Anisotropic finite element modeling for patient-specific mandible

Design and evaluation of mechanical strength of multi-material polymeric implants for mandibular reconstruction

Reconstruction of mandible implants to address segmental abnormalities is still a challenging task, both in vitro and in vivo. The mechanical strength of the materials used is a critical factor that determines how well bone is regenerated. The reconstruction technique of mandibular abnormalities widely uses polymeric implants. It is critical to evaluate the mechanical resilience under different load cases, including axial, combined, and flexural loading conditions. This study developed implants for mandibular defects using a combination of four materials: polylactic acid (PLA), polyethylene terephthalate glycol (PETG), thermoplastic polyurethane (TPU), and polycaprolactone (PCL), with the aim of mimicking the inherent characteristics of cortical and cancellous bone structures and evaluating their mechanical properties to support bone Osseo integration. The eleven of these combinations of structures result below the micro strain threshold level of <3000 µε, and the five combinations of the structures result in micro strain above the threshold value. The intact bone study results show that the stress under axial, combined, and flexural loading conditions is 27.6, 38.9, and 64.9 MPa, respectively. This study's stress results are lower than those from the intact bone study. The study found that the combinations of PLA and TPU material were most preferred for the cortical and cancellous bone regions of polymeric implants. These materials are also compatible with 3D printing. The results of this study can be used to find multi-material combinations that are strong and flexible.

Evaluation of the pattern of fracture formation from trauma to the human mandible with finite element analysis. Part 1: Symphysis region

BACKGROUND/AIM

The mandible is the largest, strongest bone in the maxillofacial region. When a fracture occurs in the mandible, its location depends on several factors: the direction of the trauma, the angle of the trauma, masticatory muscles and the quality of the bone. The aim of this study was to evaluate the stresses caused by trauma to the symphysis region from different angles.

MATERIALS AND METHODS

Computer-based mandible models were created, and a 2000 N force was applied to the symphysis at three different angles using finite element analysis. Six trauma situations were simulated with the mouth open or closed. Forces were applied to the symphysis at 90° (Model 1) in the anteroposterior direction, 45° (Model 2) in the anteroposterior-inferosuperior direction and 90° (Model 3) in the inferosuperior direction, when the mouth was open or closed. The resulting stress intensity was assessed using finite element analysis.

RESULTS

As a result of trauma applied to the symphysis region, maximum stresses were found where the impact originated and at the condyle region (Model 2, open mouth: condyle 1 [1172 MPa]). The open mouth position caused higher stress values than the closed mouth position (Model 2, open mouth: condyle 1 [1172 MPa]; closed mouth: symphysis 4 [82 MPa]). The Model 2, open-mouth state (Model 2, open mouth: condyle 1 [1172 MPa]) sustained higher stresses than all the other models.

CONCLUSION

The stress values in the mandible were affected by the force applied to the symphysis region, the angle of impact arrival and the open or closed state of the mouth. Keeping the mouth closed at the time of trauma reduced the stress value. A closed mouth during trauma directed at the symphysis reduced the possibility of mandible fractures.

Effects of assessing the bone remodeling process in biomechanical finite element stability evaluations of dental implants

BACKGROUND AND OBJECTIVE

While an accurate assessment of the biomechanical stability of implants is essential in dental prosthesis planning and associated treatment assurance, the bone remodeling process is often ignored in biomechanical studies using finite element (FE) analysis. In this study, we aimed to analyze the significance of assessing the bone remodeling process in FE analysis for evaluating the biomechanical stability of dental implants. We compared the FE results considering the bone remodeling process with FE results simulated using commonly used conditions, with no considerations of the bone remodeling process.

METHODS

The mathematical model proposed by Komarova et al. was used to calculate cell population dynamics and changes in bone density at a discrete site. The model was implemented in the FE software ABAQUS, using the UMAT subroutine. Three-dimensional FE models were constructed for two types of bone (III and IV) and three values of implant diameter (4.0, 4.5, and 5.0 mm). An average biting force of 50 N in the vertical direction was applied during the bone remodeling process for 150 days. Afterwards, the maximum biting force of 200 N in the 30° oblique direction was applied to evaluate the stability of the implant systems.

RESULTS

To understand the impact of bone remodeling on the resultant mechanical responses, we focused on peri-implant cancellous bone based on two parameters: apparent density change and microstrain distribution. The bone density decreased by an average of 5.3 % after implantation, and it was the lowest on the 6^th day. The average density increases of the peri-implant cancellous bone were 264.4 kgm³ (bone type III) and 220.0 kgm³ (bone type IV) over 150 days. For the bone stability analysis, the maximum principal strain in the peri-implant bone was used to evaluate the bone stability. If the bone remodeling process is ignored, then the bone volume within the fatigue failure range of the microstrain differs significantly from that if the bone remodeling process is considered, i.e., 60 % higher for bone type III and 33.4 % lower for bone type IV than when the bone remodeling process is considered.

CONCLUSIONS

The FE result without considering the bone remodeling process could be considered a conservative criterion for bone type III. However, in bone type IV, the FE result without considering the bone remodeling process tends to underestimate the risks. The bone remodeling process is more affected by the initial bone quality than the implant diameter.

Biomechanical Evaluation of Bone Atrophy and Implant Length in Four Implants Supporting Mandibular Full-Arch-Fixed Dentures

Residual alveolar ridge resorption often occurs after tooth extraction, which causes issues requiring further prothesis rehabilitation. A treatment concept referred to as all-on-four, involving fixed dentures supported with four implants, was recently developed. The current study aimed to determine the effect of changing bone atrophy and implant length in all-on-four treatments on stress and strain in the surrounding bone of the implant. A three-dimensional finite element method was used in this research. The stress analysis was conducted with von Mises stress values. Two types of synthetic jawbone models with mild and moderate atrophy were used. Furthermore, two different implant lengths with a similar implant design and diameter were selected, and they were classified into eight models. Then, the bone model was assessed via a computed tomography (CT) scan and was transformed into a virtual model in Geomagic and SolidWorks with implant rebuilding. After modifying bone atrophy, the von Mises stresses in the surrounding bone of the implant were as follows: mild type 2 < mild type 3 < moderate type 3 < moderate type 4. The bone quantity change rate increased more than when bone conditions were limited. Compared with changes in implant lengths, the stresses in the peri-implant surrounding bone were generally higher in the 9 mm implant length group than in the 11.5 mm group. However, the results did not significantly differ. In conclusion, the von Mises stress and strain increased in the models with moderate atrophy and low-density trabecular bone. Hence, bone atrophy and its presurgical diagnosis in long-term implant prognosis are crucial.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

In Silico Analysis of the Biomechanical Stability of Commercially Pure Ti and Ti-15Mo Plates for the Treatment of Mandibular Angle Fracture

PURPOSE

To investigate the influence of different materials and fixation methods on maximum principal stress (MPS) and displacement in reconstruction plates using in silico 3-dimensional finite element analysis (3D-FEA).

MATERIALS AND METHODS

Computer-assisted designed (CAD) models of the mandible and teeth were constructed. Champy and AO/ASIF plates and fixation screws were designed with CAD software. 3D-FEA was performed by image-based CAE software. Maximum and minimum values of biomechanical stability, MPS, and displacement distribution were compared in Champy and AO/ASIF plates made from commercially pure titanium grade 2 (cp-Ti) and a titanium-and-molybdenum (14.47% wt) alloy (Ti-15Mo).

RESULTS

For plates fixed on a model of a fractured left angle of the mandible, the maximum and minimum values of MPS in the cp-Ti-constructed Champy plate, upper AO/ASIF plate, and lower AO/ASIF plate were 19.5 and 20.3%, 15.2 and 25.3%, and 21.4 and 4.6% lower, respectively, than those for plates made from Ti-15Mo. In the same model, the maximum and minimum values of displacement in the cp-Ti-constructed Champy plate, upper AO/ASIF plate, and lower AO/ASIF plate were 1.6 and 3.8%, 3.1 and 2.7%, and 5.4 and 10.4% higher, respectively, than those for plates made from Ti-15Mo.

CONCLUSIONS

This in silico 3D-FEA shows that Ti-15Mo plates have greater load-bearing capability.

Stable Anisotropic Materials

The Finite Element Method (FEM) is commonly used to simulate isotropic deformable objects in computer graphics. Several applications (wood, plants, muscles) require modeling the directional dependence of the material elastic properties in three orthogonal directions. We investigate linear orthotropic materials, a special class of linear anisotropic materials where the shear stresses are decoupled from normal stresses, as well as general linear (non-orthotropic) anisotropic materials. Orthotropic materials generalize transversely isotropic materials, by exhibiting different stiffness in three orthogonal directions. Orthotropic materials are, however, parameterized by nine values that are difficult to tune in practice, as poorly adjusted settings easily lead to simulation instabilities. We present a user-friendly approach to setting these parameters that is guaranteed to be stable. Our approach is intuitive as it extends the familiar intuition known from isotropic materials. Similarly to linear orthotropic materials, we also derive a stability condition for a subset of general linear anisotropic materials, and give intuitive approaches to tuning them. In order to simulate large deformations, we augment linear corotational FEM simulations with our orthotropic and general anisotropic materials.

Influence of orthotropy on biomechanics of peri-implant bone in complete mandible model with full dentition

Objective. The study was to investigate the impact of orthotropic material on the biomechanics of dental implant, based on a detailed mandible with high geometric and mechanical similarity. Materials and Methods. Multiple data sources were used to elaborate detailed biological structures and implant CAD models. In addition, an extended orthotropic material assignment methodology based on harmonic fields was used to handle the alveolar ridge region to generate compatible orthotropic fields. The influence of orthotropic material was compared with the commonly used isotropic model and simplified orthotropic model. Results. The simulation results showed that the values of stress and strain on the implant-bone interface almost increased in the orthotropic model compared to the isotropic case, especially for the cancellous bone. However, the local stress concentration was more obvious in the isotropic case compared to that in orthotropic case. The simple orthotropic model revealed irregular stress and strain distribution, compared to the isotropic model and the real orthotropic model. The influence of orthotropy was little on the implant, periodontal ligament, tooth enamel, and dentin. Conclusion. The orthotropic material has significant effect on stress and strain of implant-bone interface in the mandible, compared with the isotropic simulation. Real orthotropic mechanical properties of mandible should be emphasized in biomechanical studies of dental implants.

Load transfer in Christensen(®) TMJ in alloplastic total joint replacement for two different mouth apertures

This study analyses load transfer in the fossa component based on two numerical models of total temporomandibular joint (TMJ) implants for two mouth openings. The TMJ articulation is a very complex system with muscles, ligaments and cartilage. Until now, studies of TMJ implants have analysed only condylar behaviour. The finite element models were constructed based on CT scans of a cadaveric mandible and cranium, considering the bone geometry and position. The influence of five principal muscle actions was simulated for two mouth positions, 5 mm and 15 mm openings at the incisive tooth support. Strain distributions into the surrounding bone tissue were analysed in both models in the condyle and fossa components. The results demonstrate that in Christensen(®) TJR of the temporomandibular joint the fossa component is the more critical part, presenting more stress near the screw holes and contact regions with the cranium. The most critical region is around the first two screws and the least critical is in the condyle component. For the mandible condyle reconstructed with a Christensen(®) prosthesis, the 15 mm mouth opening was more critical, as compression was increased, but for the fossa component the most critical situation occurred with the 5 mm opening. The micromovements observed suggest that the number of screws could be reduced to increase osteointegration of screws in the mandible condyle.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography–based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

Three-dimensional finite element analysis of implant-supported crown in fibula bone model

PURPOSE

The purpose of this study was to compare stress distributions of implant-supported crown placed in fibula bone model with those in intact mandible model using three-dimensional finite element analysis.

MATERIALS AND METHODS

Two three-dimensional finite element models were created to analyze biomechanical behaviors of implant-supported crowns placed in intact mandible and fibula model. The finite element models were generated from patient's computed tomography data. The model for grafted fibula was composed of fibula block, dental implant system, and implant-supported crown. In the mandible model, same components with identical geometries with the fibula model were used except that the mandible replaced the fibula. Vertical and oblique loadings were applied on the crowns. The highest von Mises stresses were investigated and stress distributions of the two models were analyzed.

RESULTS

Overall stress distributions in the two models were similar. The highest von Mises stress values were higher in the mandible model than in the fibula model. In the individual prosthodontic components there was no prominent difference between models. The stress concentrations occurred in cortical bones in both models and the effect of bicortical anchorage could be found in the fibula model.

CONCLUSION

Using finite element analysis it was shown that the implant-supported crown placed in free fibula graft might function successfully in terms of biomechanical behavior.

Three-Dimensional Nonlinear Contact Finite Element Analysis of Mandibular All-on-4 Design

The All-on-4 design was used successfully for restoring edentulous mandible. This design avoids anatomic cripples such as inferior alveolar nerve by tilting posterior implants. Moreover, tilting posterior implants of All-on-4 design had a mechanical preference than the conventional design. On the other hand, the anterior implants are parallel at the lateral incisor region. Several researches showed favorable results for tilting posterior implants. However, research did not study the influence of the anterior implant position or orientation on the mechanical aspects of this design. This study analyzes the influence of varying anterior implant position and orientation of the All-on-4 design using nonlinear contact 3D finite-element analysis. Three copied 3-dimensional models of the All-on-4 design were classified according to anterior implant position and orientation. The frictional contact between fixtures and bone was the contact type in this finite element analysis. Finally, von Mises stress and strain at implant and bone levels were recorded and analyzed using finite element software. Stress concentrations were detected mainly around the posterior implant at the loaded side. Values of the maximum equivalent stress and strain were around tilted implants of design III followed by design II, then design I. Changing the position or orientation of the anterior implants in All-on-4 design influences stress-strain distribution of the whole design.

Do erupted third molars weaken the mandibular angle after trauma to the chin region? A 3D finite element study

It has been suggested that third molars increase mandibular fragility because they do not contribute to its strength. For ethical reasons, a human study design that would permit the elucidation of this interference is not possible. This study evaluated the impact of the presence of erupted third molars on the mandibular angle of resistance when submitted to trauma. A three-dimensional (3D) mandibular model was obtained through finite element methodology using computed tomography (CT) with the geometry and mechanical properties to reproduce a normal mandibular structure. Human mandibles with no, one or two erupted third molars were evaluated. Whenever the third molar was present there was a greater concentration of tensions around the cervical part of its alveolus. Approximated Von Mises equivalent stress of the third molar region was 107.035 MPa in the mandible with teeth and 64.6948 MPa in the mandible without teeth. In the condylar region it was 151.65 MPa when the third molar was present and 184.496 MPa when it was absent. The digital models created proved that the mandibular angle becomes more fragile in the presence of third molars. When they are absent the energy concentrates on the lateral e posterior aspect of the condylar neck.

Physical modeling with orthotropic material based on harmonic fields

Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme.

Generation of mineral density distribution maps from subject-specific models of mandibles - a preliminary study

BACKGROUND

Determination of the mineral content of bone and its distribution by computed tomography (CT) enables one to define the insertion points for prosthetic devices, or determine the degree of healing in cases of fracture or surgical intervention. The use of subject-specific models allows mapping of the spatial structure and the mineral content of the bone graphically and quantitatively.

METHODS

Subject-specific models and mineral density maps from pig jaws were developed using segmentation, transcription tools and finite element analysis software. This study considered six frozen heads from pigs aged 10-12 months, and phantom solutions of K(2) HPO(4) . The predicted bone mass of each jaw was compared with its respective ash mass after incineration.

RESULTS

The tridimensional maps show highest density values at the molar cusp and within the symphysis. The average percentage error relative to the mineral density maps was -18.4%. The radiation dose was reduced by a factor of eight from the recommended maximum without compromising the precision of the models.

CONCLUSIONS

The computed tridimensional mineral density maps illustrate, numerically and graphically, the spatial distribution of the density field within the mandibular bone. These maps could facilitate the location of insertion points or determine the evolution of the mineralization level of a patient's bone tissue.

Patient-Specific Finite-Element Analyses of the Proximal Femur with Orthotropic Material Properties Validated by Experiments

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs’ surface and head’s displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models’ predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Current computational modelling trends in craniomandibular biomechanics and their clinical implications

Computational models of interactions in the craniomandibular apparatus are used with increasing frequency to study biomechanics in normal and abnormal masticatory systems. Methods and assumptions in these models can be difficult to assess by those unfamiliar with current practices in this field; health professionals are often faced with evaluating the appropriateness, validity and significance of models which are perhaps more familiar to the engineering community. This selective review offers a foundation for assessing the strength and implications of a craniomandibular modelling study. It explores different models used in general science and engineering and focuses on current best practices in biomechanics. The problem of validation is considered at some length, because this is not always fully realisable in living subjects. Rigid-body, finite element and combined approaches are discussed, with examples of their application to basic and clinically relevant problems. Some advanced software platforms currently available for modelling craniomandibular systems are mentioned. Recent studies of the face, masticatory muscles, tongue, craniomandibular skeleton, temporomandibular joint, dentition and dental implants are reviewed, and the significance of non-linear and non-isotropic material properties is emphasised. The unique challenges in clinical application are discussed, and the review concludes by posing some questions which one might reasonably expect to find answered in plausible modelling studies of the masticatory apparatus.

Finite element analysis of the human mandible at 3 different stages of life

OBJECTIVE

This study analyzed detailed models of human mandibles at 3 different stages of life with simulation of supra normal chewing forces at static conditions.

METHODS AND MATERIALS

Finite element analysis (FEA) was used to generate models from cone-beam computerized tomograms (CBCT) of 3 patients aged 12, 20, and 67 years, using numerically calculated material parameters. Estimated chewing forces were then applied to the simulations.

RESULTS

The results reflect higher elasticity in younger models in all regions of the mandible. The experimental models show that physiologic load stress and strain distributional changes of the mandible vary according to age.

CONCLUSION

The CBCT-based model generation used in this study provided high-quality model definition of the 3 individual patients of different ages. FEA has great potential to predict bone responses to paradigms of mechanical activity. Future applications of FEA will include surgical planning, surgical hardware testing, and the design of scaffolds and tissue-engineered constructs.