Concentration polarization phenomenon in the case of mechanical pressure difference on the membrane

We analyzed the transport of KCl solutions through the bacterial cellulose membrane and concentration boundary layers (CBLs) near membrane with pressure differences on the membrane. The membrane was located in horizontal-plane between two chambers with different KCL solutions. The membrane was located in horizontal-plane between two chambers with different KCL solutions. As results from the elaborated model, gradient of KCL concentration in CBLs is maximal at membrane surfaces in the case when pressure difference on the membrane equals zero. The amplitude of this maximum decreases with time of CBLs buildup. Application of mechanical pressure gradient in the direction of gradient of osmotic pressure on the membrane causes a shift of this maximum into the chamber with lower concentration. In turn, application of mechanical pressure gradient directed opposite to the gradient of osmotic pressure causes the appearance of maximum of concentration gradient in chamber with higher concentration. Besides, the increase of time of CBLs buildup entails a decrease of peak height and shift of this peak further from the membrane. Similar behavior is observed for distribution of energy dissipation in CBLs but for pressure difference on the membrane equal to zero the maximum of energy dissipation is observed in the chamber with lower concentration. We also measured time characteristics of voltage in the membrane system with greater KCl concentrations over the membrane. We can state that mechanical pressure difference on the membrane can suppress or strengthen hydrodynamic instabilities visible as pulsations of measured voltage. Additionally, time of appearance of voltage pulsations, its amplitude, and frequency depend on mechanical pressure differences on the membrane and initial quotient of KCl concentrations in chambers.     

The influence of the acetabular labrum seal,intact articular superficial zone and synovial fluid thixotropy on squeeze-film lubrication of a spherical synovial joint

A model of synovial fluid (SF) filtration by articular cartilage (AC) in a step-loaded spherical synovial joint at rest is presented. The effects of joint pathology (such as a depleted acetabular labrum, a depleted cartilage superficial zone consistent with early osteoarthritis and an inflammatory SF) on the squeezed synovial film are also investigated. Biphasic mixture models for AC (ideal fluid and elastic porous transversely isotropic two-layer matrix) and for SF (ideal and thixotropic fluids) are applied and the following results are obtained. If the acetabular labrum is able to seal the pressurised SF between the articular surfaces (as in the normal hip joint), the fluid in the synovial film and in the cartilage within the labral ring is homogeneously pressurised. The articular surfaces remain separated by a fluid film for minutes. If the labrum is destroyed or absent and the SF can escape across the contact edge, the fluid pressure is non-homogeneous and with a small jump at the articular surface at the very moment of load application. The ensuing synovial film filtration by porous cartilage is lower for the normal cartilage (with the intact superficial zone) than if this zone is already depleted or rubbed off as in the early stage of primary osteoarthritis. Compared with the inflammatory (Newtonian) SF, the normal (thixotropic) fluid applies favourably in the squeezed film near the contact centre only, yielding a thicker SF film there, but not affecting the minimum thickness in the fluid film profile at a fixed time. For all that, in the unsealed case for both the normal and pathological joint, the macromolecular concentration of the hyaluronic acid-protein complex in the synovial film quickly increases due to the filtration in the greater part of the contact. A stable synovial gel film, thick on the order of 10(-7)m, protecting the articular surfaces from the intimate contact, is formed within a couple of seconds. Boundary lubrication by the synovial gel is established if sliding motion follows until a fresh SF is entrained into the contact. This theoretical prediction is open for experimental verifications.     

Effect of cup abduction angle and head lateral microseparation on contact stresses in ceramic-on-ceramic total hip arthroplasty

A finite elements model was developed in order to evaluate the combined influence of the head lateral microseparation and the cup abduction angle on the contact pressure in Ceramic-on-Ceramic Total Hip Arthroplasty. The model's parameters were those used on the Leeds II hip simulator. A 32 mm head diameter and a 30 μm radial clearance was used. The cup was positioned with an abduction angle ranging from 45° to 90°. The medio-lateral microseparation varied from 0 to 500 μm. A load of 2500 N was applied through the head centre. For 45° abduction angle, edge loading appeared above a medial-lateral separation of 30 μm. Complete edge loading was obtained for a 60 μm medial-lateral separation. Under edge loading conditions, the contact area was found to be elliptical. For 45° abduction angle, as the head lateral separation increased, the maximal contact pressure increased from 66 MPa and converged to an asymptotic value of 205 MPa. Both cup abduction and lateral microseparation displacement induced a large increase in the stresses in Ceramic-on-Ceramic THA. However, this increase in contact pressure induced by higher abduction angle, became negligible as the lateral separation increased.     

Identification of cross-sectional parameters of lateral meniscal allografts that predict tibial contact pressure in human cadaveric knees

To guide the development of improved procedures for selecting meniscal allografts, the objective of this study was to identify which cross-sectional parameters of a lateral meniscal allograft predict the contact pressure of the articular surface of the tibia. To meet the objective, the contact pressure of the articular surface of the tibia was measured with a lateral meniscal autograft and a lateral meniscal allograft using pressure sensitive film in 15 fresh-frozen human cadaveric knees. Allografts were matched only in transverse dimensions to the autograft but not in cross-sectional dimensions. Knees were loaded to 1200 N in compression at flexion angles of 0, 15, 30 and 45 degrees using a load application system that allowed unconstrained motion in the remaining degrees of freedom. Five cross-sectional parameters for both of the grafts in each of the anterior, middle, and posterior regions were derived from measurements obtained using a laser-based non-contacting three-dimensional coordinate digitizing system (3-DCDS) (Haut et al., J. Orthop Res, 2000). Five contact variables (i.e. the maximum pressure, mean pressure, contact area, and anterior-posterior and medial-lateral locations of the centroid of contact area) were determined from the pressure sensitive film. When each allograft was paired with the corresponding autograft, the root mean squared percent differences for the cross-sectional parameters ranged from a minimum of 28% for the width of the posterior region to 572% for the height of the posterior region. The root mean squared percent differences between the contact variables for paired grafts were 29% for the maximum pressure, 19% for the mean pressure, and 24% for the contact area. Differences in the cross-sectional parameters between the grafts were related to differences in the contact variables using regression analysis. Difference in the width was most often a predictor variable in the regression models with R2 values > or = 0.45. Differences in all of the four remaining cross-sectional parameters were also important predictor variables. Because failure to match cross-sectional parameters causes substantial difference in contact variables between an allograft and autograft and because cross-sectional parameters predict the contact pressure on the tibial plateau, protocols used to prospectively select allografts should concentrate on matching cross-sectional parameters and particularly the width to those of the original meniscus.     

The thixotropic effect of the synovial fluid in squeeze-film lubrication of the human hip joint.

The thixotropic (shear-thinning) effect of the synovial fluid in squeeze-film lubrication of the human hip joint is evaluated, taking into account filtration of the squeezed synovial film by biphasic articular cartilage. A porous, homogeneous, elastic cartilage matrix filled with the interstitial ideal fluid, with the intact superficial zone (of lower permeability and stiffness in compression) already disrupted or worn away, models an early stage of arthritis. Due to a high viscosity of the normal synovial fluid at very low shear rates, the squeezed synovial film at a fixed time after the application of a steady load is found to be much thicker in a small central part of the lubricated contact area. In the remaining part, the film is thin as it corresponds to the Newtonian fluid with the same high-shear-rate viscosity. Filtration is lower for the normal cartilage with the intact superficial zone due to its lower permeability and compression stiffness. But even in the fictitious case of zero filtration, calculations show that the effect of thixotropy on the increase of the minimum synovial film thickness would manifest itself as late as after several tens of seconds since the physiologic load application. At that time, this thickness would be as low as about 0.3 microm. It follows that thixotropy of the normal synovial fluid (and so much more of the inflammatory fluid) is irrelevant in squeeze-film lubrication of both the normal and arthritic human hip joints.     

Strain-rate dependence of cartilage stiffness in unconfined compression: the role of fibril reinforcement versus tissue volume change in fluid pressurization

The strain and strain-rate-dependent response of articular cartilage in unconfined compression was studied theoretically. The transient stress and stiffness of cartilage were determined for strain rates ranging from zero to infinity. It is shown, for a given compressive strain, that the axial stress initially increases quickly as a function of strain rate, and then increases progressively more slowly towards the stress corresponding to the instantaneous response. The volume change of the tissue does not give its transient stiffness uniquely, because of the strong strain-rate dependence. The variation of tissue stiffness is primarily determined by the transient stiffness of the radial fibrils. Load sharing between the solid matrix and fluid pressurization also depends on the strain rate. At 15% axial compression, the matrix bears more than 80% of the applied load at a strain rate of 0.005%/s, while the fluid pressurization contributes more than 80% of the load at a strain rate of 0.15%/s. These results show the interplay between fibril reinforcement and fluid pressurization in articular cartilage: the fluid drives fibril stiffening which in turn produces high pore pressure at high strain rates.As a secondary objective of the present work, a fibrillar continuum element was formulated to replace the fibrillar spring element used previously in fibril-reinforced modeling, in order to eliminate the deformation incompatibility between the spring system and the nonfibrillar matrix. The results obtained using the two fibrillar elements were compared with the closed-form solutions for the static and instantaneous responses for the case of large deformation. It was found for unconfined compression that using the spring elements did not generally result in greater numerical errors than using the fibrillar continuum elements.     

A model of pulsatile flow in a uniform deformable vessel.

Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.     

Contact stress transients during functional loading of ankle stepoff incongruities

Cartilage deformation demonstrates viscoelastic behavior due to its unique structure. However, nearly all contact studies investigating incongruity-associated changes in cartilage surface stresses have been static tests. These tests have consistently measured only modest increases in contact stresses, even with large incongruities. In this study, an experimental approach measuring real-time contact stresses in human cadaveric ankles during quasi-physiologic motion and loading was used to determine how stepoff incongruities of the distal tibia affected contact stresses and contact stress gradients. Peak instantaneous contact stresses, in ankles with stepoffs between 1.0 and 4.0mm of the anterolateral articular surface, increased by between 2.3 x and 3.0 x compared to the corresponding intact ankle values. Peak instantaneous contact stress gradients in stepoff configurations increased by between 1.9 x and 2.6 x the corresponding intact configuration values. Anatomic reduction of the displaced fragment restored intact contact stresses and contact stress gradients. Intact and anatomic configurations demonstrated a heterogeneous population of low-magnitude, randomly oriented contact stress gradient vectors in contrast to high-magnitude, preferentially oriented gradients in stepoff configurations. Peak instantaneous contact stresses may be important pathomechanical determinants of post-traumatic arthritis. Abnormal contact stress gradients could cause regional pathological disturbances in cartilage stress and interstitial fluid distribution. Measuring contact stresses and contact stress gradients during motion allowed potential incongruity-associated pathologic changes in loading that occur over the complete motion cycle to be investigated.     

The inverse Womersley problem for pulsatile flow in straight rigid tubes

In this study a numerical solution for the problem of pulsating flow in rigid tubes is described. The method applies to the case of known flow rate waveform, as opposed to Womersley solution where the pressure gradient was the known quantity. The solution provides the pressure gradient and wall shear stress waveforms as well as the instantaneous velocity profiles. Results show that the method can be used to study the blood flow characteristics in large arteries.     

The transmission of load through the human hip joint

This paper describes the results of loading experiments carried out on human hip joints. The unloaded surfaces of the femoral head and the acetabulum are slightly incongruous. The location and magnitude of the contact areas between the surfaces therefore depend on the magnitude and direction of the applied load. The contact areas were determined experimentally for a variety of loads typical of normal walking. Two distinct contact areas were found on the anterior and posterior aspects of the acetabulum at light loads, gradually merging with increasing load until, at a certain transition load, the dome of the acetabulum comes into contact and contact is then complete. The value of the transition load depends on the rate of loading, due to creep of the cartilage, and was found to vary from 50 per cent of body weight in young specimens to 25 per cent of body weight for elderly specimens for rates of loading typical of normal walking. Thus, the dome of the acetabulum is out of contact for a substantial portion of the swing phase of normal walking.

The analysis of a much simplified model of the hip joint is presented. The dependence of contact area on load is demonstrated, but also a method of determining the transition load for complete contact from the load/deflection relation for the hip is suggested. The values of the transition load quoted above were obtained by this method. The analysis further indicates that the distribution of pressure between the articular surfaces depends critically on the distribution of cartilage thickness throughout the joint. It is suggested that the distribution of cartilage thickness is such as to lead to a state of uniform pressure at the upper end of the physiological load range. Some experimental evidence is presented in support of this suggestion.

It is concluded that the function of joint incongruity is to allow the articular surfaces to come out of contact at light loads so that the cartilage may be exposed to synovial fluid for the purposes of nutrition and lubrication. At large loads, the distribution of cartilage thickness ensures that a state of hydrostatic pressure is achieved in order that cartilage, with a large fluid content, may transmit large pressures without flow and consequent loss of its integrity.     

Pattern sensitivity to boundary and initial conditions in reaction-diffusion models

We consider Turing-type reaction-diffusion equations and study (via computer simulations) how the relationship between initial conditions and the asymptotic steady state solutions varies as a function of the boundary conditions. The results indicate that boundary conditions which are non-homogeneous with respect to the kinetic steady state give rise to spatial patterns which are much less sensitive to variations in the initial conditions than those obtained with homogeneous boundary conditions, such as zero flux conditions. We also compare linear pattern predictions with the numerical solutions of the full nonlinear problem.This work supported in part by U.S. Army Grant DAJA 37-81-C-0220 and the Science and Engineering Research Council of Great Britain Grant GR/c/63595     

Stresses at the meniscofemoral joint: elastostatic investigations on the applicability of interface elements

Stress distributions at the meniscofemoral joint were analysed and the applicability of nonlinear interface elements in a finite element model (FEM) were tested. Centred and 70% off-centre load cases with a complete, a partially removed or a totally removed medial meniscus were evaluated in two dimensions. Interface width was assumed to increase linearly from almost zero to 1 mm at the inner and outer border of the femoral condyles. Maximum interface forces were found at the centre of the condyles, decreasing to zero at the peripherical and intercondylar femoral border. Simulation data concerning a removed medial meniscus or medial 70% off-centre load with complete meniscus indicated higher medial contact forces in the first case. A decrease in the elastic modulus of the articular surface tissues caused two small force transfer peaks (femoral centre and intercondylar border), which were strongly influenced by the predefined gap width.     

Pullulan and dextran: uncommon composition dependent Flory-Huggins interaction parameters of their aqueous solutions

Vapor pressure measurements were performed for aqueous solutions of pullulan ( M w 280 kg/mol) and dextran ( M w 60 and 2100 kg/mol, respectively) at 25, 37.5, and 50 degrees C. The Flory-Huggins interaction parameters obtained from these measurements, plus information on dilute solutions taken from the literature, show that water is a better solvent for pullulan than for dextran. Furthermore, they evince uncommon composition dependencies, including the concurrent appearance of two extrema, a minimum at moderate polymer concentration and a maximum at high polymer concentration. To model these findings, a previously established approach, subdividing the mixing process into two clearly separable steps, was generalized to account for specific interactions between water and polysaccharide segments. Three adjustable parameters suffice to describe the results quantitatively; according to their numerical values, the reasons for the solubility of polysaccharides in water, as compared with that of synthetic polymers in organic solvents, differ in a principal manner. In the former case, the main driving force comes from the first step (contact formation between the components), whereas it is the second step (conformational relaxation) that is advantageous in the latter case.     

A method for measuring contact pressures instantaneously in articular joints

A method whereby instrumented pipes are inserted part of the way into articular cartilage from the underlying subchondral bone has been developed for measuring instantaneous contact pressures acting within articular joints. Contact pressures developed between two specimens cut from fresh cadaveric knee joints were measured with this technique and then subsequently with pressure-sensitive paper. Average contact pressures (load/contact area) were also calculated. Comparisons of the three sets of data show that contact pressures measured with the pressure pipe system are linearly related (p less than 0.001) to both the contact pressures measured with the pressure-sensitive paper and the calculated average contact pressures.     

An improved method of computing the wear factor for total hip prostheses involving the variation of relative motion and contact pressure with location on the bearing surface

A new method of computing the wear factor for total hip prostheses is presented. In the conventional method, only the resultant contact force and the track drawn by the point of its application are considered so that the product of the instantaneous force and sliding increment is integrated over one motion cycle. In the present, improved, method the contact pressure distribution is discretized by a large number of smaller normal forces, and the contribution of each is summed. This is important because the relative motion and contact pressure vary strongly with location, and because the transverse pressure component is substantial. Hence, the present surface integral represents the large contact surface better than the conventional line integral. A prerequisite for the surface integral was the method of computing the relative motion correctly anywhere on the contact surface, developed and published earlier by the present authors. For the pressure discretization, the contact surface was divided into nearly equal-sized surface elements. The contact pressure was modelled with ellipsoidal, paraboloidal and sinusoidal distributions. Two load cases were studied, double-peak and static. When an ellipsoidal contact pressure distribution extending over a hemisphere was discretized by 1000 element forces, the computed wear factor for double-peak load in a biaxial hip wear simulator was 30% lower than in the conventional resultant force case. The present method can be later developed further to involve the temporal variation of size and location of the contact surface.     

Correction of thermal gradient errors in stem thermocouple hygrometers

Stem thermocouple hygrometers were subjected to transient and stable thermal gradients while in contact with reference solutions of NaCl. Both dew point and psychrometric voltages were directly related to zero offset voltages, the latter reflecting the size of the thermal gradient. Although slopes were affected by absolute temperature, they were not affected by water potential. One hygrometer required a correction of 1.75 bars water potential per microvolt of zero offset, a value that was constant from 20 to 30 C.     

Comparative study of plantar pressure during step exercise in different floor conditions

Mechanical load has been estimated during step exercise based on ground reaction force (GRF) obtained by force platforms. It is not yet accurately known whether these measures reflect foot contact forces once the latter depend on footwear and are potentially modified by the compliant properties of the step bench. The aim of the study was to compare maximal and mean plantar pressure (PP), and maximal GRF obtained by pressure insoles after performing seven movements both over two metal force platforms and over the step bench. Fifteen step-experienced females performed the movements at the cadences of 130 and 140 beats per minute. PP and GRF (estimated from PP) obtained for each floor condition were compared. Maximal PP ranged from 29.27 +/- 9.94 to 47.07 +/- 12.88 N/cm2 as for metal platforms, and from 28.20 +/- 9.32 to 43.00 +/- 13.80 N/cm2 as for the step bench. Mean PP ranged from 11.09 +/- 1.62 to 14.32 +/- 2.06 N/cm2 (platforms) and from 10.71 +/- 1.54 to 14.22 +/- 1.77 N/cm2 (step bench). GRF (normalized body weight) ranged from 1.43 +/- 0.14 to 2.41 +/- 0.24 BW (platforms) and from 1.38 +/- 0.14 to 2.36 +/- 0.19 BW (step bench). No significant statistical differences were obtained for most of the comparisons between the two conditions tested. The results suggest that metal force platform surfaces are suitable to assess mechanical load during this physical activity. The forces applied to the foot are similar to the softer step bench and the hard force platform surface. This may reflect the ability of the performers to adapt their movement patterns to normalize the impact forces in different floor conditions.     

Mechanical and metabolic requirements for active lateral stabilization in human walking

Walking appears to be passively unstable in the lateral direction, requiring active feedback control for stability. The central nervous system may control stability by adjusting medio-lateral foot placement, but potentially with a metabolic cost. This cost increases with narrow steps and may affect the preferred step width. We hypothesized that external stabilization of the body would reduce the active control needed, thereby decreasing metabolic cost and preferred step width. To test these hypotheses, we provided external lateral stabilization, using springs pulling bilaterally from the waist, to human subjects walking on a force treadmill at 1.25 m/s. Ten subjects walked, with and without stabilization, at a prescribed step width of zero and also at their preferred step width. We measured metabolic cost using indirect calorimetry, and step width from force treadmill data. We found that at the prescribed zero step width, external stabilization resulted in a 33% decrease in step width variability (root-mean-square) and a 9.2% decrease in metabolic cost. In the preferred step width conditions, external stabilization caused subjects to prefer a 47% narrower step width, with a 32% decrease in step width variability and a 5.7% decrease in metabolic cost. These results suggest that (a). human walking requires active lateral stabilization, (b). body lateral motion is partially stabilized via medio-lateral foot placement, (c). active stabilization exacts a modest metabolic cost, and (d). humans avoid narrow step widths because they are less stable.     

An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation

We examine traveling-wave solutions for a generalized nonlinear-diffusion Fisher equation studied by Hayes [J. Math. Biol. 29, 531–537 (1991)]. The density-dependent diffusion coefficient used is motivated by certain polymer diffusion and population dispersal problems. Approximate solutions are constructed using asymptotic expansions. We find that the solution will have a corner layer (a shock in the derivative) as the diffusion coefficient approaches a step function. The corner layer at z = 0 is matched to an outer solution for z < 0 and a boundary layer for z > 0 to produce a complete solution. We show that this model also admits a new class of nonphysical solutions and obtain conditions that restrict the set of valid traveling-wave solutions. Supported by a National Science Foundation graduate fellowship. This work was performed under National Science Foundation grant DMS-9024963 and Air Force Office of Scientific Research grant AFOSR-F49620-94-1-0044.