Traction-separation law parameters for the description of age-related changes in the delamination strength of the human descending thoracic aorta.

Aortic dissection is a life-threatening disease that consists in the development of a tear in the wall of the aorta. The initial tear propagates as a discontinuity leading to separation within the aortic wall, which can result in the creation of a so-called false lumen. A fatal threat occurs if the rupture extends through the whole thickness of the aortic wall, as blood may then leak. It is generally accepted that the dissection, which can sometime extend along the entire length of the aorta, propagates via a delamination mechanism. The aim of the present paper is to provide experimentally validated parameters of a mathematical model for the description of the wall's cohesion. A model of the peeling experiment was built in Abaqus. The delamination interface was described by a piecewise linear traction-separation law. The bulk behavior of the aorta was assumed to be nonlinearly elastic, anisotropic, and incompressible. Our simulations resulted in estimates of the material parameters for the traction-separation law of the human descending thoracic aorta, which were obtained by minimizing the differences between the FEM predictions and the delamination force given by the regression of the peeling experiments. The results show that the stress at damage initiation, Tc, should be understood as an age-dependent quantity, and under the assumptions of our model this dependence can be expressed by linear regression as Tc = - 13.03·10-4·Age + 0.2485 if the crack front advances in the axial direction, and Tc = - 7.58·10-4·Age + 0.1897 if the crack front advances in the direction of the aortic circumference (Tc [MPa], Age [years]). Other model parameters were the stiffness K and the separation at failure, δf-δc (K = 0.5 MPa/mm, δf-δc = 0.1 mm). The material parameters provided by our study can be used in numerical simulations of the biomechanics of dissection propagation through the aorta especially when age-associated phenomena are studied.

Assessment of implant internal stresses under physiological femoral loading: Translation to a simplified bending load model.

The success of surgical treatment for fractures hinges on various factors, notably accurate surgical indication. The process of developing and certifying a new osteosynthesis device is a lengthy and costly process that requires multiple cycles of review and validation. Current methods, however, often rely on predecessor standards rather than physiological loads in specific anatomical locations. This study aimed to determine actual loads experienced by an osteosynthesis plate, exemplified by a standard locking plate for the femoral shaft, utilizing finite elements analysis (FEA) and to obtain the bending moments for implant development standard tests. A protocol was developed, involving the creation and validation of a fractured femur model fixed with a locking plate, mechanical testing, and FEA. The model's validation demonstrated exceptional accuracy in predicting deformations, and the FEA revealed peak stresses in the fracture bridging zone. Results of a parametric analysis indicate that larger fracture gaps significantly impact implant mechanical behavior, potentially compromising stability. This study underscores the critical need for realistic physiological conditions in implant evaluations, providing an innovative translational approach to identify internal loads and optimize implant designs. In conclusion, this research contributes to enhancing the understanding of implant performance under physiological conditions, promoting improved designs and evaluations in fracture treatments.

Analysis of load distribution on the plate and lateral hinge of a valgus opening high tibial osteotomy during weight-bearing: a finite element analysis.

INTRODUCTION: Valgus high tibial osteotomy (HTO) is indicated for managing isolated medial knee osteoarthritis in a young patient with a metaphyseal deformity of the proximal tibia. In a medial opening HTO, maintaining the integrity of the lateral hinge is crucial for ensuring proper healing and correction retention. Using a locked plate to stabilize an HTO is common practice, allowing for earlier weight-bearing. The objective of this study was therefore to measure and track the mechanical load distribution on a locked fixation plate and the lateral hinge of an HTO using a finite element (FE) model simulating single-leg stance loading. HYPOTHESIS: The working hypothesis was that during weight-bearing, the plate and the lateral hinge absorb stress asymmetrically, predominantly on the plate. MATERIAL AND METHODS: A numerical model of an HTO stabilized with a locked plate was developed based on the actual geometry of a healthy proximal tibia (using Autodesk Fusion 360 and Altair HyperWorks software). In this finite element simulation of loading, a mesh convergence study was conducted to optimize the accuracy of the numerical model results. The primary outcome measure was the maximum stress value in the affected areas (Von Mises stress, in MPa) of the plate and the lateral hinge. RESULTS: The maximum stress intensity in the plate was approximately 20.29 MPa. The maximum stress intensity in the bony hinge was about 5.6 MPa. The results of the mesh convergence study for the hinge and the plate enabled defining the most suitable model for future FE studies: a 4 mm mesh for all model elements except for the high-stress area in the plate and the hinge, which were meshed with a 0.7 mm element size. This adaptation provided greater precision in the study. DISCUSSION: There is a distribution and allocation of stress both on the plate and the hinge, underlining the significance of the plate and the absolute necessity of preserving the hinge. Predictably, the plate absorbs the majority of the load, more than three times that of the hinge. CONCLUSION: The hypothesis is confirmed; however, additional studies would be necessary to validate these numerical results: an experimental component on instrumented cadaveric bones, as well as comparative studies of different fixation plates. LEVEL OF EVIDENCE: V, expert opinion; controlled laboratory study.

Reliability Assessment of Wireless Sensor Networks by Strain-Based Region Analysis for Redundancy Estimation in Measurements on the Example of an Aircraft Wing Box.

Wireless sensor networks (WSNs) are attracting increasing research interest due to their ability to monitor large areas independently. Their reliability is a crucial issue, as it is influenced by hardware, data, and energy-related factors such as loading conditions, signal attenuation, and battery lifetime. Proper selection of sensor node positions is essential to maximise system reliability during the development of products equipped with WSNs. For this purpose, this paper presents an approach to estimate WSN system reliability during the development phase based on the analysis of measurements, using strain measurements in finite element (FE) models as an example. The approach involves dividing the part under consideration into regions with similar strains using a region growing algorithm (RGA). The WSN configuration is then analysed for reliability based on data paths and measurement redundancy resulting from the sensor positions in the identified measuring regions. This methodology was tested on an exemplary WSN configuration at an aircraft wing box under bending load and found to effectively estimate the hardware perspective on system reliability. Therefore, the methodology and algorithm show potential for optimising sensor node positions to achieve better reliability results.

PMUT-Based System for Continuous Monitoring of Bolted Joints Preload.

In this paper, we present a bolt preload monitoring system, including the system architecture and algorithms. We show how Finite Element Method (FEM) simulations aided the design and how we processed signals to achieve experimental validation. The preload is measured using a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) in pulse-echo mode, by detecting the Change in Time-of-Flight (CTOF) of the acoustic wave generated by the PMUT, between no-load and load conditions. We performed FEM simulations to analyze the wave propagation inside the bolt and understand the effect of different configurations and parameters, such as transducer bandwidth, transducer position (head/tip), presence or absence of threads, as well as the frequency of the acoustic waves. In order to couple the PMUT to the bolt, a novel assembly process involving the deposition of an elastomeric acoustic impedance matching layer was developed. We achieved, for the first time with PMUTs, an experimental measure of bolt preload from the CTOF, with a good signal-to-noise ratio. Due to its low cost and small size, this system has great potential for use in the field for continuous monitoring throughout the operative life of the bolt.

Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction.

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates.

Inverse finite element analysis for an axisymmetric model of vertical tooth extraction.

BACKGROUND AND OBJECTIVE: Tooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model. METHODS: Geometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters. RESULTS: The inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561. CONCLUSIONS: The presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

Trabecular Bone Component Assessment under Orthodontic Loads and Movements during Periodontal Breakdown-A Finite Elements Analysis.

This numerical analysis, by employing Tresca and Von Mises failure criteria, assessed the biomechanical behavior of a trabecular bone component subjected to 0.6, 1.2, and 2.4 N orthodontic forces under five movements (intrusion, extrusion, tipping, rotation, and translation) and during a gradual horizontal periodontal breakdown (0-8 mm). Additionally, they assessed the changes produced by bone loss, and the ischemic and resorptive risks. The analysis employed eighty-one models of nine patients in 405 simulations. Both failure criteria showed similar qualitative results, with Tresca being quantitatively higher by 1.09-1.21. No qualitative differences were seen between the three orthodontic loads. Quantitatively, a doubling (1.2 N) and quadrupling (2.4 N) were visible when compared to 0.6 N. Rotation and translation followed by tipping are the most stressful, especially for a reduced periodontium, prone to higher ischemic and resorptive risks. In an intact periodontium, 1.2 N can be safely applied but only in a reduced periodontium for extrusion and intrusion. More than 0.6 N is prone to increasing ischemic and resorptive risks for the other three movements. In an intact periodontium, stress spreads in the entire trabecular structure. In a reduced periodontium, stress concentrates (after a 4 mm loss-marker for the stress change distribution) and increases around the cervical third of the remaining alveolar socket.

Nested structure role in the mechanical response of spicule inspired fibers.

Euplectella aspergillummarine sponge spicules are renowned for their remarkable strength and toughness. These spicules exhibit a unique concentric layering structure, which contributes to their exceptional mechanical resistance. In this study, finite element method simulations were used to comprehensively investigate the effect of nested cylindrical structures on the mechanical properties of spicules. This investigation leveraged scanning electron microscopy images to guide the computational modeling of the microstructure and the results were validated by three-point bending tests of 3D-printed spicule-inspired structures. The numerical analyses showed that the nested structure of spicules induces stress and strain jumps on the layer interfaces, reducing the load on critical zones of the fiber and increasing its toughness. It was found that this effect shows a tapering enhancement as the number of layers increases, which combines with a threshold related to the 3D-printing manufacturability to suggest a compromise for optimal performance. A comprehensive evaluation of the mechanical properties of these fibers can assist in developing a new generation of bioinspired structures with practical real-world applications.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods.

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Modelling Inductive Sensors for Arc Fault Detection in Aviation.

Modern aircraft are being equipped with high-voltage and direct current (HVDC) architectures to address the increase in electrical power. Unfortunately, the rise of voltage in low pressure environments brings about a problem with unexpected ionisation phenomena such as arcing. Series arcs in HVDC cannot be detected with conventional means, and finding methods to avoid the potentially catastrophic hazards of these events becomes critical to assure further development of more electric and all electric aviation. Inductive sensors are one of the most promising detectors in terms of sensitivity, cost, weight and adaptability to the circuit wiring in aircraft electric systems. In particular, the solutions based on the detection of the high-frequency (HF) pulses created by the arc have been found to be good candidates in practical applications. This paper proposes a method for designing series arc fault inductive sensors able to capture the aforementioned HF pulses. The methodology relies on modelling the parameters of the sensor based on the physics that intervenes in the HF pulses interaction with the sensor itself. To this end, a comparative analysis with different topologies is carried out. For every approach, the key parameters influencing the HF pulses detection are studied theoretically, modelled with a finite elements method and tested in the laboratory in terms of frequency response. The final validation tests were conducted using the prototypes in real cases of detection of DC series arcs.

Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression.

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the range k 0 ∈ [ 0.142 , 0.203 ] mm 4 /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

Effects of different contact angles during forefoot running on the stresses of the foot bones: a finite element simulation study.

Introduction: The purpose of this study was to compare the changes in foot at different sole-ground contact angles during forefoot running. This study tried to help forefoot runners better control and improve their technical movements by comparing different sole-ground contact angles. Methods: A male participant of Chinese ethnicity was enlisted for the present study, with a recorded age of 25 years, a height of 183 cm, and a body weight of 80 kg. This study focused on forefoot strike patterns through FE analysis. Results: It can be seen that the peak von Mises stress of M1-5 (Metatarsal) of a (Contact angle: 9.54) is greater than that of b (Contact angle: 7.58) and c (Contact angle: 5.62) in the three cases. On the contrary, the peak von Mises stress of MC (Medial Cuneiform), IC (Intermediate Cuneiform), LC (Lateral Cuneiform), C (Cuboid), N (Navicular), T (Tarsal) in three different cases is opposite, and the peak von Mises stress of c is greater than that of a and b. The peak von Mises stress of b is between a and c. Conclusion: This study found that a reduced sole-ground contact angle may reduce metatarsal stress fractures. Further, a small sole-ground contact angle may not increase ankle joint injury risk during forefoot running. Hence, given the specialized nature of the running shoes designed for forefoot runners, it is plausible that this study may offer novel insights to guide their athletic pursuits.

Solar fuels design: Porous cathodes modeling for electrochemical carbon dioxide reduction in aqueous electrolytes.

The reduction of carbon dioxide emissions is crucial to reduce the atmospheric greenhouse effect, fighting climate change and global warming. Electrochemical CO2 reduction is one of the most promising carbon capture and utilization technologies, that can be powered by solar energy and used to make added-value chemicals and green fuels, providing grid-stability, energy security, and environmental benefits. A two-dimensional finite-elements model for porous electrodes was developed and validated against experimental data, allowing the design and performance improvement of a porous zinc cathode morphology and its operational conditions for an electrolyzer producing syngas via the co-electrolysis of CO2 and water. Porosity, pore length, fiber geometric shape, inlet pressure, system temperature, and catholyte flow rate were explored, and these parameters were thoroughly tuned by using the smart-search Nelder-Mead's multi-parameter optimization algorithm to achieve pronouncedly higher, industrial-relevant current density values than those previously reported, up to 263.6 mA/cm2 at an applied potential of -1.1 V vs. RHE.

Comparative evaluation of methods for obtaining the stress-free geometry of keratoconus corneas with different levels of severity.

A biomechanical model that simulates the physiological pressure load on the cornea without considering the stresses in vivo will result in an overstress or underestimation of the stress field and incorrect deformation of the corneal structure. Therefore, it is essential to propose numerical models that consider the stress-free geometry of the cornea. In this study, the Displacement and Pre-stress methods were compared to obtain the stress-free geometry (S-FG) and the physiological estimated geometry (P-EG), based on the patient-specific geometric behavior and the computational time required to reach each geometry. The same shape and contour conditions were considered in the models obtained from both methods for each of the pathological scenarios analyzed. Both methods behaved differently to obtain the free geometry, and this difference increased with the severity grade of the disease. However, they behaved in a similar way to reach the physiological estimated geometry. The Displacement method required a lower computational cost to reach the free geometry, with both methods presenting a similar computational cost to obtain the physiological geometry. The stress-free geometries obtained by both methods allowed to characterize the existing biomechanical decompensation during the progression of the diseases. In conclusion, the calculation of the stress-free corneal geometry associated to the clinically measured intraocular pressure with the Displacement and Prestress Methods in keratoconus eyes allows the development of accurate and useable models in clinical practice in real time. This displacement method shows some benefits in terms of computational cost.

Electroporation-Based Biopsy Treatment Planning with Numerical Models and Tissue Phantoms.

Molecular sampling with vacuum-assisted tissue electroporation is a novel, minimally invasive method for molecular profiling of solid lesions. In this paper, we report on the design of the battery-powered pulsed electric field generator and electrode configuration for an electroporation-based molecular sampling device for skin cancer diagnostics. Using numerical models of skin electroporation corroborated by the potato tissue phantom model, we show that the electroporated tissue volume, which is the maximum volume for biomarker sampling, strongly depends on the electrode's geometry, needle electrode skin penetration depths, and the applied pulsed electric field protocol. In addition, using excised human basal cell carcinoma (BCC) tissues, we show that diffusion of proteins out of human BCC tissues into water strongly depends on the strength of the applied electric field and on the time after the field application. The developed numerical simulations, confirmed by experiments in potato tissue phantoms and excised human cancer lesions, provide essential tools for the development of electroporation-based molecular markers sampling devices for personalized skin cancer diagnostics.

Finite element analysis in the optimization of posterior-stabilized total knee arthroplasty.

Posterior-stabilized total knee arthroplasty (PS-TKA) is associated with high rates of satisfaction and functional recovery. This is notably attributed to implant optimization in terms of design, choice of materials, positioning and understanding of biomechanics. Finite elements analysis (FEA) is an assessment technique that contributed to this optimization by ensuring mechanical results based on numerical simulation. By close teamwork between surgeons, researchers and engineers, FEA enabled testing of certain clinical impressions. However, the methodological features of the technique led to wide variations in the presentation and interpretation of results, requiring a certain understanding of numerical and biomechanical fields by the orthopedic community. The present study provides an up-to-date review, aiming to address the following questions: what are the principles of FEA? What is the role of FEA in studying PS design in TKA? What are the key elements in the literature for understanding the role of FEA in PS-TKA? What is the contribution of FEA for understanding of tibiofemoral and patellofemoral biomechanical behavior? What are the limitations and perspectives of digital simulation and FEA in routine practice, with a particular emphasis on the "digital twin" concept? LEVEL OF EVIDENCE: V, expert opinion.

The inclusion of the epithelium in numerical models of the human cornea.

We present a patient-specific finite element model of the human cornea that accounts for the presence of the epithelium. The thin anterior layer that protects the cornea from the external actions has a scant relevance from the mechanical point of view, and it has been neglected in most numerical models of the cornea, which assign to the entire cornea the mechanical properties of the stroma. Yet, modern corneal topographers capture the geometry of the epithelium, which can be naturally included into a patient-specific solid model of the cornea, treated as a multi-layer solid. For numerical applications, the presence of a thin layer on the anterior cornea requires a finer discretization and the definition of two constitutive models (including the corresponding properties) for stroma and epithelium. In this study, we want to assess the relevance of the inclusion of the epithelium in the model of the cornea, by analyzing the effects in terms of uncertainties of the mechanical properties, stress distribution across the thickness, and numerical discretization. We conclude that if the epithelium is modeled as stroma, the material properties should be reduced by 10%. While this choice represents a sufficiently good approximation for the simulation of in vivo mechanical tests, it might result into an under-estimation of the postoperative stress in the simulation of refractive surgery.

Effects of Increasing the Orthodontic Forces over Cortical and Trabecular Bone during Periodontal Breakdown-A Finite Elements Analysis.

Background and Objectives: Herein we used numerical analysis to study different biomechanical behaviors of mandibular bone subjected to 0.6 N, 1.2 N, and 2.4 N orthodontic loads during 0-8 mm periodontal breakdown using the Tresca failure criterion. Additionally, correlations with earlier FEA reports found potential ischemic and resorptive risks. Materials and Methods: Eighty-one models (nine patients) and 243 simulations (intrusion, extrusion, rotation, tipping, and translation) were analyzed. Results: Intrusion and extrusion displayed after 4 mm bone loss showed extended stress display in the apical and middle third alveolar sockets, showing higher ischemic and resorptive risks for 0.6 N. Rotation, translation, and tipping displayed the highest stress amounts, and cervical-third stress with higher ischemic and resorptive risks after 4 mm loss for 0.6 N. Conclusions: Quantitatively, rotation, translation, and tipping are the most stressful movements. All three applied forces produced similar stress-display areas for all movements and bone levels. The stress doubled for 1.2 N and quadrupled for 2.4 N when compared with 0.6 N. The differences between the three loads consisted of the stress amounts displayed in color-coded areas, while their location and extension remained constant. Since the MHP was exceeded, a reduction in the applied force to under 0.6 N (after 4 mm of bone loss) is recommended for reducing ischemic and resorptive risks. The stress-display pattern correlated with horizontal periodontal-breakdown simulations.

Orthodontic Internal Resorption Assessment in Periodontal Breakdown-A Finite Elements Analysis (Part II).

This finite elements analysis (FEA) assessed the accuracy of maximum shear stress criteria (Tresca) in the study of orthodontic internal surface resorption and the absorption-dissipation ability of dental tissues. The present study was conducted over eighty-one models totaling 324 simulations with various bone loss levels (0-8 mm), where 0.6 N and 1.2 N were applied in the intrusion, extrusion, rotation, tipping, and translation movements. Tresca criteria displayed localized high-stress areas prone to resorption for all situations, better visible in the dentine component. The internal resorptive risks are less than external ones, seeming to increase with the progression of the periodontal breakdown, especially after 4 mm. The internal and external surface high-stress areas are strictly correlated. The qualitative stress display for both forces was almost similar. The rotation and tipping displayed the highest resorptive risks for the pulp chamber, decreasing with bone loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same applied force is kept. The dentine resemblance to ductile based on its high absorption-dissipation ability seems correct. Tresca seems to supply a better predictability of the prone-to-resorption areas than the other failure criteria.