Some effects of global joint morphology on local stress aberrations near imprecisely reduced intra-articular fractures

Cadaver models of contact pressure aberration near displaced intra-articular fractures complement clinical experience, but inter-specimen variability often complicates interpretation of in vitro data. A contact finite element formulation is here used to study juxta-articular stress distributions in a plane strain model of tibial plateau step-off incongruity. Attention is focused on the influence of global morphologic parameters: intact joint surface curvatures, cartilage thickness, and cartilage stiffness. The computed stress distributions agreed well with experimental recordings for a typical 3 mm incongruity in an otherwise normal joint. Both decreased cartilage thickness and increased cartilage modulus led to elevations in the peak local contact stress, and to concentration of contact stress near the edge of the step-off incongruity. Similar effects were seen when reduction of global joint congruency was modelled by decreasing the concavity of the tibial plateau. While the observed degree of coupling between global morphology and local stress aberration was by no means negligible, the sensitivity of the stresses to variations in individual parameters was relatively mild. This suggests that the finite element results will be useful for experimental data interpretation.     

Computational and Experimental Study of Performance of an Artificial Ligament: DacronTM yarn

The success rate of reconstructing the Anterior Cruciate Ligament (ACL) with prosthetic ligaments is currently low both in humans and animals. The stress distribution in prosthetic ligaments that causes failure is very complex and not yet understood. Therefore, we have begun to develop a Finite Element Model of a prosthetic ACL. Here we describe the normal and contact stresses in Dacron(TM) yarn (a multi-fibrillar structure) using input data based on experimental measurements of the load and strain of six designed yarns. The results show that the normal and contact stresses in the fibres of the ACL yarn are directly proportional to the yarn strains. Increasing the twisting length (transverse deformation) of the yarn increases the normal stress in the fibres and the yarn modulus, but decreases the contact stresses between the fibres. The structural properties of a yarn are dependent on the specific arrangement of various filament types. Increasing the distance between the longitudinal (symmetry) axes of the filaments and the axis of symmetry of the yarn decreases the stresses.     

Computational and Experimental Study of Performance of an Artificial Ligament: DacronTM yarn

Abstract

The success rate of reconstructing the Anterior Cruciate Ligament (ACL) with prosthetic ligaments is currently low both in humans and animals. The stress distribution in prosthetic ligaments that causes failure is very complex and not yet understood. Therefore, we have begun to develop a Finite Element Model of a prosthetic ACL. Here we describe the normal and contact stresses in Dacron^TM yarn (a multi-fibrillar structure) using input data based on experimental measurements of the load and strain of six designed yarns.

The results show that the normal and contact stresses in the fibres of the ACL yarn are directly proportional to the yam strains. Increasing the twisting length (transverse deformation) of the yarn increases the normal stress in the fibres and the yarn modulus, but decreases the contact stresses between the fibres. The structural properties of a yarn are dependent on the specific arrangement of various filament types. Increasing the distance between the longitudinal (symmetry) axes of the filaments and the axis of symmetry of the yarn decreases the stresses.     

A finite element exploration of cartilage stress near an articular incongruity during unstable motion

Both instability and residual articular incongruity are implicated in the development of post-traumatic osteoarthritis (OA) following intra-articular fracture, but currently no information exists regarding cartilage stresses for unstable residual incongruities. In this study, a transversely isotropic poroelastic cartilage finite element model was implemented and validated within physiologically relevant loading ranges. This material model was then used to simulate the loading of cartilage during stable and unstable motion accompanying a step-off incongruity residual from intra-articular fracture, using load data from previous cadaver tests of ankle instability. Peak solid-phase stresses and fluid pressure were found to increase markedly in the presence of instability. Solid-phase transients of normal stress increased from 2.00 to 13.8 MPa/s for stable compared to unstable motion, and tangential stress transients increased from 17.1 to 118.1 MPa/s. Corresponding fluid pressure transients increased from 15.1 to 117.9 MPa/s for unstable motion. In the most rapidly loaded sections of cartilage, the fluid was found to carry nearly all of the normal load, with the pressurization of the fluid resulting in high solid matrix tangential stresses.     

Joint contact stresses calculated for acetabular dysplasia patients using discrete element analysis are significantly influenced by the applied gait pattern

Gait modifications in acetabular dysplasia patients may influence cartilage contact stress patterns within the hip joint, with serious implications for clinical outcomes and the risk of developing osteoarthritis. The objective of this study was to understand how the gait pattern used to load computational models of dysplastic hips influences computed joint mechanics. Three-dimensional pre- and post-operative hip models of thirty patients previously treated for hip dysplasia with periacetabular osteotomy (PAO) were developed for performing discrete element analysis (DEA). Using DEA, contact stress patterns were calculated for each pre- and post-operative hip model when loaded with an instrumented total hip, a dysplastic, a matched control, and a normal gait pattern. DEA models loaded with the dysplastic and matched control gait patterns had significantly higher (p = 0.012 and p < 0.001) average pre-operative maximum contact stress than models loaded with the normal gait. Models loaded with the dysplastic and matched control gait patterns had nearly significantly higher (p = 0.051) and significantly higher (p = 0.008) average pre-operative contact stress, respectively, than models loaded with the instrumented hip gait. Following PAO, the average maximum contact stress for DEA models loaded with the dysplastic and matched control patterns decreased, which was significantly different (p < 0.001) from observed increases in maximum contact stress calculated when utilizing the instrumented hip and normal gait patterns. The correlation between change in DEA-computed maximum contact stress and the change in radiographic measurements of lateral center-edge angle were greatest (R² = 0.330) when utilizing the dysplastic gait pattern. These results indicate that utilizing a dysplastic gait pattern to load DEA models may be a crucial element to capturing contact stress patterns most representative of this patient population.     

Assessment of the effect of mesh density on the material property discretisation within QCT based FE models: a practical example using the implanted proximal tibia

A three-dimensional, quantitative computed tomography based finite element model of a proximal implanted tibia was analysed in order to assess the effect of mesh density on material property discretisation and the resulting influence on the predicted stress distribution. The mesh was refined on the contact surfaces (matched meshes) with element sizes of 3, 2, 1.4, 1 and 0.8 mm. The same loading conditions were used in all models (bi-condylar load: 60% medial, 40% lateral). Significant variations were observed in the modulus distributions between the coarsest and finest mesh densities. Poor discretisation of the material properties also resulted in poor correlations of the stresses and risk ratios between the coarsest and finest meshes. Little difference in Young's modulus, von Mises stress and risk ratio distributions were observed between the three finest models; hence, it was concluded that for this particular case an element size of 1.4 mm on the contact surfaces was enough to properly describe the stiffness, stress and risk ratio distributions within the bone. Poor convergence of the material property distribution occurred when the element size was significantly larger than the pixel size of the source CT data. It was concluded that unless there is convergence in the Young's modulus distribution, convergence of the stress field or of other parameters of interest will not occur either.     

Assessment of the Effect of Mesh Density on the Material Property Discretisation Within QCT Based FE Models: A Practical Example Using the Implanted Proximal Tibia

A three-dimensional, quantitative computed tomography based finite element model of a proximal implanted tibia was analysed in order to assess the effect of mesh density on material property discretisation and the resulting influence on the predicted stress distribution. The mesh was refined on the contact surfaces (matched meshes) with element sizes of 3, 2, 1.4, 1 and 0.8 mm. The same loading conditions were used in all models (bi-condylar load: 60% medial, 40% lateral). Significant variations were observed in the modulus distributions between the coarsest and finest mesh densities. Poor discretisation of the material properties also resulted in poor correlations of the stresses and risk ratios between the coarsest and finest meshes. Little difference in Young's modulus, von Mises stress and risk ratio distributions were observed between the three finest models; hence, it was concluded that for this particular case an element size of 1.4 mm on the contact surfaces was enough to properly describe the stiffness, stress and risk ratio distributions within the bone. Poor convergence of the material property distribution occurred when the element size was significantly larger than the pixel size of the source CT data. It was concluded that unless there is convergence in the Young's modulus distribution, convergence of the stress field or of other parameters of interest will not occur either.     

Morphological and numerical studies of the stress compatibility of patella implants]

Failure of total knee arthroplasty is relatively often caused by problems of the patellofemoral replacement. The purpose of this study was to analyze the distribution of stresses within an anatomical patella and the changes in stress distribution after patellar resurfacing with a Miller-Galante I patellar implant using two- and three dimensional finite element models (FEM). To assess validity, FEM results were compared with morphological findings from contact radiographs and densitographs. Internal orientation of bone trabeculae is in good agreement with the orientation of theoretically calculated principal stresses. Almost unchanged principal tensile stresses after implantation, together with the lack of extreme stress peaks within the cancellous bone ensure stress compatibility of the implant. In the case of a firmly seated implant with good bone ingrowth, increased von Mises stresses are found near the fixation peg/plate junction. Their relevance for improved bone ingrowth near this part of the interface is emphasized. At the same time, material failure at the peg/plate junction can be better understood. An analysis of the early postoperative period assuming nonlinear interface conditions failed to demonstrate an uniform distribution of normal and tangential interface forces.     

Hip contact stress during normal and staircase walking: the influence of acetabular anteversion angle and lateral coverage of the acetabulum

Hip contact stress is considered to be an important biomechanical factor related to development of coxarthrosis. The effect of the lateral coverage of the acetabulum on the hip contact stress has been demonstrated in several studies of hip dysplasia, whereas the effect of the anterior anteversion remains unclear. Therefore, the joint hip contact stress during normal level walking and staircase walking, in normal and dysplastic hips, for small and large acetabular anteversion angle was computed. For small acetabular anteversion angle, the hip contact stress is slightly increased (less than 15%) in staircase walking when compared with normal walking. In hips with large angle of acetabular anteversion, walking downstairs significantly increases the maximal peak contact stress (70% in normal hips and 115% in dysplastic hips) whereas walking upstairs decreases the peak contact stress (4% in normal hips and 34% in dysplastic hips) in comparison to normal walking. Based on the presented results, we suggest that the acetabular anteversion should be considered in biomechanical evaluation of the hips, especially when the lateral coverage of the acetabulum is small.     

An analytical model of joint contact

The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.     

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.     

Tibiofemoral joint contact force in deep knee flexion and its consideration in knee osteoarthritis and joint replacement

The aim of the study was to estimate the tibiofemoral joint force in deep flexion to consider how the mechanical load affects the knee. We hypothesize that the joint force should not become sufficiently large to damage the joint under normal contact area, but should become deleterious to the joint under the limited contact area. Sixteen healthy knees were analyzed using a motion capture system, a force plate, a surface electromyography, and a knee model, and then tibiofemoral joint contact forces were calculated. Also, a contact stress simulation using the contact areas from the literature was performed. The peak joint contact forces (M +/- SD) were 4566 +/- 1932 N at 140 degrees in rising from full squat and 4479 +/- 1478 N at 90 degrees in rising from kneeling. Under normal contact area, the tibiofemoral contact stresses in deep flexion were less than 5 MPa and did not exceed the stress to damage the cartilage. The contact stress simulation suggests that knee prosthesis having the contact area smaller than 200 mm2 may be problematic since the contact stress in deep flexion would become larger than 21 MPa, and it would lead damage or wear of the polyethylene.     

Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis

Magnetic resonance (MR) imaging has been widely used to evaluate the thickness and volume of articular cartilage both in vivo and in vitro. While morphological information on the cartilage can be obtained using MR images, image processing for extracting geometric boundaries of the cartilage may introduce variations in the thickness of the cartilage. To evaluate the variability of using MR images to construct finite element (FE) knee cartilage models, five investigators independently digitized the same set of MR images of a human knee. The topology of cartilage thickness was determined using a minimal distance algorithm. Less than 8 percent variation in cartilage thickness was observed from the digitized data. The effect of changes in cartilage thickness on contact stress analysis was then investigated using five FE models of the knee. One FE model (average FE model) was constructed using the mean values of the digitized contours of the cartilage, and the other four were constructed by varying the thickness of the average FE model by +/- 5 percent and +/- 10 percent, respectively. The results demonstrated that under axial tibial compressive loading (up to 1,400 N), variations of cartilage thickness caused by digitization of MR images may result in a difference of approximately 10 percent in peak contact stresses (surface pressure, von Mises stress, and hydrostatic pressure) in the cartilage. A reduction of cartilage thickness caused increases of contact stresses, while an increase of cartilage thickness reduced contact stresses. Furthermore, the effect of variation of material properties of the cartilage on contact stress analysis was investigated. The peak contact stress increased almost linearly with the Young's modulus of the cartilage. The peak von Mises stress was dramatically reduced when the Poisson,s ratio was increased from 0.05 to 0.49 under an axial compressive load of 1,400 N, while peak hydrostatic pressure was dramatically increased. Peak surface pressure was also increased with the Poisson's ratio, but with a lower magnitude compared to von Mises stress and hydrostatic pressure. In conclusion, the imaging process may cause 10 percent variations in peak contact stress, and the predicted stress distribution is sensitive to the accuracy of the material properties of the cartilage model, especially to the variation of Poisson's ratio.     

Finite-element modelling of femoral shaft fracture fixation techniques post total hip arthroplasty.

The presence of a femoral prosthesis superior to a shaft fracture severely complicates fixation and treatment. This study uses two-dimensional, multithickness, plane stress finite-element models of a femur with prosthesis to investigate the stresses developed with the application of three popular fixation techniques: revision to a long stem prosthesis, lateral plating with a cortical bone allograft strut and cerclage wires, and custom plate application with proximal Parham band fixation with distal cortical screws (Ogden plate). The plate and bone contact as well as the fracture site contact were modelled by using orthotropic elements with custom-fit moduli so that only the normal stress to the interface was significant. A thermal analogy was used to model the cerclage and Parham band preloads so that representative preloads in the proximal fixation of the two types of plate treatments could be modelled. A parametric study was performed with the long-prosthesis model to show variations in stem lengths of one, two and three femoral diameters distal to the fracture site. The Ogden plate model showed a transfer of tensile stress near the proximal-most band, with the highest tensile stress being at the fracture site with evidence of stress shielding of the proximal lateral cortex. The cortical bone strut model showed a transfer of tensile stress to the bone strut but showed less shielding of the proximal cortex. The cerclage wires at the base of the bone strut showed the highest changes in load with the distalmost wire increasing to almost four times its original preload.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

One-legged stance as a representative static body position for calculation of hip contact stress distribution in clinical studies

It was shown in several clinical studies that static one-legged stance may be a relevant body position to describe the loads acting at the hip. However, the stress distribution averaged during movement may better describe hip load than hip contact stress distribution in the static body position. Using data on the resultant hip force during walking taken from the measurements of Bergmann (2001), spatial distribution of contact stress over the articular surface was calculated by the HIPSTRESS method and compared with the stress distribution in one-legged stance. It is shown, that the shape of the contact stress distribution during one-legged stance closely resembled the averaged contact stress distribution during the walking cycle (Pearson's correlation coefficient R2 equals; .986; p < .001). This finding presents a link between the hypothesis that the averaged contact stress distribution during a walking cycle is crucial for cartilage development and the results of clinical studies in which the calculated distribution of contact stress in one-legged stance was successfully used to predict the clinical status of the hip.     

Contact stress transients during functional loading of ankle stepoff incongruities

Cartilage deformation demonstrates viscoelastic behavior due to its unique structure. However, nearly all contact studies investigating incongruity-associated changes in cartilage surface stresses have been static tests. These tests have consistently measured only modest increases in contact stresses, even with large incongruities. In this study, an experimental approach measuring real-time contact stresses in human cadaveric ankles during quasi-physiologic motion and loading was used to determine how stepoff incongruities of the distal tibia affected contact stresses and contact stress gradients. Peak instantaneous contact stresses, in ankles with stepoffs between 1.0 and 4.0mm of the anterolateral articular surface, increased by between 2.3 x and 3.0 x compared to the corresponding intact ankle values. Peak instantaneous contact stress gradients in stepoff configurations increased by between 1.9 x and 2.6 x the corresponding intact configuration values. Anatomic reduction of the displaced fragment restored intact contact stresses and contact stress gradients. Intact and anatomic configurations demonstrated a heterogeneous population of low-magnitude, randomly oriented contact stress gradient vectors in contrast to high-magnitude, preferentially oriented gradients in stepoff configurations. Peak instantaneous contact stresses may be important pathomechanical determinants of post-traumatic arthritis. Abnormal contact stress gradients could cause regional pathological disturbances in cartilage stress and interstitial fluid distribution. Measuring contact stresses and contact stress gradients during motion allowed potential incongruity-associated pathologic changes in loading that occur over the complete motion cycle to be investigated.     

Stress analysis of the proximo-medial femur after total hip replacement

Stress-induced bone loss in the proximo-medial femur has been identified as a factor leading to loosening in the artificial hip joint. In an effort to develop a quantitative understanding of the stress distribution that causes bone loss, axial and hoop stresses in the medial calcar of the femur have been determined after total hip replacement, using finite element stress analysis. Stress distributions for a high and a low Young's modulus prosthesis material are compared for both collared and uncollared prosthesis designs. The use of a low-modulus material, and of a collar, are predicted to be advantageous, giving rise to proximo-medial stress patterns similar to those of the normal, intact femur.     

The transmission of load through the human hip joint

This paper describes the results of loading experiments carried out on human hip joints. The unloaded surfaces of the femoral head and the acetabulum are slightly incongruous. The location and magnitude of the contact areas between the surfaces therefore depend on the magnitude and direction of the applied load. The contact areas were determined experimentally for a variety of loads typical of normal walking. Two distinct contact areas were found on the anterior and posterior aspects of the acetabulum at light loads, gradually merging with increasing load until, at a certain transition load, the dome of the acetabulum comes into contact and contact is then complete. The value of the transition load depends on the rate of loading, due to creep of the cartilage, and was found to vary from 50 per cent of body weight in young specimens to 25 per cent of body weight for elderly specimens for rates of loading typical of normal walking. Thus, the dome of the acetabulum is out of contact for a substantial portion of the swing phase of normal walking.

The analysis of a much simplified model of the hip joint is presented. The dependence of contact area on load is demonstrated, but also a method of determining the transition load for complete contact from the load/deflection relation for the hip is suggested. The values of the transition load quoted above were obtained by this method. The analysis further indicates that the distribution of pressure between the articular surfaces depends critically on the distribution of cartilage thickness throughout the joint. It is suggested that the distribution of cartilage thickness is such as to lead to a state of uniform pressure at the upper end of the physiological load range. Some experimental evidence is presented in support of this suggestion.

It is concluded that the function of joint incongruity is to allow the articular surfaces to come out of contact at light loads so that the cartilage may be exposed to synovial fluid for the purposes of nutrition and lubrication. At large loads, the distribution of cartilage thickness ensures that a state of hydrostatic pressure is achieved in order that cartilage, with a large fluid content, may transmit large pressures without flow and consequent loss of its integrity.     

Stresses in polyethylene liners in a semiconstrained ankle prosthesis

A finite element model of a semiconstrained ankle implant with the tibia and fibula was constructed so that the stresses in the polyethylene liner could be computed. Two different widths of talar components were studied and proximal boundary conditions were computed from an inverse process providing a load of five times body weight appropriately distributed across the osseous structures. von Mises stresses indicated small regions of localized yielding and contact stresses that were similar to those in acetabular cup liners. A wider talar component with 36% more surface area reduced contact stress and von Mises stresses at the center of the polyethylene component by 17%.