Elasto-plastic contact analysis of an ultra-high molecular weight polyethylene tibial component based on geometrical measurement from a retrieved knee prosthesis

The wear phenomenon of ultra-high molecular weight polyethylene (UHMWPE) in knee and hip prostheses is one of the major restriction factors on the longevity of these implants. Especially in retrieved knee prostheses with anatomical design, the predominant types of wear on UHMWPE tibial components are delamination and pitting. These fatigue wear patterns of UHMWPE are believed to result from repeated plastic deformation owing to high contact stresses. In this study, the elasto-plastic contact analysis of the UHWMPE tibial insert, based on geometrical measurement for retrieved knee prosthesis, was performed using the finite element method (FEM) to investigate the plastic deformation behaviour in the UHMWPE tibial component. The results suggest that the maximum plastic strain below the surface is closely related to subsurface crack initiation and delamination of the retrieved UHMWPE tibial component. The worn surface whose macroscopic geometrical congruity had been improved due to wear after joint replacement showed lower contact stress at macroscopic level.     

A Study of Contact Temperature Due to Frictional Heating of UHMWPE

Contact temperature of ultra-high molecular weight polyethylene (UHMWPE) bearing was measured by the infrared radiometric microscope. Lubricant temperature near the contact band was measured simultaneously and compared with the contact temperature. Contact temperature increases of up to 12°C in 30 min were observed under a mean contact pressure 12.7 MPa and sliding speed 50 mm/s. Young's modulus of UHMWPE was estimated as 0.5 GPa from the contact dimensions. The coefficient of friction was evaluated for variety of contact conditions and material combinations for UHMWPE, CoCrMo alloy and sapphire glass. It was confirmed that the contact stress has a large effect on the coefficient of friction and the fluid film has little effect on the coefficient of friction. Under sliding conditions, the thermal property of the moving material has a large effect on an increment of lubricant temperature.     

An axisymmetric contact model of ultra high molecular weight polyethylene cups against metallic femoral heads for artificial hip joint replacements.

Contact mechanics of ultra high molecular weight polyethylene (UHMWPE) cups against metallic femoral heads for artificial hip joints is considered in this study. Both the experimental measurement of the contact area and the finite element prediction of the contact radius, maximum contact pressure and maximum Von Mises stress have been carried out for a wide range of contemporary artificial hip joints. Good agreement of the contact radius has been found between the experimental measurements and the finite element predictions based upon an elastic modulus of 1000 MPa and a Poisson's ratio of 0.4 for UHMWPE material under various loads up to 2.5 kN. It has been shown that the half contact angle for all the cup/head combinations considered in this study is between 40 degrees and 50 degrees under a load of 2.5 kN. The importance of this result has been discussed with respect to the anatomical position of the cup when placed in the body and the selection of a simple wear-screening test for artificial hip joints. The predicted contact radius and maximum contact pressure from the finite element model have also been compared with a simple elasticity analysis. It has been shown that the difference in the predicted contact radius between the two methods is reduced for more conforming contacts between the femoral head and the acetabular cup and smaller UHMWPE cup thickness. However, good agreement of the predicted maximum contact pressure has been found for all the combinations of the femoral head and the acetabular cup considered in this study. The importance of contact mechanics on the clinical performance of artificial hip joint replacements has also been discussed.     

The effect of kinematic conditions on the wear of ultra-high molecular weight polyethylene (UHMWPE) in orthopaedic bearing applications

It is known that wear mechanisms differ between the ultra-high molecular weight polyethylene (UHMWPE) components of total hip replacement (THR) and total knee replacement (TKR). The difference in relative contact position or 'kinematic conditions of contact' between the metal and polymer components is thought to contribute to the contrast in observed wear mechanisms. A reciprocating wear tester was used to evaluate three basic kinematic contact conditions: sliding, in which the relative contact position on the polymer remains stationary; gliding, where the contact position on the polymer reciprocates; and rolling, where the contact position on the polymer varies and the relative velocities of both components are equal. All static load tests used cast Co-Cr alloy and irradiated Chirulen UHMWPE in a 37 degrees C environment lubricated with bovine serum albumin. UHMWPE test sample wear was measured gravimetrically at intervals of 600,000 cycles. The results indicated a difference in wear factor (volume lost due to wear per unit load per unit sliding distance) between the three groups with varying relative motion. The study indicates that screening tests which evaluate wear properties of new materials for total joint replacement should reflect the different kinematic contact conditions.     

Steady-state elastohydrodynamic lubrication analysis of a metal-on-metal hip implant employing a metallic cup with an ultra-high molecular weight polyethylene backing

The elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a 28 mm diameter metal-on-metal hip prosthesis employing a metallic cup with an ultra-high molecular weight polyethylene (UHMWPE) backing under a simple steady state rotation representing the flexion/extension during walking. Both Reynolds and elasticity equations were coupled and solved numerically by the finite difference method. The elastic deformation was determined by means of the fast Fourier transform (FFT) technique using the displacement coefficients obtained from the finite element method. Excellent agreement of the predicted elastic deformation was obtained between the FFT technique and the conventional direct summation method. The number of grid points used in the lubrication analysis was found to be important in predicting accurate film thicknesses, particularly at low viscosities representative of physiological lubricants. The effect of the clearance between the femoral head and the acetabular cup on the predicted lubricant film thickness was shown to be significant, while the effect of load was found to be negligible. Overall, the UHMWPE backing was found not only to reduce the contact pressure as identified in a previous study by the authors (Liu et al., 2003) but also significantly to increase the lubricant film thickness for the 28 mm diameter metal-on-metal hip implant, as compared with a metallic mono-block cup.     

Transient elastohydrodynamic lubrication in artificial knee joint with non-Newtonian fluids

This paper presents the transient analysis of a human artificial knee joint under elastohydrodynamic lubrication (EHL) for point contact with non-Newtonian lubricants. The artificial knee joints use ultra high molecular weight polyethylene (UHMWPE) against metal with time-varying speed and load during walking. This numerical simulation employed a perturbation method, Newton Raphson method and multigrid method with full approximation technique to solve simultaneously both the time-dependent Reynolds equation, with non-Newtonian fluid based on a Carreau model, and the elasticity equation.The general numerical schemes are implemented to investigate the characteristics of elastohydrodynamic lubrication in human artificial knee joints; profiles of pressure and film thickness are determined, with varying material and lubricant properties, applied loads and speeds. The results show that the elastohydrodynamic fluid film thickness between the metallic component of the artificial knee joint and the soft polyethylene bearing becomes larger as the contact area increases and the fluid film pressure decreases. At the beginning of the first walking cycle, the film thickness is lower than in subsequent cycles because of the time required to develop the fluid film; after the first cycle, the fluid film is similar for every cycle and is dependent on transient applied load and speed during human movement.     

Measurement and theoretical determination of frictional temperature rise between sliding surfaces of artificial hip joints

Frictional heating of articulating surfaces may influence the rate of wear, fatigue, creep and oxidative degradation of bearing materials. Also temperature rise can damage the surrounding tissue and lubricant around the artificial joint and contributes insert loosening. The objective of this study is to determine temperature rise between sliding surface of vitamin E blended UHMWPE and conventional UHMWPE acetabular component paired with a cobalt–chromium–molybdenum (CoCrMo) femoral component, as a function of sliding time and applied load. Besides the experimental studies, the frictional temperature rise of conventional UHMWPE was theoretically calculated. Frictional measurements of the joints were carried out on a custom made hip joint friction simulator. The diameter of the prostheses was 28 mm. Applied static loads were changed from 200 N to 1500 N. In flexion–extension plane, a simple harmonic oscillatory motion between ±24° was applied to the UHMWPE acetabular component. The period of motion was 1 Hz and the tests were run up to 11,000 cycles. Temperature rise in acetabular and femoral component was recorded with embedded thermocouples. Both the experimental temperature rise values and theoretical calculations results were compared and evaluated.     

A simulator study of friction in total replacement hip joints.

Frictional behaviour of 22 different femoral head-acetabular cup combinations was studied on a new servo-hydraulic microcomputer-controlled hip joint simulator using various flexion-extension angle and superior-inferior load set value waveforms and using distilled water at 37 +/- 1 degrees C as lubricant. Six different head materials were included in the study, whereas all cups were ultra-high molecular weight polyethylene (UHMWPE). Most head-cup combinations studied are commercially available. No distinctly superior joint design can be pointed out, but the frictional behaviour of alumina ceramic against UHMWPE proved overall most favourable (mu min was 0.02), whereas that of non-ion-implanted titanium alloy Ti-6Al-4V against UHMWPE proved strikingly poor (mu max was 0.15). The lowest frictional torque was in 22 mm joints, but frictional torque did not always increase straightforwardly with increasing diameter of the femoral head. The measurements form an extensive comparison between a wide variety of head-cup combinations. The simulator is apparently a useful instrument in the study of frictional behaviour of new designs, materials, surface treatments and coatings that are frequently introduced.     

Nanoindentation properties of compression-moulded ultra-high molecular weight polyethylene

This paper investigates the elastic modulus and hardness of untreated and treated compression-moulded ultra-high molecular weight polyethylene (UHMWPE) tibial inserts of a total knee replacement (TKR) prosthesis. Investigations were carried out at a nanoscale using a Nanoindenter at penetration depths of 100,250 and 500 nm. The nanomechanical properties of surface and subsurface layers of the compression-moulded tibial inserts were studied using the untreated UHMWPE. The nanomechanical properties of intermediate and core layers of the compression-moulded tibial insert were studied using the cryoultrasectioned and etched UHMWPE treated samples. The cryoultrasectioning temperature (-150 degrees C) of the samples was below the glass transition temperature, Tg (-122 +/- 2 degrees C ), of UHMWPE. The measurement of the mechanical response of crystalline regions within the nanostructure of UHMWPE was accomplished by removing the amorphous regions using a time-varying permanganic-etching technique. The percentage crystallinity of UHMWPE was measured using differential scanning calorimetry (DSC) and the Tg of UHMWPE was determined by dynamic mechanical analysis (DMA). Atomic force microscopy (AFM) was used to assess the effect of surface preparation on the samples average surface roughness, Ra. In this study, it was demonstrated that the untreated UHMWPE samples had a significantly lower (p < 0.0001) elastic modulus and hardness relative to treated UHMWPE cryoultrasectioned and etched samples at all penetration depths. No significant difference (p > 0.05) in elastic modulus and hardness between the cryoultrasectioned and etched samples was observed. These results suggest that the surface nanomechanical response of an UHMWPE insert in a total joint replacement (TJR) prosthesis is significantly lower compared with the bulk of the material. Additionally, it was concluded that the nanomechanical response of material with higher percentage crystallinity (67 per cent) was predominantly determined by the crystalline regions within the semi-crystalline UHMWPE nanostructure.     

Effect of stair descent loading on ultra-high molecular weight polyethylene wear in a force-controlled knee simulator

A loading protocol approximating forces, torques and motions at the knee during stair descent was developed from previously published data for input into a force-controlled knee simulator. A set of total knee replacements (TKRs) was subjected to standard walking cycles and stair descent cycles at a ratio of 70: 1 for 5 million cycles. Another set of implants with similar articular geometry and the same ultra-high molecular weight polyethylene (UHMWPE) resin (GUR 415), sterilization and packaging was tested with standard walking cycles only. Implant kinematics, gravimetric wear and surface roughness of the UHMWPE inserts were analysed for both sets of implants. Contact stresses were calculated for both loading protocols using a Hertzian line contact model. Significantly greater weight loss (p < 0.05) and more severe surface damage of UHMWPE inserts resulted with the walking + stair descent loading protocol compared to walking cycles only. Anterior-posterior (AP) tibiofemoral contact point displacements were lower during stair descent than walking, but not significantly different (p = 0.05). Contact stresses were significantly higher during stair descent than walking, owing to higher axial loads and the smaller radius of curvature of the femoral components at higher flexion angles. High contact stresses on UHMWPE components are likely to accelerate the fatigue of the material, resulting in more severe wear, similar to what is observed in retrieved implants. Thus the inclusion of loading protocols for activities of daily living in addition to walking is warranted for more realistic in vitro testing of TKRs.     

Demonstration of a New Technique Using Radioisotope Tracers to Measure the Backside Wear Rate on Tibial Inserts

Local backside wear measurements on ultra-high molecular weight polyethylene (UHMWPE) tibial inserts in LCS mobile bearing knee prostheses have been performed using a new radioisotope tracing technique. The radioisotope tracers ⁹⁷Ru and ^101mRh were synthesized via a fusion evaporation reaction and recoil-implanted into cylindrical plugs of UHMWPE. The labelled plugs were carefully fitted into tibial inserts at two relevant locations. With bovine serum acting as a lubricant, the tibial inserts were then worn in vitro for 500,000 and 780,000 cycles, respectively, in a pneumatic knee motion simulator. Results reflect the non-linear change of wear during the wear-in phase and its evolution to a long-term steady-state rate. This new technique shows potential for extracting localized wear rates across the backside of a tibial insert in order to develop a comprehensive backside wear model.     

A new formulation for the prediction of polyethylene wear in artificial hip joints

Artificial joints employing ultra-high molecular weight polyethylene (UHMWPE) are widely used to treat joint diseases and trauma. Wear of the polymer bearing surface largely limits the use of these joints in younger and more active patients. Previous studies have shown the wear factor used in Archard's law for the conventional polyethylene to be highly dependent on contact pressure and this has produced variability in experimental data and has constrained the reliability and applicability of previous computational predictions. A new wear law is proposed, based on wear volume being dependent on, and proportional to, the product of the sliding distance and contact area. The dimensionless proportional constant, wear coefficient, which was independent of contact pressure, was determined from a multi-directional pin on plate study. This was used in computational predictions of the wear of the conventional UHMWPE hip joints. The wear of the polyethylene cup was independently experimentally determined in physiological full hip joint simulator studies. The predicted wear rate from the new computational model was generally increased, with an improved agreement with the experimental measurement compared with the previous computational model. It was shown that wear in the UHMWPE hip joints increased as head size and contact area increased. This resulted in a much larger increase in the wear rate as the head size increased, compared with the previous computational model, and is consistent with clinical observations. This new understanding of the wear mechanism in artificial joints using the UHMWPE bearing surfaces, and the improved ability to predict wear independently and to address previously described discrepancies offer new opportunities to optimize design parameters.     

Fretting Wear Behavior of UHMWPE—Influence of Load and Stroke

In this study, the tribological behavior of ultra-high-molecular-weight polyethylene (UHMWPE) against a GCr 15 steel ball during fretting wear conditions was investigated using an oscillating reciprocating tribometer. The aim of this study was to characterize the critical value of normal load and stroke corresponding to this transition in UHMWPE worn surface at room temperature. Results showed that there existed a critical value of load or stroke at fixed condition. The friction coefficient and wear volume loss of UHMWPE at or near the critical values of load and stroke exhibited extreme changes. Based on observation of the worn surface by scanning electron microscopy (SEM) and 3D surface profiler measurements, it can be found that damage to the worn surface can be linked to the contact load and stroke. In addition, results showed that during the process of fretting wear under different load or stroke conditions, the gross slip regime dominated throughout the whole test period.     

A machine for the preliminary investigation of design features influencing the wear behaviour of knee prostheses

Degradation of tibial inserts in vivo has been found to be multifactorial in nature, resulting in a complex interaction of many variables. A range of kinematic conditions occurs at the tibio-femoral interface, giving rise to various degrees of rolling and sliding at this interface. The movement of the tibio-femoral contact point may be an influential factor in the overall wear of ultra-high molecular weight polyethylene (UHMWPE) tibial components. As part of this study a three-station wear-test machine was designed and built to investigate the influence of rolling and sliding on the wear behaviour of specific design aspects of contemporary knee prostheses. Using the machine, it is possible to monitor the effect of various slide roll ratios on the performance of contemporary bearing designs from a geometrical and materials perspective.     

Measurement of laxity in the anterior cruciate ligament-deficient knee: a comparison of three different methods in vitro

The aim of this study was to compare in-vitro measurements of anteroposterior laxity in the anterior cruciate ligament (ACL)-deficient knee using three different methods: an Instron materials-testing machine, then a KT-2000 arthrometer, and finally by Roentgen stereophotogrammetric analysis (RSA). Eight ACL-deficient human cadaver knees were used. Total displacement was measured between 90 N anterior and 90 N posterior tibiofemoral drawer forces at both 20 degrees and 90 degrees knee flexion. Laxity ranged from 11.5 to 27.6 mm at 20 degrees and from 8.7 to 23.9 mm at 90degrees. A statistically significant difference was not found between the mean RSA and KT-2000 measurements. However, the mean Instron measurements of laxity were significantly (3-4 mm) higher than both RSA and KT-2000 measurements. The clinical methods of RSA and the KT-2000 measurements agreed well but appeared to underestimate tibiofemoral anteroposterior laxity compared with the materials-testing machine. These findings may be helpful in the future comparison of different studies.     

A simple fully integrated contact-coupled wear prediction for ultra-high molecular weight polyethylene hip implants

A fully coupled contact and wear model was developed in the present study for hip implants employing an ultra-high molecular weight polyethylene (UHMWPE) cup in combination with a metallic or ceramic femoral head. A simple elasticity equation based on the concept of constrained column model was employed to solve the contact mechanics between the acetabular cup and the femoral head under the three-dimensional physiological loading condition. The wear model was based on the classical Archard-Lancaster equation in common with all other studies reported in the literature. The fully coupled contact and wear model was applied to both conventional and cross-linked UHMWPE cups under a wide range of design parameters such as the clearance and the femoral head radius. The predicted linear and volumetric wear as well as their rates for conventional UHMWPE cups were found to be in good agreement with those obtained from a similar analysis by Maxian but using the finite element method for the contact mechanics analysis. The predicted maximum contact pressure was found to decrease rapidly within the first 10(6) cycles, and below the limit to cause plastic deformation within the UHMWPE cup with a nominal radial clearance of 0.2 mm. The effect of the clearance between the head and the cup on the predicted wear was found to be negligible. For the cross-linked UHMWPE cup with relatively large diameters up to 48 mm and a fixed outside diameter of 50 mm, the predicted wear, which was found to increase with increasing femoral head radius, remained small owing to the small wear factor associated with these materials. Furthermore, if the head diameter increases beyond 42 mm, a rapid increase in the contact pressure was predicted, owing to the decrease in the wall thickness of the cross-linked UHMWPE cup.     

Effect of contact pressure on wear and friction of ultra-high molecular weight polyethylene in multidirectional sliding

Computational wear models need input data from valid tribological tests. For the wear model of a total hip prosthesis, the contact pressure dependence of wear and friction of ultra-high molecular weight polyethylene (UHMWPE) against polished CoCr in diluted calf serum lubricant was studied, and useful input data produced. Two test devices were designed and built: a heavy load circularly translating pin-on-disc (HL-CTPOD) wear test device and an HL-CTPOD friction measurement device. Both can be used with a wide range of loads. The wear surface diameter of the test pin was kept constant at 9 mm, whereas the load was varied so that the nominal contact pressure ranged from 0.1 to 20 MPa. The wear factor decreased with increasing contact pressure, whereas the coefficient of friction first increased with increasing contact pressure with low pressure values and then decreased. Up to the pressure of 2.0 MPa, the wear mechanisms and wear factors were in good agreement with clinical findings. In the critical range of 2.0-3.5 MPa, the wear mechanisms and wear factors started to differ from clinical ones, and the decrease of the wear factor steepened. The discrepancy became more and more evident as the pressure was gradually increased beyond 3.5 MPa. It appears that the pressure value of 2.0 MPa should not be exceeded in pin-on-disc wear tests that are to reproduce the clinical wear of UHMWPE acetabular cups.     

The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: a mathematical analysis

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.     

Relative movements between Kinemax Plus tibial inserts and the tibial base-plates

Tests were performed on six large Kinemax Plus knee bearings (snap-fit design) to evaluate the amount of movement between 10- and 15-mm-thick tibial inserts and the tibial base plates. The knee bearings were tested up to 1 x 10(6) cycles on the Durham six-station knee wear simulator which subjected the bearings to similar motion and loading profiles that would be experienced by the natural knee during walking. Although passive internal/external (I/E) rotation was allowed, no active I/E rotation was applied. The movement of the tibial inserts was measured with dial gauges (accuracy +/-0.01 mm) before and after the bearings were tested on the simulator, when unloaded, and throughout the tests while the bearings were being dynamically loaded in the simulator. Movement occurred between the tibial insert and the tibial base plate after initial assembly due to the snap-fit mechanism used to locate the tibial insert within the tibial base plate. However this decreased appreciably when the bearings were loaded in the simulator. The amount of movement did not change with time when the bearings were continuously loaded in the simulator. However, after each test the amount of movement of the tibial inserts, when unloaded, was only 65 per cent (anterior-posterior) and 46 per cent (medial-lateral) of the values before the test. This was thought to be due to creep of the ultra-high molecular weight polyethylene (UHMWPE) inserts. The movement between the tibial insert and tibial base plate in situ is likely to be much less than that observed by a surgeon at the time of assembly due to loading of the knee bearing in the body. However, the amount of movement when the tibial inserts are loaded may still be great enough to produce a second interface where wear of the tibial insert may take place.     

On the pressure dependence of the wear of ultrahigh molecular weight polyethylene

The wear of polyethylene in bovine serum was evaluated as a function of load and molecular weight. The range and distribution of contact loadings simulated those which exist in currently available total hip and total knee prostheses. The wear increased exponentially with load at constant molecular weight. An increasing molecular weight parametrically displaced the exponential curve to higher loads, lowering the overall rate. It is proposed that the behavior of these materials be described in terms of a critical pressure-velocity product although the specific mechanisms for wear acceleration are not known in this case.