Application of the u-p finite element method to the study of articular cartilage.

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.     

Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses

Organization of the collagen network is known to be different in healthy, osteoarthritic and repaired cartilage. The aim of the study was to investigate how the structure and properties of collagen network of cartilage modulate stresses in a knee joint with osteoarthritis or cartilage repair. Magnetic resonance imaging (MRI) at 1.5 T was conducted for a knee joint of a male subject. Articular cartilage and menisci in the knee joint were segmented, and a finite element mesh was constructed based on the two-dimensional section in sagittal projection. Then, the knee joint stresses were simulated under impact loads by implementing the structure and properties of healthy, osteoarthritic and repaired cartilage in the models. During the progression of osteoarthritis, characterized especially by the progressive increase in the collagen fibrillation from the superficial to the deeper layers, the stresses were reduced in the superficial zone of cartilage, while they were increased in and under menisci. Increased fibril network stiffness of repair tissue with randomly organized collagen fibril network reduced the peak stresses in the adjacent tissue and strains at the repair–adjacent cartilage interface. High collagen fibril strains were indicative of stress concentration areas in osteoarthritic and repaired cartilage. The collagen network orientation and stiffness controlled the stress distributions in healthy, osteoarthritic and repaired cartilage. The evaluation of articular cartilage function using clinical MRI and biomechanical modeling could enable noninvasive estimation of osteoarthritis progression and monitoring of cartilage repair. This study presents a step toward those goals.     

An approach for the stress analysis of transversely isotropic biphasic cartilage under impact load.

Stress analysis of contact models for isotropic articular cartilage under impacting loads shows high shear stresses at the interface with the subchondral bone and normal compressive stresses near the surface of the cartilage. These stress distributions are not consistent, with lesions observed on the cartilage surface of rabbit patellae from blunt impact, for example, to the patello-femoral joint. The purpose of the present study was to analyze, using the elastic capabilities of a finite element code, the stress distribution in more morphologically realistic transversely isotropic biphasic contact models of cartilage. The elastic properties of an incompressible material, equivalent to those of the transversely isotropic biphasic material at time zero, were derived algebraically using stress-strain relations. Results of the stress analysis showed the highest shear stresses on the surface of the solid skeleton of the cartilage and tensile stresses in the zone of contact. These results can help explain the mechanisms responsible for surface injuries observed during blunt insult experiments.     

Biomechanical assessment of tissue retrieved after in vivo cartilage defect repair: tensile modulus of repair tissue and integration with host cartilage

Failure to restore the mechanical properties of tissue at the repair site and its interface with host cartilage is a common problem in tissue engineering procedures to repair cartilage defects. Quantitative in vitro studies have helped elucidate mechanisms underlying processes leading to functional biomechanical changes. However, biomechanical assessment of tissue retrieved from in vivo studies of cartilage defect repair has been limited to compressive tests. Analysis of integration following in vivo repair has relied on qualitative histological methods. The objectives of this study were to develop a quantitative biomechanical method to assess (1) the tensile modulus of repair tissue and (2) its integration in vivo, as well as determine whether supplementation of transplanted chondrocytes with IGF-I affected these mechanical properties. Osteochondral blocks were obtained from a previous 8 month study on the effects of IGF-I on chondrocyte transplantation in the equine model. Tapered test specimens were prepared from osteochondral blocks containing the repair/native tissue interface and adjacently located blocks of intact native tissue. Specimens were then tested in uniaxial tension. The tensile modulus of repair tissue averaged 0.65 MPa, compared to the average of 5.2 MPa measured in intact control samples. Integration strength averaged 1.2 MPa, nearly half the failure strength of intact cartilage samples, 2.7 MPa. IGF-I treatment had no detectable effects on these mechanical properties. This represents the first quantitative biomechanical investigation of the tensile properties of repair tissue and its integration strength in an in vivo joint defect environment.     

Finite-element-analysis and experimental investigation in a femur with hip endoprosthesis

The stress distribution in a human femur with an endoprosthesis was determined. The finite element method (FEM) was used for a three-dimensional model with more than 15000 degrees of freedom. Geometrical and material data had been taken for this model from a left femur with endoprosthesis. On the contralateral bone a strain gauge investigation was performed to validate the calculations. Reasonable agreement was achieved. Various modes of loading were investigated. A perfect bond at the interface between materials of different elastic moduli was assumed. The results are valid for endoprosthesis with such structured stem surfaces as allow transfer of tensile and shear stresses.     

A collagen-based interface construct for the assessment of cell-dependent mechanical integration of tissue surfaces

The interface between any newly engineered tissue and pre-existing tissue is of great importance to tissue engineering; however, this process has so far been largely ignored, with few reports regarding the mechanical strength of newly integrated connective tissues surfaces. A new model system has been developed to generate a well-defined interface between two collagen lattices: one pre-contracted by resident fibroblasts and the other a cell-free wrapping gel. This construct can be cultured for prolonged periods (>2 weeks) and can also be fitted onto a mechanical testing system to measure the interface adhesive strength at the end of the culture time. Interface adhesive strength shows a six-fold increase after 1 week in culture, compared with the time-zero baseline. Observations of cell migration across the interface suggest that cell translocation in the three-dimensional matrix might play an important role in the integration process. In this new controlled geometry, normal and shear stresses at the interface can be analysed by finite element modelling and the areas at which debonding starts can be defined. The current experimental design permits solid multiple (homogeneous or heterogeneous) interface formation in vitro with a well-defined geometry and the possibility of measuring mechanical linkage. This design should enable many other factors affecting cell-driven interface strengthening to be investigated. This study was supported by the Fifth Framework Programme of the European Commission, “Biomechanical Interactions in Tissue Engineering and Surgical Repair (BITES)”.     

Contact models of repaired articular surfaces: influence of loading conditions and the superficial tangential zone

The superficial tangential zone (STZ) plays a significant role in normal articular cartilage’s ability to support loads and retain fluids. To date, tissue engineering efforts have not replicated normal STZ function in cartilage repairs. This finite element study examined the STZ’s role in normal and repaired articular surfaces under different contact conditions. Contact area and pressure distributions were allowed to change with time, tension-compression nonlinearity modeled collagen behavior in the STZ, and nonlinear geometry was incorporated to accommodate finite deformation. Responses to loading via impermeable and permeable rigid surfaces were compared to loading via normal cartilage, a more physiologic condition, anticipating the two rigid loading surfaces would bracket that of normal. For models loaded by normal cartilage, an STZ placed over the inferior repair region reduced the short-term axial compression of the articular surface by 15%, when compared to a repair without an STZ. Covering the repair with a normal STZ shifted the flow patterns and strain levels back toward that of normal cartilage. Additionally, reductions in von Mises stress (21%) and an increase in fluid pressure (13%) occurred in repair tissue under the STZ. This continues to show that STZ properties of sufficient quality are likely critical for the survival of transplanted constructs in vivo. However, response to loading via normal cartilage did not always fall within ranges predicted by the rigid surfaces. Use of more physiologic contact models is recommended for more accurate investigations into properties critical to the success of repair tissues.     

A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading

Bone has a capability to repair itself when it is fractured. Repair involves the generation of intermediate tissues, such as fibrous connective tissue, cartilage and woven bone, before final bone healing can occur. The intermediate tissues serve to stabilise the mechanical environment and provide a scaffold for differentiation of new tissues. The repair process is fundamentally affected by mechanical loading and by the geometric configuration of the fracture fragments. Biomechanical analyses of fracture healing have previously computed the stress distribution within the callus and identified the components of the stress tensor favouring or inhibiting differentiation of particular tissue phenotypes. In this paper, a biphasic poroelastic finite element model of a fracture callus is used to simulate the time-course of tissue differentiation during fracture healing. The simulation begins with granulation tissue (post-inflammation phase) and finishes with bone resorption. The biomechanical regulatory model assumes that tissue differentiation is controlled by a combination of shear strain and fluid flow acting within the tissue. High shear strain and fluid flows are assumed to deform the precursor cells stimulating formation of fibrous connective tissue, lower levels stimulate formation of cartilage, and lower again allows ossification. This mechano-regulatory scheme was tested by simulating healing in fractures with different gap sizes and loading magnitudes. The appearance and disappearance of the various tissues found in a callus was similar to histological observation. The effect of gap size and loading magnitude on the rate of reduction of the interfragmentary strain was sufficiently close to confirm the hypothesis that tissue differentiation phenomena could be governed by the proposed mechano-regulation model.     

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.     

Finite element simulations of a focal knee resurfacing implant applied to localized cartilage defects in a sheep model

Articular resurfacing metal implants have recently been tested in animal models to treat full thickness localized articular cartilage defects, showing promising results. However, the mechanical behavior of cartilage surrounding the metal implant has not been studied yet as it is technically challenging to measure in vivo contact areas, pressures, stresses and deformations from the metal implant. Therefore, we implemented a detailed numerical finite element model by approximating one of the condyles of the sheep tibiofemoral joint and created a defect of specific size to accommodate the implant. Using this model, the mechanical behavior of the surrounding of metal implant was studied. The model showed that the metal implant plays a significant role in the force transmission. Two types of profiles were investigated for metal implant. An implant with a double-curved profile, i.e., a profile fully congruent with the articular surfaces in the knee, gives lower contact pressures and stresses at the rim of the defect than the implant with unicurved spherical profile. The implant should be placed at a certain distance into the cartilage to avoid damage to opposing biological surface. Too deep positions, however, lead to high shear stresses in the cartilage edges around the implant. Mechanical sealing was achieved with a wedge shape of the implant, also useful for biochemical sealing of cartilage edges at the defect.     

Influence of aspect ratios on the creep behaviour of articular cartilage in indentation

Indentation tests are commonly used to determine the mechanical behaviour of articular cartilage with varying properties, thickness, and geometry. This investigation evaluated the effect of changing geometric parameters on the properties determined from creep indentation tests. Finite element analyses simulated the indentation behaviour of two models, an excised cylindrical specimen of cartilage with either normal and repair qualities and an osteochondral defect represented as a cylindrical region of repair cartilage integrated with a surrounding layer of normal tissue. For each model, the ratios of indenter radius to cartilage height (a/h=0.5,1.5) and cartilage radius to indenter radius (r/a=2,5) were varied. The vertical displacement of the cartilage under the indenter obtained through finite element analysis was fitted to a numerical algorithm to determine the aggregate modulus, permeability, and Poisson's ratio. Indentation behaviours of cartilage specimens for either model with a/h=1.5 were not affected by r/a for values of 2 and 5. Aggregate modulus was not greatly affected by the geometric changes studied. Permeability was affected by changes in the ratio of specimen to indenter radii for a/h=0.5. These findings suggest that experimental configurations of excised cylindrical specimens, also representing osteochondral defects with no or unknown degree of integration, where the cartilage layer has a/h=0.5 should not have r/a values on the order of 2 for confidence in the mechanical properties determined. Indentation of osteochondral defects where the repair cartilage is fully integrated to the surrounding cartilage can be performed with confidence for all cases tested.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

Effect of repeated microwave disinfections on bonding of different commercial teeth to resin denture base

doi: 10.1111/j.1741‐2358.2011.00516.x Effect of repeated microwave disinfections on bonding of different commercial teeth to resin denture base Objective: To verify the influence of repeated microwave disinfections on the shear bond strength of two commercial types of teeth to acrylic resin, when the ridge lap surfaces were unmodified, bur abraded, bur grooved or etched by monomer. Material and methods: Eighty specimens (n = 10) were adhered to the tooth ridge lap surface, polymerised in a water bath at 74°C for 9 h. Microwaved specimens were individually immersed in 150 ml of water and submitted to five simulated disinfections in a microwave oven calibrated at 650 W for 3 min. Control specimens were not microwave treated. Shear bond strength tests were performed in an Instron machine with a cross‐speed of 1 mm/min. The fracture load values were transformed into shear bond strength as a function of the bonding area (0.28 cm²). Data were submitted to anova and Tukey’s test (α = 0.05). Fractured areas were classified as adhesive, cohesive (resin or tooth) or mixed failures. Results: Repeated microwave disinfections increased the shear strength of the tooth/resin bond. Mechanical retention in microwaved and non‐microwaved procedures improved the shear bond strength. Conclusions: The different commercial types of teeth influenced shear bond strength values, with Biotone teeth showing the lower values.     

Finite element estimates of interface stress in the trans-tibial prosthesis using gap elements are different from those using automated contact

When compared with automated contact methods of finite element (FE) analyses, gap elements have certain inherent disadvantages in simulating large slip of compliant materials on stiff surfaces. However, automated contact has found limited use in the biomechanical literature. A non-linear, three-dimensional, geometrically accurate, FE analysis of the trans-tibial limb-socket prosthetic system was used to compare an automated contact interface model with a gap element model, and to evaluate the sensitivity of automated contact to interfacial coefficient of friction (COF). Peak normal stresses and resultant shear stresses were higher in the gap element model than in the automated contact model, while the maximum axial slip was less. Under proximally directed load, compared with automated contact, gap elements predicted larger areas of stress concentration that were located more distally. Gap elements did not predict any relative slip at the distal end, and also transmitted a larger proportion of axial load as shear stress. Both models demonstrated non -linear sensitivity to COF, with larger variation at lower magnitudes of COF. By imposing physical connections between interface surfaces, gap elements distort the interface stress distributions under large slip. Automated contact methods offer an attractive alternative in applications such as prosthetic FE modeling, where the initial position of the limb in the socket is not known, where local geometric features have high design significance, and where large slip occurs under load.     

A dynamic finite element analysis of impulsive loading of the extension-splinted rabbit knee

A dynamic nonlinear finite element model was developed to study juxtarticular stresses in the splinted rabbit knee, an established laboratory model for creating osteoarthrosis due to impulsive loading. Plane strain finite element results were validated by comparison with corresponding experimental data. Parametric effects studied included the input tibial displacement speed, the local bone density distribution, and the modulus of cartilage and subchondral bone. While the computed resultant contact force magnitude was sensitive to a number of model parameters, the stress patterns, when normalized to a given resultant force magnitude, were not. Despite comparable force peaks, the finite element results showed approximately six-fold higher effective strain rate levels for a severely impulsive loading protocol known to induce rapid osteoarthrosis, versus those for a mildly impulsive loading protocol not usually associated with cartilage damage. A propensity for elevated shear in the deep cartilage layer near the contact periphery, observed in nearly all computed stress distributions, is consistent with previous experimental findings of fissuring at that level in the impulsively loaded rabbit knee.     

Finite element stress analysis of a push-out test. Part 1: Fixed interface using stress compatible elements.

In this first part of a two-part paper, interelement stress compatible finite elements are developed and used to perform the stress analysis of a push-out test with a fixed interface. In the formulation, the required continuity of some of the stresses along either a specific interface or all interelement interfaces is enforced by a penalty procedure. The model is axisymmetric and consists of two cylinders attached to each other through the interface. Various relative material properties and boundary conditions are simulated in order to examine their effects on the interface stresses. Both loadings of axial compression force and axial torque are considered. The predicted results exhibit identical interelement stresses and displacements even when highly dissimilar materials are used. They also exhibit a complex state of interface stresses which depend on the geometry, material arrangement, boundary conditions, and loading. The variation of the shear stress is often highly nonuniform and the radial normal stresses are likely to be large. The present results, therefore, disagree with the common assumptions made in the pull-out tests in the orthopaedic applications. Finally, stress analysis of a number of possible testing configurations could lead to the design of an optimal pull-out test which maximizes the usefulness of the measured results in terms of the interface bond strength and factors affecting it.     

Structural characterization and reliable biomechanical assessment of integrative cartilage repair

Structural and functional characterization of integrative cartilage repair in controlled model systems can play a key role in the development of innovative strategies to improve the long-term outcome of many cartilage repair procedures. In this work, we first developed a method to reproducibly generate geometrically defined disk/ring cartilage composites and to remove outgrown fibrous layers which can encapsulate cartilaginous tissues during culture. We then used the model system to test the hypothesis that such fibrous layers lead to an overestimation of biomechanical parameters of integration at the disk/ring interface. Transmission electron microscopy images of the composites after 6 weeks of culture indicated that collagen fibrils in the fibrous tissue layer were well integrated into the collagen network of the cartilage disk and ring, whereas molecular bridging between opposing disk/ring cartilage surfaces was less pronounced and restricted to regions with narrow interfacial regions (< 2 microm). Stress-strain profiles generated from mechanical push-out tests for composites with the layers removed displayed a single and distinct peak, whereas profiles for composites with the layers left intact consisted of multiple superimposed peaks. As compared to composites with removed layers, composites with intact layers had significantly higher adhesive strengths (161+/-9 vs. 71+/-11 kPa) and adhesion energies (15.0+/-0.7 vs. 2.7+/-0.4 mJ/mm2). By combining structural and functional analyses, we demonstrated that the outgrowing tissue formed during in vitro culture of cartilaginous specimens should be eliminated in order to reliably quantify biomechanical parameters related to integrative cartilage repair.     

The effects of different articulate curvature of artificial disc on loading distribution

Purpose: Deeper insights into the mechanical behavior of lumbar disc prostheses are required. Prior studies on the biomechanical performance of artificial discs were mostly performed with finite element analyses, but this has never been analyzed with altering articulate curvature. This study aimed to ascertain the influence of the geometry of a ball-and-socket disc prosthesis for the lumbar spine. Materials and Methods: Three-dimensional finite element model of human L4-L5 was reconstructed. Convex, concave, and elliptic artificial disc models were also established with Computer-Aided-Design software. Simulations included: (1) three articulate types of polyethylene (PE) insert were implanted inferiorly and (2) concave and convex PE inserts were implanted on the superior or inferior sides in flexion/extension, lateral bending, and axial rotation in the lumbar spine. Shear stresses and von Mises stresses on PE insert were assessed for their loading distributions. Results: High shear stresses of all articulate types occurred in flexion, and convex PE insert performed the maximum stress of 23.81 MPa. Under all conditions, stresses on concave PE inserts were distributed more evenly and lower than those on the convex type. Elliptic geometry enabled confining the rotation of the motion unit. The shear force on the convex PE insert on the inferior side could induce transverse crack because the shear stress exceeded yielding shear stress. Conclusions: The concave PE insert on the inferior side not only decreased loading concentration but had relatively low stress. Such a design may be applicable for artificial discs.     

Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing

A new quantitative tissue differentiation theory which relates the local tissue formation in a fracture gap to the local stress and strain is presented. Our hypothesis proposes that the amounts of strain and hydrostatic pressure along existing calcified surfaces in the fracture callus determine the differentiation of the callus tissue. The study compares the local strains and stresses in the callus as calculated from a finite element model with histological findings from an animal fracture model. The hypothesis predicts intramembranous bone formation for strains smaller approximately +/- 5% and hydrostatic pressures smaller than +/- 0.15 MPa. Endochondral ossification is associated with compressive pressures larger than about -0.15 MPa and strains smaller than +/- 15%. All other conditions seemed to lead to connective tissue or fibrous cartilage. The hypothesis enables a better understanding of the complex tissue differentiation seen in histological images and the mechanical conditions for healing delayed healing or nonunions.     

Various Effects of Sandblasting of Dental Restorative Materials

Background

Sandblasting particles which remain on the surfaces of dental restorations are removed prior to cementation. It is probable that adhesive strength between luting material and sandblasting particle remnants might exceed that with restorative material. If that being the case, blasting particles adhere to sandblasted material surface could be instrumental to increasing adhesive strength like underlying bonding mechanism between luting material and silanized particles of tribochemical silica coating-treated surface. We hypothesize that ultrasonic cleaning of bonding surfaces, which were pretreated with sandblasting, may affect adhesive strength of a resin luting material to dental restorative materials.

Methods

We therefore observed adhesive strength of resin luting material to aluminum oxide was greater than those to zirconia ceramic and cobalt-chromium alloy beforehand. To measure the shear bond strengths of resin luting material to zirconia ceramic and cobalt-chromium alloy, forty specimens of each restorative material were prepared. Bonding surfaces were polished with silicon abrasive paper and then treated with sandblasting. For each restorative material, 40 sandblasted specimens were equally divided into two groups: ultrasonic cleaning (USC) group and non-ultrasonic cleaning (NUSC) group. After resin luting material was polymerized on bonding surface, shear test was performed to evaluate effect of ultrasonic cleaning of bonding surfaces pretreated with sandblasting on bond strength.

Results

For both zirconia ceramic and cobalt-chromium alloy, NUSC group showed significantly higher shear bond strength than USC group.

Conclusions

Ultrasonic cleaning of dental restorations after sandblasting should be avoided to retain improved bonding between these materials.