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Article

Evaluation of Miniscrew Stability in Posterior Teeth Intrusion—A Three-Dimensional Finite Element Analysis

by
Khaled Omran Ben Khalil
1,*,
R. Lale Taner
2,3,
K. Müfide Dinçer
1 and
Orhan Özdiler
1
1
Department of Orthodontics, Faculty of Dentistry, Cyprus Health and Social Sciences University, Mersin 99700, Turkey
2
Department of Orthodontics, Faculty of Dentistry, Gazi University, Ankara 06490, Turkey
3
Department of Orthodontics, Faculty of Dentistry, Cyprus International University, Mersin 99258, Turkey
*
Author to whom correspondence should be addressed.
Appl. Sci. 2026, 16(4), 1783; https://doi.org/10.3390/app16041783
Submission received: 21 January 2026 / Revised: 2 February 2026 / Accepted: 6 February 2026 / Published: 11 February 2026
(This article belongs to the Special Issue Advances in Orthodontic Treatment, 2nd Edition)
Browse Figures
Versions Notes

Abstract

This Finite Element Analysis (FEA) study examined the stability of Polyetheretherketone (PEEK) miniscrews and tissue response in the posterior maxilla under varying angulations. A Cone beam computed tomography (CBCT)-derived three-dimensional model of the fully dentate maxilla was generated, featuring anatomical structures (teeth, periodontal ligament (PDL), alveolar bone) and orthodontic components (brackets, transpalatal arch, archwires). PEEK miniscrews were positioned bilaterally in the regions of the second premolar-first molar and first molar-second molar. A force of 100 g was applied perpendicular to the archwire. Four insertion angulations (45°, 70°, 90°, and 110°) were simulated. FEA revealed a consistent posterior displacement pattern: crowns tipped distally and buccally, while roots moved mesially, with intrusion. The first molar’s PDL peaked at 110°. Cortical bone stress was greatest in molars (1.41 × 105 Pa at 70–110°). Cancellous bone stress peaked under 70° loading in the second molar (1.25 × 105 Pa). PEEK miniscrews exhibited minimal deformation and low interfacial stress, confirming stable anchorage across all angles. Posterior PEEK miniscrews demonstrated excellent stability across all insertion angles, with 70° providing optimal biomechanical efficiency for intrusion. The first molar’s PDL experienced the highest stress concentrations at extreme angles. These findings offer clinical guidance for miniscrew placement to achieve effective intrusion while maintaining tissue safety.

1. Introduction

Orthodontic intrusion, defined as the apical movement of a tooth along its longitudinal axis, is a fundamental strategy for correcting vertical discrepancies [1]. For conditions like anterior open bite and molar overeruption, intrusion facilitates counterclockwise mandibular rotation, improving occlusal function and facial esthetics [1,2]. Conventional mechanics, such as active vertical correctors [1], springs and magnets within bite blocks [2,3], occipital headgear [4,5], and maxillary traction devices [5,6], often lack absolute anchorage control, leading to unpredictable outcomes [7]. The use of temporary skeletal anchorage devices (e.g., miniscrews) has markedly increased the predictability of intrusion, as they provide a stationary reactive unit for force application [8,9]. Their application for maxillary molar intrusion is well-established in the literature [10,11,12,13,14,15]. Mini-implants are frequently utilized for intruding incisors in deep bite cases and molars in patients needing posterior intrusion for open-bite correction. A key benefit is the ability to achieve bodily movement without substantial tipping, which is an advantage over traditional mechanics that often cause unwanted side effects, such as the extrusion of neighboring teeth [16].
For posterior intrusion, Lin et al. (2006) [17] reported that using bilateral mini-implants in the posterior maxilla led to a mean molar intrusion of 1.5–2 mm, which aided in anterior open-bite correction. Posterior intrusion is especially useful for managing excessive vertical growth in hyperdivergent patients, improving both facial aesthetics and stability. Effectively intruding molars has also been associated with better temporomandibular joint (TMJ) function, as changes to the occlusal plane can reduce strain on TMJ structures [16].
Compared to other skeletal devices like miniplates, miniscrews offer notable clinical advantages, including less invasive placement, reduced patient discomfort, greater versatility in site selection, and broad acceptance [18]. Nonetheless, their clinical performance is not without challenges, with failure rates reported around 20%, often attributed to a loss of primary stability linked to biomechanical factors such as miniscrew design, dimension, and placement angulation [19,20,21,22].
In addition to biomechanical factors, certain clinical and anatomical limitations exist. Contraindications for miniscrew use include compromised systemic health, poor oral hygiene, pathological bone quality, and smoking [23,24]. Failure of temporary anchorage devices (TADs) can also arise from root or periodontal ligament contact, inadequate insertion torque, soft tissue inflammation, and anatomical complications such as sinus perforation or nerve injury [25]. Furthermore, higher failure rates are observed in the mandible, which are attributed to greater bone density and the associated requirement for increased insertion torque [26].
A key factor determining miniscrew success is the biomechanical interface established with the host bone. Titanium (Ti), the conventional material employed, is characterized by excellent biocompatibility and a high degree of corrosion resistance [27]. However, its high Young’s modulus (110 GPa) results in a substantial rigidity mismatch with bone (~14 GPa). This disparity can induce stress shielding, localized bone loss (resorption), and potential implant failure [28,29]. Furthermore, Ti may be susceptible to ion release in the oral environment and can cause undesirable light scattering [30,31]. These limitations have prompted the exploration of alternative materials. PEEK, a high-performance polymer, presents a compelling option due to its intermediate modulus, which better approximates bone stiffness, potentially reducing stress shielding. Its chemical inertness, biocompatibility, and favorable aesthetic profile further support its investigation for orthodontic anchorage [31,32].
The biomechanical effects of intrusion mechanics, particularly the stress distribution within the periodontal ligament, alveolar bone, and around the anchorage unit, are complex and difficult to assess clinically. Finite element analysis enables detailed simulation of these structures under orthodontic loads, providing insights into stress and strain fields [33,34,35]. A precise understanding of the biomechanics of molar intrusion is essential to optimize clinical protocols, minimize adverse effects like root resorption, and maximize the efficiency of tooth movement and implant stability [36].
Therefore, this finite element analysis aims to: (1) investigate stress distribution patterns in the posterior maxilla during molar intrusion using miniscrews; (2) compare stresses in bone and periodontal ligaments resulting from different implant placement angulations; and (3) identify the optimal insertion angle to apply efficient forces while minimizing stresses that contribute to root resorption and peri-implant strain, thereby ensuring tooth movement efficiency and miniscrew stability.

2. Materials and Methods

2.1. Study Design

This finite element analysis focused on the effects of insertion angulation and force direction on stress distribution, miniscrew displacement, and the mechanical response of surrounding periodontal and bone structures. A single loading configuration was simulated, involving the bilateral placement of PEEK miniscrews in the interradicular spaces between the second premolar and first molar and between the first and second molars. A 100 g force was applied perpendicular to the archwire from each side. Four insertion angulations were tested: 45°, 70°, 90°, and 110°.

2.2. Three-Dimensional Model Development

A three-dimensional finite element (FE) model (Figure 1) was developed based on a CBCT scan of a fully dentate maxilla from a 35-year-old male. The CBCT scan was acquired at 120 kVp and 7 mA with a 0.25 mm voxel size (FOV: 16 cm diameter × 4 cm height) using a Carestream CS 9600 system (Carestream Dental, Atlanta, GA, USA). Volumetric Digital Imaging and Communications in Medicine (DICOM) data were used for subsequent digital reconstruction.
The DICOM datasets were then imported into Mimics Research software 21.0 (Materialise NV, Leuven, Belgium) for segmentation. Utilizing threshold-based techniques, the compact and cancellous bone regions of the maxilla were precisely isolated, with careful attention paid to replicate the natural thickness of the buccal alveolar bone. Key anatomical dimensions, such as the interdental bone thickness of 1.0 to 1.26 mm in the buccal segments and the 1.00 to 1.20 mm thickness characteristic of the premolar area, were digitally preserved to ensure anatomical fidelity [37]. Furthermore, individual posterior teeth were digitally separated at their interproximal contacts to permit the independent simulation of rotational movements in later analyses (Figure 2). A critical step involved the creation of a uniform 0.2 mm space around all tooth roots to represent the PDL [38]. These initial reconstructions of the maxillary bone, dentition, and PDL space were subsequently transferred to Geomagic Design X v2022 (3D Systems, Rock Hill, SC, USA) for critical surface smoothing, refinement, and artifact correction, thereby ensuring a high degree of anatomical accuracy for the model’s core structures.
The necessary orthodontic components were designed using computer-aided design (CAD) software. The TPA was digitally created in Exocad 3.2 (Exocad GmbH, Darmstadt, Germany). All other components, including brackets, archwires, and miniscrews, were designed within SolidWorks 2026 (SolidWorks Corp., Concord, Dassault Systèmes, MA, USA) based on exact manufacturer specifications and catalog measurements. The final assembly was constructed in SolidWorks, integrating the refined anatomical model with these engineered components. The assembly included all maxillary teeth from the first premolar to the second molars, upon which MBT brackets with a 0.022 × 0.028-inch slot (3M Unitek Dental Products, Monrovia, CA, USA) were virtually positioned. A segmented stainless-steel archwire (Ormco, Scafati, Italy) with dimensions of 0.019 × 0.025 inches was modeled from the first premolar to the second molars. The TPA was modeled as a 1.2 mm stainless-steel structure connecting the first molars. For skeletal anchorage, PEEK miniscrews measuring 1.6 × 8 mm (Invibio, Ltd., Thornton-Cleveleys, UK) were placed at a vertical level of 5 mm apical to the alveolar crest. These implants, reverse-engineered in SolidWorks from manufacturer data, were positioned at specified angulations for simulation (45°, 70°, 90°, and 110°). Finally, a Boolean subtraction operation was performed to simulate osteotomy sites within the maxillary bone model, ensuring the correct three-dimensional alignment and biomechanical fit of all dental and implant components within the accurately proportioned bony architecture.

2.3. Finite Element Analysis Setup

Pre-processing and finite element analysis were carried out using the Transient Structural module in ANSYS Workbench 2022 R2 (ANSYS Inc., Pennsylvania, PA, USA). The simulation was conducted on a system running the Windows 11 Pro (64-bit) operating system. Computational hardware consisted of an Intel Core i9 13900KF processor, 64 GB of DDR5 RAM, an NVIDIA RTX 4090 GPU, and a 2 TB SSD for data storage. The model was discretized using 10-node tetrahedral elements (Solid 187).
Material properties are detailed in Table 1. Interfaces were defined to replicate clinical biomechanics: a nonlinear viscoelastic model for the PDL-tooth interface, a fixed interface with slight mobility for the PDL-to-bone connection, and a rigid interface for PEEK miniscrews to bone. The brackets-to-archwire and spring-to-archwire interfaces used frictional contact (μ = 0.3), while the TPA-to-teeth and hook-to-archwire interfaces were perfectly bonded. Finally, the spring-to-archwire interface utilized a frictional contact definition. A convergence study informed the meshing strategy, where stress results stabilized below a 0.1 mm element size. Consequently, a fine mesh with an element size of approximately 0.2 mm was applied to the teeth, PDL, and maxilla, while a coarser mesh was used for the soft tissues. The resulting mesh, composed predominantly of Tet10 elements, was evaluated for quality. The distribution of element quality metrics, with prominent peaks at 0.13 and 0.25, confirmed a predominantly high-quality mesh suitable for biomechanical simulation. A summary of node and element counts for the model is provided in Table 2. For the posterior intrusion simulation, bilateral PEEK miniscrews were placed between the second premolar and first molar and between the first and second molars, each loaded with a 100 g perpendicular force. Four distinct angulation sets were tested for the miniscrews relative to the archwire (Figure 3). The posterior maxilla was fully constrained in all directions to prevent rigid-body motion. In the post-processing phase, von Mises stress distributions were analyzed to evaluate the biomechanical performance of the posterior miniscrews. Principal stress analysis was conducted on the alveolar bone to identify regions at risk of remodeling. The PDL was analyzed for hydrostatic pressure and shear stress to evaluate potential tissue response. Finally, total deformation and directional displacements (X, Y, Z) were analyzed for the miniscrews, PDL, dentin, and bone to assess mechanical stability and movement patterns.

2.4. Data Analysis

Mechanical performance was analyzed using von Mises stress in miniscrews, stress distributions (shear, principal, hydrostatic) in the alveolar bone and PDL, and 3D displacements of screws and posterior teeth. Displacement of miniscrews and posterior teeth was measured along the X, Y, and Z axes to evaluate stability and movement patterns. Evaluation across the four insertion angles clarified their impact on both the biomechanical efficiency of the system and the safety of the surrounding tissues.

2.5. Model Validation

The FEA model was validated by qualitative comparison of PDL hydrostatic pressure distribution under intrusive loading with the finite element study of Mazhari et al. (2022) [39] which investigated full-arch intrusion using temporary skeletal anchorage. For consistency with the reference model, a 150 g intrusive force was applied in the present validation simulation. Despite differences between the two studies in treatment scope (full-arch versus segmental intrusion), miniscrew configuration, and boundary conditions, the present model demonstrated comparable qualitative trends in PDL hydrostatic pressure. Specifically, the central incisor exhibited the highest hydrostatic pressure, followed by the lateral incisor and canine, reproducing the stress hierarchy reported by Mazhari et al. (2022) [39]. This similarity in pressure distribution reflects analogous load transfer mechanisms within the dentoalveolar complex under intrusive forces. A direct quantitative comparison of hydrostatic pressure magnitudes was not performed due to inherent methodological differences between the models. However, the agreement in relative pressure patterns and tooth-wise distribution under an equivalent intrusive load supports the validity of the present model in capturing clinically relevant biomechanical behavior. Such pattern-based validation using PDL hydrostatic pressure is an established and accepted approach in orthodontic finite element analysis when an identical reference model is unavailable [40,41].

3. Results

3.1. Posterior Teeth Displacement

Superimposition of pre- and post-loading models revealed a consistent biomechanical pattern across all four loading angles. Crowns demonstrated distal and buccal movement with intrusion, while roots exhibited mesial displacement with intrusion (Table 3 and Figure 4). Key findings include:
  • Crown Displacement: Maximum distal tipping occurred at the first premolar (−0.0000705 mm at 110°).
  • Root Displacement: Maximum mesial movement occurred at the first molar (+0.0000387 mm at 90°).
  • Intrusion: Intrusion values ranged from +0.000104 mm to +0.000135 mm, with the second premolar showing the greatest intrusion and the second molar the least.

3.2. Posterior Periodontal Ligament (PDL) Analysis

PDL stress levels increased with load angle, peaking at 110°. The first molar recorded the highest tensile principal stress (74,608 Pa), while the second molar exhibited the highest von Mises stress (88,939 Pa) (Table 4 and Figure 5). Hydrostatic pressure within the PDL was significantly elevated in the first molar across all angles, reaching 34,591 Pa at 110°. Premolars exhibited moderate pressure (~8000–9000 Pa) (Table 5 and Figure 6).

3.3. Bone Analysis

3.3.1. Cortical Bone Stress Analysis Under Orthodontic Loading

Cortical bone stress increased with loading angle, with molars sustaining significantly higher von Mises and principal stresses than premolars (Table 6 and Figure 7). The highest equivalent stress (141,000 Pa) was recorded for the first and second molars at 70° and 110°. Tensile stresses consistently dominated the stress state. Maximum principal stress at the cortical bone interface with the PEEK miniscrews was moderate, ranging from 18,100 Pa (110°) to 36,500 Pa (90°). The screw placed between the first and second molars typically experienced slightly higher stress (Figure 8).

3.3.2. Cancellous Bone Stress Analysis

Stress in the cancellous bone was most pronounced under 70° loading. The second molar had the highest von Mises stress (124,920 Pa). Tensile stresses predominated across all conditions. Principal stress at the cancellous bone–screw interface remained low (<9140 Pa), indicating favorable load distribution into the trabecular structure (Table 7 and Figure 9).

3.4. Miniscrew Stress Analysis

The PEEK miniscrews exhibited excellent stability across all loading conditions (Table 8, Figure 10), with deformation (<0.0000799 mm), displacement (<0.0000866 mm), and maximum von Mises stress (206,300 Pa at 45°) well within material safety limits. The miniscrew between the second premolar and first molar consistently showed marginally higher mechanical values than the more distal screw.

4. Discussion

This FEA study analyzed how force angulation affects miniscrew-assisted posterior intrusion. By evaluating tooth displacement, periodontal ligament stress, bone response, and anchorage behavior, it clarifies how force direction influences stress distribution while achieving intended intrusion. FEA was selected for its ability to provide a controlled, reproducible evaluation of orthodontic biomechanics, overcoming the ethical and practical limitations of in vivo studies. The main advantage of this analysis is the systematic isolation of parameters, such as implant design, placement, and force application under consistent boundary conditions, free from the confounding variables of patient-specific biology [42].
This reliable FEA utilized a patient-specific maxillary model from CBCT scans [43], processed to remove surface irregularities, preventing unrealistic stress results [44]. Bone, teeth, and miniscrews were modeled as linearly elastic; the PDL received time-sensitive properties [45]. To simulate a clinically stable miniscrew, its connection to the bone was defined as perfectly bonded [44]. The virtual mesh was made especially fine around critical areas like the miniscrew and bone interfaces to ensure stress patterns were captured accurately [46]. The forces applied were 200 g distributed posteriorly to reflect common clinical loads, with points of application chosen to model realistic clinical mechanics. This simulation used a bilateral intrusive load of 200 g (100 g per side), which is within the range of clinically reported posterior intrusion forces [47,48]. The model was properly secured at the posterior maxilla to allow for stable calculation of tooth movement [49]. This consistent and validated modeling approach ensures that the differences observed in the results are due to the changes in force angle and implant position, not inconsistencies in the model itself [50].
Across all angulations, tooth movement showed a consistent pattern: slight outward crown movement along with small root shifts, confirming that posterior intrusion occurred as a combination of tipping and downward movement, rather than straight vertical movement. This is the biomechanically expected outcome when the applied force has a lateral direction, creating a rotational effect around the segment’s center of resistance [51].
Quantitatively, posterior crowns exhibited consistent distal and buccal displacement combined with intrusion. Crown intrusion ranged between 0.000104 mm and 0.000135 mm, with the highest values at the second premolar. Roots consistently showed mesial displacement (up to 0.0000387 mm at the first molar, 90°) and intrusion values similar to or slightly lower than crowns, confirming a rotational movement pattern. The second molar demonstrated smaller lateral displacements across angulations, suggesting a buffering effect due to its posterior position and root morphology. PDL stress analysis revealed marked, angle-dependent redistribution. von Mises stress was highest in molar regions, particularly at oblique angulations (124,000 Pa at the second molar, 45°), confirming molars as primary stress-bearing units under oblique vectors.
Maximum principal stress analysis clarified the loading mode. Tensile stresses frequently exceeded compressive stresses, especially in the first molar (reaching 74,600 Pa at 110°), indicating a tension-dominant PDL environment under these intrusion-type vectors. This distinction is clinically relevant, as compressive zones are associated with different biological risks, including ischemia and root resorption. Hydrostatic pressure results reinforced these findings. The first molar consistently demonstrated the highest PDL hydrostatic pressure across all angulations, measuring 27,458 Pa at 45°, 35,850 Pa at 70°, 31,059 Pa at 90°, and 34,591 Pa at 110°. In contrast, premolars and the second molar generally exhibited lower values (8000–12,000 Pa). Given the increasing recognition of hydrostatic pressure as a mechanobiological driver of vascular compression and external apical root resorption, these results suggest that the first molar represents a biologically sensitive site during posterior intrusion mechanics.
When comparing angulations, the data suggest that changing the posterior force angle primarily modulated stress concentrations rather than fundamentally altering the overall displacement direction (which remained an intrusion with buccal/distal components). This pattern is consistent with the notion that within a narrow displacement range, the PDL–bone complex may respond with relatively similar kinematics, while internal stress distributions shift as the ratio of vertical to horizontal components changes. Similar conclusions have been drawn in miniscrew biomechanics papers where altering vector direction changes stress localization and anchorage demand more than it changes the basic direction of initial tooth movement [36,52].
Cortical bone analysis demonstrated high equivalent stresses in molar regions across multiple angulations, with principal stresses indicating that both tensile and compressive components can become substantial at posterior sites. This is clinically meaningful because cortical bone is the primary load-bearing envelope and commonly exhibits concentrated stresses adjacent to force application pathways and anchorage sites. Recent miniscrew-supported molar intrusion FE studies similarly emphasize that posterior cortical bone can become a peak stress region under intrusion mechanics, particularly when force vectors include off-axis components. Cancellous bone stresses exhibited nonlinear dependence on angulation. For example, cancellous von Mises stress in the second molar increased markedly at 70° (125,000 Pa) compared with 45° (69,000 Pa) and decreased substantially at 90° (28,100 Pa). This non-monotonic behavior reflects the sensitivity of trabecular bone stress to force direction and boundary constraints rather than a simple increase with obliquity.
Peri-implant bone stresses were consistently higher at the cortical interface than at the cancellous interface. Maximum principal stress at the cortical interface reached 27,400 Pa (45°), 32,600 Pa (70°), 36,500 Pa (90°), and 22,700 Pa (110°), whereas cancellous interface stresses remained lower (2750–9140 Pa). This confirms the dominant mechanical role of cortical engagement in miniscrew stability.
A clinically significant observation was the variation in anchorage load across the evaluated miniscrew insertion sites. The miniscrew positioned between the second premolar and first molar consistently demonstrated superior susceptibility to deformation, displacement, and von Mises stress compared to the screw placed between the first and second molars. This suggests a less favorable mechanical environment at the premolar-molar site, likely related to interradicular geometry and proximity to the primary load path. Despite this, absolute miniscrew deformations and stresses remained very small, indicating high mechanical stability for PEEK miniscrews under all tested conditions [53].
The results demonstrate that altering the posterior force angle between 45° and 110° primarily modulates stress concentrations and anchorage demand rather than fundamentally altering the initial displacement direction, which remained an intrusion with buccal/distal components. This is consistent with the concept that within a narrow displacement range, the tooth-PDL-bone complex may respond with relatively similar kinematics, while internal stress distributions shift with the changing ratio of force components. These findings reinforce contemporary orthodontic biomechanics principles: effective posterior intrusion requires not only achieving vertical displacement but also optimizing force vectors to minimize unfavorable PDL pressure, cortical bone stress, and anchorage overload, particularly in biologically sensitive regions like the first molar [54]. Additionally, orthodontic tooth movement is time-dependent and involves biological remodeling; most FE studies, including the present analysis, capture the “initial response” rather than staged movement over time. This limitation is frequently noted in recent orthodontic FE work, and it reinforces that the present results are best used to compare immediate biomechanical tendencies (stress localization, likely tipping direction, relative anchorage demand) across loading angulations rather than predicting final clinical outcomes directly [55].
Overall, the study found that oblique loading (45–110°) for posterior intrusion consistently produces intrusion with accompanying buccal/distal crown tipping and mesial root movement. Stress concentrations varied by tooth, with the first molar showing high PDL hydrostatic pressure and molar regions showing high cortical bone stress. While miniscrew stability was high, anchorage demand was greater at the second premolar-first molar site. Changes in the oblique angle primarily redistributed stresses rather than reversing the direction of movement, underscoring that the force vector dictates both primary intrusion and secondary tipping moments.
The present investigation has limitations inherent to finite element analysis. Although qualitative validation was performed through comparison of hydrostatic pressure distribution patterns with previously published finite element models, direct quantitative experimental validation was not conducted. The assumptions of material homogeneity, isotropy, and idealized boundary conditions may not fully replicate the biological variability of clinical conditions. Additionally, the model reflects the initial mechanical response to loading and does not account for time-dependent bone remodeling or periodontal adaptation. Therefore, the absolute stress magnitudes should be interpreted with caution, and future in vitro and clinical studies are required to quantitatively validate these findings.

5. Conclusions

Within the methodological framework and limitations of this finite element analysis:
  • Posterior PEEK miniscrews demonstrated mechanical stability under all evaluated insertion angulations during intrusion mechanics. Variations in insertion angle influenced stress distribution within the periodontal ligament and surrounding alveolar bone; however, the general pattern of posterior intrusion with associated tipping tendencies remained consistent across models.
  • Among the tested configurations, the 70° angulation exhibited a comparatively balanced biomechanical response in terms of stress distribution and miniscrew behavior. Nevertheless, increased angulations were associated with higher localized stress concentrations, particularly in the first molar region.

Author Contributions

K.O.B.K.: Responsible for conceptualization, methodological development, analysis, investigation, data management, manuscript writing and revision, and visualizations. R.L.T.: Assisted with methodology, analysis, investigation, data management, and original draft preparation. K.M.D.: Oversaw conceptualization, methodology, validation, resources, manuscript review, supervision, and project administration. O.Ö.: Contributed to conceptualization, validation, investigation, manuscript review, and project administration. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Ethical approval for this research (Project No: KSTU/2024/356) was granted by the Scientific Re-search Ethics Committee of the Cyprus Health and Social Sciences University on 15 January 2025.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to patient privacy/ethical restrictions.

Acknowledgments

The authors gratefully acknowledge the professional technical assistance of Mohamed Gamal Askar in performing the finite element analysis for this study. The simulations were conducted under a service agreement, and the authors recognize the significant value of his expertise during the modeling phase.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
PEEKPolyetheretherketone
FEAFinite Element Analysis
CBCTCone beam computed tomography
PDLPeriodontal Ligament
TPATranspalatal arch
FEFinite Element
DICOMDigital Imaging and Communications in Medicine
CADcomputer-aided design

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Figure 1. CBCT Scan image acquisition and 3D creation.
Figure 1. CBCT Scan image acquisition and 3D creation.
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Figure 2. Digital separation of individual posterior teeth.
Figure 2. Digital separation of individual posterior teeth.
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Figure 3. Three-dimensional Model Assembly with different loading angulations: (A) 45°, (B) 70°, (C) 90°, and (D) 110°.
Figure 3. Three-dimensional Model Assembly with different loading angulations: (A) 45°, (B) 70°, (C) 90°, and (D) 110°.
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Figure 4. Anatomical coordinate axes for displacement analysis (mm) and a summary of anterior tooth stress under varied loading angles.
Figure 4. Anatomical coordinate axes for displacement analysis (mm) and a summary of anterior tooth stress under varied loading angles.
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Figure 5. Periodontal ligament stress distribution under different orthodontic loading angles.
Figure 5. Periodontal ligament stress distribution under different orthodontic loading angles.
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Figure 6. Distribution of hydrostatic pressure (Pa) within the PDL of each tooth under different orthodontic loading.
Figure 6. Distribution of hydrostatic pressure (Pa) within the PDL of each tooth under different orthodontic loading.
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Figure 7. Distribution of von Mises stress in cortical bone surrounding posterior teeth under different orthodontic loading.
Figure 7. Distribution of von Mises stress in cortical bone surrounding posterior teeth under different orthodontic loading.
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Figure 8. Maximum principal stress at the interface of PEEK miniscrews and cortical bone for two implant positions across all loading angles.
Figure 8. Maximum principal stress at the interface of PEEK miniscrews and cortical bone for two implant positions across all loading angles.
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Figure 9. Representative finite element analysis results showing von Mises and principal stress fields in the cancellous bone surrounding the posterior teeth under different loading angles.
Figure 9. Representative finite element analysis results showing von Mises and principal stress fields in the cancellous bone surrounding the posterior teeth under different loading angles.
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Figure 10. Representative finite element analysis results showing directional deformation, total displacement and maximum Von Mises stress of PEEK miniscrews.
Figure 10. Representative finite element analysis results showing directional deformation, total displacement and maximum Von Mises stress of PEEK miniscrews.
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Table 1. A summary of the material properties relevant to this study.
Table 1. A summary of the material properties relevant to this study.
MaterialModulus of Elasticity (GPa)Poisson’s Ratio
Compact Bone13.70.30
Cancellous Bone0.1420.3
PEEK Miniscrews3.60.36
0.019 × 0.025″ Stainless steel wire193.00.29
TPA210.00.30
PDL0.070.45
Gingiva (Soft Tissue)0.00010.4
Preadjusted bracket (MBT slot 0.022″)197.00.29
NiTi closed coli spring480.3
Table 2. Mesh Nodes and Element distribution for the model.
Table 2. Mesh Nodes and Element distribution for the model.
ModelNodesElements
Loading Condition
Case 1: Implant at 45° (Posterior)1,325,870787,287
Case 2: Implant at 70° (Posterior)2,274,8881,448,492
Case 3: Implant at 90° (Posterior)2,216,5311,391,108
Case 4: Implant at 110° (Posterior)1,532,466910,973
Table 3. Three-dimensional crown and root displacements (distal/mesial, palatal/buccal, intrusion/extrusion) for posterior teeth under orthodontic loading at 45°, 70°, 90°, and 110°.
Table 3. Three-dimensional crown and root displacements (distal/mesial, palatal/buccal, intrusion/extrusion) for posterior teeth under orthodontic loading at 45°, 70°, 90°, and 110°.
Distal (−)/Mesial (+) (mm)Palatal (+)/Buccal (−) (mm)Intrusion (+)/Extrusion (−) (mm)
CrownRootCrownCrownRootCrown
Angle 45°
First premolar−0.0000661230.000010797−0.000062562−0.0000045390.00012370.000123
Second premolar−0.0000665520.000017436−0.0000499320.00000387420.000134720.00010695
First molar−0.0000675280.000035668−0.0000450680.0000101710.000121360.0001182
Second molar−0.0000272980.000026897−0.0000179070.00000636560.000104220.000080915
First premolar−0.000069790.000010776−0.000061505−0.0000046290.000122580.00012204
Second premolar−0.0000659350.000017298−0.0000514770.00000423010.000134180.0001074
First molar−0.000068550.000037757−0.0000464460.0000107470.000123990.00012173
Second molar−0.0000268840.000027356−0.0000178070.00000688020.000104120.000068484
Angle 90°
First premolar−0.0000631060.000011135−0.000052881−0.00000437430.000122650.00012207
Second premolar−0.0000663730.000017764−0.0000487540.00000447010.000133380.00010666
First molar−0.0000634480.000038703−0.0000425390.0000109090.000122190.00011954
Second molar−0.0000271390.000028864−0.0000199460.00000693390.000102160.000067619
Angle 110°
First premolar−0.0000705310.00001046−0.000061187−0.00000436970.000122940.00012243
Second premolar−0.0000662630.00001742−0.0000501720.00000438110.000134110.00010719
First molar−0.0000663340.0000379−0.0000447130.0000105860.000122420.00011995
Second molar−0.0000268980.000028198−0.0000184820.00000696030.000103310.000068274
Table 4. von Mises and principal stress (tensile and compressive) (Pa) in the periodontal ligament of posterior teeth under different orthodontic loading angles.
Table 4. von Mises and principal stress (tensile and compressive) (Pa) in the periodontal ligament of posterior teeth under different orthodontic loading angles.
TeethStress AnalysisAngle 45°Angle 70°Angle 90°Angle 110°
First premolarVon Mises stress35,58235,85935,86239,005
Principal stress “Tensile”21,61220,97421,49621,467
Principal stress “Compressive”3763.43823.53785.22766.3
Second premolarVon Mises stress27,57727,57927,39727,757
Principal stress “Tensile”23,10525,92522,36822,931
Principal stress “Compressive”771.26666.53489.71159
First molarVon Mises stress48,58962,37848,80261,054
Principal stress “Tensile”54,71670,23956,71474,608
Principal stress “Compressive”2109.46229.83402.94508.2
Second molarVon Mises stress124,330100,24053,08888,939
Principal stress “Tensile”31,15524,29935,89031,201
Principal stress “Compressive”59054210.749303520.7
Table 5. Hydrostatic pressure (Pa) within the PDL for posterior teeth under different orthodontic loading angles.
Table 5. Hydrostatic pressure (Pa) within the PDL for posterior teeth under different orthodontic loading angles.
Angle 45°Angle 70°Angle 90°Angle 110°
First premolar8226.48077.98285.48423.1
Second premolar9050.98999.78786.98868.7
First molar27,45835,85031,05934,591
Second molar9629.58050.214,27512,080
Table 6. von Mises and principal stress values (Pa) in cortical bone for posterior teeth under different orthodontic loading angles.
Table 6. von Mises and principal stress values (Pa) in cortical bone for posterior teeth under different orthodontic loading angles.
Tooth Angle 45°Angle 70°Angle 90°Angle 110°
First premolarVon Mises stress61,69361,9385662062,403
Principal stress “Tensile”51,64642,95841,72340,434
Principal stress “Compressive”582.75451.11364.683714.2
Second premolarVon Mises stress50,73848,84843,38746,930
Principal stress “Tensile”24,32826,38123,66050,189
Principal stress “Compressive”641.44531.64203.22487.35
First molarVon Mises stress135,760135,000134,440140,680
Principal stress “Tensile”97,41282,78794,66759,633
Principal stress “Compressive”13,31411,10112,1909220.7
Second molarVon Mises stress135,760135,000134,440140,680
Principal stress “Tensile”63,71180,14253,03754,373
Principal stress “Compressive”13,31411,10112,1907236.2
Table 7. von Mises and principal stress (tensile and compressive) (Pa) in the cancellous bone surrounding posterior teeth under different orthodontic loading angles.
Table 7. von Mises and principal stress (tensile and compressive) (Pa) in the cancellous bone surrounding posterior teeth under different orthodontic loading angles.
ToothStress AnalysisAngle 45°Angle 70°Angle 90°Angle 110°
First premolarVon Mises stress36,30731,22726,61428,843
Principal stress “Tensile”22,23221,53318,02317,832
Principal stress “Compressive”2947.61172.65899.92799.3
Second premolarVon Mises stress37,17870,58114,81653,497
Principal stress “Tensile”26,76244,22311,91139,219
Principal stress “Compressive”2234.823,2201090.57460.7
First molarVon Mises stress58,87155,01323,99530,607
Principal stress “Tensile”69,37739,97915,29323,545
Principal stress “Compressive”9749.611,0951325.81287.9
Second molarVon Mises stress69,027124,92028,13938,934
Principal stress “Tensile”41,94156,53918,57924,515
Principal stress “Compressive”1131.51885.92747.23934.3
Table 8. Biomechanical performance of PEEK miniscrews: directional deformation, total displacement, and maximum von Mises stress under different orthodontic loading.
Table 8. Biomechanical performance of PEEK miniscrews: directional deformation, total displacement, and maximum von Mises stress under different orthodontic loading.
Biomechanical PerformanceAngle 45°Angle 70°Angle 90°Angle 110°
Direction deformation (mm)Between
second premolar and first molar		0.00007450.0000791420.0000791910.000079845
Between
first molar and second molar		0.0000328240.000035960.0000404310.000041688
Total displacement (mm)Between
second premolar and first molar		0.0000852680.000086620.0000841080.00008303
Between
first molar and second molar		0.0000463310.0000476090.0000482620.00004812
Maximum Von Mises Stress (Pa)Between
second premolar and first molar		206,300144,11058,26662,528
Between
first molar and second molar		94,00774,32756,58647,564
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Khalil, K.O.B.; Taner, R.L.; Dinçer, K.M.; Özdiler, O. Evaluation of Miniscrew Stability in Posterior Teeth Intrusion—A Three-Dimensional Finite Element Analysis. Appl. Sci. 2026, 16, 1783. https://doi.org/10.3390/app16041783

AMA Style

Khalil KOB, Taner RL, Dinçer KM, Özdiler O. Evaluation of Miniscrew Stability in Posterior Teeth Intrusion—A Three-Dimensional Finite Element Analysis. Applied Sciences. 2026; 16(4):1783. https://doi.org/10.3390/app16041783

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Khalil, Khaled Omran Ben, R. Lale Taner, K. Müfide Dinçer, and Orhan Özdiler. 2026. "Evaluation of Miniscrew Stability in Posterior Teeth Intrusion—A Three-Dimensional Finite Element Analysis" Applied Sciences 16, no. 4: 1783. https://doi.org/10.3390/app16041783

APA Style

Khalil, K. O. B., Taner, R. L., Dinçer, K. M., & Özdiler, O. (2026). Evaluation of Miniscrew Stability in Posterior Teeth Intrusion—A Three-Dimensional Finite Element Analysis. Applied Sciences, 16(4), 1783. https://doi.org/10.3390/app16041783

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