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.     

Analysis of red blood cell motion through cylindrical micropores: effects of cell properties.

Filtration through micropores is frequently used to assess red blood cell deformability, but the dependence of pore transit time on cell properties is not well understood. A theoretical model is used to simulate red cell motion through cylindrical micropores with diameters of 3.6, 5, and 6.3 microns, and 11-microns length, at driving pressures of 100-1000 dyn/cm2. Cells are assumed to have axial symmetry and to conserve surface area during deformation. Effects of membrane shear viscosity and elasticity are included, but bending resistance is neglected. A time-dependent lubrication equation describing the motion of the suspending fluid is solved, together with the equations for membrane equilibrium, using a finite difference method. Predicted transit times are consistent with previous experimental observations. Time taken for cells to enter pores represents more than one-half of the transit time. Predicted transit time increases with increasing membrane viscosity and with increasing cell volume. It is relatively insensitive to changes in internal viscosity and to changes in membrane elasticity except in the narrowest pores at low driving pressures. Elevating suspending medium viscosity does not increase sensitivity of transit time to membrane properties. Thus filterability of red cells is sensitively dependent on their resistance to transient deformations, which may be a key determinant of resistance to blood flow in the microcirculation.     

Prediction of lubrication regimes in wrist implants with spherical bearing surfaces

The wrist joint is frequently affected by rheumatoid arthritis, resulting in wrist pain, deformity and ultimately loss of function. Artificial wrist implants have been introduced to treat the rheumatoid wrist, to attempt to alleviate pain and restore some function to the joint. The aim of this study was to predict the likely lubrication regimes that occur in wrist implants with spherical bearing surfaces. The implant was modelled as an equivalent ball-on-plane. Elastohydrodynamic lubrication theory was used to determine the minimum film thickness for the implant under different load, entraining velocity, lubricant viscosity, size of implant and material combinations. The results show that the highest film thickness is found in large implants, with high viscosity, high entraining velocity and low load. Hard-on-soft material combinations will operate with a boundary lubrication regime. Material combinations involving ceramic bearing surfaces have the potential to operate with a mixed lubrication regime.     

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.     

The Influence of Normal Load and Sliding Speed on Frictional Properties of Skin

The study of frictional properties of human skin is important for medical research, skin care products and textile exploi- tation. In order to investigate the influence of normal load and sliding speed on the frictional properties of skin and its possible mechanism, tests were carded out on a multi-specimen friction tester. When the normal load increases from 0.1 N to 0.9 N, normal displacement and the friction coefficient of skin increase. The friction coefficient is dependent on the load, indicating that both adhesion and deformation contribute to the friction behaviour. The deformation friction was interpreted using the plough model of friction. When sliding speed increases from 0.5 mm·s^-1 to 4 mm·s^-1, the friction coefficient increases and ＂stick-slip＂ phenomena increase, indicating that hysteretic friction contributes to the friction. The hysteretic friction was in- terpreted using schematic of energy translation during the rigid spherical probe sliding on the soft skin surface, which provides an explanation for the influence of the sliding speed on the frictional characteristics of the skin.     

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.     

Effect of surface roughness on squeeze film poroelastic bearings with special reference to synovial joints

A simplified mathematical model has been developed for understanding the combined effects of surface roughness and couple stresses on lubrication aspects of synovial joints. The modified Reynolds equation which incorporates the elastic as well as randomized surface roughness structure of cartilage with couple-stress fluid as lubricant is derived. The mean pressure, load carrying capacity and time of approach as functions of film thickness during normal articulation of joints are obtained by using Christensen stochastic theory with the assumption that the roughness asperity heights are to be small compared to the film thickness. The effects of surface roughness and elasticity are considerably pronounced for the poroelastic bearings with couple-stress fluid as lubricant compared with classical case.     

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.     

Swimming of spermatozoa in a linear viscoelastic fluid.

A modified resistive force theory is developed for a spermatozoon swimming in a general linear viscoelastic fluid. The theory is based on a Fourier decomposition of the flagellar velocity, which leads to solving the Stokes flow equations with a complex viscosity. We use a model spermatozoon with a spherical head which propagates small amplitude sinusoidal waves along its flagellum. Results are obtained for the velocity of propulsion and the rate of working for a free swimming spermatozoon and the thrust on a fixed spermatozoon. There is no change in propulsive velocity for a viscoelastic fluid compared to a Newtonian fluid. The rate of working does change however, decreasing with increasing elasticity of the fluid, for a Maxwell fluid. Thus the theory predicts that a spermatozoon can swim faster in a Maxwell fluid with the same expenditure of energy for a Newtonian fluid.     

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.     

Hydrodynamic theory of swimming of flagellated microorganisms.

A theory of the type commonly used in polymer hydrodynamics is developed to calculate swimming properties of flagellated microorganisms. The overall shape of the particle is modeled as an array of spherical beads which act, at the same time, as frictional elements. The fluid velocity field is obtained as a function of the forces acting at each bead through Oseen-type, hydrodynamic interaction tensors. From the force and torque equilibrium conditions, such quantities as swimming velocity, angular velocity, and efficiency can be calculated. Application is made to a spherical body propelled by a helical flagellum. A recent theory by Lighthill, and earlier formulations based on tangential and normal frictional coefficients of a curved cylinder, CT and CN, are analyzed along with our theory. Although all the theories predict similar qualitative characteristics, such as optimal efficiency and the effect of fluid viscosity, they lead to rather different numerical values. In agreement with Lighthill, we found the formalisms based on CN and CT coefficients to be somewhat inaccurate, and head-flagellum interactions are shown to play an important role.     

The role of interstitial fluid pressurization in articular cartilage lubrication

Over the last two decades, considerable progress has been reported in the field of cartilage mechanics that impacts our understanding of the role of interstitial fluid pressurization on cartilage lubrication. Theoretical and experimental studies have demonstrated that the interstitial fluid of cartilage pressurizes considerably under loading, potentially supporting most of the applied load under various transient or steady-state conditions. The fraction of the total load supported by fluid pressurization has been called the fluid load support. Experimental studies have demonstrated that the friction coefficient of cartilage correlates negatively with this variable, achieving remarkably low values when the fluid load support is greatest. A theoretical framework that embodies this relationship has been validated against experiments, predicting and explaining various outcomes, and demonstrating that a low friction coefficient can be maintained for prolonged loading durations under normal physiological function. This paper reviews salient aspects of this topic, as well as its implications for improving our understanding of boundary lubrication by molecular species in synovial fluid and the cartilage superficial zone. Effects of cartilage degeneration on its frictional response are also reviewed.     

Measurement of the Internal Frictional Drag of the Bacterial Flagellar Motor by Fluctuation Analysis

The bacterial flagellar motor generates the torque that drives the rotation of bacterial flagellar filaments. The torque it generates depends sensitively on the frictional viscous drag on the motor, which includes the frictional viscous drag on the filaments (external load) and the internal frictional viscous drag on the rotor (internal load). The internal load was roughly estimated previously by modeling it as a sphere of a radius of 20 nm rotating in a lipid of viscosity of 100 cp but was never measured experimentally. Here, we measured the internal load by fluctuation analysis of the motor velocity traces. A similar approach should be applicable to other molecular motors.     

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.     

Elasticity imaging of polymeric media

Viscoelastic properties of soft tissues and hydropolymers depend on the strength of molecular bonding forces connecting the polymer matrix and surrounding fluids. The basis for diagnostic imaging is that disease processes alter molecular-scale bonding in ways that vary the measurable stiffness and viscosity of the tissues. This paper reviews linear viscoelastic theory as applied to gelatin hydrogels for the purpose of formulating approaches to molecular-scale interpretation of elasticity imaging in soft biological tissues. Comparing measurements acquired under different geometries, we investigate the limitations of viscoelastic parameters acquired under various imaging conditions. Quasi-static (step-and-hold and low-frequency harmonic) stimuli applied to gels during creep and stress relaxation experiments in confined and unconfined geometries reveal continuous, bimodal distributions of respondance times. Within the linear range of responses, gelatin will behave more like a solid or fluid depending on the stimulus magnitude. Gelatin can be described statistically from a few parameters of low-order rheological models that form the basis of viscoelastic imaging. Unbiased estimates of imaging parameters are obtained only if creep data are acquired for greater than twice the highest retardance time constant and any steady-state viscous response has been eliminated. Elastic strain and retardance time images are found to provide the best combination of contrast and signal strength in gelatin. Retardance times indicate average behavior of fast (1-10 s) fluid flows and slow (50-400 s) matrix restructuring in response to the mechanical stimulus. Insofar as gelatin mimics other polymers, such as soft biological tissues, elasticity imaging can provide unique insights into complex structural and biochemical features of connectives tissues affected by disease.     

Tribological characteristics of healthy tendon

Tendons transfer muscular forces efficiently and painlessly, facilitating joint motion. Whilst the tribology of articular cartilage is constantly explored, a poorer understanding remains of tendon lubrication and friction. This study reports experimental data describing the tribological characteristics of tendon and its surrounding tissue, before presenting an arithmetic solution to facilitate numerical modelling. The experimental characteristics of the tensile (i.e. mid-substance) and compressive (i.e. fibrocartilaginous) regions of bovine flexor tendon were investigated using a pin-on-plate tribometer, with immunofluroscence analysis describing the relative intensity and distribution of surface-bound lubricin. Arithmetic analysis considering the digital extensor tendon determined that, in physiological conditions, the tensile tendon region was able to generate elastohydrodynamic lubrication (EHL). The equivalent region of compressive tendon exhibited a higher intensity of surface-bound lubricin which, it is hypothesised, serves to minimise the increased frictional resistance due to generating only mixed or boundary lubrication regimes. Arithmetic analysis indicates that, given a more favourable biomechanical environment, this region can also generate EHL. Whilst acknowledging the limitations of transferring data from an animal model to a clinical environment, by providing the first data and equations detailing the film thicknesses and lubrication regime for these two tendon regions it is hoped that clinicians, engineers and scientists can consider improved clinical strategies to tackle both tendinopathy and tendon rupture.     

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.     

Fluid and solid mechanics in a poroelastic network induced by ultrasound

We made a theoretical analysis on the fluid and solid mechanics in a poroelastic medium induced by low-power ultrasound. Using a perturbative approach, we were able to linearize the governing equations and obtain analytical solutions. We found that ultrasound could propagate in the medium as a mechanical wave, but would dissipate due to frictional forces between the fluid and the solid phase. The amplitude of the wave depends on the ultrasonic power input. We applied this model to the problem of drug delivery to soft biological tissues by low-power ultrasound and proposed a mechanism for enhanced drug penetration. We have also found the coexistence of two acoustic waves under certain circumstances and pointed out the importance of very accurate experimental determination of the high-frequency properties of brain tissue.     

Hydrostatic pressurization and depletion of trapped lubricant pool during creep contact of a rippled indenter against a biphasic articular cartilage layer

This study presents an analysis of the contact of a rippled rigid impermeable indenter against a cartilage layer, which represents a first simulation of the contact of rough cartilage surfaces with lubricant entrapment. Cartilage was modeled with the biphasic theory for hydrated soft tissues, to account for fluid flow into or out of the lubricant pool. The findings of this study demonstrate that under contact creep, the trapped lubricant pool gets depleted within a time period on the order of seconds or minutes as a result of lubricant flow into the articular cartilage. Prior to depletion, hydrostatic fluid load support across the contact interface may be enhanced by the presence of the trapped lubricant pool, depending on the initial geometry of the lubricant pool. According to friction models based on the biphasic nature of the tissue, this enhancement in fluid load support produces a smaller minimum friction coefficient than would otherwise be predicted without a lubricant pool. The results of this study support the hypothesis that trapped lubricant decreases the initial friction coefficient following load application, independently of squeeze-film lubrication effects.