Transient Elastohydrodynamic Lubrication Models for the Human Ankle Joint

Unsteady squeezing flow of a magnetized nano-lubricant between parallel disks with Robin boundary conditions

The aim of the present work is to examine the impact of magnetized nanoparticles (NPs) in enhancement of heat transport in a tribological system subjected to convective type heating (Robin) boundary conditions. The regime examined comprises the squeezing transition of a magnetic (smart) Newtonian nano-lubricant between two analogous disks under an axial magnetism. The lower disk is permeable whereas the upper disk is solid. The mechanisms of haphazard motion of NPs and thermophoresis are simulated. The non-dimensional problem is solved numerically using a finite difference method in the MATLAB bvp4c solver based on Lobotto quadrature, to scrutinize the significance of thermophoresis parameter, squeezing number, Hartmann number, Prandtl number, and Brownian motion parameter on velocity, temperature, nanoparticle concentration, Nusselt number, factor of friction, and Sherwood number distributions. The obtained results for the friction factor are validated against previously published results. It is found that friction factor at the disk increases with intensity in applied magnetic field. The haphazard (Brownian) motion of nanoparticles causes an enhancement in thermal field. Suction and injection are found to induce different effects on transport characteristics depending on the specification of equal or unequal Biot numbers at the disks. The main quantitative outcome is that, unequal Biot numbers produce significant cooling of the regime for both cases of disk suction or injection, indicating that Robin boundary conditions yield substantial deviation from conventional thermal boundary conditions. Higher thermophoretic parameter also elevates temperatures in the regime. The nanoparticles concentration at the disk is boosted with higher values of Brownian motion parameter. The response of temperature is similar in both suction and injection cases; however, this tendency is quite opposite for nanoparticle concentrations. In the core zone, the resistive magnetic body force dominates and this manifests in a significant reduction in velocity, that is damping. The heat build-up in squeeze films (which can lead to corrosion and degradation of surfaces) can be successfully removed with magnetic nanoparticles leading to prolonged serviceability of lubrication systems and the need for less maintenance.

Synovial Joints. Tribology, Regeneration, Regenerative Rehabilitation and Arthroplasty

Synovial joints are unique biological tribosystems that allow a person to perform a wide range of movements with minimal energy consumption. In recent years, they have been increasingly called “smart friction units” due to their ability to self-repair and adapt to changing operating conditions. However, in reality, the elements of the internal structure of the joints under the influence of many factors can degrade rather quickly, leading to serious disease such as osteoarthritis. According to the World Health Organization, osteoarthritis is already one of the 10 most disabling diseases in developed countries. In this regard, at present, fundamental research on synovial joints remains highly relevant. Despite the fact that the synovial joints have already been studied fully, many issues related to their operating, prevention, development of pathology, diagnosis and treatment require more detailed consideration. In this article, we discuss the urgent problems that need to be solved for the development of new pharmacological agents, biomaterials, scaffolds, implants and rehabilitation devices for the prevention, rehabilitation and improvement of the treatment effectiveness of synovial joints at various stages of osteoarthritis.

Articular cartilage and meniscus reveal higher friction in swing phase than in stance phase under dynamic gait conditions

Most previous studies investigated the remarkably low and complex friction properties of meniscus and cartilage under constant loading and motion conditions. However, both load and relative velocity within the knee joint vary considerably during physiological activities. Hence, the question arises how friction of both tissues is affected by physiological testing conditions occurring during gait. As friction properties are of major importance for meniscal replacement devices, the influence of these simulated physiological testing conditions was additionally tested for a potential meniscal implant biomaterial. Using a dynamic friction testing device, three different friction tests were conducted to investigate the influence of either just varying the motion conditions or the normal load and also to replicate the physiological gait conditions. It could be shown for the first time that the friction coefficient during swing phase was statistically higher than during stance phase when varying both loading and motion conditions according to the physiological gait pattern. Further, the friction properties of the exemplary biomaterial were also higher, when tested under dynamic gait parameters compared to static conditions, which may suggest that static conditions can underestimate the friction coefficient rather than reflecting the in vivo performance.

Friction properties of a new silk fibroin scaffold for meniscal replacement

The menisci protect the articular cartilage by reducing contact pressure in the knee. To restore their function after injury, a new silk fibroin replacement scaffold was developed. To elucidate its tribological properties, friction of the implant was tested against cartilage and glass, where the latter is typically used in tribological cartilage studies. The silk scaffold exhibited a friction coefficient against cartilage of 0.056, which is higher than meniscus against cartilage but in range of the requirements for meniscal replacements. Further, meniscus friction against glass was lower than cartilage against glass, which correlated with the surface lubricin content. Concluding, the tribological properties of the new material suggest a possible long-term chondroprotective function. In contrast, glass always produced high, non-physiological friction coefficients.

The Role of Fluid Dynamics in Distributing Ankle Stresses in Anatomic and Injured States

BACKGROUND

In 1976, Ramsey and Hamilton published a landmark cadaveric study demonstrating a dramatic 42% decrease in tibiotalar contact area with only 1 mm of lateral talar shift. An increase in maximum principal stress of at least 72% is predicted based on these findings though the delayed development of arthritis in minimally misaligned ankles does not appear to be commensurate with the results found in dry cadaveric models. We hypothesized that synovial fluid could be a previously unrecognized factor that contributes significantly to stress distribution in the tibiotalar joint in anatomic and injured states.

METHODS

As it is not possible to directly measure contact stresses with and without fluid in a cadaveric model, finite element analysis (FEA) was employed for this study. FEA is a modeling technique used to calculate stresses in complex geometric structures by dividing them into small, simple components called elements. Four test configurations were investigated using a finite element model (FEM): baseline ankle alignment, 1 mm laterally translated talus and fibula, and the previous 2 bone orientations with fluid added. The FEM selected for this study was the Global Human Body Models Consortium-owned GHBMC model, M50 version 4.2, a model of an average-sized male (distributed by Elemance, LLC, Winston-Salem, NC). The ankle was loaded at the proximal tibia with a distributed load equal to the GHBMC body weight, and the maximum principal stress was computed.

RESULTS

All numerical simulations were stable and completed with no errors. In the baseline anatomic configuration, the addition of fluid between the tibia, fibula, and talus reduced the maximum principal stress computed in the distal tibia at maximum load from 31.3 N/mm² to 11.5 N/mm². Following 1 mm lateral translation of the talus and fibula, there was a modest 30% increase in the maximum stress in fluid cases. Qualitatively, translation created less high stress locations on the tibial plafond when fluid was incorporated into the model.

CONCLUSIONS

The findings in this study demonstrate a meaningful role for synovial fluid in distributing stresses within the ankle that has not been considered in historical dry cadaveric studies. The increase in maximum stress predicted by simulation of an ankle with fluid was less than half that projected by cadaveric data, indicating a protective effect of fluid in the injured state. The trends demonstrated by these simulations suggest that bony alignment and fluid in the ankle joint change loading patterns on the tibia and should be accounted for in future experiments.

CLINICAL RELEVANCE

Synovial fluid may play a protective role in ankle injuries, thus delaying the onset of arthritis. Reactive joint effusions may also function to additionally redistribute stresses with higher volumes of viscous fluid.

Biphasic and boundary lubrication mechanisms in artificial hydrogel cartilage: A review

Various studies on the application of artificial hydrogel cartilage to cartilage substitutes and artificial joints have been conducted. It is expected in clinical application of artificial hydrogel cartilage that not only soft-elastohydrodynamic lubrication but biphasic, hydration, gel-film and boundary lubrication mechanisms will be effective to sustain extremely low friction and minimal wear in daily activities similar to healthy natural synovial joints with adaptive multimode lubrication. In this review article, the effectiveness of biphasic lubrication and boundary lubrication in hydrogels in thin film condition is focused in relation to the structures and properties of hydrogels. As examples, the tribological behaviors in three kinds of poly(vinyl alcohol) hydrogels with high water content are compared, and the importance of lubrication mechanism in biomimetic artificial hydrogel cartilage is discussed to extend the durability of cartilage substitute.

Role of interstitial fluid pressurization in TMJ lubrication

In temporomandibular joints (TMJs), the disc and condylar cartilage function as load-bearing, shock-absorbing, and friction-reducing materials. The ultrastructure of the TMJ disc and cartilage is different from that of hyaline cartilage in other diarthrodial joints, and little is known about their lubrication mechanisms. In this study, we performed micro-tribometry testing on the TMJ disc and condylar cartilage to obtain their region- and direction-dependent friction properties. Frictional tests with a migrating contact area were performed on 8 adult porcine TMJs at 5 different regions (anterior, posterior, central, medial, and lateral) in 2 orthogonal directions (anterior-posterior and medial-lateral). Some significant regional differences were detected, and the lateral-medial direction showed higher friction than the anterior-posterior direction on both tissues. The mean friction coefficient of condylar cartilage against steel was 0.027, but the disc, at 0.074, displayed a significantly higher friction coefficient. The 2 tissues also exhibited different frictional dependencies on sliding speed and normal loading force. Whereas the friction of condylar cartilage decreased with increased sliding speed and was independent of the magnitude of normal force, friction of the disc showed no dependence on sliding speed but decreased as normal force increased. Further analysis of the Péclet number and frictional coefficients suggested that condylar cartilage relies on interstitial fluid pressurization to a greater extent than the corresponding contact area of the TMJ disc.

Ultrastructural analysis of healthy synovial fluids in three mammalian species

A better knowledge of synovial fluid (SF) ultrastructure is required to further understand normal joint lubrication and metabolism. The aim of the present study was to elucidate SF structural features in healthy joints from three mammalian species of different size compared with features in biomimetic SF. High-resolution structural analysis was performed using transmission electron microscopy (TEM) and scanning electron microscopy (SEM) and environmental SEM/wet scanning transmission electron microscopy mode complemented by TEM and SEM cryogenic methods. Laser-scanning confocal microscopy (LCM) was used to locate the main components of SF with respect to its ultrastructural organization. The present study showed that the ultrastructure of healthy SF is built from a network of vesicles with a size range from 100 to a few hundred nanometers. A multilayered organization of the vesicle membranes was observed with a thickness of about 5 nm. LCM study of biological SF compared with synthetic SF showed that the microvesicles consist of a lipid-based membrane enveloping a glycoprotein gel. Thus, healthy SF has a discontinuous ultrastructure based on a complex network of microvesicles. This finding offers novel perspectives for the diagnosis and treatment of synovial joint diseases.

Compliant-layer tibial bearing inserts: Friction testing of different materials and designs for a new generation of prostheses that mimic the natural joint

Total joint replacements (TJRs) have a limited lifetime, but the introduction of devices that exhibit good lubricating properties with low friction and low wear could well extend this. A novel tibial bearing design, using polyurethane (PU) as a compliant layer, to mimic the natural joint, has been developed. To determine accurately the mode of lubrication under which these joints operate, a synthetic lubricant was used in all these tests. Friction tests were carried out to assess the effects of material modulus and surface roughness, together with bearing design parameters such as bearing thickness and conformity, on lubrication. Corethane 80A was the preferred material and was chosen as the compliant layer for subsequent testing. A low surface roughness resulted in lower asperity contact as the asperities were depressed by the pressurized entraining fluid and full-fluid-film lubrication was approached. The three different tibial bearing conformities (low, medium, and high) did not appear to influence the mode of lubrication and all these bearings performed with extremely low friction. Similarly, the bearing thickness effects on lubrication at the levels tested (2 mm, 3 mm, and 4 mm) were minimal, although the effects of layer thickness on interface shear stress could be expected to be significant. This study describes a series of friction tests that have been used to select the most appropriate material and to optimize the design parameters to establish optimum conditions for these compliant layer joints.

Compliant layer bearings in artificial joints. Part 2: Simulator and fatigue testing to assess the durability of the interface between an elastomeric layer and a rigid substrate

Artificial joints have been much improved since their introduction but they still have a limited lifetime. In an attempt to increase their life by improving the lubrication acting within these prostheses, compliant layered polyurethane (PU) joints have been devised. These joints mimic the natural synovial joint more closely by promoting fluid film lubrication. In this study, tests were performed on compliant layer joints to determine their ability to function under a range of conditions. Both static and dynamic compression tests were undertaken on compliant artificial hip joints of two different radial clearances. Friction tests were also performed before and after static loading. In addition to this, knee wear tests were conducted to determine the suitability of a compliant layer in these applications. In the knee tests, variations in experimental testing conditions were investigated using both active and passive rotation and severe malalignment of the tibial inserts. The static compression tests together with the friction studies suggest that a small radial clearance is likely to result in ‘grabbing’ contact between the head and cup. The larger radial clearance (0.33 μm) did not exhibit these problems. The importance of the design of the compliant layer joints was highlighted with delamination occurring on the lateral bearings during the knee wear studies. The bearings with a layer 2 mm thick performed better than the bearings with a layer 3 mm thick. Tests conducted on flat PU bearings resulted in no delamination; therefore, it was concluded that the layer separation was caused by design issues rather than by material issues. It was found that, with careful material choice, consideration of design, and effective manufacturing techniques, the compliant layer joint functioned well and demonstrated durability of the union between the hard and soft layers. These results give encouragement for the suitability of these joints for clinical use.

Compliant layer acetabular cups: friction testing of a range of materials and designs for a new generation of prosthesis that mimics the natural joint

Total joint replacements (TJRs) have a limited lifetime, but the introduction of components that exhibit good lubricating properties with low friction and low wear could extend the life of TJRs. A novel acetabular cup design using polyurethane (PU) as a compliant layer (to mimic the natural joint) has been developed. This study describes a series of friction tests that have been used to select the most appropriate material, optimize the design parameters, and fine-tune the manufacturing processes of these joints. To determine accurately the mode of lubrication under which these joints operate, a synthetic lubricant was used in all these tests. Friction tests were carried out to assess the lubrication of four PU bearing materials. Corethane 80A was the preferred material and was subjected to subsequent testing. Friction tests conducted on acetabular cups, manufactured using Corethane 80A articulating against standard, commercially available femoral heads, demonstrated friction factors approaching those for full-fluid-film lubrication with only approximately 1 per cent asperity contact. As the joint produces these low friction factors within less than half a walking cycle after prolonged periods of loading, start-up friction was not considered to be a critical factor. Cups performed well across the full range of femoral head sizes, but a number of samples manufactured with reduced radial clearances performed with higher than expected friction. This was caused by the femoral head being gripped around the equator by the low clearance cup. To avoid this, the cup design was modified by increasing the flare at the rim. In addition to this the radial clearance was increased. As the material is incompressible, a radial clearance of 0.08 mm was too small for a cup diameter of 32 mm. A clearance of between 0.10 and 0.25 mm produced a performance approaching full-fluid-film lubrication. This series of tests acted as a step towards the optimization of the design of these joints, which has now led to an in vivo ovine model.

Effect of phospholipidic boundary lubrication in rigid and compliant hemiarthroplasty models

Hemiarthroplasty may benefit from materials which produce lower friction and improved boundary lubrication protection during start-up conditions. The purpose of this study was to evaluate the effect of phospholipidic boundary lubrication in both rigid and compliant hemiarthroplasty. An in vitro model was designed to dissociate the relative contribution of implant material compliance and the presence of phospholipid to the overall friction of a hemiarthroplasty contact using bovine articular cartilage. Normal bovine articular cartilage was articulated against four flat materials using reciprocating motion: (a) borosilicate glass: (b) borosilicate glass coated with dipalmitoylphosphatidylcholine (DPPC); (c) polyurethane (PU) elastomer (Tecoflex SG93A, a medical-grade aliphatic thermoplastic PU, Thermedics Incorporated. Woburn, Massachusetts); and (d) surface-coated PU (Tecoflex SG93A substrate coated with lipid-attracting copolymer poly[methacryloyloxyethyl phosphorylcholine (MPC)-co-butyl methacrylate (BMA)]. Tests were conducted in physiologically simulated tribological conditions for a non-conformal point contact. Friction and lubrication analysis was performed using both static and kinetic coefficients of friction mu measured for each group as a function of time for a sliding distance of up to 60 m. Results showed that the inclusion of supplemental phospholipid, DPPC, on a rigid substrate significantly decreased mu in comparison with the control (cartilage-glass). Additionally, removal of phospholipid components from the articular cartilage surface produced a significantly greater start-up mu in comparison with normal cartilage at the test onset. The use of a material with a lower modulus resulted in lower mu for the entire duration of the test. Polyurethane elastomer coated with the lipid-attracting copolymer, poly(MPC-co-BMA), resulted in the lowest frictional response. As seen in this study, the improvement of low-modulus hemiarthroplasty may involve the optimization of chemical modification and incorporation of lipid-attracting MPC copolymers onto compliant materials. However, further tests are warranted to determine whether lipid-attracting MPC copolymers perform as well during long-time, in vivo wear studies.

Development of artificial articular cartilage

Attempts have been made to develop an artificial articular cartilage on the basis of a new viewpoint of joint biomechanics in which the lubrication and load-bearing mechanisms of natural and artificial joints are compared. Polyvinyl alcohol hydrogel (PVA-H), 'a rubber-like gel', was investigated as an artificial articular cartilage and the mechanical properties of this gel were improved through a new synthetic process. In this article the biocompatibility and various mechanical properties of the new improved PVA-H is reported from the perspective of its usefulness as an artificial articular cartilage. As regards lubrication, the changes in thickness and fluid pressure of the gap formed between a glass plate and the specimen under loading were measured and it was found that PVA-H had a thicker fluid film under higher pressures than polyethylene (PE) did. The momentary stress transmitted through the specimen revealed that PVA-H had a lower peak stress and a longer duration of sustained stress than PE, suggesting a better damping effect. The wear factor of PVA-H was approximately five times that of PE. Histological studies of the articular cartilage and synovial membranes around PVA-H implanted for 8-52 weeks showed neither inflammation nor degenerative changes. The artificial articular cartilage made from PVA-H could be attached to the underlying bone using a composite osteochondral device made from titanium fibre mesh. In the second phase of this work, the damage to the tibial articular surface after replacement of the femoral surface in dogs was studied. Pairs of implants made of alumina, titanium or PVA-H on titanium fibre mesh were inserted into the femoral condyles. The two hard materials caused marked pathological changes in the articular cartilage and menisci, but the hydrogel composite replacement caused minimal damage. The composite osteochondral device became rapidly attached to host bone by ingrowth into the supporting mesh. The clinical implications of the possible use of this material in articular resurfacing and joint replacement are discussed.

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.

Prediction of transient lubricating film thickness in knee prostheses with compliant layers

The transient lubricating film thickness in knee prostheses using compliant layers has been predicted under simulated walking conditions based upon the elastohydrodynamic lubrication theory. Qualitative agreement has been found between the present theoretical predictions and the experimental measurements using an electric resistance technique reported earlier. It has been shown that the contact geometry plays an important role in the generation of fluid film lubrication in knee prostheses using compliant layers. The maximum lubricating film thickness is predicted for the maximized contact area of a transverse conjunction where the semi-minor contact radius lies in the direction of entraining. The additional advantage of the transverse contact conjunction is that the possibility of lubricant starvation due to small stroke length can be minimized. All these factors, together with the kinematic requirements in the natural knee joint, should be taken into consideration when designing artificial knee joint replacements.

The influence of articular surface incongruity on lubrication and contact pressure distribution of loaded synovial joints

In the model intended for short-term loading (such as during the walking cycle) of a human synovial joint in the lower extremities, cartilage lubricated by Newtonian synovial fluid is considered to be incompressible elastic and subchondral bone is considered to be rigid. The model is non-diffusional, i.e. no interstitial fluid flow occurs across the articular surfaces. A simple plane strain case of the human ankle joint is considered. For high steady loading applied in the centre of the stationary tibial arc and for steady sliding of the talar arc, this model shows that individual physiological variations in the geometry of the articular surfaces have only a small effect on the contact stress distribution and the fluid film thickness. If this load is applied eccentrically in the tibial arc, the contact pressure distribution varies more with surface geometry, but the minimum fluid film thickness differs little from that for symmetric loading. The maximum contact pressure is placed eccentrically in this case, but its value is changed only little when compared to the central loading of the same value. In order to explain different distribution patterns of subchondral bone mineralization, it is anticipated that the total load peaks of periodic time-dependent loads are transmitted centrally in some incongruent joints and eccentrically in others.

Friction of composite cushion bearings for total knee joint replacements under adverse lubrication conditions

Conventional joint replacements consist of a polished metallic or ceramic component articulating against a layer of polyethylene. Although the friction in the contact between these articulating surfaces is low, polyethylene wear is produced as a result of a boundary/mixed lubrication regime. Wear debris is generated by direct asperity contact, abrasion, adhesion and fatigue, and has been shown to cause adverse tissue reactions which can lead to joint failure. The introduction of soft compliant materials, similar in stiffness to articular cartilage, has shown that with cyclic loading and relative motion between the articulating surfaces typical of normal walking, a fluid film can be maintained through combined entraining and squeeze-film actions, and hence wear can be minimized. For 95 per cent of the time, however, we are not walking but standing still or moving slowly. A pendulum simulator has been used in the present study to investigate the effect of adverse tribological conditions which may lead to fluid film breakdown, such as severe cyclic loading, particularly in the swing phase, reduced sliding velocity, reduced stroke length and start-up after a period of constant loading. Friction of a model composite cushion knee bearing, manufactured from a graded modulus (20-1000 MPa) layer of polyurethane, sliding against a polished metal cylinder has been measured for various lubricants and the results have been analysed using a Stribeck assessment. Severe cyclic loading, decreased sliding velocity and decreased stroke length have been found to limit the degree of fluid entrainment previously allowed during the swing phase of normal walking, thus allowing breakdown of fluid films and elevated levels of friction and surface damage. Soft layer joint replacements must therefore be designed to operate with thick elastohydrodynamic fluid films to provide some degree of protection when tribological conditions become severe, or alternatively incorporate alternative boundary or mixed lubrication mechanisms. This study quantifies a potential limitation of the cushion bearing concept.

The normal stress effect and equilibrium friction coefficient of articular cartilage under steady frictional shear

During creep or stress relaxation, articular cartilage exhibits a time-dependent friction coefficient which has been shown to reach an equilibrium value, mu eq, as the tissue deformation equilibrates. This study investigates the frictional properties of articular cartilage explants under steady frictional shear and constant compressive strain after the tissue reaches stress-relaxation equilibrium. The two parameters measured are the normal force and frictional torque, from which the friction coefficient was then calculated. It is shown in this experimental study that: (1) Under a prescribed infinitesimal compressive strain, cartilage supports higher compressive normal stress under steady shear than it does in the absence of frictional shear. Furthermore, the normal stress increases with increasing sliding velocity, resulting in a velocity-dependent value of mu eq. The observed normal stress effectively increases the compressive stiffness of cartilage by a factor up to 3.1. (2) Under a prescribed steady frictional shear both the normal stress and frictional shear stress increase, though not proportionally, with increasing compressive strain, producing a decreasing friction coefficient. (3) This velocity-dependent normal stress effect is also shown to result, at least partly, from intrinsic properties of cartilage. The normal stress effect has not been previously reported for articular cartilage, and represents an intriguing mechanical response not commonly encountered in solids, though common in non-Newtonian fluids.

Analysis of fluid film lubrication in artificial hip joint replacements with surfaces of high elastic modulus

Lubrication mechanisms and contact mechanics have been analysed for total hip joint replacements made from hard bearing surfaces such as metal-on-metal and ceramic-on-ceramic. A similar analysis for ultra-high molecular weight polyethylene (UHMWPE) against a hard bearing surface has also been carried out and used as a reference. The most important factor influencing the predicted lubrication film thickness has been found to be the radial clearance between the ball and the socket. Full fluid film lubrication may be achieved in these hard/hard bearings provided that the surface finish of the bearing surface and the radial clearance are chosen correctly and maintained. Furthermore, there is a close relation between the predicted contact half width and the predicted lubrication film thickness. Therefore, it is important to analyse the contact mechanics in artificial hip joint replacements. Practical considerations of manufacturing these bearing surfaces have also been discussed.

Determination of lubricating film thickness for permeable hydrogel and non-permeable polyurethane layers bonded to a rigid substrate with particular reference to cushion form hip joint replacements

The lubricating film thickness in a model of compliant layered bearings, using both permeable hydrogels and non-permeable polyurethane elastomers for total hip joint replacements, has been measured using optical interferometry, under both entraining and squeeze-film motion. The film thickness in the lubricated contact was measured for both water and a 40 per cent glycerol solution in water as a function of entraining velocity and squeeze-film time. The measured lubricating film thickness for the permeable hydrogel was compared to that of the non-permeable polyurethane elastomer and little difference was found when the lubricating film thickness was sufficiently large (greater than 150 nm). Comparison of the experimental results and the theoretical predictions based upon elastohydrodynamic lubrication analysis showed good agreement in the entraining experiments where the film thickness was greater than 150 nm. In the squeeze-film experiments the experimental measurements were greater than the theoretical predictions for all squeeze times due to the formation of a central pocket of fluid which was not predicted by the simple theory used. This also occurred for the hydrogels for films greater than 150 nm. For longer squeeze times the film thickness for the hydrogel fell below the theoretical prediction. This was considered to be due to the permeability of the hydrogel reducing the film thickness when the film thickness was less than 150 nm. The permeability of the hydrogel was not modelled in the theoretical lubrication analysis used in this study.

A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers

Previous studies have shown that interstitial fluid pressurization plays an important role in the load support mechanism of articular cartilage under normal step loading. These studies have demonstrated that interstitial fluid pressurization decreases with time if the applied load is maintained constant. In the present study, a theoretical solution is obtained for another common loading of articular cartilage, namely the contact of surfaces in rolling motion. Pure rolling of symmetrical frictionless cylindrical cartilage layers is analyzed under steady state. The linear biphasic model of Mow et al. [J. Biomech. Engng 102, 73-84 (1980)] is used to describe the mechanical response of articular cartilage. The solution of this contact problem reduces to simultaneously solving a set of four integral equations, akin to the dual integral problem of elastic contact. It is found that the solution is dependent on four non-dimensional parameters: Rh = Vb/HAk, W/2 mu b, R/b, and v, where V is the surface velocity, b the cartilage thickness, HA the aggregate modulus, mu the shear modulus, v Poisson's ratio, k the permeability, R the radius of cylindrical surfaces, and W the applied load per unit cylinder length. For Rh << 1, interstitial fluid pressurization is found to be negligible, and all the applied load is supported by the solid collagen-proteoglycan phase of the tissue, thus causing significant cartilage deformation. As Rh increases to a physiological level (Rh approximately 10(4)), interstitial fluid pressurization may support more than 90% of the total applied load, shielding the solid matrix from high effective stresses and reducing matrix strains and deformation. The protective effect of interstitial fluid pressurization is observed to increase with increasing joint congruence (R/b); similarly, as the applied load (W/2 mu b) is increased, a greater proportion of it is supported by the fluid. In degenerative cartilage, Rh may drop by one or more orders of magnitude, primarily as a result of increased permeability. Thus, the protective stress-shielding effect of interstitial fluid pressurization may become less effective in diseased tissue, possibly setting a pathway for further tissue degeneration.

Cushion form bearings for total knee joint replacement. Part 1: Design,friction and lubrication

Cushion knee prostheses have been designed and constructed that produce approximately equal initial contact areas and theoretical film thicknesses compared with a conventional UHMWPE (ultra-high molecular weight polyethylene) joint. These compliant bearings had a flat tibial component which imposed fewer biomechanical constraints and allowed a greater range of movement. Friction experiments have been carried out on a pendulum simulator apparatus. The results showed that the cushion knee joints operated just within the mixed lubrication regime, but that they benefited from a substantial measure of fluid film lubrication. Microelastohydrodynamic lubrication was effective in preserving low friction and thin but effective lubricating films.

An asymptotic solution for the contact of two biphasic cartilage layers

This study addresses the hypothesis that interstitial fluid plays a major role in the load support mechanism of articular cartilage. An asymptotic solution is presented for two contacting biphasic cartilage layers under compression. This solution is valid for identical thin (i.e. epsilon = h'/a'0 << 1), frictionless cartilage layers, and for the 'early' time response (i.e. t' << (h')2/HAk) after the application of a step load. An equilibrium asymptotic solution is also presented (i.e.t'-->infinity). Here h' is the thickness, a'0 is a characteristic contact radius, HA is the aggregate modulus and k is the permeability of the cartilage layer. A main conclusion from this analysis is that the fluid phase of cartilage plays a major role in providing load support during the first 100-200 s after contact loading. Further, the largest component of stress in cartilage is the hydrostatic pressure developed in the interstitial fluid. For tissue fluid volume fraction (porosity) in the range 0.6 < or = phi f < or = 0.8, k = O(10(-15) m4/Ns) and HA = O(1 MPa), the peak magnitude of the principal effective (or elastic) stress may be as low as 14% of the peak hydrostatic pressure within the tissue, or the contact stress at the surface. In effect, the interstitial fluid shields the solid matrix from high normal stresses and strains. The asymptotic solution also shows that pressure-sensitive film measurements of intra-articular contact stress do not measure the elastic stress at the surface, but they rather provide a measure of the interstitial fluid pressure. Finally, this analysis provides strong support for the hypothesis that, if sudden loading causes shear failure within the cartilage-bone layer structure, this failure would take place at the cartilage-bone interface, and the plane of failure would be either parallel or perpendicular to this interface.

Asperity lubrication in human joints

The asperity lubrication in human joints is examined in the present paper, with particular reference to the tertiary undulation with wavelengths of around 20-45 microns. It was found that, under dynamic physiological loading conditions, the secondary waviness of the cartilaginous surface (typically 0.5 mm wavelength) could be effectively flattened to sustain a fluid film of 0.1-0.3 micron thick, while the tertiary waviness could be squashed to sustain a much thinner fluid film of 0.01 micron (10 nm) thick with normal synovial fluid as the lubricant. The calculated film thickness for the tertiary undulation was less than 5 nm when the ankle joint was lubricated by Ringer's solution or pathological synovial fluids, or when only quasi-static loading conditions were considered, while a sufficiently thick fluid film could still be formed when the secondary undulations were considered alone. It was thus suggested that the fluid film lubrication mechanism was operative for human joints with normal synovial fluid as the lubricant under physiological dynamic loading conditions and the mixed lubrication mechanism could take over when static loading conditions prevailed or when watery lubricants (eta approximately 0.001 Pa s) were used.

A full numerical solution to the problem of microelastohydrodynamic lubrication of a stationary compliant wavy layered surface firmly bonded to a rigid substrate with particular reference to human synovial joints

A full numerical solution procedure has been developed for the microelastohydrodynamic lubrication analysis of a stationary compliant wavy layered surface firmly bonded to a rigid substrate. The results obtained have been compared with those using a simplified method adopted by Dowson and Jin(1) and good agreement has been obtained.

The effect of porosity of articular cartilage on the lubrication of a normal human hip joint

The effect of porosity of articular cartilage on the lubrication of a normal human hip joint has been studied. The poroelasticity equation of articular cartilage and the modified Reynolds equation for the synovial fluid lubricant have been successfully solved under squeeze-film motion and for the conditions experienced in a normal human hip joint. It has been shown that porosity of the articular cartilage depletes the lubricant film thickness, rather than increasing it, particularly when the lubricant film thickness becomes small. Furthermore, it has been shown that articular cartilage can be treated as a single-phase incompressible elastic material in the lubrication modelling under physiological walking conditions.

Evaluation of metallic personalized hemiarthroplasty: a canine patellofemoral model

The purpose of this study was to characterize the response of articular cartilage to weight bearing against a metallic personalized hemiarthroplasty prosthesis. Ten dogs each underwent surgery in which an elastomeric replica of the left femoral patellar groove was made. Using this replica, a 0.5-mm-thick prosthesis was cast in Co-Cr alloy and subsequently the surface was polished to a mirror finish which had a center line average roughness value in the range of human hemiarthroplasty implants. A second surgery was performed to resurface the left trochlea with this prosthesis. Five animals were sacrificed at 3 months and 5 at 6 months. Cartilage damage occurred primarily in the distal region of the patella, and was especially evident at 6 months. Mechanical indentation tests conducted on patellar cartilage in a saline bath at 37 degrees C indicated both increased deformation and residual deformation in the affected areas, indicative of degenerative change. Areas of fibrillation with a depletion of proteoglycans were identified histologically. These areas were only superficial at 3 months but became more extensive at 6 months. Rheological analysis of the synovial fluid of tests joints indicated that a decrease in viscosity occurred from 3 to 6 months, an additional indicator of progressive degeneration. This novel implant model showed that even if a metallic hemiarthroplasty implant had an identical geometry as the joint surface being replaced and had a reasonably smooth surface, cartilage degeneration inevitably resulted.

Design considerations for cushion form bearings in artificial hip joints

Lubrication mechanisms and contact mechanics have been analysed in a new generation of 'cushion form' bearings for artificial hip joints, which comprise low elastic modulus layers on the articulating surfaces. Comparisons have been made with 'hard' bearings used in existing prostheses and also with the natural hip joint. Lubricating film thicknesses are enhanced by larger contact areas and lower contact pressures. For a fixed contact area, simultaneous changes in layer thickness and radial clearance have been shown to have a small effect on elastohydrodynamic film thickness. Hard bearings designed with the same contact area as the cushion bearings produced a similar film thickness, but lubricant film thickness is not optimized in current designs. The main advantage of using a cushion bearing with low elastic modulus layers was found to be associated with microelastohydrodynamic lubrication. Careful selection of the elastic modulus is important in order to ensure that this lubrication regime was effective. Low elastic modulus layers may also produce local deformations, which enhance squeeze film action. The elastic modulus of the material should not be lower than necessary to produce effective microelastohydrodynamic lubrication, as a further reduction in modulus only increases the strain distribution in the material. A lubricant film thickness of 0.3 microns has been predicted for a cushion hip prosthesis with a femoral head diameter of 32 mm and radius of contact zone of 16 mm, using a 2 mm thick layer with an elastic modulus of 20 MPa.

Tribology of total artificial joints

The tribology of total artificial replacement joints is reviewed. The majority of prosthesis currently implanted comprise a hard metallic component which articulates on ultra high molecular weight polyethylene surface. These relatively hard bearing surfaces operate with a mixed or boundary lubrication regime, which results in wear and wear debris from the ultra high molecular weight polyethylene surface. This debris can contribute to loosening and ultimate failure of the prostheses. The tribological performance of these joints has been considered and a number of factors which may contribute to increased wear rates have been identified. Cushion bearing surfaces consisting of low elastic modulus materials which can articulate with full fluid film lubrication are also described. These bearing surfaces have shown the potential for greatly reducing wear debris.