Biomechanical evaluation of implant options for unilateral maxillary defects: a finite element analysis

Abstract

Objective

This study aimed to evaluate stress distribution in unilateral maxillary defects using finite element analysis (FEA) to compare subperiosteal (SI) and zygomatic implants (ZI).

Materials and methods

A 3D model of a unilaterally atrophied maxilla was reconstructed from CT scans. Five scenarios were simulated: (1) quad zygoma implants (SC1), (2) zygoma and conventional implants (SC2), (3) two-piece SI and conventional implants (SC3), (4) one-piece SI and conventional implants (SC4) and (5) one-piece SI implant (SC5). Mechanical properties were assigned based on data in the literature; a 450 N force for occlusal loading and a 93 N force for oblique loads were applied.

Results

Under vertical loading, SC2 exhibited the highest tensile stress (Pmax) in the atrophic region (R-AM), while SC4 showed the lowest Pmax across the entire maxilla, indicating better stress distribution. Under oblique forces, SC2 also showed the highest Pmax in R-AM, while SC5 had the lowest Pmax overall. Minimum principal stress (Pmin) followed similar patterns, with SC4 and SC5 demonstrating lower stress levels than the other scenarios. Abutment stresses were highest in SC2 and lowest in SC4. Overall, the SI scenarios (SC3–SC5) exhibited lower stress transmission to the alveolar bone than the ZI scenarios (SC1 and SC2), with SC4 providing the most balanced stress distribution across all regions.

Conclusions

SI implants, mainly the one-piece SI (SC4), offered a more favourable stress distribution than ZI implants in unilateral maxillary defects, reducing the risk of excessive bone stress. This finding suggests that SI implants may be superior for such cases, although individual patient anatomy should guide implant selection. Further clinical studies are necessary to confirm these biomechanical findings in vivo.

Clinical relevance

This study underscores the crucial role of implant selection in minimising stress on the alveolar bone in unilateral maxillary defects. Based on these findings, we recommend personalised implant strategies based on biomechanical insights to enhance outcomes in maxillofacial reconstruction.

Introduction

Maxillary defects, often the result of tumours, trauma or severe atrophy, present a complex reconstruction challenge. The intricate anatomy of the maxilla and maxillary sinus, coupled with decreased bone quality and increased sinus pneumatisation, particularly in hemi-maxillary defects, contribute to the complexity of this task [1].

Various methods of maxillary defect reconstruction have been proposed, including obturator prostheses, bone grafts with titanium plates or meshes, and regional pedicled flaps [2]. However, regional pedicled flaps may be insufficient for the functional reconstruction of oral structures, such as dental implants and denture restoration [3]. On the other hand, bone grafts require a second operation and microvascular techniques, leading to longer recovery times and increased patient discomfort [4, 5]. Advanced grafting surgical techniques may not be appropriate for cases involving tumours and traumatic injuries, either due to the patient’s physiological state or the complexity of the required reconstruction in the affected area [6]. In certain cases, implant utilisation may be deemed the sole therapeutic option. However, the heterogeneity of defects may render certain options unsuitable for the intended purpose [7].

In cases of trauma, tumour or atrophy, different parts of the jaw may be affected unequally, leading to varying bone levels. This variation can create complications when planning treatment for edentulous mouths and confuse clinicians. In situations where all implant options for reconstruction are being considered, conventional implants are recommended in areas where sufficient bone levels exist for high success rates [8]. Conventional implants have demonstrated significantly higher success rates, are a minimally invasive treatment option, and exhibit fewer drawbacks than alternative implant options [9]. However, studies have shown that conventional implants are highly influenced by bone quality, with high interfacial stress concentrations forming near the implant–cortical bone junction in the presence of thin cortical bone [10]. This may lead to bone failure or implant instability caused by fatigue or overload. Therefore, optimising implant geometry and determining the appropriate implant treatment based on the patient’s anatomical and individual characteristics may enhance clinical success [11, 12].

When the placement of conventional dental implants is unfeasible due to inadequate bone availability or highly invasive surgical techniques, alternative implant procedures should be considered. Subperiosteal (SI) and zygomatic implants (ZI) may be alternative procedures that avoid invasive surgical protocols and patient discomfort for severely atrophic maxillas. ZI has emerged over the last two decades as a reliable and effective option for managing atrophic edentulous maxilla and maxillectomy defects [13]. The ZI utilises the bone of the zygomatic arch as an anchor for a long implant, which can be used in conjunction with conventional implants to support prostheses and obturators. While no randomised controlled trials have directly compared the clinical effectiveness of ZIs versus other rehabilitation techniques, many published studies have reported positive long-term outcomes [14, 15]. However, the current literature has not addressed the need for a comprehensive biomechanical comparison between SI and ZI implants in unilateral maxillary defects, leaving a crucial gap in understanding their long-term success rates and optimal implant selection for various clinical scenarios. Although the extent of stress, such as increasing occlusal force, is high, dynamic techniques for examining stress due to supporting implants are unavailable.

SI was initially introduced by Dahl in 1943 as a treatment option for patients with severe bone loss [16]. However, they gradually lost popularity due to a lack of technology, the need for two-stage surgery, and biomechanically inadequate designs. In recent years, with the development of advanced technologies, such as computer-aided design and computer-aided manufacturing, the use of new materials, and a better understanding of bone biomechanics, SIs have regained attention as a viable option for treating advanced bone loss [17]. Despite these advances, there is still limited data on how SI implants perform under varying loads compared to ZI implants, especially in highly resorbed maxillary regions. Thus, this study seeks to provide a detailed biomechanical comparison to fill this gap. In the long term, inappropriate or unbalanced force accumulation can lead to screw loosening or abutment fractures. In addition, it can exacerbate resorption in an already severely atrophic maxilla and result in a loss of bone–implant compatibility [18].

Accurate estimation of the peak stress level is a crucial step in ensuring the successful rehabilitation of a prosthesis. The potential for excessive stress at the implant-bone interface, leading to peri-implant-bone loss and failure of osseointegration, underscores the necessity of this process. Finite element analysis (FEA), a powerful tool, helps address this need by breaking down complex problems into manageable elements and providing numerical results for insight into implant loading biomechanics.

ZIs primarily derive support from the zygomatic bone, whereas SIs typically rely on the maxillary buttress region for support. These regions exhibit high resistance to resorption under masticatory forces. Conversely, the alveolar bone region, particularly the posterior maxillary area with high spongy bone content, is susceptible to resorption under high-stress conditions [19]. Therefore, it is imperative to consider the alveolar crest region when analysing stress distribution in relation to alveolar resorption during long-term implant use. This consideration is especially critical in implant systems designed for patients with unilateral maxillary defects, as it influences the long-term outcomes of implants. While there are analyses in the literature regarding the use of these two implant designs alone, there is no comprehensive study comparing the stress transmission of these implant types in unilateral maxillary defects [2, 4–12, 17]. Our study aims to evaluate the effects of these two implants on alveolar bone under different clinical scenarios and to provide more specific recommendations for clinical applications. In particular, the simulation performed in five different scenarios, considering different loading conditions, provides a new and unique approach to understanding the effect of implant selection on clinical outcomes. These findings contribute significantly to the existing literature by demonstrating that implant selection should be based on individualised factors.

The novelty of this study lies in its approach to simulating various clinical scenarios to evaluate the optimal implant configuration in terms of stress distribution. Doing so aims to provide biomechanical insights that can inform clinicians on the most suitable implant type for improving long-term clinical outcomes in maxillofacial reconstruction.

The rationale for this study is to fulfil the need for a deeper biomechanical understanding to determine the optimal choice of implant for unilateral maxillary defects. The complexity of maxillary anatomy and severe bone loss limit the effectiveness of conventional implants and may necessitate the use of subperiosteal and ZI as alternative solutions. However, more data on these implants’ effects on stress distribution must be collected. With this study, we aim to guide clinicians and patients towards better outcomes by presenting the main biomechanical factors that should be considered during implant selection.

Materials and methods

This study was performed in the Hacettepe University Faculty of Dentistry Oral and Maxillofacial Surgery Department. A 3D representation of an unilaterally atrophied maxillary bone was generated from a computed tomography scan of an adult patient and saved in stereolithography (STL) format. The resolution per slice obtained from these scans was 0.625 mm, which allowed for detailed modeling of both the cortical and spongy bone structures. The topographical scan was obtained from the archive of the ALGOR FEMPRO^® version 19 (ALGOR, Inc. 150 Beta Drive Pittsburgh, PA 15238–2932 USA) sofware. A linear static stress analysis was conducted using a Sparse solver, enabling efficient handling of the complex geometry and high element count. This analysis evaluated the stress distributions in both the zygomatic and subperiosteal implants, as well as the surrounding bone tissue. The Sparse solver was employed to effectively manage the complex geometry and high element count. Linear static stress analysis was applied to evaluate the stress distributions in both the zygomatic and subperiosteal implants, as well as in the surrounding bone tissue. The mesh density was maintained at a high level, utilizing a tetrahedral mesh type with an average element size of 0.2 mm. The solid geometry of the maxilla, encompassing both cortical and spongy bone, was reconstructed from the STL data into Digital Imaging and Communications in Medicine (DICOM) format using 3D–Doctor software (Able Software Corp., MA, USA. Implants and other prosthetic components were integrated into the model using CAD models provided by the manufacturer. The mechanical properties of materials, Poisson’s ratio, and Young modulus were obtained from the literature (Table 1) [20, 21], and the boundary conditions were determined. All models used in the study were fixed in the upper, anterior and posterior regions of the jaw to have zero motion in each degree of freedom [22, 23]. The models receive support from these regions when force is applied [24].

Table 1.

Mechanical properties of materials

Material	Young Modulus (MPa)	Poisson Ratio
Cortical Bone	13,700	0.3
Spongıose Bone	1,370	0.3
Titanium	110,000	0.35
Subperiosteal Implant	116,000	0.32
Prothesis (acrylic)	3000	0.35
Prothesis Metal Frame (cr-co)	218,000	0.33

In creating the unilateral maxillary defect model, the right side of the maxilla represented the severely atrophic hemi-maxilla (R-AM), while the left side represented the non-atrophic hemi-maxilla (L-NAM) (Fig. 1). The R-AM bone borders were created as follows: 2.5 mm length between the nasal cavity and alveolar crest in the anterior maxilla and 2.5 mm length between the floor of the maxillary sinus and the alveolar crest in the posterior maxilla (Fig. 1). The L-NAM bone borders were created as follows: an 8 mm length between the nasal cavity and the alveolar crest in the anterior maxilla and an 8 mm length between the floor of the maxillary sinus and the alveolar crest in the posterior maxilla (Fig. 1). The alveolar crest diameter of the maxilla model used in all models was uniformly set to 5 mm.

Fig. 1.

A 3D representation of an unilaterally atrophied maxillary bone and bone borders

Five scenarios were created in the hemiatrophic maxilla model in this study:

• Scenario 1 (SC1): Quad ZIs (4.1 × 35 mm) were placed at a 55-degree angle using the extrasinus technique (Fig. 2a).

• Scenario 2 (SC2): Two ZIs (4.1 × 35 mm) were placed at a 55-degree angle in the R-AM region, and two conventional implants (4.1 × 10 mm) were placed in the L-NAM region (Fig. 2b).

• Scenario 3 (SC3): Two-piece SI, each piece with two wings, were placed in the R-AM region. The posterior piece of the SI had one wing in the canine region and the other in the zygomatic buttress region. In contrast, the anterior piece of the SI had wings positioned in the right and left nasal buttress regions. Two conventional implants (4.1 × 10 mm) were placed in the L-NAM region (Fig. 2c).

• Scenario 4 (SC4): A one-piece SI featuring three wings was placed in the R-AM region, one each on the right and left nasal buttress and one in the zygomatic buttress region. Two conventional implants (4.1 × 10 mm) were placed in the L-NAM region (Fig. 2d).

• Scenario 5 (SC5): A one-piece SI was placed in the entire maxilla, featuring four wings: two in the right and left nasal buttress regions and two in the right and left zygomatic buttress regions (Fig. 2e).

Fig. 2.

Modelling of the scenarios (a) Scenario 1 (b) Scenario 2 (c) Scenario 3 (d) Scenario 4 (e) Scenario 5

Zygomatic implants (Straumann^® Zygoma Implant System-Flat type) used in SC1 and SC2 were 4.1 mm in diameter and 35 mm in length and were placed at a 55-degree angle. Conventional implants (Straumann^® Implant System) used in SC2, SC3, and SC4 were 4.1 mm in diameter and 10 mm in length. Due to the nature of the study, which compared different implant options, implants in all groups could not be standardised. However, the abutments of all implants used were 3.75 mm in diameter, based on the platform-switching concept. All SIs had a thickness of 1.8 mm, made of 5-grade titanium, with two holes in each wing. Each SI was stabilised using titanium screws measuring 7 mm in length and 2 mm in width.

In this study, the extent of osseointegration of implants within the bone was assessed based on the existing literature. The current models were developed to replicate a fully osseointegrated implant with high mineralisation in the surrounding bone [25]. This approach was referenced from a previous FEA study by Ihde et al., who divided implant healing into five stages and defined stage 5 as a scenario in which long-term integration of the implant body results in complete corticalisation of all endosseous surfaces. Accordingly, all implant-bone interfaces in our models were simulated using ‘HARD’ contact definitions to reflect this fully integrated state [26].

To mimic mastication forces, a total force of 450 Newtons (N) in a vertical direction was applied to the first premolar, second premolar, and first molar (28 N, 94 N, and 108 N, respectively) and 93 N in a 45-degree angle from the palatinal direction to the canine teeth at the models [21, 27]. This force application aimed to replicate the centric relationship in canine-guarded occlusion [21]. We conducted stress analysis to measure stresses in the zygoma and subperiosteal implants, the maxillary cortical bone, implant abutments, and the metal substructure in units of MPa (N/mm²). The analysis visually represents areas with high stress levels in red and low stress levels in blue, providing insights into stress distribution patterns. In these scenarios, the number of nodes is as follows: SC1 356,998, SC2 324,035, SC3 448,143, SC4 423,637 and SC5 347,627. The number of elements is as follows: SC1 1,295,810, SC2 1,205,428, SC3 1,686,266, SC4 1,583,053 and SC5 1,350,204. In this study, highly detailed and realistic 3D models were created using the Mesh First Approach. The number of nodes and elements incorporated into the model ensured sufficient accuracy, thus eliminating the need for further mesh refinement. Model validation was achieved by confirming that the model exhibited the expected physical behavior under the applied loads.

This study measures tensile (Pmax) and compressive (Pmin) principal stress values at consistent sites in all scenarios. For scenarios involving zygoma implants, the anterior zygoma implant was positioned at the 1st premolar level, while the posterior zygoma implant was placed at the 1st molar level. In a parallel and systematic manner, conventional implants were situated in the 1st premolar and 1st molar regions. All conventional (10 mm long) implants were placed using the transalveolar sinus lift technique. Four abutments were planned for SC1 and SC2, with six abutments planned for SC3, SC4, and SC5. The abutments were consistently placed at the lateral, 1st premolar, and 1st molar tooth levels in all scenarios. In all scenarios, alveolar bone stress was measured and evaluated at the alveolar crest level in the abutment area.

Results

Under vertical forces, the highest Pmax value in the R-AM was observed in the 1st premolar region in SC2 (Table 2), while the lowest Pmax values were found in SC4 when the entire maxilla was considered (Figs. 3 and 4). Under vertical forces, the highest Pmin value in R-AM was noted in the 1st molar region in SC1 (Table 2), with the overall highest Pmin value observed in SC2 and the lowest in SC5 (Fig. 5). When the scenarios were subjected to oblique forces, the highest Pmax values in R-AM were observed in the 1st molar region in SC2 (Table 3) and the lowest in SC5 across the entire maxilla evaluated (Figs. 4 and 6). For oblique forces, the highest Pmin values in R-AM were observed in SC1 (Table 3) and the lowest in SC5 (Fig. 7).

Table 2.

Distribution of Tensile (Pmax), Compressive (Pmin) and Von Mises Stresses (Abutment, Prothesis) under Vertical forces in scenarios

		Stress Values Under Vertical Forces (MPa)
		R-AM			L-NAM			Totally
		12	14	16	22	24	26
Pmax. (MPa)	SC1	0.04	1.59	2.05	0.09	1.94	2.13	7.8
	SC2	0.06	1.33	6.5	0.44	16.09	5.66	30.02
	SC3	0.56	1.46	1.07	0.64	1.10	2.29	6.57
	SC4	0.19	0.32	0.29	0.09	0.03	1.71	2.44
	SC5	0.37	0.39	1.62	0.06	1.32	1.36	4.76
Pmin. (MPa)	SC1	0.44	4.1	17.57	0.54	6.11	13.95	42.71
	SC2	0.95	6.32	11.1	1.96	2.42	23.18	45.93
	SC3	0.42	2.29	4.2	0.41	3.31	17.57	28.2
	SC4	0.04	0.47	0.42	0.02	2.06	10.96	13.98
	SC5	0.28	0.73	2.54	0.39	0.63	1.83	6.43
Abutment (MPa)	SC1		41.64	178.46		37.49	100.58	358.17
	SC2		20.59	137.09		148.87	202.86	509.41
	SC3	23.24	28.17	56.83	10.38	23.45	56.01	198.08
	SC4	3.04	12.53	23.3	2.53	43	15.22	99.62
	SC5	9.89	8.79	28.56	11.96	8.77	46.09	114.06
Prothesis (MPa)	SC1		19.02	45.69		18.02	39.56	122.29
	SC2		24.29	41.51		35.69	62.86	164.35
	SC3	27.29	31.73	53.42	13.65	13.11	27.63	166.83
	SC4	2.38	18.57	27.61	3.94	13.8	25.97	92.27
	SC5	6.04	15.74	28.65	12.66	10.18	28.63	101.9

R-AM: Right athophied hemi-maxilla, L-NAM: Left non-atrophied hemi-maxilla, Pmax.: Tensile stress, Pmin.: Compressive Stress, N/mm² = MPa

Fig. 3.

Pmax stress distributions on bones under vertical forces (a) Coloring conditions and coordinate layout (b) Scenario 1 (c) Scenario 2 (d) Scenario 3 (e) Scenario 4 (f) Scenario 5

Fig. 4.

Bar chart shows Pmax (left) and Pmin (right) stress values among the models

Fig. 5.

Pmin stress distributions on bones under vertical forces (a) Coloring conditions and coordinate layout (b) Scenario 1 (c) Scenario 2 (d) Scenario 3 (e) Scenario 4 (f) Scenario 5

Table 3.

Distribution of tensile (Pmax), compressive (Pmin) and von mises stresses (Abutment, Prothesis) under oblique forces in scenarios

		Stress Values Under Oblique Forces (MPa)
		R-AM			L-NAM			Totally
		12	14	16	22	24	26
Pmax. (MPa)	SC1	0.41	0.97	2.45	0.39	2.25	6.36	12.83
	SC2	0.13	3.53	8.57	1.25	1.98	13.55	29.01
	SC3	0.53	0.206	0.38	0.34	2.29	10.4	14.14
	SC4	0.6	2.09	1.47	0.36	0.69	6.97	12.18
	SC5	0.5	1.49	1.74	0.11	0.55	0.99	5.38
Pmin. (MPa)	SC1	0.38	11.45	4.76	1.59	12.99	6.49	37.66
	SC2	0.17	12.34	2.1	0.68	12.12	6.13	33.54
	SC3	0.25	0.18	0.08	0.63	4.11	1.71	6.96
	SC4	0.26	1.97	0.02	0.1	2.67	1.16	6.18
	SC5	0.33	0.08	0.16	0.08	0.21	0.1	0.96
Abutment (MPa)	SC1		72.88	32.25		57.58	37.58	200.29
	SC2		101.91	63.03		58.07	34.07	257.08
	SC3	28.36	17.11	10.78	21.28	26.26	30.6	134.39
	SC4	13.71	12.88	7.06	15.06	6.07	22.35	77.13
	SC5	17.07	18.58	9.03	17.5	21.83	8.36	92.37
Prothesis (MPa)	SC1		26.28	13.21		35.31	16.19	90.99
	SC2		23.92	24.16		37.49	20.95	106.52
	SC3	36.2	17.24	9.29	29.46	13.04	19.23	124.46
	SC4	10.27	12.79	8.31	11.2	17.62	8.6	68.79
	SC5	11.35	9.16	8.49	13.79	22.17	7.62	72.58

R-AM: Right athophied hemi-maxilla, L-NAM: Left non-atrophied maxilla, Pmax.: Tensile stress, Pmin.: Compressive Stress, MPa = N/mm²

Fig. 6.

Pmax stress distributions on bones under oblique forces (a) Coloring conditions and coordinate layout (b) Scenario 1 (c) Scenario 2 (d) Scenario 3 (e) Scenario 4 (f) Scenario 5

Fig. 7.

Pmin stress distributions on bones under oblique forces (a) Coloring conditions and coordinate layout (b) Scenario 1 (c) Scenario 2 (d) Scenario 3 (e) Scenario 4 (f) Scenario 5

Regarding forces on the abutments, under vertical forces, the lowest forces were recorded at SC4, while the highest forces were found at SC2 (Table 2), which were four times greater (Fig. 8). Specifically, in the L-NAM, the Von Mises stress value on the abutment in the 1st molar region in SC2 was more than two times higher than the total Von Mises stress value on the abutments in SC4 under vertical and oblique forces (Fig. 9) (Tables 2 and 3). In the prosthetic metal frame, as with all measurements, the lowest Von Mises stress values were measured at SC4 under vertical and oblique forces (Figs. 9 and 10) (Tables 2 and 3).

Fig. 8.

Von Mises stress distributions on abutments and subperiosteal implants under vertical forces (left) and oblique forces (right) SC1) Scenario 1 SC2) Scenario 2 SC3) Scenario 3 SC4) Scenario 4 SC5) Scenario 5

Fig. 9.

Bar chart shows Von Mises stress values in Abutment (left) and Prothesis (right) among the models

Fig. 10.

Von Mises stress distributions on prosthesis under vertical forces (upper) and oblique forces (bottom) SC1) Scenario 1 SC2) Scenario 2 SC3) Scenario 3 SC4) Scenario 4 SC5) Scenario 5

Discussion

FEA is a numerical method widely employed in engineering and biomechanics. Researchers prefer this technique due to its non-invasive and flexible nature. It allows for the simulation of various defects and corresponding reconstruction plans within a single model. The analysis process is highly visual and vivid, enabling investigators to easily evaluate and examine regions of interest. While histological studies suggest the possibility of incomplete osseointegration between bone and implant interfaces, this study adopts the assumption of 100% osseointegration for implants, consistent with assumptions made in other relevant studies [25]. To accurately portray complete integration, all contact definitions were simulated as ‘HARD’, and all implants were modelled assuming stage 5 osseointegration in alignment with the existing literature [26].

This study provides a unique contribution to the field of maxillary reconstruction by offering a detailed biomechanical comparison of SI and ZI in the context of unilateral maxillary defects. While previous studies have explored the individual performance of ZI and SI implants, a significant gap exists in understanding their comparative biomechanical behaviour under different loading conditions.

This study aimed to evaluate the stress distribution in bone and implants of implant treatment options for unilateral maxillary defects. For this analysis, the final models with prostheses were transferred to the ALGOR FEMPRO^® software; a total of 93 N oblique load and 450 N occlusal load were applied. Titanium alloys are known for their high strength-to-weight ratio and excellent mechanical properties, including their ability to withstand stress levels of up to 900 N/mm2 without irreversible deformation. Studies have shown that values of 25 MPa and above can damage bone tissue [28]. This study investigated the stress levels experienced by the implant or bone tissue; no scenario in which the stress exceeded this limit was identified.

The biomechanical forces exerted on implant-supported prostheses influence the resistance of the alveolar bone to chewing force and the remodelling process of the bone surrounding the implant. The heightened forces placed on the alveolar bone are an important factor in implant treatment failure [28]. Research findings indicate that compressive and tensile stresses impact the force resistance of the alveolar bone and the bone remodelling process surrounding the implant [28, 29]. Accordingly, this study evaluated the compressive and tensile stresses of the alveolar bone in which the implants and abutments were placed.

Upon analysis of the Pmax values under vertical and oblique forces transmitted to the alveolar bone surrounding the implants, this study found that the scenarios utilising subperiosteal implants (SC3, SC4, SC5) exhibited significantly lower stress transmission to the bone than those utilising zygoma implants (SC1, SC2). This finding is consistent with previous studies comparing zygoma and subperiosteal implants, albeit with varying force values [30, 31].

The placement of ZI is highly dependent on the shape of the zygomatic bone, as vertical loads on the abutment are transmitted to the alveolar bone at an angle [15, 32]. Forces acting along the long axis of the implant show a more even stress distribution. Forces acting obliquely on the long axis increase stress at the bone–implant interface. Although some short-term studies indicate that implant inclination of 45–60 degrees does not alter clinical success, it is essential to acknowledge the potential for excessive loads to induce microscopic fractures and perturb the osseointegration between the implant and alveolar bone [33]. These loads may increase the risk of bone fractures and render the alveolar bone more susceptible to fragility. Anatomical features, such as the maxillary sinus, zygomatic bone anatomy, and the position of the alveolar ridge, may influence the ideal implantation angle of ZI.

However, placing ZI as close to the alveolar ridge as possible and at an angle that minimises the cantilever length may be more appropriate. There is still no consensus on the ideal technique for the placement of ZI, according to the degree of bone anchorage and implant inclination. Little is known about the amount of zygomatic bone around ZI placed with different techniques, which may affect initial mechanical implant stability. However, a cadaveric study by Corvello et al. demonstrated that ZI placed with the extrasinus technique could be placed in a more lateralised position, allowing greater penetration of the implants into the zygomatic bone [34, 35]. Compared to the original Branemark protocol, the extrasinus technique provides a shorter cantilever length, since the exit position of the implant is in the crestal ridge [35]. Thus, the incoming forces are more parallel to the long axis of the implant, resulting in relatively less stress at the bone–implant interface.

Therefore, in this study, ZIs were placed using the extrasinus technique. Anatomical investigations have demonstrated that the zygomatic bone presents a greater surface area and bone length to support the zygomatic implant than the maxilla. Most studies have confirmed that support from the zygomatic bone region is advantageous for stress distribution in the atrophic maxilla [15, 36]. However, Varghese et al. conducted an FEA [37] comparing zygoma and endosseous implants while also considering the masticatory muscles. The research findings indicated that stress distribution was not concentrated in the zygomatic bones and that alveolar bone support played a significant role in zygoma implants. Furthermore, the quad zygoma model demonstrated a more evenly balanced and reduced stress distribution than did the model incorporating endosseous implants with zygoma. Consistent with these results, SC2 exhibited the greatest susceptibility to stress transmitted to the alveolar bone in the study. As a result, when zygoma implants are preferred, quad zygoma application is more advantageous concerning Pmax and Pmin to the alveolar bone.

After thoroughly evaluating various implant scenarios in this study, it was determined that SC4 yielded the most favourable results regarding the maximum tensile stresses transmitted to the bone. Specifically, SC4 involved using a one-piece subperiosteal implant in the atrophic region of the maxilla coupled with two endosseous implants in the non-atrophic region. This scenario transmitted the least stress to the bone in oblique and vertical forces. Conversely, of the scenarios using subperiosteal implants, S3 was the most disadvantageous, based on the observed outcomes. Although studies have shown that lower stress values are obtained in two-piece subperiosteal implant designs, these studies evaluate the stress on the implant and do not comment on the stress transmitted to the bone [38]. In addition, these studies assessed symmetrical maxilla models [30]. When developing personalised subperiosteal implant designs, it is crucial to consider the anatomical geometry of the underlying bone. Applying the findings of this study to unilateral maxillary defects may significantly enhance the long-term success rates of these implants.

Upon detailed examination of the Pmin and Pmax values transmitted to the bone under oblique and vertical forces, the highest values were localised in the bone surrounding the most posterior implants in S1, S2 and S3. The impact of uneven stress distribution on the resorption pattern is a key aspect to consider. This phenomenon is more pronounced in the hemi-maxilla without defects, where the posterior region of the maxilla, the least dense region of the jaw bones, exhibits more rapid resorption under stress, a well-documented occurrence in the literature [39, 40]. Uneven stress distribution, particularly in the hemi-maxilla without defects, contributes to a more pronounced resorption pattern on the side with healthy bone [41]. Considering the long-term use of the implants, it is likely that the resorption pattern is more pronounced on the side without atrophy due to this uneven stress distribution, adding to the complexity of the situation [41, 42].

Although SC5 had stress distribution values closest to SC4, issues may arise when adapting one-piece subperiosteal implants to the underlying asymmetrical bone during production, which could negatively impact stress distributions. Furthermore, having conventional implants in the non-atrophied hemi-maxilla region may eliminate the problem of subperiosteal implant incompatibility due to potential resorption in this region, making it potentially more successful in the long term. A meticulously planned and designed implant tailored to the specific anatomy of the underlying bone will ensure long-term success by promoting optimal integration, stability, and functionality.

In the analysis of Von Mises stress values on the abutment and prosthesis, similar results were observed with the Pmax and Pmin values. The highest Von Mises stress values on the abutment and prosthesis superstructure were recorded at S2; the lowest values were recorded at S4. In particular, at S2, the total load transmitted to the abutments (509.41 N/mm²) exceeded the total load applied to the prosthesis (250 N). Although these values do not exceed the upper limit of titanium alloys (900 N/mm²), a load of 200 N/mm² transmitted to the abutment of a conventional implant in the posterior region in a non-atrophic hemi-maxilla could lead to adverse effects over time. In this study, regular occlusal forces were evaluated. In the presence of excessive force (such as that caused by bruxism), the stress on the abutment fragments at S2 increases. This finding highlights the importance of selecting implants that can withstand these forces, especially in semi-atrophic maxilla scenarios. Such considerations can significantly improve long-term clinical success.

The findings of this study demonstrated that one-piece SI implants (SC4) exhibited the most favourable stress distribution, a finding not previously reported in the literature. This suggests that one-piece SI implants may offer a biomechanical advantage over ZI in severe unilateral atrophy, especially when conventional implants cannot be placed. By highlighting this finding, our study adds a new layer of understanding to implant selection strategies, potentially shifting clinical preferences towards SI implants in specific scenarios.

The literature includes studies that classify implants based on their degree of osseointegration with the bone [25, 26]. Future research incorporating varying stages of implant integration could enhance the anatomical accuracy of jawbone models, thereby enriching the field. This current study represents the most extensive comparison of treatment options for unilateral maxillar defects. Consequently, an assumed 100% osseointegration was employed for all implants, which may be a limitation due to the absence of data reflecting variable osseointegration levels. Ihde et al. investigated different osseointegration stages in an FEA analysis [43].

Despite the strengths of this study, several limitations should be acknowledged. First, the finite element model, while based on realistic anatomical data, reduces the complexities of biological systems. This analysis did not consider real-life factors, such as bone quality, patient-specific anatomical variations, and biological responses to implant loading. Second, although the simulated loading conditions reflect typical masticatory forces, they may not fully replicate the dynamic nature of actual occlusion in patients. Future studies could enhance the accuracy of these findings by incorporating in vivo data and clinical assessments to validate biomechanical predictions. Finally, while this study focused on biomechanical performance, the clinical effectiveness of the implant options in terms of patient outcomes requires further investigation through long-term clinical trials.

Conclusions

This study’s findings indicate that subperiosteal implants generally exhibit lower alveolar bone stress levels than zygoma implants, which is consistent with the existing literature. Specifically, scenario S4 demonstrated the most favourable stress distribution, suggesting that it may offer the most advantageous clinical outcomes for patients with atrophic maxillary regions. On the other hand, the quad zygoma model (SC1) showed better stress distribution than the combination of endosseous and zygoma implants (SC2), although it still transmitted higher stress levels than the subperiosteal options. This study emphasises the importance of considering the anatomical geometry of the underlying bone when developing personalised subperiosteal implant designs.

Furthermore, this study adds new biomechanical insights by directly comparing ZI and SI implants in a controlled, simulated environment, offering clinicians evidence-based guidance for optimising implant choices in maxillofacial reconstruction. Each case of atrophy should be evaluated individually. However, FEA studies have enabled the assessment of stress distribution on bone and titanium structures for different implant designs, allowing for a mechanical, if not clinical, evaluation. The meticulous selection and design of implants based on individual anatomical and mechanical considerations can significantly enhance the long-term clinical success of implant treatments for unilateral maxillary defects.

Future research should prioritise long-term clinical studies to validate these findings and further investigate the biomechanical behaviour of various implant designs under different loading conditions.

Author contributions

G.A.; conceptualization, data curation, writing-original draft, preparation, I.A.; preparation, data analysis, sample and data collection, E.T.; methodology, reviewing, supervision.

Funding

Open access funding is provided by the Authors.

Data availability

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

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.