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Stress wave effects in a finite element analysis of an impulsively loaded articular joint.

A dynamic contact finite element formulation was used to study transient stresses in the impulsively loaded rabbit knee, an established experimental model of mechanically induced osteoarthrosis. The computations were used to test the hypothesis that stress wave propagation and reflection, from juxtarticular interfaces of material property discontinuity, could be responsible for markedly increased levels of transient local cartilage stress. The finite element results demonstrated intuitively credible stress wave propagation and interfacial reflection phenomena. However, the magnitude of these waves was not nearly large enough to appreciably alter the quasi-static stress distributions otherwise prevailing. Thus, local stress wave reflection from interfaces of modulus discontinuity (for example the cartilage/subchondral plate) probably does not contribute appreciably to the heightened tissue sensitivity to impulsive loading experimentally observed in this animal model.

Animals↗

Finite element analysis of bioelectric phenomena.

This article reviews the application of finite element methods to models of bioelectric phenomena. The models represent the electrical fields created in the body as a result of membrane current sources or external current applied for diagnostic or therapeutic purposes. We formulate the governing equations for these models and then derive the finite element equations for the generalized bioelectric problem. The 32 papers reviewed here, all those appearing in the literature to date, cover the areas of electrocardiology, therapeutic and functional electrical stimulation in the cerebellum, cochlea, spinal cord, and peripheral nerves, cardiac defibrillation, electrical impedance tomography, bidomain cardiac models, electroporation, and therapeutic electrical stimulation of bone. For each, we summarize the purpose of the study, the model details and assumptions, the major results, and the applicability of the study. The models are then considered as a group to critique the appropriateness of the finite element method, the means of implementation, and the factors affecting accuracy, thus providing an overview of the state of finite element modeling of bioelectric phenomena.

Central Nervous System Diseases↗

Three-dimensional finite element analysis of stress-distribution around single tooth implants as a function of bony support, prosthesis type, and loading during function.

The elastic limit of bone surrounding implants may be surpassed and thus produce microfractures in bone. The purpose of this study was to use computer simulations to examine clinical situations with IMZ implants in edentulous mandibles and to identify loading conditions that could lead to bone microfractures. Three-dimensional finite element analysis models were used to examine effects of: (1) types of edentulous mandibles, (2) veneering materials, (3) the absence of cortical bone, (4) different intramobile elements, (5) loading directions, and (6) loading levels. Stress distribution patterns were compared and interfacial stresses were monitored specifically at four heights along the bone-implant interface. Stresses were concentrated toward cortical bone (0.8 to 15.0 MPa). There were no differences between types of veneering materials and the absence of cortical bone increased interfacial stresses. The use of a titanium intramobile element decreased stresses. Minor stress increases were associated with smaller mandibles. Oblique loads increased stresses 15 times, and 200 N loads increased stresses 10 times. Conditions for bone microfracturing were associated with oblique loads, high occlusal stress magnitudes, and the absence of cortical bone.

Bite Force↗

A perturbation method for predicting the temperature and stress sensitivities of quartz vibrating structures simulated by finite-element analysis.

Thermal and mechanical sensitivities of vibrating structures and wave guides are key parameters for the optimization of high stability resonant devices operating in the ultrasonic frequency range (from a few tenth of kilohertz to a few gigahertz). In this paper, the possibility to simulate and predict temperature coefficients of frequency (TCF) of quartz transducers of any shape as well as their stress sensitivity coefficients is addressed. The theoretical developments based on harmonic finite-element analysis coupled with a variational perturbation method are detailed, showing how to derive the regarded parameters. The proposed approach is validated using a two-dimensional (2-D) model of a plane face-bulk acoustic resonator for which an analytical model can give access to both TCF and stress sensitivity coefficients. It is then applied to a 2-D model of convex plane bulk acoustic resonator of singly rotated quartz and used to compute the first order TCF of a 3-D model of a tuning fork structure. In the latter case, the importance of considering the actual excitation of the device is demonstrated, allowing for the accurate definition of angular loci for which thermal compensation can be expected, in agreement with literature. Possible extensions and improvements of the proposed method is discussed in conclusion.

Journal Article↗

In-situ simulation of one-piece metacarpophalangeal joint implants using finite element analysis.

Generally, reconstruction of the rheumatoid metacarpophalangeal (MCP) joint is achieved by means of implantation of a hinged silastic prosthesis. Whereas these implants restore some degree of mobility to the joint, they are prone to failure after a relatively short life-span, and little is known about their dynamical behaviour within the joint. In this study, the Swanson and Sutter designs of MCP implant were examined in an idealized joint environment by means of two-dimensional finite element analysis. The purpose was to assess how the differing geometry affected their behaviour as replacement joints, and whether they were inherently prone to abrasion and high stress concentrations during flexion. The results revealed the changing points of contact between the implant and the bone ends, and clearly showed the implant stems 'pistoning' in the intramedullary canals. This was found to be an effective way to provide preliminary information on the dynamic behaviour of an implant in a simulated joint. This would facilitate further optimization of design in advance of fabrication.

Computer Simulation↗

Prediction of fatigue failure of a total knee replacement tibial plateau using finite element analysis.

Recent reports of total knee prosthesis fractures have raised concerns over the long-term structural integrity of metal-backed tibial components. Both the development of a fibrous tissue membrane under the tibial plateau of a total knee prosthesis and loading conditions may seriously alter the fatigue life of the metal tibial tray. The effects of the cement and fibrous tissue at the bone-prosthesis interface were studied. Using the method of three-dimensional finite element analysis, peak loads of normal gait were simulated at several locations on the plateau of a generic, single-stemmed, porous-coated, CoCrMo tibial component model, providing information on the effect of abnormal loading patterns. According to the analysis, stresses below the material endurance limit are predicted throughout the prosthesis prior to the development of the fibrous membrane. However, stresses exceeding the yield strength of the material are predicted in a prosthesis that is supported by a fully developed 1 mm membrane, meaning that it has a markedly increased risk of low-cycle fatigue failure. Lateral displacement of the loading is detrimental to prosthesis life because maximum stress increases 100% while posterior displacement of the loading increases maximum stress by only 30%. Anterior loading creates stresses similar to those created by central loading. Because of their susceptibility to low-cycle fatigue failure, simple, single-stemmed prostheses are not recommended in cases of questionable bone stock unless modified. Several design alternatives are proposed.

Bone Cements↗

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression.

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.

Biomechanical Phenomena↗

Adaptive silicon monochromators for high-power wigglers; design, finite-element analysis and laboratory tests.

Multipole wigglers in storage rings already produce X-ray power in the range up to a few kilowatts and planned devices at third-generation facilities promise up to 30 kW. Although the power density at the monochromator position is an order of magnitude lower than that from undulators, the thermal strain field in the beam footprint can still cause severe loss of performance in X-ray optical systems. For an optimized adaptive design, the results of finite-element analysis are compared with double-crystal rocking curves obtained with a laboratory X-ray source and, in a second paper [Quintana, Hart, Bilderback, Henderson, Richter, Setterson, White, Hausermann, Krumrey & Schulte-Schrepping (1995). J. Synchotron Rad. 2, 1-5], successful tests at wiggler sources at CHESS and ESRF and in an undulator source at HASYLAB are reported.

Journal Article↗

Force transmission of one- and two-piece morse-taper oral implants: a nonlinear finite element analysis.

PURPOSE: To compare force transmission behaviors of one-piece (1-P) and two-piece (2-P) morse-taper oral implants. MATERIAL AND METHODS: A three-dimensional finite element model of a morse-taper oral implant and a solid abutment was constructed separately. The implant-abutment complex was embedded in a phi 1.5 cm x 1.5 cm acrylic resin cylinder. Vertical and oblique forces of 50 N and 100 N were applied on the abutment and solved by two different analyses. First, contact analysis was performed in the implant-abutment complex to evaluate a 2-P implant. Then, the components were bonded with a separation force of 10(20) N to analyze a 1-P implant. RESULTS: Von Mises stresses in the implant, principal stresses, and displacements in the resin were the same for both designs under vertical loading. Under oblique loading, principal stresses and displacement values in the resin were the same, but the magnitudes of Von Mises stresses were higher in the 2-P implant. The principal stress distributions around both implants in the acrylic bone were similar under both loading conditions. CONCLUSION: 2-P implants experience higher mechanical stress under oblique loading. Nevertheless, the 1-P- or 2-P morse-taper nature of an implant is not a decisive factor for the magnitude and distribution of stresses, and displacements in supporting tissues.

Compressive Strength↗

Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques.

In this study, we investigate if finite element (FE) analyses of human trabecular bone architecture based on 168 microm images can provide relevant information about the bone mechanical characteristics. Three human trabecular bone samples, one taken from the femoral head, one from the iliac crest, and one from the lumbar spine, were imaged with micro-computed tomography (micro-CT) using a 28 microm resolution. After reconstruction the resolution was coarsened to 168 microm. First, all reconstructions were thresholded and directly converted to FE-models built of hexahedral elements. For the coarser resolutions of two samples, this resulted in a loss of trabecular connections and a subsequent loss of stiffness. To reduce this effect, a tetrahedral element meshing based on the marching cubes algorithm, as well as a modified hexahedron meshing, which thresholds the image such that load carrying bone mass is preserved, were employed. For each sample elastic moduli and tissue Von Mises stresses of the three different 168 microm models were compared to those from the hexahedron 28 microm model. For one sample the hexahedron meshing at 168 microm produced excellent results. For the other two samples the results obtained from the hexahedral models at 168 microm resolution were poor. Considerably better results were attained for these samples when using the mass-compensated or tetrahedron meshing techniques. We conclude that the accuracy of the FE-models at 168 microm strongly depends on the bone morphology, in particular its trabecular thickness. A substantial loss of trabecular connections during the hexahedron meshing process indicates that poor FE results will be obtained. In this case the tetrahedron or mass-compensated hexahedron meshing techniques can reduce the loss of connections and produce better results than the plain hexahedron meshing techniques.

Algorithms↗

Fatigue behavior of zirconia hip joint heads: experimental results and finite element analysis.

Crack propagation in a commercial surgical grade zirconia ceramic was performed under static and cyclic loading. The slow crack growth (SCG) parameters were determined in both cases. The results reveal the existence of threshold values of applied stress intensity factor, for both static and cyclic loadings, below which no slow crack growth occurs. Such threshold values represent one of the best advantages of the present zirconia ceramic compared with other ceramic materials used in orthopedics, which could lead to a strong enhancement of implant lifetime. This threshold value was also identified by cyclic fatigue tests performed on zirconia femoral heads. From a new statistical approach based on the Monte Carlo method, the knowledge of SCG behavior, and the help of finite element analysis, an estimate of the lifetime prediction has been made and discussed.

Biocompatible Materials↗

3-D Finite element analysis of all-ceramic posterior crowns.

The purpose of this study was to evaluate the stress distribution under various loading conditions within posterior all-ceramic crowns. A three-dimensional finite element model representing a lower first molar was constructed. Variations of the model had two types of single layer all-ceramic crowns (Dicor and Empress) and two types of double layer all-ceramic crowns (In-Ceram and Empress2) cemented. A load of 600 N, simulating the maximum bite force, was applied vertically to the crowns. Loads of 225 N, simulating masticatory force, were applied from three directions (vertically, at a 45 degrees angle, and horizontally). In the test simulating maximum bite force, the maximum tensile stresses on all crowns (17.4-19.4 MPa) concentrated around the loading points. In the masticatory force simulation test, the specimens experienced maximum tensile stresses of 19.7-27.0 MPa under a horizontal load and 10.8-10.9 MPa under a vertical load. When the load was applied horizontally, the maximum tensile stress was observed around the loading points on the surface in the case of the single layer crowns, and of the cervical area of the inner core of the double layer crowns. Within the limitation of this study, it was found that the strength of occlusal contact points is important to the integrity of posterior all-ceramic crowns and that bite forces applied from the horizontal direction are a critical factor.

Bite Force↗

Finite element analysis of indentation tests on pyrolytic carbon.

The stresses which cause failure at contact areas between leaflets and orifices in pyrolytic carbon heart valves are evaluated. These contact stresses have previously been studied using Hertzian crack models that apply to monolithic material. Many heart valves are not monolithic pyrolytic carbon but a pyrolytic carbon deposited on graphite. Contact loads on these layered structures cause initial cracking in the pyrolytic carbon at the interface between pyrolytic carbon and graphite rather than Hertzian surface cracks. Increasing the load on layered structures will cause a secondary cracking (of Hertzian cracks) on the surface. The contact loading was simulated with a 5.1 mm diameter ball pressing against a flat sample of graphite coated with 0.26 mm of pyrolytic carbon on each surface. Finite element analysis of this model calculated the stresses associated with a range of loads causing no cracks through initial interface cracks and secondary surface cracks to complete failure. The calculated stresses are correlated with parallel laboratory experiments. A failure criterion for contact stresses is developed. The initial cracks at the graphite/pyrolytic carbon interface occur when the tensile stress in the pyrolytic carbon reaches 207 to 276 MPa and the compression stress in the graphite reaches 414 to 483 MPa. These initial cracks do not propagate immediately to the surface since they run into a high triaxial compression stress field. Circular surface cracks occur at the edge of the ball/pyrolytic carbon contact area at higher loads. These cracks require a shear stress of about 241 MPa and also require a tensile stress component. The results provide a criterion for designing contact regions in pyrolytic heart valves.

Biocompatible Materials↗

Stochastic finite element analysis of biological systems: comparison of a simple intervertebral disc model with experimental results.

Statistical methods allow the effects of uncertainty to be incorporated into finite element models. This has potential benefits for the analysis of biological systems where natural variability can give rise to substantial uncertainty in both material and geometrical properties. In this study, a simple model of the intervertebral disc under compression was created and analysed as both a deterministic and a stochastic system. Factorial analysis was used to determine the important parameters to be included in the stochastic analysis. The predictions from the model were compared to experimental results from 21 sheep discs. The size and shape of the distribution of the axial deformations predicted by the model was consistent with the experimental results given that the number of model solutions far exceeded the number of experimental results. Stochastic models could be valuable in determining the range and most likely value of stress in a tissue or implant.

Animals↗

Effects of lumbar spinal fusion on the other lumbar intervertebral levels (three-dimensional finite element analysis).

The risk of accelerating the degeneration of adjacent disc levels after lumbar spinal fusion is a controversial issue. A finite element model consisting of L1 to L5 lumbar spines was used to assess the effect on adjacent disc level after lumbar spinal fusion. We compared intact, L4/5 posterior interbody fusion (PLF), and L4/5 posterior lumbar interbody fusion (PLIF) models. The loading conditions applied were compressive force, compressive force plus flexion moment, and compressive force plus extension moment. Evaluations were made for von Mises stress on each vertebral end-plate, Tresca stress of all the annulus fibrosus, and Tresca stress of the annulus fibrosus from the posterior surface of the disc to the neural foramen. As the result, the von Mises stress adjacent to the fusion level was higher than the other nonfusion levels; it was higher under conditions of flexion moment loading plus compression loading [112% (2.59 PMa) in the PLF model and 117% (2.72 Mpa) in the PLIF model] than in the intact model. The Tresca stress of all the annulus fibrosus adjacent to the fusion level was higher than that on other nonfusion intervertebral levels; it was higher under conditions of flexion moment loading plus compression loading [127% (0.57 PMa) in the PLF model and 209% (0.89 Mpa) in the PLIF model] than in the intact model. The Tresca stress of the annulus fibrosus from the posterior surface of the disc to the neural foramen adjacent to the fusion level was higher than that on other nonfusion intervertebral levels; and it was higher under conditions of flexion moment loading plus compression loading [107% (1.48 PMa) in the PLF model and 112% (1.54 Mpa) in the PLIF model] than in the intact model. These findings demonstrate that with lumbar fusion, stresses on the vertebral end-plate and the annulus fibrosus were high adjacent to the fusion level; furthermore, stresses were higher in the PLIF model than in the PLF model. These results suggested that lumbar spinal fusion might bring with it a risk of damage to the annulus fibrosus and the vertebral end-plate adjacent to the fusion level.

Compressive Strength↗

Acoustic-structural coupled finite element analysis for sound transmission in human ear--pressure distributions.

A three-dimensional (3D) finite element (FE) model of human ear with accurate structural geometry of the external ear canal, tympanic membrane (TM), ossicles, middle ear suspensory ligaments, and middle ear cavity has been recently reported by our group. In present study, this 3D FE model was modified to include acoustic-structural interfaces for coupled analysis from the ear canal through the TM to middle ear cavity. Pressure distributions in the canal and middle ear cavity at different frequencies were computed under input sound pressure applied at different locations in the canal. The spectral distributions of middle ear pressure at the oval window, round window, and medial site of the umbo were calculated and the results demonstrated that there was no significant difference of pressures between those locations at frequency below 3.5 kHz. Finally, the influence of TM perforation on pressure distributions in the canal and middle ear cavity was investigated for perforations in the inferior-posterior and inferior sites of the TM in the FE model and human temporal bones. The results show that variation of middle ear pressure is related to the perforation type and location, and is sensitive to frequency.

Acoustic Stimulation↗

Microdamage and osteocyte-lacuna strain in bone: a microstructural finite element analysis.

Damage accumulation in living tissues occurs when the rate of damage formation is greater than the rate of damage repair. For very large increases in the loading rate of bones, this can result in "stress fractures" due to the growth and coalescence of fatigue related microdamage. At lower increases of loading rates, the damage accumulation process is halted because there is time for adaptive bone-remodeling to occur in response to the new load. However, it is not known if there is a relationship between microdamage and bone remodeling per se. One hypothesis for the control of bone remodeling is that osteocytes sense strains and mediate osteoblastic and osteoclastic activity. The purpose of this study was to investigate whether damage generates strains which may trigger bone remodeling. If this were true, then accumulative damage would cause adaptive bone remodeling. This study applies the methods of finite element analysis to determine the effect of observed damage mechanisms on the proposed sensors of remodeling in Haversian bone. Individual lamellae are modeled and osteocyte-lacunae are included in a generalized plane strain geometric representation. It is predicted that microdamage alters the local deformation behavior around lacunae, and that the changes increase as microdamage accumulates. Hence, if damage accumulates in a bone, it could be sensed as a change in strain at a microstructural level. The results give theoretical support to the experimental studies that have shown a correlation between microdamage and the initiation of resorption as a first step in bone remodeling.

Bone Remodeling↗