An analysis of the squeeze-film lubrication mechanism for articular cartilage.

An asymptotic analysis of a lubrication problem is presented for a model of articular cartilage and synovial fluid under the squeeze-film condition. This model is based upon the following constitutive assumptions: (1) articular cartilage is a linear porous-permeable biphasic material filled with a linearly viscous fluid (i.e. Newtonian fluid); (2) synovial fluid is also a linearly viscous fluid. The geometry of the problem is defined by assuming that (1) cartilage is a uniform layer of thickness H; (2) synovial fluid is a very thin layer compared to H; (3) the radius R of the load-supporting area (or the effective radius of curvature of joint surface, Ri) is large compared to H. Squeeze-film action is generated in the lubricant by a step loading function applied onto the two bearing surfaces. The model assumptions and the material properties yield two small parameters in the mathematical formulation. Based on these two small parameters, two coupled nonlinear partial differential equations were derived from an asymptotic analysis of the problem: one for the lubricant (analogous to the Reynolds equation) and one for the cartilage. For known properties of normal cartilage, our calculations show: (1) the cartilage layer deforms to enlarge the load-supporting area; (2) cartilage deformation acts to reduce the lateral fluid speed in the lubricant, thus prolonging the squeeze-film time which ranges from 1 to 10 s; (3) lubricant fluid in the gap is forced from the central high-pressure region into cartilage, and expelled from the tissue at the low-pressure periphery of the load-bearing region; and (4) tensile hoop stress exists at the cartilage surface despite the compressive squeeze-film loading condition. This hoop stress results directly from the radial flow of the interstitial fluid in the cartilage layer.     

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.     

A novel method for in vivo knee prosthesis wear measurement

Wear remains an important cause of failure in knee replacement. Of the current methods of early performance assessment or prediction, simulators have been un-physiological, single X-ray film analyses remain limited by accuracy and retrieval and survival methods have a prohibitive time scale. An accurate method is needed to allow a timely assessment of polyethylene component wear in vivo, when a new design is introduced, in order to predict likely outcome. We present a new method for measuring wear in vivo that we believe will allow this prediction of long-term wear. X-ray film pairs were taken of implanted prosthetic metal components. When the X-ray system was calibrated, projections of the appropriate Computer Aided Design (CAD) model could be matched to the shapes on the scanned X-ray films to find component positions. Interpenetration of the metal femoral component into the polyethylene component could then be established and represents our estimate of "wear". This method was used to measure in vivo prosthesis wear to an accuracy of 0.11 mm.     

Adaptative control of above knee electro-hydraulic prosthesis.

Conventional designs of an above-knee prosthesis are based on mechanisms with mechanical properties (such as friction, spring and damping coefficients) that remain constant during changing cadence. These designs are unable to replace natural legs due to the lack of active knee joint control. Since the nonlinear and time-varying dynamic coupling between the thigh and the prosthetic limb is high during swing phase, an adaptive control is employed to control the knee joint motion. Two dimensional simulation indicates that the adaptive controller can improve the appearance of gait pattern. It is adaptable to walking speed and can compensate for the variations of hip moment, hip trajectory and toe-off conditions.     

Numerical investigations and analysis on the effects of geometrical parameters on the group velocity of transverse magnetic pump mode and free electron laser instability

In this paper, we have numerically investigated the effects of various geometrical parameters of a backward wave oscillator, filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate R ₀ of a seeded free electron laser. On changing mean radius corrugation amplitude h and corrugation period z ₀ of backward wave oscillator; the ponderomotive potential of space charge wave changes. This in turn, changes the coupling strength of TM mode with negative beam space charge mode and hence the growth rate of parametric instability of free electron laser. A dispersion relation is derived and numerically solved for various geometrical parameters of backward wave oscillator and beam profile. A relation for Γ is also derived and computed numerically. The instability growth scales directly to the square root of beam density and inversely as seven power of relativistic gamma factor γ₀. Published in Russian in Fizika Plazmy, 2009, Vol. 35, No. 2, pp. 179–184. This text was submitted by the authors in English.     

Numerical model proposed for a temporomandibular joint prosthesis based on the recovery of the healthy movement

The temporomandibular joint (TMJ) is an anatomical set of the buco-maxillary system that allows the movement of the mandible in most varied ways. Several factors can influence the malfunctioning of the joint and lead to the use of a total prosthesis. However, current prostheses do not supply the maximum amplitude of movement during protrusion and opening, due to mainly the anatomical differences between patients. For this reason, this article aims to study the patient’s kinematic characteristics for a better comprehension of the problem and, consequently, to develop a numerical model for TMJ prostheses able to recover the healthy movement. The numerical model is based on the development of a mechanical joint whose profile is able to reproduce the movement of the health system. The results obtained through the developed model showed a good agreement with the experimental results, representing, therefore, a promising alternative to approach the problems related to TMJ.     

NMR simulation analysis of statistical effects on quantifying cerebrovascular parameters

Determining tissue structure and composition from the behavior of the NMR transverse relaxation during free induction decay and spin echo formation has seen significant advances in recent years. In particular, the ability to quantify cerebrovascular network parameters such as blood volume and deoxyhemoglobin concentration from the NMR signal dephasing has seen intense focus. Analytical models have been described, based on statistical averaging of randomly oriented cylinders in both the static and slow diffusion regimes. However, the error in estimates obtained from these models when applied to systems in which the statistical assumptions of many, randomly oriented perturbers are violated has not been systematically investigated. Using a deterministic simulation that can include diffusion, we find that the error in estimated venous blood volume fraction and deoxyhemoglobin concentration obtained using a static dephasing regime statistical model is inversely related to the square root of number of blood vessels. The most important implication of this is that the minimum imaging resolution for accurate deoxyhemoglobin and blood volume estimation is not bound by hardware limitations, but rather by the underlying tissue structure.     

The design of a model for a three dimensional stress analysis of the cement layer beneath the medial plateau of a knee prosthesis

Factors which have influenced the design of a large scale model for an analysis of the strain in three dimensions of the cement layer beneath the medial plateau of a knee prosthesis are discussed. Materials were selected to model the medial tibial plateau, underlying cement and bone for a typical prosthesis and a two dimensional finite element analysis was used to indicate where the strain gauges should be embedded in the model.     

Limited rotation of the mobile-bearing in a rotating platform total knee prosthesis

The hypothesis of this study was that the polyethylene bearing in a rotating platform total knee prosthesis shows axial rotation during a step-up motion, thereby facilitating the theoretical advantages of mobile-bearing knee prostheses. We examined 10 patients with rheumatoid arthritis who had a rotating platform total knee arthroplasty (NexGen LPS mobile, Zimmer Inc. Warsaw, USA). Fluoroscopic data was collected during a step-up motion six months postoperatively. A 3D-2D model fitting technique was used to reconstruct the in vivo 3D kinematics. The femoral component showed more axial rotation than the polyethylene mobile-bearing insert compared to the tibia during extension. In eight knees, the femoral component rotated internally with respect to the tibia during extension. In the other two knees the femoral component rotated externally with respect to the tibia. In all 10 patients, the femur showed more axial rotation than the mobile-bearing insert indicating the femoral component was sliding on the polyethylene of the rotating platform during the step-up motion. Possible explanations are a too limited conformity between femoral component and insert, the anterior located pivot location of the investigated rotating platform design, polyethylene on metal impingement and fibrous tissue formation between the mobile-bearing insert and the tibial plateau.     

A planar model of the knee joint to characterize the knee extensor mechanism

A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.     

Novel route to fatigue-resistant fully sintered ultrahigh molecular weight polyethylene for knee prosthesis

The role of entanglements in obtaining a homogeneous product of ultrahigh molecular weight polyethylene (UHMW-PE) has been explored. Studies performed in this report show that a disentangled state before melting is a prerequisite to obtain homogeneous products of an intractable polymer like UHMW-PE. The disentangled state is obtained directly from the reactor by controlling the polymerization conditions or in the solid state when there is enhanced chain mobility along the c axis of a unit cell. The disentangled state is maintained in the melt over a period of time, invoking implications in polymer rheology. This approach is applicable to polymers in general. The homogeneous fully sintered UHMW-PE, obtained for the first time, shows a considerable decrease in oxygen permeability and an increase in toughness and fatigue resistance. Such homogeneous products of UHMW-PE are beneficial in highly demanding applications, especially in knee prosthesis, where the polymer is used as an inlay between the human bone and a metal or ceramic part, which slides against the polyethylene component during normal gait.     

Computer-aided material balancing for prediction of fermentation parameters.

Despite the importance of biomass as a parameter in fermentation processes, there are no commercially available sensors suitable for its measurement. An indirect approach for the assessment of biomass concentration can be based on material balances and on the direct monitoring of fermentation parameters for which there are established sensors (e.g., gaseous oxygen and carbon dioxide). As a consequence, this method requires no assumption of cellular yield coefficients or rate constants. This approach is also readily adaptable to general use since it requires only some knowledge of the compositions of the substrate, cells, and noncellular products.     

Effect of severity of knee osteoarthritis on the variability of gait parameters

Gait analysis has provided important information concerning gait patterns and variability of gait in patients with knee osteoarthritis (OA) of varying severity. The objective of this study was to clarify how the variability of gait parameters is influenced by the severity of knee OA. Gait analysis was performed at three different controlled walking speeds in three groups of subjects with varying degrees of knee OA (20 healthy subjects with no OA and 90 patients with moderate or severe OA). The variability of gait parameters was characterized by the coefficient of variance (CV) of spatial-temporal parameters, as well as by the mean coefficient variance (MeanCV) of angular parameters. Based on our results, we conclude that the complexity of gait decreases if the walking speed differs from the self-selected speed. In patients with knee OA, the decreased variability of angular parameters on the affected side represents decreased joint flexibility. This leads to decreased consistency in movements of the lower limbs from stride-to-stride, as shown by increased variability of spatial-temporal parameters. Decreased joint flexibility and consistency of movement can be associated with decreased complexity of movement. Other joints of the kinetic chain, such as joints of the non-affected side and the pelvis, play an important role in compensation and adaptation of step-by step motion and in the ability of secure gait. Results suggest that the variability of gait associated with knee osteoarthritis is gender-dependent. During rehabilitation, particular attention must be paid to improving gait stability and proprioception and gender differences should be taken into account.     

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

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

The catalytic mechanism of carbonic anhydrase. Hydrogen-isotope effects on the kinetic parameters of the human C isoenzyme.

1. The steady-state kinetics of the interconversion of CO2 and HCO3 catalyzed by human carbonic anhydrase C was studied using 1H2O and 2H2O as solvents. The pH-independent parts of the parameters k(cat) and Km are 3-4 times larger in 1H2O than in 2H2O for both directions of the reaction, while the ratios k(cat)/Km show much smaller isotope effects. With either CO2 or HCO3 as substrate the major pH dependence is observed in k(cat), while Km appears independent of pH. The pKa value characterizing the pH-rate profiles is approximately 0.5 unit larger in 2H2O than in 1H2O. 2. The hydrolysis of p-nitrophenyl acetate catalyzed by human carbonic anhudrase C is approximately 35% faster in 2H2O than in 1H2O. In both solvents the pKa values of the pH-rate profiles are similar to those observed for the CO2-HCO3 interconversion. 3. It is tentatively proposed that the rate-limiting step at saturating concentrations of CO2 or HCO3 is an intramolecular proton transfer between two ionizing groups in the active site. It cannot be decided whether the transformation between enzyme-bound CO2 and HCO3 involves a proton trnasfer or not.     

Numerical analysis of the flux and force generated by a correlation ratchet mechanism

 The correlation ratchet (CR) has been proposed as a possible mechanism for the operation of biomolecular motors. To test whether a CR mechanism is applicable to any particular motor, it is necessary to evaluate the unloaded velocity and the stall force of the CR mechanism. This paper is concerned with efficient numerical procedures for the determination of these quantities. In particular, the numerical results indicate that the stall force of a CR mechanism is quite limited, despite wide variations of the CR parameters. Received: 24 May 2000 / Revised version: 5 November 2001 / Published online: 8 May 2002     

Numerical analysis of an osseointegrated prosthesis fixation with reduced bone failure risk and periprosthetic bone loss

Currently available implants for direct attachment of prosthesis to the skeletal system after transfemoral amputation (OPRA system, Integrum AB, Sweden and ISP Endo/Exo prosthesis, ESKA Implants AG, Germany) show many advantages over the conventional socket fixation. However, restraining biomechanical issues such as considerable bone loss around the stem and peri-prosthetic bone fractures are present. To overcome these limiting issues a new concept of the direct intramedullary fixation was developed. We hypothesize that the new design will reduce the peri-prosthetic bone failure risk and adverse bone remodeling by restoring the natural load transfer in the femur. Generic CT-based finite element models of an intact femur and amputated bones implanted with 3 analyzed implants were created and loaded with a normal walking and a forward fall load. The strain adaptive bone remodeling theory was used to predict long-term bone changes around the implants and the periprosthetic bone failure risk was evaluated by the von Mises stress criterion. The results show that the new design provides close to physiological distribution of stresses in the bone and lower bone failure risk for the normal walking as compared to the OPRA and the ISP implants. The bone remodeling simulations did not reveal any overall bone loss around the new design, as opposed to the OPRA and the ISP implants, which induce considerable bone loss in the distal end of the femur. This positive outcome shows that the presented concept has a potential to considerably improve safety of the rehabilitation with the direct fixation implants.