The influence of the root cross-section on the stress distribution in teeth restored with a positive-locking post and core design: a finite element study

Human teeth with substantial coronal defects are subject to reconstruction by means of post and core restorations. Typically, such a restoration comprises a slightly cylindrical post onto which an abutment of varying shape, depending on the designated restoration, is attached. As clinical results are not satisfactory to date, we proposed a new proprietary post and core design which makes use of positive locking. As this prefabricated system is not customised to an individual root's cross-sectional geometry (usually oval), a varying amount of radicular dentin is left in periphery of the core's outer edge. The aim of this study was to assess the implications of this fact, i.e., whether the root has to endure higher overall stress levels which ultimately may lead to failure of one of the components involved. A series of finite element simulations were performed to evaluate stress and strain on the system, in which the proposed post and core was embedded into a virtual dentin cylinder of different diameters, ranging from flush mounting of the restoration to a dentin excess of 4 mm, and subsequently loaded with forces with two angles of attack (90 degrees and 130 degrees ). The results show that flush mounting yields an agreeable stress and strain distribution within the radicular dentin, but overall stress levels drop significantly with an excess of 0.5 mm of surrounding dentin. More than 1 mm excess was not found to have profound positive effects.     

Experiments to determine the time dependent material properties of the periodontal ligament]

The periodontal ligament is a tissue that attaches the tooth (root) to its alveolar socket, and thus plays an important role in the regulation of tooth movements. Detailed knowledge of the material properties of the periodontal ligament is therefore essential to an understanding of tooth reaction to forces applied during orthodontic treatment. A knowledge of material parameters can also be used in simulations of long-term tooth movements with the aim of improving orthodontic treatment. To this end, this study investigated time-dependent material properties, namely the hysteresis behaviour of the periodontal ligament under constant-velocity loading, the influence of loading velocity on the hysteresis, and its failure under constant loading. Specimens obtained from pigs were used for testing purposes, and the experiments were conducted in a special test setup using a material testing device. The material behaviour of the periodontal ligament was shown to be viscoelastic, and the elastic parameters of material behaviour were also determined. Under constant-velocity loading, material behaviour showed a nonlinear course of the stress-strain curve, also known as hysteresis. When loading was repeated several times, the maximum stress of the hysteresis decreased with each cycle. Determination of the deflection of the specimen at different velocities showed maximum stress to be dependent on the loading rate. The measured stress-strain curves were approximated by bilinear behaviour, permitting the use of finite element calculations. Also investigated was the failure behaviour of the periodontal ligament, which revealed tissue rupture to be inconstant.     

Mechanical vulnerability of lower second premolar utilising visco-elastic dynamic stress analysis

Stress analysis determines vulnerability of dental tissues to external loads. Stress values depend on loading conditions, mechanical properties and constrains of structural components. The critical stress levels lead to tissue damage. The aim of this study is to analyse dynamic stress distribution of lower second premolar due to physiological cyclic loading, and dependency of pulsatile stress characteristics to visco-elastic property of dental components by finite element modelling. Results show that visco-elastic property markedly influences stress determinants in major anatomical sites including dentin, cementum–enamel and dentin–enamel junctions. Reduction of visco-elastic parameter leads to mechanical vulnerability through elevation of stress pulse amplitude, maximum stress value; and reduction of stress phase shift as a determinant of stress wave propagation. The results may be applied in situations in which visco-elasticity is reduced such as root canal therapy and post and core restoration in which teeth are more vulnerable to fracture.     

Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

Relation between subject-specific hip joint loading, stress distribution in the proximal femur and bone mineral density changes after total hip replacement

In the prediction of bone remodelling processes after total hip replacement (THR), modelling of the subject-specific geometry is now state-of-the-art. In this study, we demonstrate that inclusion of subject-specific loading conditions drastically influences the calculated stress distribution, and hence influences the correlation between calculated stress distributions and changes in bone mineral density (BMD) after THR.For two patients who received cementless THR, personalized finite element (FE) models of the proximal femur were generated representing the pre- and post-operative geometry. FE analyses were performed by imposing subject-specific three-dimensional hip joint contact forces as well as muscle forces calculated based on gait analysis data. Average values of the von Mises stress were calculated for relevant zones of the proximal femur. Subsequently, the load cases were interchanged and the effect on the stress distribution was evaluated. Finally, the subject-specific stress distribution was correlated to the changes in BMD at 3 and 6 months after THR.We found subject-specific differences in the stress distribution induced by specific loading conditions, as interchanging of the loading also interchanged the patterns of the stress distribution. The correlation between the calculated stress distribution and the changes in BMD were affected by the two-dimensional nature of the BMD measurement.Our results confirm the hypothesis that inclusion of subject-specific hip contact forces and muscle forces drastically influences the stress distribution in the proximal femur. In addition to patient-specific geometry, inclusion of patient-specific loading is, therefore, essential to obtain accurate input for the analysis of stress distribution after THR.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Optimal mechanical design of anatomical post-systems for endodontic restoration

This paper analyses the mechanical behaviour of a new reinforced anatomical post-systems (RAPS) for endodontic restoration. The composite restorative material (CRM) completely fills the root canal (as do the commonly used cast metal posts) and multiple prefabricated composite posts (PCPs) are employed as reinforcements. Numerical simulations based on 3D linearly elastic finite element models under parafunctional loads were performed in order to investigate the influence of the stiffness of the CRM and of the number of PCPs. Periodontal ligament effects were taken into account using a discretised anisotropic nonlinearly elastic spring system, and the full discrete model was validated by comparing the resulting stress fields with those obtained with conventional restorations (cast gold-alloy post, homogeneous anatomical post and cemented single PCP) and with the natural tooth. Analysis of the results shows that stresses at the cervical/middle region decrease as CRM stiffness increases and, for large and irregular root cavities that apical stress peaks disappear when multiple PCPs are used. Accordingly, from a mechanical point of view, an optimal RAPS will use multiple PCPs when CRM stiffness is equal to or at most twice that of the dentin. This restorative solution minimises stress differences with respect to the natural tooth, mechanical inhomogeneities, stress concentrations on healthy tissues, volumes subject to shrinkage phenomena, fatigue effects and risks of both root fracture and adhesive/cohesive interfacial failure.     

Finite element analysis of a new customized composite post system for endodontically treated teeth

This paper investigated the mechanical behavior of a new customized post system built up with a composite framework presently utilized for crowns, bridges, veneers and inlay/onlay dental restorations. The material has been shaped so to follow perfectly the profile of the root canal in order to take advantage of the better mechanical properties of composites with respect to metallic alloys commonly used for cast posts.

The analysis has been carried out with 3D finite element models previously validated on the basis of experimental work. The new post system has been compared to a variety of restorations using either prefabricated or cast posts. The structural efficiency of the new restoration has been evaluated for an upper incisor under different loading conditions (mastication, bruxism, impact).

Results prove that maximum stress values in restored teeth are rather insensitive to post types and materials. However, the new customized composite restoration allows to reduce significantly the stresses inside the dentinal regions where conservative clinical interventions are not possible.     

Physiologically based boundary conditions in finite element modelling

Finite element analysis has been used extensively in the study of bone loading and implant performance, such as in the femur. The boundary conditions applied vary widely, generally producing excessive femoral deformation, and although it has been shown that the muscle forces influence femoral deflections and loading, little consideration has been given to the displacement constraints. It is hypothesised that careful application of physiologically based constraints can produce physiological deformation, and therefore straining, of the femur. Joint contact forces and a complete set of muscle forces were calculated based on the geometry of the Standardised Femur using previously validated musculoskeletal models. Five boundary condition cases were applied to a finite element model of the Standardised Femur: (A) diaphyseally constrained with hip contact and abductor forces; (B) case A plus vasti forces; (C) case A with complete set of muscle forces; (D) distally constrained with all muscle forces; (E) physiological constraints with all muscle forces. It was seen that only the physiological boundary conditions, case E, produced physiological deflections (< 2.0mm) of the femoral head in both the coronal and sagittal planes, which resulted in minimal reaction forces at the constrained nodes. Strains in the mid-diaphysis varied by up to 600 micro-strain under walking loads and 1000 micro-strain under stair climbing loads. The mode of loading, as indicated by the strain profiles on the cortex also varied substantially under these boundary conditions, which has important consequences for studies that examine localised bone loading such as fracture or bone remodelling simulations.     

Three-dimensional finite element analysis of glass-ceramic dental crowns

Because of the improved esthetic potential of glass-ceramic crowns as dental restorations, they are sometimes preferred over metal-ceramic crowns for restoration of anterior teeth. Because of their relatively high strength, these ceramic crowns are also frequently used for restoration of posterior teeth. However, due to the larger magnitude of biting forces on posterior teeth, intraoral fracture of all-ceramic crowns tends to occur more frequently in posterior crowns (Moffa, 1988). The objective of this study was to determine the relative influence of load orientation and the occlusal thickness of posterior ceramic crowns on the stress distribution which develops under these loading and design conditions. Three-dimensional finite element models for a molar crown were developed to determine the stress distribution under simulated applied loads. Glass-ceramic crowns with occlusal thicknesses of 0.5, 1.5, and 3.0 mm were considered. The largest principal tensile stresses induced in ceramic due to a distributed load of 600 N applied in a cuspal region were approximately 12 and 182 MPa for vertical and horizontal loading orientations, respectively. Stresses which developed in the facial and lingual marginal regions were primarily compressive under vertical loads. However, tensile stresses developed when the load was applied horizontally. Differences in stress distribution within crowns with the three occlusal thicknesses occurred only near the site of loading. Because of the relatively large failure rates of ceramic crowns in the posterior regions, these restorations should be strengthened by improvement in design, composition, and thermal processing conditions. Before any significant progress is made in these areas, these restorations should be used for the anterior teeth. The results of this study suggest that orientation of the applied load has a more important effect on development of large tensile stresses than the occlusal thickness of ceramic.     

Finite element analysis of anterior tooth root stresses developed during endodontic treatment

Vertical tooth root fractures are diagnostically challenging, frustrating, and an increasingly common cause of failure of tooth restoration. These vertical root fractures have been associated with many causes, including the endodontic process itself. To investigate these endodontic causes, various phases of crown replacement for an anterior tooth were modeled using nonlinear, plane strain finite element (FE) analysis. Stresses developed during obturation, post positioning, crown placement, and masticatory and occlusal loading of the restored tooth were estimated using this analysis method. The minimum (compressive) principal stress was greatest during obturation of cones 1 and 2, and during mastication of the restored tooth. Although these stresses were significant (-150 to -280 MPa), they did not exceed the compressive strength of dentin. The maximum (tensile) principal stresses, 160 to 300 MPa, were also observed during obturation of cones 1 and 2. These peak stresses exceed the dentin tensile strength.     

Measuring the transverse Young’s modulus of maize rind and pith tissues

Wind-induced bending loads frequently cause failure of maize (corn) stalks. When failure occurs, it usually manifests as transverse buckling. Because this failure mode is closely related to transverse tissue stiffness, the purpose of this study was to develop a method for measuring the transverse Young’s modulus of maize stalk rind and pith tissues. Short, disc-shaped stalk segments were used for this purpose. X-ray computed tomography was used to obtain the geometry of each specimen prior to testing. Each specimen was tested in two different configurations. Computed tomography data was used to create a specimen-specific finite element model of each test specimen. Data from the first testing configuration was used in conjunction with the finite element model to determine the Young’s Modulus values for each specimen. The specimen-specific finite element models provided estimates of the stress states in the stem under transverse loading, and these stress states accurately predicted the location of failure in transverse test specimens. The entire testing method was validated using data from one test configuration to predict the structural response of each specimen during the second test configuration.     

Mechanical and failure properties of single attached cells under compression

Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7+/-2.5 microN at an axial strain of 72+/-4%. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force-deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo-Hookean constitutive model, excellent agreement between predicted and measured force-deformation curves was obtained, yielding an average Young's modulus of 1.14+/-0.32 kPa.     

Stress distribution and displacement analysis during an intermaxillary disjunction--a three-dimensional FEM study of a human skull

The goal of this study was to contribute to an understanding of how much expansion force is needed during a maxillary expansion (ME) and where bony reaction takes place. A finite element (FE) model of a dry human male skull was generated from CT scans. The FE model, which consists of cortical and cancellous bone and teeth, was loaded with the same force magnitudes, directions and working points as in rapid maxillary expansion (RME). A three-dimensional finite element stress analysis (FESA) of the forces and displacement was performed. The highest stress was observed in the maxilla in the region where the forces were applied, and spreads more or less throughout almost the whole frontal skull structures. The displacement distribution which causes stress in the skull is highly dependant on the thickness of the bone and its structure. All areas with high compressive and tensile stress are exactly the regions which determine the maximal amount of force to be used during the maxillary expansion and should be examined in case of any complication during a patient's treatment. Regions with significant compressive and tensile stress are the regions observed to have an increase in cellular activity. Further simulations with a given displacement (0.5mm) showed that displacement simulations need extra caution otherwise they will lead to very high forces which are not realistic in an orthodontic treatment.     

Biology meets engineering: The structural mechanics of fossil and extant shark teeth

The majority of studies on the evolution and function of feeding in sharks have focused primarily on the movement of cranial components and muscle function, with little integration of tooth properties or function. As teeth are subjected to sometimes extreme loads during feeding, they undergo stress, strain, and potential failure. As attributes related to structural strength such as material properties and overall shape may be subjected to natural selection, both prey processing ability and structural parameters must be considered to understand the evolution of shark teeth. In this study, finite element analysis was used to visualize stress distributions of fossil and extant shark teeth during puncture, unidirectional draw (cutting), and holding. Under the loading and boundary conditions here, which are consistent with bite forces of large sharks, shark teeth are structurally strong. Teeth loaded in puncture have localized stress concentrations at the cusp apex that diminish rapidly away from the apex. When loaded in draw and holding, the majority of the teeth show stress concentrations consistent with well designed cantilever beams. Notches result in stress concentration during draw and may serve as a weak point; however they are functionally important for cutting prey during lateral head shaking behavior. As shark teeth are replaced regularly, it is proposed that the frequency of tooth replacement in sharks is driven by tooth wear, not tooth failure. As the tooth tip and cutting edges are worn, the surface areas of these features increase, decreasing the amount of stress produced by the tooth. While this wear will not affect the general structural strength of the tooth, tooth replacement may also serve to keep ahead of damage caused by fatigue that may lead to eventual tooth failure. J. Morphol., 2011. © 2010 Wiley‐Liss, Inc.     

Mixed-mode loading of the cement-bone interface: a finite element study

While including the cement-bone interface of complete cemented hip reconstructions is crucial to correctly capture their response, its modelling is often overly simplified. In this study, the mechanical mixed-mode response of the cement-bone interface is investigated, taking into account the effects of the well-defined microstructure that characterises the interface. Computed tomography-based plain strain finite element analyses models of the cement-bone interface are built and loaded in multiple directions. Periodic boundaries are considered and the failure of the cement and bone fractions by cracking of the bulk components are included. The results compare favourably with experimental observations. Surprisingly, the analyses reveal that under shear loading no failure occurs and considerable normal compression is generated to prevent interface dilation. Reaction forces, crack patterns and stress fields provide more insight into the mixed-mode failure process. Moreover, the cement-bone interface analyses provide details which can serve as a basis for the development of a cohesive law.     

A micromechanically-based, three-dimensional interface finite element for the modelling of the periodontal ligament

Some ideas are presented for the implementation of an interface finite element capable to model in 3-dimensions several mechanical features of the periodontal ligament. Such an element is based on a simple 2-cable micromechanical model, able to reproduce the periodontal ligament stiffness and strength under any loading condition, including the pure torsion of a tooth. A single cable represents a sufficiently populated sample of collagen fibres, each with an initially crimped geometry; a single collagen fibre can provide a mechanical response, in tension, only when it is completely uncoiled. The macroscopic interface behaviour is obtained by statistical integrations over the uncoiled length of each collagen fibre, up to the fibre failure. Such a model can reproduce the periodontal ligament anisotropy due to the variable fibre orientation along the tooth root, its different behaviour in tension/compression/shear, its different behaviour for extrusive/intrusive loading, and so forth. Some numerical examples illustrate the potentialities of this interface element, quite simple in essence but rather complete from an engineering viewpoint.     

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.