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.     

Effect of bearing geometry and structure support on transient elastohydrodynamic lubrication of metal-on-metal hip implants

An effective lubrication can significantly reduce wear of metal-on-metal artificial hip joints. The improvement of the lubrication can be achieved through the optimisation of the bearing geometry in terms of a small clearance and/or the structural support such as a polyethylene backing underneath a metallic bearing in a sandwich acetabular cup form. The separate effects of these two factors on fluid film lubrication of 28 mm diameter metal-on-metal total hip joints under walking conditions were numerically investigated in this paper. The results show that a larger lubricant film due to the polyethylene backing can be significantly enhanced by the transient squeeze-film action, particularly during the stance phase, and a similar lubricant film can be developed for both the monolithic cup relying on the smaller clearance and the sandwich cup benefiting from the polyethylene backing. Both cup systems can function in a wide range of lubrication regimes, covering both mixed and fluid film, under the current design and manufacture conditions.     

Prediction of lubricating film thickness in UHMWPE hip joint replacements

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

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.     

Hard-on-Hard Lubrication in the Artificial Hip under Dynamic Loading Conditions

The tribological performance of an artificial hip joint has a particularly strong influence on its success. The principle causes for failure are adverse short- and long-term reactions to wear debris and high frictional torque in the case of poor lubrication that may cause loosening of the implant. Therefore, using experimental and theoretical approaches models have been developed to evaluate lubrication under standardized conditions. A steady-state numerical model has been extended with dynamic experimental data for hard-on-hard bearings used in total hip replacements to verify the tribological relevance of the ISO 14242-1 gait cycle in comparison to experimental data from the Orthoload database and instrumented gait analysis for three additional loading conditions: normal walking, climbing stairs and descending stairs. Ceramic-on-ceramic bearing partners show superior lubrication potential compared to hard-on-hard bearings that work with at least one articulating metal component. Lubrication regimes during the investigated activities are shown to strongly depend on the kinematics and loading conditions. The outcome from the ISO gait is not fully confirmed by the normal walking data and more challenging conditions show evidence of inferior lubrication. These findings may help to explain the differences between the in vitro predictions using the ISO gait cycle and the clinical outcome of some hard-on-hard bearings, e.g., using metal-on-metal.     

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.     

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

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

Predictive Simulation Generates Human Adaptations during Loaded and Inclined Walking

Predictive simulation is a powerful approach for analyzing human locomotion. Unlike techniques that track experimental data, predictive simulations synthesize gaits by minimizing a high-level objective such as metabolic energy expenditure while satisfying task requirements like achieving a target velocity. The fidelity of predictive gait simulations has only been systematically evaluated for locomotion data on flat ground. In this study, we construct a predictive simulation framework based on energy minimization and use it to generate normal walking, along with walking with a range of carried loads and up a range of inclines. The simulation is muscle-driven and includes controllers based on muscle force and stretch reflexes and contact state of the legs. We demonstrate how human-like locomotor strategies emerge from adapting the model to a range of environmental changes. Our simulation dynamics not only show good agreement with experimental data for normal walking on flat ground (92% of joint angle trajectories and 78% of joint torque trajectories lie within 1 standard deviation of experimental data), but also reproduce many of the salient changes in joint angles, joint moments, muscle coordination, and metabolic energy expenditure observed in experimental studies of loaded and inclined walking.     

Influence of walking speed on gait parameters

Modern three-dimensional gait analysis systems give information on joint angles and moments in the sagittal and coronal planes, for which normal ranges may not be readily available in the literature. Since patients with joint disease tend to walk slowly and with a short stride, it is essential that normal ranges for gait parameters should be defined with reference to speed of walking. This we have done using a population of 10 normal male subjects agea from 18 to 63 years, walking at speeds which range from very slow to very fast. The ranges of knee angle and moment are given, together with the changes in these parameters with walking speed. Peak knee flexion moment is strongly related to walking speed, whereas coronal plane knee angle is virtually independent of it. The stride length is probably the best basis for deciding the normal range for a particular measurement.     

A probabilistic method to estimate gait kinetics in the absence of ground reaction force measurements

Human joint torques during gait are usually computed using inverse dynamics. This method requires a skeletal model, kinematics and measured ground reaction forces and moments (GRFM). Measuring GRFM is however only possible in a controlled environment. This paper introduces a probabilistic method based on probabilistic principal component analysis to estimate the joint torques for healthy gait without measured GRFM. A gait dataset of 23 subjects was obtained containing kinematics, measured GRFM and joint torques from inverse dynamics in order to obtain a probabilistic model. This model was then used to estimate the joint torques of other subjects without measured GRFM. Only kinematics, a skeletal model and timing of gait events are needed. Estimation only takes 0.28 ms per time instant. Using cross-validation, the resulting root mean square estimation errors for the lower-limb joint torques are found to be approximately 0.1 Nm/kg, which is 6–18% of the range of the ground truth joint torques. Estimated joint torque and GRFM errors are up to two times smaller than model-based state-of-the-art methods. Model-free artificial neural networks can achieve lower errors than our method, but are less repeatable, do not contain uncertainty information on the estimates and are difficult to use in situations which are not in the learning set. In contrast, our method performs well in a new situation where the walking speed is higher than in the learning dataset. The method can for example be used to estimate the kinetics during overground walking without force plates, during treadmill walking without (separate) force plates and during ambulatory measurements.     

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.     

Gait analysis using gravitational acceleration measured by wearable sensors

A novel method for measuring human gait posture using wearable sensor units is proposed. The sensor units consist of a tri-axial acceleration sensor and three gyro sensors aligned on three axes. The acceleration and angular velocity during walking were measured with seven sensor units worn on the abdomen and the lower limb segments (both thighs, shanks and feet). The three-dimensional positions of each joint are calculated from each segment length and joint angle. Joint angle can be estimated mechanically from the gravitational acceleration along the anterior axis of the segment. However, the acceleration data during walking includes three major components; translational acceleration, gravitational acceleration and external noise. Therefore, an optimization analysis was represented to separate only the gravitational acceleration from the acceleration data. Because the cyclic patterns of acceleration data can be found during constant walking, a FFT analysis was applied to obtain some characteristic frequencies in it. A pattern of gravitational acceleration was assumed using some parts of these characteristic frequencies. Every joint position was calculated from the pattern under the condition of physiological motion range of each joint. An optimized pattern of the gravitational acceleration was selected as a solution of an inverse problem. Gaits of three healthy volunteers were measured by walking for 20 s on a flat floor. As a result, the acceleration data of every segment was measured simultaneously. The characteristic three-dimensional walking could be shown by the expression using a stick figure model. In addition, the trajectories of the knee joint in the horizontal plane could be checked by visual imaging on a PC. Therefore, this method provides important quantitive information for gait diagnosis.     

Repeatability of 3D gait kinematics obtained from an electromagnetic tracking system during treadmill locomotion

The purpose of this paper was to describe a technique that enables three-dimensional (3D) gait kinematics to be obtained using an electromagnetic tracking system, and to report the intra-trial, intra-day/inter-tester and inter-day/intra-tester repeatability of kinematic gait data obtained using this technique. Ten able-bodied adults underwent four gait assessments; the same two testers tested each subject independently on two different days. Gait assessments were conducted on a custom-built long-bed treadmill with no metal components between the rollers. Each gait assessment involved familiarisation to treadmill walking, subject anatomical and functional calibration, and a period of steady-state treadmill walking at a self-selected speed. Following data collection, 3D joint kinematics were calculated using the joint coordinate system approach. 3D joint angle waveforms for 10 left and right strides were extracted and temporally normalised for each trial. Intra-trial, intra-day/inter-tester and inter-day/intra-tester repeatability of the temporally normalised kinematic waveforms were quantified using the coefficient of multiple determination (CMD). CMDs for joint kinematics averaged 0.942 intra-trial, 0.849 intra-day/inter-tester and 0.773 inter-day/intra-tester. In general, sagittal plane kinematics were more repeatable than frontal or transverse plane kinematics, and kinematics at the hip were more repeatable than at the knee or ankle. The level of repeatability of kinematic gait data obtained during treadmill walking using this protocol was equal or superior to that reported previously for overground walking using image-based protocols.     

Lubrication mode analysis of articular cartilage using Stribeck surfaces

Lubrication of articular cartilage occurs in distinct modes with various structural and biomolecular mechanisms contributing to the low-friction properties of natural joints. In order to elucidate relative contributions of these factors in normal and diseased tissues, determination and control of lubrication mode must occur. The objectives of these studies were (1) to develop an in vitro cartilage on glass test system to measure friction coefficient, mu; (2) to implement and extend a framework for the determination of cartilage lubrication modes; and (3) to determine the effects of synovial fluid on mu and lubrication mode transitions. Patellofemoral groove cartilage was linearly oscillated against glass under varying magnitudes of compressive strain utilizing phosphate buffered saline (PBS) and equine and bovine synovial fluid as lubricants. The time-dependent frictional properties were measured to determine the lubricant type and strain magnitude dependence for the initial friction coefficient (mu(0)=mu(t-->0)) and equilibrium friction coefficient (mu(eq)=mu(t-->infinity)). Parameters including tissue-glass co-planarity, normal strain, and surface speed were altered to determine the effect of the parameters on lubrication mode via a 'Stribeck surface'. Using this testing apparatus, cartilage exhibited biphasic lubrication with significant influence of strain magnitude on mu(0) and minimal influence on mu(eq), consistent with hydrostatic pressurization as reported by others. Lubrication analysis using 'Stribeck surfaces' demonstrated clear regions of boundary and mixed modes, but hydrodynamic or full film lubrication was not observed even at the highest speed (50mm/s) and lowest strain (5%).     

An upper-body can improve the stability and efficiency of passive dynamic walking

The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker.     

Gait synchronized force modulation during the stance period of one limb achieved by an active partial body weight support system

Our purpose was to demonstrate the ability of an actively controlled partial body weight support (PBWS) system to provide gait synchronized support during the stance period of a single lower extremity while examining the affect of such a support condition on gait asymmetry. Using an instrumented treadmill and a motion capture system, we compared gait parameters of twelve healthy elderly subjects (age 65-80 years) during unsupported walking to those while walking with 20% body weight support provided during only the stance period of the right limb. Specifically, we examined peak three-dimensional ground reaction force (GRF) data and the symmetry of lower extremity sagittal plane joint angles and of time and distance parameters. A reduction in all three GRF components was observed for the supported limb during modulated support. Reductions observed in the vertical GRF were comparable to the desired 20% support level. Additionally, GRF components examined for the unsupported limb during modulated support were consistently similar to those measured during unsupported walking. Modulated support caused statistically significant increases in asymmetry for knee flexion during stance (increased 5.9%), hip flexion during late swing (increased 9.1%), and the duration of single limb support (increased 2.8%). However, the observed increases were similar or considerably less than the natural variability in the asymmetry of these parameters during unsupported walking. The ability of the active PBWS device to provide unilateral support may offer new and possibly improved applications of PBWS rehabilitation for patients with unilateral walking deficits such as hemiparesis or orthopaedic injury.     

Influence of altered gait patterns on the hip joint contact forces

Children who exhibit gait deviations often present a range of bone deformities, particularly at the proximal femur. Altered gait may affect bone growth and lead to deformities by exerting abnormal stresses on the developing bones. The objective of this study was to calculate variations in the hip joint contact forces with different gait patterns. Muscle and hip joint contact forces of four children with different walking characteristics were calculated using an inverse dynamic analysis and a static optimisation algorithm. Kinematic and kinetic analyses were based on a generic musculoskeletal model scaled down to accommodate the dimensions of each child. Results showed that for all the children with altered gaits both the orientation and magnitude of the hip joint contact force deviated from normal. The child with the most severe gait deviations had hip joint contact forces 30% greater than normal, most likely due to the increase in muscle forces required to sustain his crouched stance. Determining how altered gait affects joint loading may help in planning treatment strategies to preserve correct loading on the bone from a young age.     

Hip contact forces and gait patterns from routine activities.

In vivo loads acting at the hip joint have so far only been measured in few patients and without detailed documentation of gait data. Such information is required to test and improve wear, strength and fixation stability of hip implants. Measurements of hip contact forces with instrumented implants and synchronous analyses of gait patterns and ground reaction forces were performed in four patients during the most frequent activities of daily living. From the individual data sets an average was calculated. The paper focuses on the loading of the femoral implant component but complete data are additionally stored on an associated compact disc. It contains complete gait and hip contact force data as well as calculated muscle activities during walking and stair climbing and the frequencies of daily activities observed in hip patients. The mechanical loading and function of the hip joint and proximal femur is thereby completely documented. The average patient loaded his hip joint with 238% BW (percent of body weight) when walking at about 4 km/h and with slightly less when standing on one leg. This is below the levels previously reported for two other patients (Bergmann et al., Clinical Biomechanics 26 (1993) 969-990). When climbing upstairs the joint contact force is 251% BW which is less than 260% BW when going downstairs. Inwards torsion of the implant is probably critical for the stem fixation. On average it is 23% larger when going upstairs than during normal level walking. The inter- and intra-individual variations during stair climbing are large and the highest torque values are 83% larger than during normal walking. Because the hip joint loading during all other common activities of most hip patients are comparably small (except during stumbling), implants should mainly be tested with loading conditions that mimic walking and stair climbing.     

Single photon radioluminescence. I. Theory and spectroscopic properties.

The excitation of a fluorescent molecule by a beta-decay electron (radioluminescence) depends upon the electron energy, the distance between radioactive 'donor' and fluorescent 'acceptor', and the excitation characteristics and solvent environment of the fluorophore. The theory for calculation of single photon radioluminescence (SPR) signals is developed here; in the accompanying paper, measurement methods and biological applications are presented. To calculate the three-dimensional spatial profile for electron energy deposition in an aqueous environment, a Monte Carlo calculation was performed incorporating theories of electron energy distributions, energy loss due to interactions with matter, and deflections in electron motion due to collisions. For low energy beta emitters, 50% of energy deposition occurs within 0.63 micron (3H, 18.5 keV), 22 microns (14C, 156 keV), 25 microns (35S, 167 keV), and 260 microns (36Cl, 712 keV) of the radioisotope. In close proximity to the beta emitter (100 nm, 3H; 10 microns, 14C) the probability for fluorophore excitation is approximately proportional to the inverse square of the distance between the beta emitter and fluorophore. To investigate the other factors that determine the probability for fluorophore excitation, SPR measurements were carried out in solutions containing 3H and a series of fluorophores in different solvents. In water, the probability of fluorescence excitation was nearly proportional to the integrated absorbance over a > 1,000-fold variation in absorbances. The probability of fluorescence excitation was enhanced up to 2,600-fold when the fluorophore was in a "scintillant" aromatic or hydrocarbon solvent. SPR emission spectra were similar to fluorescence emission spectra obtained with photon excitation. The single photon signal due to Bremsstrahlung increased with wavelength in agreement with theory. The distance dependence for the SPR signal predicted by the model was in good agreement with measurements in which a 14C donor was separated by known thicknesses of water from a fluorescently-coated coverglass. Quantitative predictions for radioluminescence signal as a function of donor-acceptor distance were developed for specific radioisotope-fluorophore geometries in biological samples.