Contact mechanics and elastohydrodynamic lubrication in a novel metal-on-metal hip implant with an aspherical bearing surface

Diameter and diametral clearance of the bearing surfaces of metal-on-metal hip implants and structural supports have been recognised as key factors to reduce the dry contact and hydrodynamic pressures and improve lubrication performance. On the other hand, application of aspherical bearing surfaces can also significantly affect the contact mechanics and lubrication performance by changing the radius of the curvature of a bearing surface and consequently improving the conformity between the head and the cup. In this study, a novel metal-on-metal hip implant employing a specific aspherical bearing surface, Alpharabola, as the acetabular surface was investigated for both contact mechanics and elastohydrodynamic lubrication under steady-state conditions. When compared with conventional spherical bearing surfaces, a more uniform pressure distribution and a thicker lubricant film thickness within the loaded conjunction were predicted for this novel Alpharabola hip implant. The effects of the geometric parameters of this novel acetabular surface on the pressure distribution and lubricant thickness were investigated. A significant increase in the predicted lubricant film thickness and a significant decrease in the dry contact and hydrodynamic pressures were found with appropriate combinations of these geometric parameters, compared with the spherical bearing surface.     

Transient elastohydrodynamic lubrication analysis of metal-on-metal hip implant under simulated walking conditions

The transient elastohydrodynamic lubrication (EHL) analysis was performed in this study for a typical metal-on-metal bearing employing a polyethylene backing underneath a metallic cup inlay under dynamic operating conditions of load and speed representative of normal walking. A ball-in-socket configuration was adopted to represent the articulation between the femoral head and the acetabular cup. The governing Reynolds and elasticity equations were solved simultaneously by using both finite difference and finite element methods. The predicted transient film thickness from the present study was compared with the estimation based on the quasi-static analysis. It was found that the polyethylene backing employed in the typical metal-on-metal hip bearing, combined with dynamic squeeze-film action, significantly improved the transient lubricant film thickness under cyclic walking and consequently a fluid film lubrication regime was possible for smooth bearing surfaces with an average roughness less than 0.005 microm.     

Time-dependent elastohydrodynamic lubrication analysis of total knee replacement under walking conditions

This work is concerned with the lubrication analysis of artificial knee joints, which plays an increasing significant role in clinical performance and longevity of components. Time-dependent elastohydrodynamic lubrication analysis for normal total knee replacement is carried out under the cyclic variation in both load and speed representative of normal walking. An equivalent ellipsoid-on-plane model is adopted to represent an actual artificial knee. A full numerical method is developed to simultaneously solve the Reynolds and elasticity equations using the multigrid technique. The elastic deformation is based on the constrained column model. Results show that, under the combined effect of entraining and squeeze-film actions throughout the walking cycle, the predicted central film thickness tends to decrease in the stance phase but keeps a relatively larger value at the swing phase. Furthermore, the geometry of knee joint implant is verified to play an important role under its lubrication condition, and the length of time period is a key point to influence the lubrication performance of joint components.     

Time-dependent elastohydrodynamic lubrication analysis of total knee replacement under walking conditions

This work is concerned with the lubrication analysis of artificial knee joints, which plays an increasing significant role in clinical performance and longevity of components. Time-dependent elastohydrodynamic lubrication analysis for normal total knee replacement is carried out under the cyclic variation in both load and speed representative of normal walking. An equivalent ellipsoid-on-plane model is adopted to represent an actual artificial knee. A full numerical method is developed to simultaneously solve the Reynolds and elasticity equations using the multigrid technique. The elastic deformation is based on the constrained column model. Results show that, under the combined effect of entraining and squeeze-film actions throughout the walking cycle, the predicted central film thickness tends to decrease in the stance phase but keeps a relatively larger value at the swing phase. Furthermore, the geometry of knee joint implant is verified to play an important role under its lubrication condition, and the length of time period is a key point to influence the lubrication performance of joint components.     

Prediction of lubricating film thickness in UHMWPE hip joint replacements

An elastohydrodynamic lubrication model developed for a ball-in-socket configuration in a previous studies by the present authors (Jalali-Vahid et al., Thinning films and tribological interfaces, 26th Leeds-Lyon Symposium on Tribology, 2000, pp. 329-339) was applied to analyse the lubrication problem of a typical artificial hip joint replacement, consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup against a metallic or ceramic femoral head. The cup was assumed to be stationary whilst the ball was assumed to rotate at a steady angular velocity and under a constant load. A wide range of main design parameters were considered. It has been found that the predicted lubricating film thickness increases with a decrease in the radial clearance, an increase in the femoral head radius, an increase in UHMWPE thickness and a decrease in UHMWPE modulus. However, the predicted lubricating film thicknesses are not found to be sufficiently large in relation to the surface roughness of the cup and head to indicate separation of the two articulating surfaces. It should also be noted that if the design features are unable to secure full fluid film lubrication, it may be preferable to select them for minimum wear rather than maximum film thickness. For example, an increase in head radius will enhance the film thickness, but it will also increase the sliding distance and hence wear in mixed or boundary lubrication conditions. Furthermore, it is pointed out that an increase in the predicted lubricant film thickness is usually associated with an increase in the contact area, and this may cause lubricant starvation and stress concentration at the edge of the cup, and adversely affect the tribological performance of the implant. The effect of running-in process on the lubrication in UHMWPE hip joint replacements is also discussed.     

3-D model of a total hip replacement in vivo providing hydrodynamic pressure and film thickness for walking and bicycling

Formulation of a 3-D lubrication simulation of a total hip replacement in vivo is presented using a finite difference approach. The goal is to determine if hydrodynamic lubrication is taking place, how thick the joint fluid film is and over what percentage of two gait cycles, (walking and bicycling), the hydrodynamic lubricating action is occurring, if at all. The assumption of rigid surfaces is made, which is conservative in the sense that pure hydrodynamic lubrication is well known to predict thinner films than elasto-hydrodynamic lubrication (EHL) for the same loading. The simulation method includes addressing the angular velocity direction changes and accurate geometry configuration for the acetabular cup and femoral head components and provides a range of results for material combinations of CoCrMo-on-UHMWPE, CoCrMo-on-CoCrMo, and alumina-on-alumina components. Results are in the form of the joint fluid film pressure distributions, load components and film thicknesses of the joint fluid, for the gait cycles of walking and bicycling. Results show hydrodynamic action occurs in only about 10% of a walking gait cycle and throughout nearly 90% of a bicycling gait. During the 10% of the walking cycle that develops hydrodynamic lubrication, the minimum fluid film thicknesses are determined to be between 0.05 micron and 1.1 microns, while the range of film thicknesses for bicycling is between 0.1 micron and 1.4 microns, and occurs over 90% of the bicycling gait. Pressure distributions for these same periods are in the range of 2 MPa to 870 MPa for walking and 1 MPa to 24 MPa for bicycling.     

Determinants of friction in soft elastohydrodynamic lubrication

Elastohydrodynamic lubrication (EHL) protects soft tissues from damage and wear in many biological systems (e.g. synovial joints, cornea of the eye, and pleural surfaces of the lung and chest wall). Among studies of lubrication of deformable solids, few have examined the effects of external loads, geometry, and material properties on EHL of soft tissues. To examine these effects, we studied the tribology of soft tissues in a two-dimensional finite element simulation of a thin layer of fluid separating a sliding rigid surface from a soft asperity or bump with an initial sinusoidal shape. We computed the frictional force, deformation of the solid, and change in fluid thickness as functions of independent variables: sliding velocity, normal load, material properties, and bump amplitude and length. Double-logarithmic regression was used to determine the exponents of the scaling relationships of friction coefficient and minimum fluid thickness to the independent variables. The analysis showed that frictional shear force is strongly dependent on velocity, viscosity, and load, moderately dependent on bump length and elasticity, and only weakly dependent on the bump amplitude. The minimum fluid thickness is strongly dependent on velocity and viscosity, and changes moderately with load, elasticity, amplitude, and length. The shape of the bump has little effect. The results confirm that the shear-induced deformation of an initially symmetrical shape, including generalizations to other symmetrical geometries such as quadratic or piecewise linear bumps, leads to load-supporting behavior.     

Friction in metal-on-metal total disc arthroplasty: effect of ball radius

Total disc arthroplasty (TDA) can be used to replace a degenerated intervertebral disc in the spine. There are different designs of prosthetic discs, but one of the most common is a ball-and-socket combination. Contact between the bearing surfaces can result in high frictional torque, which can then result in wear and implant loosening. This study was designed to determine the effects of ball radius on friction. Generic models of metal-on-metal TDA were manufactured with ball radii of 10, 12, 14 and 16 mm, with a radial clearance of 0.015 mm. A simulator was used to test each sample in flexion-extension, lateral bending and axial rotation at frequencies of 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 Hz under loads of 50, 600, 1200 and 2000 N, in new born calf serum. Frictional torque was measured and Stribeck curves were plotted to illustrate the lubrication regime in each case. It was observed that implants with a smaller ball radius showed lower friction and showed boundary and mixed lubrication regimes, whereas implants with larger ball radius showed boundary lubrication only. This study suggests designing metal-on-metal TDAs with ball radius of 10 or 12 mm, in order to reduce wear and implant loosening.     

Elastohydrodynamic lubrication analysis of metal-on-metal hip-resurfacing prostheses

The elastohydrodynamic lubrication analysis was carried out in this study for a typical metal-on-metal hip-resurfacing prosthesis under a simple steady-state rotation. Both the Reynolds equation and the elasticity equation were coupled and solved numerically by the finite difference method. The finite element method was used to determine the elastic deformation of both the femoral and the acetabular components required for the lubrication analysis. The effect of the radial clearance between the femoral head and the acetabular cup on the predicted film thickness and pressure distribution was investigated. The predicted minimum lubricating film thickness was found to compare favourably with the prediction using the Hamrock and Dowson [J. Lubrication Technol. 100 (1978) 236] formula based on the assumption of ball-on-plane semi-infinite solids. This implies that the non-metallic materials such as bone and cement underlying the metallic components have a small effect on the predicted lubrication performance for the particular metal-on-metal hip-resurfacing prosthesis considered in this study. Under realistic physiological walking conditions, a decrease in the radial clearance from 150 to 50 microm resulted in a 137% increase in the predicted minimum film thickness from 19 to 45 nm. Consequently, given a surface roughness of 0.01 microm for both the metallic femoral and acetabular bearing surfaces, the predicted mixed lubrication regime for the larger clearance was changed to a full fluid film lubrication regime for the smaller clearance. This clearly highlighted the importance of the design and manufacturing parameters on the tribological performance of these hard-on-hard hip prostheses.     

The thixotropic effect of the synovial fluid in squeeze-film lubrication of the human hip joint.

The thixotropic (shear-thinning) effect of the synovial fluid in squeeze-film lubrication of the human hip joint is evaluated, taking into account filtration of the squeezed synovial film by biphasic articular cartilage. A porous, homogeneous, elastic cartilage matrix filled with the interstitial ideal fluid, with the intact superficial zone (of lower permeability and stiffness in compression) already disrupted or worn away, models an early stage of arthritis. Due to a high viscosity of the normal synovial fluid at very low shear rates, the squeezed synovial film at a fixed time after the application of a steady load is found to be much thicker in a small central part of the lubricated contact area. In the remaining part, the film is thin as it corresponds to the Newtonian fluid with the same high-shear-rate viscosity. Filtration is lower for the normal cartilage with the intact superficial zone due to its lower permeability and compression stiffness. But even in the fictitious case of zero filtration, calculations show that the effect of thixotropy on the increase of the minimum synovial film thickness would manifest itself as late as after several tens of seconds since the physiologic load application. At that time, this thickness would be as low as about 0.3 microm. It follows that thixotropy of the normal synovial fluid (and so much more of the inflammatory fluid) is irrelevant in squeeze-film lubrication of both the normal and arthritic human hip joints.     

Biomechanical analysis of the Universal 2 implant in total wrist arthroplasty: a finite element study

Little is known about the mechanics of in vivo loading on total wrist prostheses where many studies have looked at the mechanics of other types of arthroplasty such as for the hip and the knee which has contributed to the overall success of these types of procedures. Currently surgeons would prefer to carry out arthrodesis on the wrist rather than consider arthroplasty as clinical data have shown that the outcome of total wrist arthroplasty is poorer than compared to the hip and knee. More research is needed on the loading mechanisms of the implants in order to enhance the design of future generation implants. This study looks at the load transfer characteristics of the Universal 2 implant using a finite element model of a virtually implanted prosthesis during gripping. The results showed that the loading on the implant is higher on the dorsal and ulnar aspect than on the volar and radial aspect of the implant. The whole load is transmitted through the radius and none through the ulna.     

Constituents and pH changes in protein rich hyaluronan solution affect the biotribological properties of artificial articular joints.

The relationship between the coefficient of friction and pH value or protein constituents of lubricating fluid, together with viscosity, were studied within a bearing surface model for artificial joint, ultra-high molecular weight polyethylene (UHMWPE) against stainless steel (SUS), using a mechanical spectrometer. Four lubricants were tested in this study: sodium hyaluronate (HA), HA with albumin, HA with gamma-globulin, and HA with (L)alpha-dipalmitoyl phosphatidylcholine ((L)alpha-DPPC). The coefficient of friction between UHMWPE and SUS in HA with albumin or HA with gamma-globulin varied from 0.035 to 0.070 depending on angular velocity and pH. The coefficient of friction in HA or HA with (L)alpha-DPPC varied from 0.023 to 0.045 depending on angular velocity and pH. The variation in pH for HA with albumin had a large effect on the coefficient of friction at low range of angular velocity with viscosity independence. The variation in pH for HA with gamma-globulin had a large effect on the coefficient of friction with viscosity dependence at high angular velocity. The addition of (L)alpha-DPPC showed a small effect on the coefficient of friction at low angular velocity. This study confirms that the presence of albumin in the lubricant promotes pH dependence and viscosity independence of the tribological properties at low speed while the presence of globulin promotes pH and viscosity independence at low speed and promotes pH and viscosity dependence at high speed in the lubrication of UHMWPE against SUS. This study supports the clinical hypothesis that the effect of constituents and pH changes in periprosthetic fluid for the lubrication is a clue toward resolving many complications after total joint replacement.     

Dependence of nanoscale friction and adhesion properties of articular cartilage on contact load

Boundary lubrication of articular cartilage by conformal, molecularly thin films reduces friction and adhesion between asperities at the cartilage-cartilage contact interface when the contact conditions are not conducive to fluid film lubrication. In this study, the nanoscale friction and adhesion properties of articular cartilage from typical load-bearing and non-load-bearing joint regions were studied in the boundary lubrication regime under a range of physiological contact pressures using an atomic force microscope (AFM). Adhesion of load-bearing cartilage was found to be much lower than that of non-load-bearing cartilage. In addition, load-bearing cartilage demonstrated steady and low friction coefficient through the entire load range examined, whereas non-load-bearing cartilage showed higher friction coefficient that decreased nonlinearly with increasing normal load. AFM imaging and roughness calculations indicated that the above trends in the nanotribological properties of cartilage are not due to topographical (roughness) differences. However, immunohistochemistry revealed consistently higher surface concentration of boundary lubricant at load-bearing joint regions. The results of this study suggest that under contact conditions leading to joint starvation from fluid lubrication, the higher content of boundary lubricant at load-bearing cartilage sites preserves synovial joint function by minimizing adhesion and wear at asperity microcontacts, which are precursors for tissue degeneration.     

Lubrication of the human ankle joint in walking with the synovial fluid filtrated by the cartilage with the surface zone worn out: steady pure sliding motion.

A mixture model of synovial fluid filtration by cartilage in the human ankle joint during walking is presented for steady sliding motion of the articular surfaces. In the paper the cartilage surface zone is assumed worn out. The same model has been recently applied to the squeeze-film problem for the human hip joint loaded by the body weight during standing (Hlavácek, Journal of Biomechanics 26, 1145-1150, 1151-1160, 1993; Hlavácek and Novák, Journal of Biomechanics 28, 1193-1198, 1199-1205, 1995). The linear biphasic model for cartilage (elastic porous matrix + ideal fluid) due to Prof. V. C. Mow and his co-workers and the biphasic model for synovial fluid (viscous fluid + ideal fluid), as used in the above-mentioned squeeze-film problem, are applied. For the physiologic parameters of the ankle joint during walking, a continuous synovial fluid film about 1 microm thick is maintained under steady entraining motion according to the classical model without the fluid transport across the articular surface. This is not the case in the filtration model with the cartilage surface zones worn out. On the contrary, this filtration model indicates that synovial fluid is intensively filtrated by such cartilage, so that no continuous fluid film is maintained and a synovial gel layer, about 10(-8) m thick, develops over the majority of the contact. Thus, if the cartilage surface zones are worn out, boundary lubrication should prevail in the ankle joint under steady sliding motion for the mean values of loading and the sliding velocity encountered in walking cycle.     

Computational hip joint simulator for wear and heat generation

This paper presents a computational simulator for the hip to compute the wear and heat generation on artificial joints. The friction produced on artificial hip joints originates wear rates that can lead to failure of the implant. Furthermore, the frictional heating can increase the wear. The developed computational model calculates the wear in the joint and the temperature in the surrounding zone, allowing the use of different combinations of joint materials, daily activities and different individuals. The pressure distribution on the joint bearing surfaces is obtained with the solution of a contact model. The heat generation by friction and the volumetric wear is computed from the pressure distribution and the sliding distance. The temperature is obtained from the solution of a transient heat conduction problem that includes the time-dependent heat generated by friction. The contact and heat conduction problems are solved numerically with the Finite Element Method. The developed computational model performs a full simulation of the acetabular bearing surface behaviour, which is useful for acetabular cup design and material selection. The results obtained by the present model agree with experimental and clinical data, as well as other numerical studies.     

Biomechanical validation of finite element models for two silicone metacarpophalangeal joint implants

Silicone implants are used for prosthetic arthroplasty of metacarpophalangeal (MCP) joints severely damaged by rheumatoid arthritis. Different silicone elastomer MCP implant designs have been developed, including the Swanson and the NeuFlex implants. The goal of this study was to compare the in vitro mechanical behavior of Swanson and NeuFlex MCP joint implants. Three-dimensional (3D) finite element (FE) models of the silicone implants were modeled using the commercial software ANSYS and subjected to angular displacement from 0 deg to 90 deg. FE models were validated using mechanical tests of implants incrementally bent from 0 deg to 90 deg in a joint simulator. Swanson size 2 and 4 implants were compared with NeuFlex size 10 and 30 implants, respectively. Good agreement was observed throughout the range of motion for the flexion bending moment derived from 3D FE models and mechanical tests. From 30 deg to 90 deg, the Swanson 2 demonstrated a greater resistance to deformation than the NeuFlex 10 and required a greater bending moment for joint flexion. For larger implant sizes, the NeuFlex 30 had a steeper moment-displacement curve, but required a lower moment than the Swanson 4, due to implant preflexion. On average, the stress generated at the implant hinge from 30 deg to 90 deg was lower in the NeuFlex than in the Swanson. On average, starting from the neutral position of 30 deg for the preflexed NeuFlex implant, higher moments were required to extend the NeuFlex implants to 0 deg compared with the Swanson implants, which returned spontaneously to resting position. Implant toggling within the medullary canals was less in the NeuFlex than in the Swanson. The differential performance of these implants may be useful in implant selection based on the preoperative condition(s) of the joint and specific patient functional needs.     

The influence of the acetabular labrum seal,intact articular superficial zone and synovial fluid thixotropy on squeeze-film lubrication of a spherical synovial joint

A model of synovial fluid (SF) filtration by articular cartilage (AC) in a step-loaded spherical synovial joint at rest is presented. The effects of joint pathology (such as a depleted acetabular labrum, a depleted cartilage superficial zone consistent with early osteoarthritis and an inflammatory SF) on the squeezed synovial film are also investigated. Biphasic mixture models for AC (ideal fluid and elastic porous transversely isotropic two-layer matrix) and for SF (ideal and thixotropic fluids) are applied and the following results are obtained. If the acetabular labrum is able to seal the pressurised SF between the articular surfaces (as in the normal hip joint), the fluid in the synovial film and in the cartilage within the labral ring is homogeneously pressurised. The articular surfaces remain separated by a fluid film for minutes. If the labrum is destroyed or absent and the SF can escape across the contact edge, the fluid pressure is non-homogeneous and with a small jump at the articular surface at the very moment of load application. The ensuing synovial film filtration by porous cartilage is lower for the normal cartilage (with the intact superficial zone) than if this zone is already depleted or rubbed off as in the early stage of primary osteoarthritis. Compared with the inflammatory (Newtonian) SF, the normal (thixotropic) fluid applies favourably in the squeezed film near the contact centre only, yielding a thicker SF film there, but not affecting the minimum thickness in the fluid film profile at a fixed time. For all that, in the unsealed case for both the normal and pathological joint, the macromolecular concentration of the hyaluronic acid-protein complex in the synovial film quickly increases due to the filtration in the greater part of the contact. A stable synovial gel film, thick on the order of 10(-7)m, protecting the articular surfaces from the intimate contact, is formed within a couple of seconds. Boundary lubrication by the synovial gel is established if sliding motion follows until a fresh SF is entrained into the contact. This theoretical prediction is open for experimental verifications.     

Time-dependent behavior of cartilage surrounding a metal implant for full-thickness cartilage defects of various sizes: a finite element study

Recently, physiological and biomechanical studies on animal models with metal implants filling full-thickness cartilage defects have resulted in good clinical outcomes. The knowledge of the time-dependent macroscopic behavior of cartilage surrounding the metal implant is essential for understanding the joint function after treating such defects. We developed a model to investigate the in vivo time-dependent behavior of the tibiofemoral cartilages surrounding the metal implant, when the joint is subjected to an axial load for various defect sizes. Results show that time-dependent effects on cartilage behavior are significant, and can be simulated. These effects should be considered when evaluating the results from an implant. In particular, the depth into the cartilage where an implant is positioned and the mechanical sealing due to solidification of the poroelastic material need a time aspect. We found the maximal deformations, contact pressures and contact forces in the joint with time for the implant positioned in flush and sunk 0.3 mm into the cartilage. The latter position gives the better joint performance. The results after 60 s may be treated as the primary results, reflecting the effect of accumulation in the joint due to repeated short-time loadings. The wedge-shaped implant showed beneficial in providing mechanical sealing of cartilages surrounding the implant with time.     

The Phan-Thien and Tanner model applied to thin film spherical coordinates: applications for lubrication of hip joint replacement

The Phan-Thien and Tanner (PTT) model is one of the most widely used rheological models. It can properly describe the common characteristics of viscoelastic non-Newtonian fluids. There is evidence that synovial fluid in human joints, which also lubricates artificial joints, is viscoelastic. Modeling the geometry of the total hip replacement, the PTT model is applied in spherical coordinates for a thin confined fluid film. A modified Reynolds equation is developed for this geometry. Several simplified illustrative problems are solved. The effect of the edge boundary condition on load-carrying normal stress is discussed. Solutions are also obtained for a simple squeezing flow. The effect of both the relaxation time and the PTT shear parameter is to reduce the load relative to a Newtonian fluid with the same viscosity. This implies that the Newtonian model is not conservative and may overpredict the load capacity. The PTT theory is a good candidate model to use for joint replacement lubrication. It is well regarded and derivable from molecular considerations. The most important non-Newtonian characteristics can be described with only three primary material parameters.     

Effect of swing phase load on metal-on-metal hip lubrication, friction and wear

There is renewed interest in metal-on-metal (MOM) total hip replacements (THRs), however, variable wear rates have been observed clinically. It is hypothesised that changes in soft tissue tensioning during surgery may alter loading of THRs during the swing phase of gait leading to changes in fluid film lubrication, friction and wear. This study aimed to assess the effect of swing phase load on the lubrication, friction and wear of MOM hip replacements. Theoretical lubrication modelling was carried out using elastohydrodynamic theory. All the governing equations were solved numerically for the lubricant film thickness between the articulating surfaces under the transient dynamic conditions with low and high swing phase loads. Friction testing was completed using a single axis pendulum simulator, simplified loading cycles were applied with low and high swing phase loads. MOM hip replacements were tested in a hip simulator, modified to provide different swing phase loading regimes; a low (100 N) and a high load (as per ISO 14242-1; 280 N). Results demonstrated that the performance of MOM bearings is highly dependent on swing phase load. Hence, changes in the tension of the tissues at surgery and variations in muscle forces may increase swing phase load, reduce lubrication, increase friction and accelerate wear. This may explain some of the variations that have been observed with clinical wear rates.