Enhancing the mechanical stability of restored teeth with interfacial cracks: Finite element analysis.

OBJECTIVES: This study aims to enhance the mechanical stability of restored molar teeth with class II occlusal-distal (OD) cavities. We seek to achieve this goal through a comprehensive investigation of three primary factors: (1) the choice of restoration material properties, (2) internal cavity geometries, and (3) the impact of double-layered restoration configurations. METHODS: To achieve our objectives, we initiated by creating two-dimensional (2D) models of restored teeth featuring class II OD cavities, utilizing scanned and segmented images of maxillary molar teeth. We drew 2D profiles of dentine and enamel, which were then imported into finite element analysis (FEA) software. To explore various cavity geometries, we implemented a total of thirteen different designs, encompassing straight, oblique, grooved, curved, and double-layered configurations. We utilized a semi-circular stone to simulate the application of contact load on the restored tooth. We applied identical boundary conditions and contact loading across all models. To assign material properties, we developed a Python code, enabling the automatic assignment of seven elastic moduli ranging from 2 GPa to 26 GPa to the restoration materials. Meanwhile, constant material properties were assigned to the enamel and dentine. In total, we conducted 133 FEA simulations to comprehensively analyse the effects of the aforementioned factors on the strength and performance of restored molar teeth. RESULTS: Our analysis revealed two key factors significantly influencing the mechanical resistance of treated teeth, particularly in the presence of a crack or debonding: (1) the marginal geometry of the OD cavity and (2) the elastic modulus of the restorative material. However, altering the internal cavity angle and implementing a double-layered restoration did not significantly influence the restored tooth's overall strength and performance in the face of crack or debonding situations. SIGNIFICANCE: The findings of this study have substantial implications for designing and restoring class II OD cavities to enhance resistance to cracks or debonding. The use of curved marginal geometries in restoration design can significantly improve fracture resistance, with double-curved geometries reducing stress concentrations by approximately 43% compared to straight cavities. These results offer valuable guidance for strengthening the structural integrity of restored teeth, calling for further experimental investigations to explore practical applications and benefits.

The influence of dental restoration depth, internal cavity angle, and material properties on biomechanical resistance of a treated molar tooth.

OBJECTIVES: To assess the hypotheses that a restored tooth structure for a class II occlusal-distal (OD) cavity can be reinforced by optimizing the cavity geometry and choosing composites with adequate mechanical properties. METHODS: A human maxillary molar tooth was scanned, and segmented. The 2D profiles of dentin and enamel were drawn and imported to ABAQUS software. Eighteen restored tooth models with different cavity occlusal depths (OcDs) and internal cavity angles were developed. A semi-circular stone part was used to apply contact loads to the restored tooth model. After setting up the required interactions and boundary conditions, a written Python code was used to automatically assign a wide range of elastic moduli, from 2 GPa to 26 GPa, to the composite restorations, and assign constant material properties to the enamel and dentine. For simplicity, the behaviour of the mechanical material was postulated homogeneous and elastic, while the FE analyses were linearly carried out in this study. Also, the code enabled the FEA software to conduct the stress analyses, determine maximum principal stresses, and record the obtained results. RESULTS: The internal cavity angle formed between the mesial wall and the pulpal floor of the cavity significantly changed the peak maximum principal stress both in the enamel and restoration. The peak stress concentrations were observed mostly at the enamel-restoration interface, with an almost perpendicular orientation to this interface. Regarding the effect of occlusal cavity depth (OcD), the model with the shallowest cavity (OcD = 1.5 mm) represented greater resistance to applied loads than the model with deeper cavities (OcD = 2.0 mm and OcD 2.5 mm). The composite modulus (CM) in the range of 10-18 GPa reduced the maximum principal stress concentrations in the enamel. The lowest result for maximum principal stress was observed in the model with OcD = 1.5 mm, CM = 10 GPa and internal cavity angles = 100°, which was the strongest model against contact loads. SIGNIFICANCE: Class II OD cavities with optimal geometry have reduced induced stress levels, thus being able to be more mechanically robust against contact load transmitted by a stone. Cavity geometry designs with obtuse (more than 90°) internal cavity angles were significantly efficient in minimizing peak stress concentrations. The results indicated that for the model with obtuse internal cavity angles, choosing a composite with optimised properties can diminish stress, particularly at the tooth-restoration interface. Furthermore, the shallowest the cavity, the sturdier the restoration was, especially when the interface tooth-restoration laid on enamel and not on dentine.

Influence of thermal and thermomechanical stimuli on a molar tooth treated with resin-based restorative dental composites.

OBJECTIVES: In-vivo experimental techniques to understand the biomechanical behavior of a restored tooth, under varying oral conditions, is very limited because of the invasive nature of the study and complex tooth geometry structure. Therefore, 3D-Finite element analyses are used to understand the behavior of a restored tooth under varying oral conditions. In this study, the distribution of maximum principal stress (MaxPS) and the location of MaxPS on a restored tooth using six different commercially available dental resin composites under the influence of thermal and thermomechanical stimuli are performed. METHODS: An intact tooth was scanned using µ-CT and segmented to obtain separate geometric models of the tooth, including enamel and dentine. Then, a class II mesial-occlusal-distal (MOD) cavity was constructed for the tooth model. The restored tooth model was further meshed and imported to the commercial Finite Element (FE) software ANSYS. Thermal hot and cold stimuli at 50 °C and 2 °C, respectively, were applied on the occlusal and lingual surface of the tooth model with the tooth's ambient temperature set at 37 °C. A uniform loading of 400 N was applied on the occlusal surface of the tooth to imitate the masticatory forces during the cyclic thermal stimuli. RESULTS: The results of this study showed that the restorative materials with higher thermal conductivity showed a lower temperature gradient between the restoration and enamel, during the application of thermal stimuli, leading to a higher value of MaxPS on the restoration. Moreover, on applying thermal stimuli, the location of MaxPS at the restoration-enamel junction (REJ) changes based on the value of the coefficient of thermal expansion (CTE). The MaxPS distribution on the application of simultaneous thermal and mechanical stimuli was not only dependent on the elastic modulus of restorative materials but also their thermal properties such as the CTE and thermal conductivity. The weakest part of the restoration was at the REJ, as it experienced the peak stress level during the application of thermomechanical stimuli. SIGNIFICANCE: The findings from this study suggest that restorative materials with lower values of elastic modulus, lower coefficient of thermal expansion and higher values of thermal conductivity result in lower stresses on the restoration. The outcomes from this study also suggest that the thermal and mechanical properties of a restorative material can have a considerable effect on the selection of restorative materials by dental clinicians over conventional restorative materials.

The effect of dental restoration geometry and material properties on biomechanical behaviour of a treated molar tooth: A 3D finite element analysis.

OBJECTIVES: To test the hypothesis that restoration of class II mesio-occlusal-distal (MOD) cavities can be strengthened through judicious choice of restoration geometry and material properties. METHODS: An intact extracted human maxillary molar tooth was digitized, segmented, reconstructed, and four 3D restored tooth models were developed with four different restoration geometries: one straight, one single-curved, and two double-curved. Stress analysis was conducted for representative loading using finite element analysis, and maximum principal stresses were determined at the dentine-enamel and restoration-enamel junctions. A range of restorative material elastic moduli (5-80 GPa) and Poisson's ratios (0.25-0.35) were studied. Vertical loads of 400 N were applied on occlusal points, while the roots of the molar teeth, below the crevices, were supported in all directions. All the materials were modelled as homogeneous, isotropic, and elastic. RESULTS: The maximum principal stresses at the restoration-enamel junctions were strongly dependent on the MOD restoration geometries. Peak stresses occurred along the palatal surface of the restoration rather than the opposite buccal surface. Double-curved restorations showed the lowest peak stress at restoration-enamel junctions. Choice of the mechanical properties of restorative material in the range of 5-35 GPa further reduced stress concentrations on the enamel. SIGNIFICANCE: Class II MOD restorations may be stronger if designed with double-curved marginal geometries that can reduce stress concentrations. Designs with convex and concave geometries were particularly effective because they reduced stress concentrations dramatically. Results suggest that relatively minor changes to the geometry of a restoration can have a substantial effect on stress at the restoration-enamel junction and motivate future experimental analysis.

FWNNet: Presentation of a New Classifier of Brain Tumor Diagnosis Based on Fuzzy Logic and the Wavelet-Based Neural Network Using Machine-Learning Methods.

In this paper, we present a novel classifier based on fuzzy logic and wavelet transformation in the form of a neural network. This classifier includes a layer to predict the numerical feature corresponded to labels or classes. The presented classifier is implemented in brain tumor diagnosis. For feature extraction, a fractal model with four Gaussian functions is used. The classification is performed on 2000 MRI images. Regarding the results, the accuracy of the DT, KNN, LDA, NB, MLP, and SVM is 93.5%, 87.6%, 61.5%, 57.5%, 68.5%, and 43.6%, respectively. Based on the results, the presented FWNNet illustrates the highest accuracy of 100% with the fractal feature extraction method and brain tumor diagnosis based on MRI images. Based on the results, the best classifier for diagnosis of the brain tumor is FWNNet architecture. However, the second and third high-performance classifiers are the DT and KNN, respectively. Moreover, the presented FWNNet method is implemented for the segmentation of brain tumors. In this paper, we present a novel supervised segmentation method based on the FWNNet layer. In the training process, input images with a sweeping filter should be reshaped to vectors that correspond to reshaped ground truth images. In the training process, we performed a PSO algorithm to optimize the gradient descent algorithm. For this purpose, 80 MRI images are used to segment the brain tumor. Based on the results of the ROC curve, it can be estimated that the presented layer can segment the brain tumor with a high true-positive rate.

Magnetic Resonance Elastography Reconstruction for Anisotropic Tissues.

Elastography has become widely used clinically for characterising changes in soft tissue mechanics that are associated with altered tissue structure and composition. However, some soft tissues, such as muscle, are not isotropic as is assumed in clinical elastography implementations. This limits the ability of these methods to capture changes in anisotropic tissues associated with disease. The objective of this study was to develop and validate a novel elastography reconstruction technique suitable for estimating the linear viscoelastic mechanical properties of transversely isotropic soft tissues. We derived a divergence-free formulation of the governing equations for acoustic wave propagation through a linearly transversely isotropic viscoelastic material, and transformed this into a weak form. This was then implemented into a finite element framework, enabling the analysis of wave input data and tissue structural fibre orientations, in this case based on diffusion tensor imaging. To validate the material constants obtained with this method, numerous in silico phantom experiments were run which encompassed a range of variations in wave input directions, material properties, fibre structure and noise. The method was also tested on ex vivo muscle and in vivo human volunteer calf muscles, and compared with a previous curl-based inversion method. The new method robustly extracted the transversely isotropic shear moduli (G⊥', G∥', G″) from the in silico phantom tests with minimal bias, including in the presence of experimentally realistic levels of noise in either fibre orientation or wave data. This new method performed better than the previous method in the presence of noise. Anisotropy estimates from the ex vivo muscle phantom agreed well with rheological tests. In vivo experiments on human calf muscles were able to detect increases in muscle shear moduli with passive muscle stretch. This new reconstruction method can be applied to quantify tissue mechanical properties of anisotropic soft tissues, such as muscle, in health and disease.

A multi-objective optimization of stent geometries.

Stents are scaffolding cardiovascular implants used to restore blood flow in narrowed arteries. However, the presence of the stent alters local blood flow and shear stresses on the surrounding arterial wall, which can cause adverse tissue responses and increase the risk of adverse outcomes. There is a need for optimization of stent designs for hemodynamic performance. We used multi-objective optimization to identify ideal combinations of design variables by assessing potential trade-offs based on common hemodynamic indices associated with clinical risk and mechanical performance of the stents. We studied seven design variables including strut cross-section, strut dimension, strut angle, cell alignment, cell height, connector type and connector arrangement. Optimization objectives were the percentage of vessel area exposed to adversely low time averaged WSS (TAWSS) and adversely high Wall Shear Stress (WSS) assessed using computational fluid dynamics modeling, as well as radial stiffness of the stent using FEA simulation. Two multi-objective optimization algorithms were used and compared to iteratively predict ideal designs. Out of 50 designs, three best designs with respect to each of the three objectives, and two designs in regard to overall performance were identified.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix.

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry.

Characterizing the mechanical behavior of living tissue presents an interesting challenge because the elasticity varies by eight orders of magnitude, from 50Pa to 5GPa. In the present work, a non-destructive optical fiber photoelastic polarimetry system is used to analyze the mechanical properties of resected samples from porcine liver, kidney, and pancreas. Using a quasi-linear viscoelastic fit, the elastic modulus values of the different organ systems are determined. They are in agreement with previous work. In addition, a histological assessment of compressed and uncompressed tissues confirms that the tissue is not damaged during testing.

Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching.

The time- and frequency-dependent properties of connective tissue define their physiological function, but are notoriously difficult to characterize. Well-established tools such as linear viscoelasticity and the Fung quasi-linear viscoelastic (QLV) model impose forms on responses that can mask true tissue behavior. Here, we applied a more general discrete quasi-linear viscoelastic (DQLV) model to identify the static and dynamic time- and frequency-dependent behavior of rabbit medial collateral ligaments. Unlike the Fung QLV approach, the DQLV approach revealed that energy dissipation is elevated at a loading period of ∼10s. The fitting algorithm was applied to the entire loading history on each specimen, enabling accurate estimation of the material's viscoelastic relaxation spectrum from data gathered from transient rather than only steady states. The application of the DQLV method to cyclically loading regimens has broad applicability for the characterization of biological tissues, and the results suggest a mechanistic basis for the stretching regimens most favored by athletic trainers.

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen.

UNLABELLED: The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2s and 10-30s. Different finite time constants in the range of 1-7000s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000s, and to merge relaxation finite time constants in the 0.5-2s range into a single time content in the 1s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction. STATEMENT OF SIGNIFICANCE: As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans.

Microstructural properties and mechanics vary between bundles of the human anterior cruciate ligament during stress-relaxation.

Previous studies have shown different elastic properties between the anteromedial (AM) and posterolateral (PL) bundles of the human anterior cruciate ligament (ACL). However, it is unknown if the two bundles of the ACL exhibit distinct time-dependent properties and microstructural organization, which have important implications for fully understanding the structure-function relationships of this oft-injured ligament. The goal of this study was to quantify the viscoelastic material properties and collagen fiber alignment of the AM and PL bundles in 16 human ACLs during stress-relaxation mechanical tests using the quasi-linear viscoelastic (QLV) model and a quantitative polarization imaging technique. We hypothesized that the AM and PL bundles would exhibit differences in the instantaneous mechanical and organizational properties (i.e., immediately following a step increase in strain), but similar time-dependent changes during stress-relaxation. Results showed that AM samples exhibited larger peak/equilibrium stresses and less stress-relaxation during a 300-s hold compared to PL samples. The AM bundle demonstrated stronger and more uniform collagen fiber alignment (i.e., higher degree of linear polarization (DoLP) values and less distributed angle of polarization (AoP) values) compared to the PL bundle, and larger changes in alignment strength during the hold. Results suggest that the AM bundle is the more "dominant" bundle, with significantly different mechanical and material properties in stress-relaxation. While more research is needed to better understand how these findings relate to the pathophysiology of ACL tears and can best guide treatment, the findings provide additional insight into the microstructural properties and biomechanics of the human ACL.

Efficient and optimized identification of generalized Maxwell viscoelastic relaxation spectra.

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here an efficient algorithm that enables rapid identification of viscoelastic relaxation spectra. The algorithm was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen, revealing an extensive distribution of viscoelastic time constants.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials.

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.