Abstract
Background
This study validated a patient-specific three-dimensional (3D) finite element (FE) model utilizing cone-beam computed tomography (CBCT) scans and occlusal records from a bruxism patient exhibiting a fractured right maxillary first molar. The model analyzed lateral mandibular movements linked to fracture initiation and evaluated its clinical utility in optimizing implant-supported prosthetic designs through biomechanical stress profiling.
Method
Lateral mandibular movements were simulated by the FE model from patient with bruxism to pinpoint the displacements that cause fracture-related stress concentrations. Three zirconia/resin implant crowns with cusp inclinations were modeled on the fracture geometry. Simulated biomechanical stress distribution was analyzed to assess effects on peri-implant bone, fixtures, and prosthetics.
Results
The pre-fracture model revealed stress concentrations coinciding with clinical root fracture sites during lateral mandibular movements defined by displacement parameters (x=-0.5 mm, y=-0.2 mm, z = 0 mm). In implant-supported prostheses, increased cusp inclination elevated stress in both implants and peri-implant bone, with zirconia crowns exhibiting higher stress than resin counterparts. The prosthetic abutment showed maximal stress concentration, approaching titanium’s yield strength at 30° inclination.
Conclusions
Three-dimensional finite element analysis (3D-FEA) effectively simulates abnormal occlusal stress directions in root-fractured teeth, proposing a novel clinical method to determine occlusal stress vectors. Additionally, for bruxism patients, implant prostheses should prioritize low cusp inclinations and use materials with low elastic modulus to mitigate stress concentration and mechanical complication risks.
Keywords: Maxillary first molar, Three-dimensional finite element analysis, Implant prosthodontic, Root fracture, Cusp inclination
Introduction
A middle-aged female patient was clinically evaluated by this research group. CBCT scans revealed a root fracture located at the cervical of the root of her right maxillary first molar. Through comprehensive clinical and anamnestic investigations, a long period of nocturnal bruxism and clenching habits were identified, with generalized occlusal surface attrition and partial dentin exposure observed across the entire dentition. Based on multi-disciplinary analysis, abnormal occlusal patterns were determined to be the primary causative factor for right maxillary molar root fracture for her.
Root fracture, defined as cracks or complete separations confined to the dental root while preserving crown integrity, disrupts root continuity [1, 2]. Molar root fracture is common in clinical practice, with recent studies reporting an increasing incidence [3]. The etiological factors of molar root fracture are predominantly associated with inherent structural defects of the teeth and occlusal trauma, where traumatic occlusal stress has been considered a primary causative factor [4]. Prolonged exposure to traumatic occlusal stress can lead to internal or external root resorption, weakening the root and making it more prone to fracture. Patients with nocturnal bruxism or abnormal oral function often experience pathological tooth wear. This wear can alter the morphology of the occlusal surface and reduce crown height [5]. The resulting excessive occlusal stress and abnormal force vectors are key risk factors for root fracture [4, 6]. Although multiple clinical methods exist for measuring occlusal stress magnitude, effective determination of occlusal stress direction remains elusive.
3D-FEA is a computational modeling technique that enables the simulation and analysis of complex structures and materials under diverse conditions [7]. In implant research, it non-invasively visualizes stress distributions and evaluates impacts of loading conditions, material properties, and geometries on bone-implant interfaces [8]. By modeling lateral occlusal movements linked to molar root fracture, 3D-FEA identifies critical occlusal stress vectors under clinically or experimentally constrained scenarios, enabling predictive clinical analysis through simulation of anatomically inaccessible regions.
As a parafunctional behavior involving rhythmic masticatory muscle contractions, bruxism contributes to pathological tooth attrition, myofascial hyperactivity [9]and temporomandibular dysfunction. Such biomechanical overload may further propagate non-physiological stress to implant-prosthetic systems, exacerbating risks of mechanical fatigue and interfacial failure [10]. Despite the recognized high-risk factor for failure of implant restorations in abnormal occlusion, implant restorations remain the mainstay of treatment for edentulism due to their clinical advantages. Thus, implant rehabilitation remains a necessary clinical consideration for patients with potential bruxism.
To reduce the adverse effects of parafunctional oral movements, such as bruxism, on implant-supported dentures, the current study combines medical image data from genuine root fracture cases with 3D-FEA. It reconstructs patient-specific 3D models of the jawbone, dentition, and periodontal tissues, and utilizes 3D-FEA to analyze the principal occlusal direction of lateral mandibular occlusion. This method allows a systematic investigation of optimal implant-supported prosthodontic designs protocols for patients with bruxism.
Materials and methods
Modeling of natural tooth
This study utilizes CBCT images and intraoral occlusal records from patients with bilateral maxillary first molar root fracture treated at the Affiliated Hospital of Guizhou Medical University as modeling materials (research protocol approved by the Ethics Committee of the Affiliated Hospital of Guizhou Medical University) (Fig. 1). The CBCT data were imported into Mimics 21.0 software (Materialise, Leuven, Belgium). Following digital reconstruction of the fractured root segments of the right maxillary first molar, three-dimensional models of the maxillary jawbone, maxillary dentition, and mandible were separately extracted.
Fig. 1.
CBCT image of root fracture. red arrow show root fold
The extracted models were optimized using Geomagic Wrap 2021 software (3D Systems, Rock Hill, SC). Due to the limited resolution of CBCT image, the precise boundaries of the periodontal ligament could not be accurately segmented Therefore, the periodontal ligament was modeled as a homogeneous layer with a thickness of 0.2 mm [11]. The periodontal ligament model was generated by offsetting the entire tooth model outward by 0.2 mm in Geomagic Wrap 2021. Cortical bone thickness around bilateral maxillary first molars was measured as approximately 0.75 mm using patient CBCT data. Consequently, cortical bone was assumed to have a uniform thickness of 0.75 mm.
To achieve precise occlusal surface morphology and occlusal relationships, plaster models of the dentition were scanned into STL files using a CAD/CAM dental 3D scanner. The intermaxillary occlusal relationship was reconstructed through the multi-point alignment function in Geomagic Wrap, and the DICOM-derived mandibular model was replaced with the scanned mandibular model. Finally, the optimized and smoothed triangular mesh models were converted into three-dimensional volumetric models.
The final assembly was completed in SolidWorks by removing interferences among the maxillary cortical bone, maxillary cancellous bone, teeth, periodontal ligament, and mandibular assembly (including teeth), resulting in a pre-fracture model with validated occlusal relationships (Fig. 2A).
Fig. 2.
(A)The final assembly of maxillary cortical bone, maxillary cancellous bone, teeth, periodontium and mandible (with teeth) is completed to obtain a natural tooth model with occlusal relationship before root fracture. (B) The upper right first molar undergoes a final implant denture restoration and is designed with restorative crowns with three apical inclinations (10°, 20°, and 30°)
Modeling of implant prosthodontic
A bone-level implant model with a diameter of 4.8 mm and length of 8 mm was placed at the site of the right maxillary first molar using SolidWorks (Dassault Systems, Waltham, USA). The prosthetic abutment and central screw were subsequently assembled onto the implant fixture. Based on the occlusal relationships within the model, crown cusp inclination angles were designed at 10°, 20°, and 30°. A cementation layer model was generated by applying a 50 μm-thick surface offset to the prosthetic abutment [12]. Following interference removal in SolidWorks, three implant prosthodontic models with distinct cusp inclination angles were finalized (Fig. 2B).
Material parameter setting and meshing
The models were imported into Abaqus software (Dassault Systems Simulia Corp, Johnston, USA), where Poisson’s ratios and elastic moduli of each component were assigned according to published data [13–16] (Table 1). A coincident node configuration was implemented across all assembly components. Two-dimensional meshes were initially generated, followed by three-dimensional meshes. Tetrahedral elements were utilized for mesh generation, with localized refinement performed at geometrically complex regions. The number of elements and nodes for each model was determined (Table 2).
Table 1.
Material accessories parameters
| Material | Young’s modulus (MPa) | Poisson’s ratio |
|---|---|---|
| Teeth | 1.86 × 104 | 0.31 |
| Periodontal membrane | 68.9 | 0.45 |
| Cancellous bone | 1.37 × 103 | 0.30 |
| Cortical bone | 1.37 × 104 | 0.30 |
| Titanium (Implant, Abutment, Screw) | 1.1 × 105 | 0.35 |
| Resin | 2.22 × 104 | 0.28 |
| Zirconia | 2.1 × 105 | 0.27 |
| Glass-ionomer cement (bonding layer) | 1.59 × 104 | 0.33 |
Table 2.
Number of model cells in each group
| groups | number of element types | the number of node |
|---|---|---|
| Pre-fracture Model | 4803478 | 1188317 |
| Implant Model 10° | 4687022 | 1169867 |
| Implant Model 20° | 4688427 | 1170186 |
| Implant Model 30° | 4690293 | 1170607 |
Boundary and load condition settings
Boundary Conditions for Pre-fracture Model (Fig. 3): The inferior surface of the maxillary cortical bone adjacent to the maxillary sinus is fixed as the primary constraint. Frictional contacted with a coefficient of 0.2 [17] is defined between adjacent teeth. Bonded contacts are established at the interfaces of teeth-periodontal ligament, periodontal ligament-jawbone, and cortical-cancellous bone to ensure continuous stress transfer.
Fig. 3.
Boundary setting of the model
Initial displacement magnitudes of 0.5 mm are prescribed along all three coordinate axes of the mandibular model, corresponding to the general mandibular movement direction [18]. These displacements are iteratively adjusted based on stress distribution patterns from preliminary simulations. The adjustment protocol included:
Maintaining the x-axis displacement at 0.5 mm;
Systematically varying y- and z-axis displacements.
Through this methodology, lateral mandibular movements were simulated by controlled displacement, thereby applying occlusal loading to the maxillary dentition.
Boundary conditions for implant prosthodontic models: A 100% osseointegration rate [19] mechanical interlock was established at the implant-abutment interface to eliminate abutment loosening. The crown was rigidly bonded to the abutment with glass ionomer cement, preventing crown displacement. Consequently.
No relative displacement between the jawbone and implant was permitted;
Frictionless bonded contacts were defined at all interfaces (implant-abutment, abutment-central screw, screw-crown);
Frictional contact with a coefficient of 0.217 was applied between crown surfaces.
The mandibular movement direction that induced stress concentration at the mesiobuccal root cervical region in the pre-fracture model was adopted as the loading condition for the implant prosthodontic models.
Results
Determination of lateral mandibular movement directions
The meshed models were imported into Abaqus to simulate intraoral occlusal relationships. Through multi-directional lateral displacement of the mandibular model (Fig. 4), stress concentration predominantly occurred at the mesiobuccal root cervical region when mandibular displacements are set to:
Fig. 4.
Cloud diagram of von Mises stress distribution in the right maxillary first molar
x-axis: −0.5 mm;
y-axis: −0.2 mm;
z-axis: 0 mm.
The results of the numerical analysis demonstrate high-stress zones (displayed in red) localized at the furcation area of the mesiobuccal root of the right maxillary first molar. Among all tested displacement directions, the maximum stress magnitude consistently occurred at the mesiobuccal root cervical region. The spatial distribution of stress concentration corresponded with the actual root fracture site was identified in CBCT image (Fig. 1).
Stress analysis of Implant-Supported prosthetic models
Under simulated right lateral mandibular movement with prescribed displacements (x=−0.5 mm, y=−0.2 mm, z = 0 mm), the biomechanical performance of peri-implant bone tissue, implant fixtures, and prosthetic components was analyzed for two crown materials (zirconia and resin) and three cusp inclination angles (10°, 20°, 30°). The von Mises stress distribution patterns and peak stress values are presented in Table 3; Fig. 5, 6, 7, 8, 9.
Table 3.
Von mises peak stress table for bone tissue, implant, abutment and abutment screw (MPa)
| Bone | Screw | Implant | Abutment | ||
|---|---|---|---|---|---|
| Zirconia crown | 10° | 60.278 | 415.564 | 416.901 | 635.315 |
| 20° | 75.446 | 493.741 | 533.830 | 703.666 | |
| 30° | 95.158 | 620.948 | 624.596 | 939.415 | |
| Resin crown | 10° | 55.508 | 364.142 | 364.813 | 555.720 |
| 20° | 67.488 | 435.840 | 468.636 | 619.743 | |
| 30° | 85.106 | 544.533 | 547.322 | 821.137 | |
Fig. 5.
Three-dimensional histogram of peak von Mises stress in bone tissue, implant, abutment and abutment screw. In dental implant models with crowns of the same material, the peak stress values of the bone tissue, implant, restorative abutment, and central screw tend to increase with the increase of the apical slope, whereas the resin crown restoration model have the smallest stress values in the same apical slope
Fig. 6.
von Mises stress distribution map of the bone tissue around the implant. The maximum equivalent stresses in the bone tissue are concentrated at the cortical and cancellous bone junction on the distal mid-palatal side. In the model with the same crown material, the alveolar bone stress increased with the apical slope increase. Compared to the model with zirconia crowns, the resin crown restorations have the least stress on the bone tissue in the same apical slope
Fig. 7.
von Mises stress distribution map of the center screw. The stresses in the screw are concentrated in the neck of the central screw. In models with the same crown material, the stress in the restorative screw increased with increasing apical slope. Compared to the model with zirconia crowns, the abutment of the resin crown restoration model has the least stress in the same apical slope
Fig. 8.
von Mises stress distribution map of the implant. The stresses in the implant are concentrated in the buccal connection of the implant to the abutment. In models with the same crown material, the stress in the implant increased with increasing apical slope. Compared to the model with zirconia crowns, the implant in the resin crown restoration model has the least stress in the same apical obliquity
Fig. 9.
von Mises stress distribution map of the abutment. The stresses in the abutment are concentrated in the buccal connection of the abutment to the implant. In models with the same crown material, the stress in the abutment increased with increasing apical slope. Compared to the model with zirconia crowns, the abutment of the resin crown restoration model has the least stress in the same apical slope
Table 3; Fig. 5 present the maximum von Mises stress values in peri-implant bone tissue, the implant fixture, prosthetic abutment, and central screw under different crown restoration conditions of the right maxillary first molar during lateral mandibular movement. During lateral movement, under identical cusp inclination angles, the zirconia crown group exhibited higher peak stress values in the implant and its supporting components compared to the resin crown group. Furthermore, under crown restorations with cusp inclination angles of 10°, 20°, and 30°, the stress magnitude in the implant-supported prosthesis demonstrated a positive correlation with increasing cusp inclination angles.
Fig. 6, 7, 8, 9 visually demonstrate the equivalent stress distribution in peri-implant bone tissue, abutment screws, implants, and abutments under resin and zirconia crown restorations with three cusp inclination angles during lateral mandibular movement. When lateral loading is applied to the right maxillary first molar by the mandible, the maximum stress in peri-implant bone tissue occurred at the junction between distopalatal cancellous bone and cortical bone (Fig. 6). The highest stress on the abutment screw is observed at its neck region, particularly in the 30° cusp inclination zirconia crown restoration model (Fig. 7). Stress within the implant was primarily concentrated in the cervical area, with the maximum equivalent stress located at the buccal cervical region (Fig. 8). Stress in the abutment is focused at the buccal interface connecting to the implant (Fig. 9).
Discussion
Bruxism, characterized by involuntary non-functional oral activities of teeth grinding or clenching [10, 20]may lead to clinical manifestations including masticatory muscle hypertrophy, dental hard tissue defects, prosthetic or tooth fracture, dentin hypersensitivity/pain, and loss of periodontal supporting tissues [21]. Additionally, bruxism has been associated with implant-related complications such as implant fracture, screw loosening, central screw fracture, and peri-implant marginal bone loss [22]where excessive occlusal stress and aberrant force vectors are considered primary causative factors [21, 22]. Although implant-supported prostheses effectively restore missing tooth function, current clinical methods for detecting and adjusting occlusal stress magnitude remain insufficient to determine force direction. Consequently, the ability to identify abnormal occlusal stress vectors has become critical for maintaining the long-term stability of implant prostheses in bruxism patients.
In this study, we performed a biomechanical analysis of the fractured tooth was employed to identify the specific occlusal stress vector that caused stress concentration in the fracture region. The primary lateral occlusal stress direction was determined through this analysis. Prosthodontic designs for implant-supported crowns were subsequently optimized based on this identified force vector. This methodology provides critical clinical significance for guiding implant rehabilitation strategies in bruxism patients.
Through finite element analysis of the pre-fracture model, the mandibular displacement direction corresponding to maximum stress concentration in the root fracture region was determined. This displacement vector was oriented inferolaterally relative to the mandibular occlusal plane, aligning with the typical mandibular movement trajectory during lateral occlusal function [18, 23]. These findings indicate that the experimentally derived direction corresponds to the border movement pathway of the mandible during physiological lateral excursions. However, within the equivalent stress nephograms of the dental root, the maximum stress values concentrated at the mesiobuccal cervical region were lower than the fracture resistance strength of dentin (100–200 MPa) [24]. This discrepancy arises because root fracture and periodontal support loss in bruxism patients develop through prolonged exposure to aberrant occlusal stress vectors. Chronic stress concentration at specific root regions induces microcrack initiation, which significantly reduces dentin fracture resistance. Under sustained lateral occlusal loading, dentin undergoes fatigue accumulation. Fracture occurs when accumulated stress exceeds the material’s fatigue strength.
The rigid osseointegrated connection between the implant and alveolar bone lacks the protective periodontal ligament and its associated proprioceptive feedback mechanisms. Consequently, abnormal occlusal overload frequently induces implant-related complications such as implant fracture and screw loosening. Particularly among patients with parafunctional oral activities like bruxism, excessive occlusal stress combined with aberrant force vectors generated during unconscious grinding or clenching constitutes a primary contributor to prosthetic and implant complications [25]. However, the definitive correlation between bruxism and implant failure remains controversial [26]. Given the high prevalence of parafunctional habits in clinical populations, implant rehabilitation for these patients remains clinically unavoidable. Therefore, selecting optimal prosthodontic designs may substantially reduce the risk of implant complications in this patient cohort.
This study employs 3D-FEA to identify the lateral mandibular movement direction that induced root fracture in the patient. The identified movement vector can be regarded as the primary lateral occlusal trajectory during bruxism episodes in this patient. By incorporating this clinically derived lateral occlusal movement pattern into the biomechanical designs of implant-supported prostheses for parafunctional conditions, the stress distribution analysis achieves enhanced anatomical fidelity in simulating human mandibular kinematics during lateral occlusal function.
During lateral mandibular movement, finite element analysis of the implant-supported prosthesis revealed that the von Mises stress magnitude on the implant increased proportionally with cusp inclination angles, with stress predominantly concentrated at the buccal cervical region of the implant. Among all cusp inclination designs, the maximum stress value on the implant was observed in the 30° cusp inclination zirconia crown group. This phenomenon may be attributed to the bonded contact interfaces between the crown, cement layer, abutment, central screw, and implant. When the mandible applies an inferolaterally directed load to the maxillary buccal cusp, the cusp inclination generates a superomedially oriented resultant force component through geometric interaction. The magnitude of this force component escalates with increasing cusp inclination angles, thereby enabling indirect modulation of peri-implant stress distribution through cusp inclination adjustment [13, 27].
Additionally, the experimental results indicate that the prosthetic abutment exhibited the highest stress magnitudes within each model. In the 30° inclination group, stress values in the abutment under both crown materials fell within the yield strength range of titanium (780–950 MPa) [28]while peak stress magnitudes in the implant and central screw approached this threshold at higher cusp inclinations. This suggests that the implant-abutment junction may represent the primary site for mechanical complication initiation in implant prostheses for patients with parafunctional habits. Furthermore, lateral occlusal movements constitute a repetitive biomechanical process, with each cycle transmitting occlusal stress to stress-concentrated regions. Under such cyclic loading conditions, the implant and its supporting components undergo progressive fatigue accumulation, ultimately predisposing to mechanical complications including screw loosening, abutment fracture, and implant failure.
In the peri-implant bone tissue, the equivalent stress magnitude increased proportionally with cusp inclination angles, with peak stress values predominantly localized in the palatal cortical bone. This phenomenon arises because cortical bone, compared to cancellous bone, possesses a higher elastic modulus and consequently greater resistance to deformation, leading to stress concentration within this region. Under implant-supported prostheses with high cusp inclination angles, peri-implant bone experiences elevated stress magnitudes, thereby increasing the risk of marginal bone resorption [29]. One possible solution for marginal bone resorption after implant restoration is to use a material with a lower Young’s modulus, such as porous titanium, which allows for a better fit to the bone and reduces the risk of marginal bone resorption after implantation [30].
However, in models restored with resin crowns, the von Mises stress values within the implant, abutment, central screw, and peri-implant bone tissue were significantly lower than those in zirconia crown restorations. This phenomenon could be attributed to the energy-absorbing capacity exhibited by low elastic modulus crown materials, which dissipate occlusal stress thereby reducing stress transmission to the underlying implant components [31]. Therefore, for patients with parafunctional oral activities, prosthodontic designs featuring low cusp inclination angles combined with low elastic modulus crown materials can effectively mitigate abnormal stress magnitudes in the implant and its superstructure under non-axial loading conditions.
Despite these findings, the experimental conditions failed to fully replicate clinical complexities. In the 3D finite element modeling, material properties were simplified as isotropic, linearly elastic, and homogeneous, while adjacent anatomical structures within the oral cavity were neglected. Furthermore, the biomechanical analysis of root fracture omitted the physiological kinematics of the mandible, and critical factors such as oral temperature variations, masticatory force dynamics, and material fatigue were excluded from the simulation, reflecting the inherent limitations of the experimental designs.
Conclusions
This study employed 3D-FEA to simulate lateral occlusal movement patterns in non-traumatically root-fractured teeth, providing a novel methodology for clinically determining occlusal stress vectors. Compared to direct occlusal surface loading methods, mandibular displacement-based loading protocols demonstrated enhanced biomechanical credibility by replicating physiological lateral movement kinematics. The experimental results indicate that for edentulous patients with bruxism, reducing cusp inclination angles and selecting low elastic modulus materials (e.g., resin) for crown fabrication can effectively mitigate the incidence of mechanical and biological complications in implant-supported prostheses.
Acknowledgements
None.
Abbreviations
- 3D
Three-dimensional
- FE
Finite element
- CBCT
Cone-beam computed tomography
- 3D-FEA
Three-dimensional finite element analysis
Authors’ contributions
Z.A: Conceptualization, Data curation, Writing- Original draft preparation, Experimental operation, Reviewing, Editing, Methodology, Modeling & Simulation and Software. Y.Q: Reviewing, Editing, Methodology, Methodology, Modeling & Simulation and Software. W.H: Conceptualization, Methodology, Supervision. S.L, J.L: Experimental site, Experimental operation. All authors reviewed the manuscript.
Funding
Guizhou Provincial Foundation for Excellent Scholars Program(no.GCC[2023]080).
Graduate Research Fund Program(2024YJSKYJJ276).
Data availability
The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.
Declarations
Ethics approval and consent to participate
All experimental protocols were approved by the Medical Ethics Committee of the Affiliated Stomatology Hospital of Guizhou Medical University (Reference number: Ethics Review No. 27, 2023). The study was conducted in accordance with the Declaration of Helsinki. Informed consent was obtained from all subjects.
Consent for publication
not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Zheqing An and Yuhan Qi contributed equally to this work.
Contributor Information
Siyang Luo, Email: luosfpro@foxmail.com.
Jian Liao, Email: 7860552@qq.com.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.