acts as a central structural pillar in the anterior maxilla, directly aligned with the direction of force application from anterior and premolar regions. As a result, occlusal forces are transmitted more directly to this region, leading to localized stress accumulation. In contrast, the zygomatic buttress, although structurally robust, is positioned more laterally and is capable of distributing loads over a broader surface area, thereby reducing localized stress concentrations. Furthermore, the geometric continuity and relative stiffness of the nasal buttress may contribute to its function as a primary load-bearing pathway in subperiosteal implant-supported prosthetic systems. Both the nasal and zygomatic buttress regions are known to be relatively resistant to resorption and serve as key anchorage sites for subperiosteal implants. The lower tensile stress values in the M5 (12.6 MPa) and M6 (13.7 MPa) models indicate that these designs may protect the cortical bone from overload by distributing the load more evenly. According to the literature, the safe compression limit for cortical bone is generally accepted as 50 MPa. In our study, the minimum principal stress value of -42 MPa obtained in the M3 model, while within this safe limit, approaches the threshold associated with bone resorption. In contrast, the lower stress values exhibited by the M5 and M6 models around the 2nd screw socket in the buccal region suggest that these designs are advantageous for preserving bone health.

Mommaerts et al. proposed rehabilitation using 2 separate implants instead of a single implant. They listed the advantages of this approach as the ability to manage only one surgical area at a time, which reduces bleeding and limits the spread of local anesthesia; the elimination of the need for extensive separation of the palatal fibro mucosa and preservation of the nasopalatine nerve; and the fact that if infection occurs in part of the implant, only the affected portion needs to be removed [5]. Despite the potential benefits of one-piece implants in stress distribution and immediate loading, the surgical challenges associated with their placement must be carefully considered. Precise positioning and alignment are essential for proper fit and optimal load distribution. Surgeons require advanced technical skills, extensive experience, and thorough preoperative planning to achieve successful outcomes.

There is no definitive data in the literature regarding the minimum number of osteosynthesis screws required for subperiosteal implants. However, various studies recommend using as many osteosynthesis screws as possible to enhance the osseointegration potential of the titanium framework with the underlying bone and to ensure adequate primary stability [10, 30, 31]. Vaira et al. performed surgical procedures using at least 4 screws [36]. Dimitroulis et al. conducted surgeries involving at least eight screws buccally and at least 2 screws palatally or lingually, depending on the size of the subperiosteal implant [10]. In the present study, stabilization was achieved with 6 screws on each buccal side in each model, 1 bar on palatal side in single-piece models, and 2 screw on each the palatal side in 2-piece models.

Traditional endosseous implants generally cause higher localized stress at the cortical bone/implant interface, which can contribute to marginal bone loss over time [18]. In contrast, subperiosteal implants, especially those with dual-configuration designs, have demonstrated a more even stress distribution along the alveolar ridge, potentially reducing the risk of bone resorption. Acar et al. and Ari et al. found that subperiosteal implants exhibited lower peak stress values compared to conventional implants under similar loading conditions, particularly in atrophic ridges where endosseous implants may lack adequate bone support [27, 28]. However, subperiosteal implants also present some biomechanical challenges. Their reliance on periosteal fixation rather than bone integration means that micromovements can occur if sufficient stabilization is not achieved.

Subperiosteal implants offer a less invasive alternative to zygomatic implants, avoiding transantral placement and reducing the risk of sinus-related and orbital complications. While zygomatic implants demonstrate high survival rates, they are associated with increased surgical complexity and a distinct complication profile [32–34]. In contrast, subperiosteal implants allow for design customization and may facilitate re-intervention in case of failure. These differences highlight the importance of individualized treatment planning based on anatomical and clinical considerations.

The differences observed among the 6 implant designs can be explained by variations in load transfer pathways and structural support distribution. Designs with increased surface area and multiple fixation zones demonstrated a more homogeneous stress distribution, reducing peak stress concentrations in cortical bone. In contrast, configurations with more localized support tended to concentrate stresses within the implant structure. The presence of a palatal connection in single-piece designs contributed to improved structural continuity, allowing forces to be redistributed across the arch and reducing localized stress accumulation within the implant. However, this configuration was associated with increased stress transfer to surrounding bone in certain models. Similarly, mesh-type designs altered the biomechanical balance by localizing stress within the implant framework while reducing stress transmission to the abutment, prosthetic framework, and bone tissue. These findings indicate that stress distribution is governed by the interaction of multiple design parameters, including surface area, support geometry, and structural continuity. From a clinical perspective, optimizing these variables is essential to achieve a balance between implant durability and preservation of peri-implant bone in the rehabilitation of severely atrophic maxillae.

From a clinical standpoint, the choice between single-piece and 2-piece subperiosteal implant designs should be guided by the primary treatment objective. If the priority is to minimize mechanical stress within the implant and enhance structural continuity, single-piece designs may be preferable. Conversely, if the goal is to reduce stress transfer to the surrounding bone—particularly in patients with compromised bone quality—2-piece configurations may offer a biomechanical advantage. Mesh-type designs may provide an additional benefit by redistributing stress away from peri-implant bone, potentially contributing to improved long-term tissue preservation. Therefore, implant design selection should be individualized based on patient-specific anatomical and biomechanical considerations.

Although direct experimental validation was not performed, the present finite element model demonstrates consistency with previously published biomechanical studies on subperiosteal and maxillary implant systems. In particular, the localization of peak stress concentrations in the nasal buttress region and around the implant–bone interface observed in this study is in agreement with earlier reports identifying these regions as primary load-bearing pathways in the atrophic maxilla [17, 18, 20]. Furthermore, the magnitude of von Mises stresses within the implant and principal stresses in cortical bone falls within the ranges reported in comparable finite element analyses under similar loading conditions [17, 20, 28, 29]. Previous studies have also demonstrated that implant design parameters, such as monoblock versus multi-piece configurations, significantly influence stress distribution patterns, with single-piece systems tending to concentrate stress within the implant structure and multi-piece systems facilitating stress dissipation to surrounding bone [20, 28, 29]. These trends are consistent with the findings of the present study. Taken together, the agreement between the present results and existing finite element literature supports the validity and reliability of the computational model and suggests that the observed stress patterns are biomechanically plausible.

Within the limitations of this study, several simplifying assumptions should be considered when interpreting the results. The analyses were performed under linear static loading conditions, and all materials were modeled as homogeneous, isotropic, and linearly elastic. In particular, the assumption of isotropic bone behavior represents a limitation, as cortical bone is known to exhibit anisotropic mechanical properties that may influence stress distribution patterns, especially in the thin cortical shell of the atrophic maxilla. Furthermore, the absence of dynamic loading conditions and biological factors such as bone remodeling may limit the direct clinical translation of the findings. Despite these limitations, the present results suggest that custom-made titanium subperiosteal implants represent a biomechanically viable and less invasive alternative for the rehabilitation of severely atrophic maxillae.

Conclusion

This study demonstrated distinct biomechanical differences among the evaluated implant designs. Single-piece configurations showed lower von Mises stress values within the implant, suggesting improved load absorption and structural continuity. In contrast, two-piece designs were more effective in reducing stress transfer to the surrounding bone, which may be advantageous for minimizing cortical bone loading. Mesh-type designs exhibited a tendency to localize stress within the implant while reducing stress transmission to adjacent components. Stress concentrations were consistently observed in the nasal buttress region, highlighting its role as a primary load-bearing anatomical structure in subperiosteal implant fixation.

All evaluated designs remained within physiologically acceptable limits for cortical bone and below the yield strength of titanium, indicating adequate mechanical safety under simulated loading conditions. However, these findings are based on static linear finite element analysis and do not account for biological factors such as bone remodeling, dynamic loading conditions, or long-term clinical response. Therefore, the results should be interpreted as comparative biomechanical insights rather than direct predictors of clinical performance.

From a clinical perspective, implant design selection may be guided by the primary treatment objective: single-piece designs may be preferred when implant-level stress reduction and structural continuity are prioritized, whereas two-piece designs may be more suitable for minimizing stress transfer to peri-implant bone, particularly in patients with compromised bone quality.

Among the evaluated designs, M3 demonstrated the lowest von Mises stress values within the implant, indicating the most favorable mechanical behavior at the implant level. In contrast, mesh-type designs (M5 and M6) showed lower stress values in cortical bone, suggesting a more advantageous biomechanical profile for bone preservation. Overall, two-piece configurations exhibited a consistent tendency to reduce stress transfer to surrounding bone, supporting their potential benefit in maintaining peri-implant bone integrity.

Authors’ contributions

K.A.D. and Y.F. conceptualized the study K.A.D. and Y.F. curated the data and provided resources, software, and visualization. K.A.D. and Y.F. performed formal analysis and investigation and developed the methodology. K.A.D. and Y.F. administered the project and supervised the research. K.A.D. and Y.F. validated the findings. K.A.D. and Y.F. wrote the original draft and reviewed and edited the manuscript.

Funding

None.

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 does not involve human or animal participants, and thus, ethical approval was not required. The research was conducted using computational simulations, adhering to standard scientific and ethical guidelines.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.