Hydraulic conductivity of polymer matrices

Hydraulic permeability of multilayered collagen gel scaffolds under plastic compression-induced unidirectional fluid flow

Under conditions of free fluid flow, highly hydrated fibrillar collagen gels expel fluid and undergo gravity driven consolidation (self-compression; SC). This process can be accelerated by the application of a compressive stress (plastic compression; PC) in order to generate dense collagen scaffolds for tissue engineering. To define the microstructural evolution of collagen gels under PC, this study applied a two-layer micromechanical model that was previously developed to measure hydraulic permeability (k) under SC. Radially confined PC resulted in unidirectional fluid flow through the gel and the formation of a dense lamella at the fluid expulsion boundary which was confirmed by confocal microscopy of collagen immunoreactivity. Gel mass loss due to PC and subsequent SC were measured and applied to Darcy's law to calculate the thickness of the lamella and hydrated layer, as well as their relative permeabilities. Increasing PC level resulted in a significant increase in mass loss fraction and lamellar thickness, while the thickness of the hydrated layer dramatically decreased. Permeability of lamella also decreased from 1.8×10(-15) to 1.0×10(-15) m(2) in response to an increase in PC level. Ongoing SC, following PC, resulted in a uniform decrease in mass loss and k with increasing PC level and as a function SC time. Experimental k data were in close agreement with those estimated by the Happel model. Calculation of average k values for various two-layer microstructures indicated that they each approached 10(-15)-10(-14) m(2) at equilibrium. In summary, the two-layer micromechanical model can be used to define the microstructure and permeability of multi-layered biomimetic scaffolds generated by PC.

Artificial lymphatic drainage systems for vascularized microfluidic scaffolds

The formation of a stably perfused microvasculature continues to be a major challenge in tissue engineering. Previous work has suggested the importance of a sufficiently large transmural pressure in maintaining vascular stability and perfusion. Here we show that a system of empty channels that provides a drainage function analogous to that of lymphatic microvasculature in vivo can stabilize vascular adhesion and maintain perfusion rate in dense, hydraulically resistive fibrin scaffolds in vitro. In the absence of drainage, endothelial delamination increased as scaffold density increased from 6 to 30 mg/mL and scaffold hydraulic conductivity decreased by a factor of 20. Single drainage channels exerted only localized vascular stabilization, the extent of which depended on the distance between vessel and drainage as well as scaffold density. Computational modeling of these experiments yielded an estimate of 0.40-1.36 cm H2O for the minimum transmural pressure required for vascular stability. We further designed and constructed fibrin patches (0.8 × 0.9 cm(2)) that were perfused by a parallel array of vessels and drained by an orthogonal array of drainage channels; only with the drainage did the vessels display long-term stability and perfusion. This work underscores the importance of drainage in vascularization, especially when a dense, hydraulically resistive scaffold is used.

Computational design of drainage systems for vascularized scaffolds

This computational study analyzes how to design a drainage system for porous scaffolds so that the scaffolds can be vascularized and perfused without collapse of the vessel lumens. We postulate that vascular transmural pressure--the difference between lumenal and interstitial pressures--must exceed a threshold value to avoid collapse. Model geometries consisted of hexagonal arrays of open channels in an isotropic scaffold, in which a small subset of channels was selected for drainage. Fluid flow through the vessels and drainage channel, across the vascular wall, and through the scaffold were governed by Navier-Stokes equations, Starling's Law of Filtration, and Darcy's Law, respectively. We found that each drainage channel could maintain a threshold transmural pressure only in nearby vessels, with a radius-of-action dependent on vascular geometry and the hydraulic properties of the vascular wall and scaffold. We illustrate how these results can be applied to microvascular tissue engineering, and suggest that scaffolds be designed with both perfusion and drainage in mind.

Osmotic flow caused by polyelectrolytes

Osmotic flow of water caused by high concentrations of anionic polyelectrolytes across semipermeable membranes, permeable only to solvent and simple electrolyte, has been measured in a newly designed flow cell. The flow cell features small solution and solvent compartments and an efficient stirring mechanism. We have demonstrated that, while the osmotic pressure of the anionic polyelectrolytes is determined primarily by micro-counterions, the osmotic flow is determined by solution-dependent properties as embodied in the hydrodynamic frictional coefficient which is determined by the polymer backbone segment of the polyelectrolyte. The variation of the osmotic permeability coefficient, L(p)(o), with concentration and osmotic pressure closely correlated with the concentration dependence of this frictional coefficient. These studies confirm previous work that the kinetics of osmotic flow across a membrane impermeable to the osmotically active solute is primarily determined by the diffusive mobility of the solute.

Darcy permeability of agarose-glycosaminoglycan gels analyzed using fiber-mixture and donnan models

Agarose-glycosaminoglycan (GAG) membranes were synthesized to provide a model system in which the factors controlling the Darcy (or hydraulic) permeability could be assessed in composite gels of biological relevance. The membranes contained a GAG (chondroitin sulfate) that was covalently bound to agarose via terminal amine groups, and the variables examined were GAG concentration and solution ionic strength. The addition of even small amounts of GAG (0.4 vol/vol %) resulted in a twofold reduction in the Darcy permeability of 3 vol/vol % agarose gels. Electrokinetic coupling, caused by the negative charge of the GAG, resulted in an additional twofold reduction in the open-circuit permeability when the ionic strength was decreased from 1 M to 0.01 M. A microstructural hydrodynamic model was developed, based on a mixture of neutral, coarse fibers (agarose fibrils), and fine, charged fibers (GAG chains). Heterogeneity within agarose gels was modeled by assuming that fiber-rich, spherical inclusions were distributed throughout a fiber-poor matrix. That model accurately predicted the Darcy permeability when the ionic strength was high enough to suppress the effects of charge, but underestimated the influence of ionic strength. A more macroscopic approach, based on Donnan equilibria, better captured the reductions in Darcy permeability caused by GAG charge.

The contribution of solute-solvent exchange at the membrane surface to the reduction by albumin of the hydraulic permeability coefficient of an artificial semipermeable membrane

Infusion of synthetic colloids for tissue edema in inflammatory conditions reduces the hydraulic permeability coefficient (L(p)) of capillary membranes. However, the molecular mechanisms governing the modulation of L(p) of capillary membranes by these colloidal macromolecules are not known. In this study, I examined the effect of albumin on the L(p) of an artificial semipermeable membrane to determine whether solute-solvent exchange at the membrane surface may contribute to reduction of the L(p) of capillary membranes by colloidal macromolecules. The artificial membrane was used because of its well known molecular weight cutoff size and the absence of any specific interaction of albumin with such membranes. L(p) values of ultrafiltration membranes (molecular weight cutoff, 30,000) were measured by using an osmotic flow cell at a hydrostatic pressure difference (DeltaP) of 30 cm H(2)O in the absence of albumin or in the presence of albumin (2.4-8 wt%) at a DeltaP of 0 or 30 cm H(2)O. At all concentrations, albumin decreased L(p) values at both DeltaP values of 0 and 30 cm H(2)O compared with those in the absence of albumin (P < 0.05). These reductions were almost in a concentration-dependent manner and by almost half at 8 wt% albumin. This finding may be appropriately explained by slowed solute-solvent exchange at the membrane surface as the albumin concentration is increased. It is concluded that the reduction in the L(p) of capillary membranes by colloidal macromolecules is not caused solely by plugging of the capillary pores, but also by solute-solvent exchange at the capillary membrane surface.

IMPLICATIONS

Albumin concentrations more than 2.4 wt% decreased the water permeabilities of ultrafiltration membranes compared with those measured in the absence of albumin. The finding may be explained by slowed solute-solvent exchange at the membrane surface, suggesting that the reduction in water permeability of capillary membranes by colloidal macromolecules may not be caused solely by plugging of the capillary pores.

Non-linear dependence of interstitial fluid pressure on joint cavity pressure and implications for interstitial resistance in rabbit knee

AIMS

Synovium retains lubricating fluid in the joint cavity. Synovial outflow resistance estimated as dPj/dQs (Pj, joint fluid pressure and Qs trans-synovial flow) is greater, however, than expected from interstitial glycosaminoglycan concentration. This study investigates whether subsynovial fluid pressure increases with intra-articular pressure, as this would reduce the estimated resistance estimate.

METHODS

Interstitial fluid pressure (Pif) was measured as a function of distance from the joint cavity in knees of anaesthetized rabbits, using servo-null pressure-measuring micropipettes and using an external 'window'. Joint fluid pressure Pj was either endogenous (-2.4 +/- 0.4 cmH2O, mean +/- SEM) or held at approximately 4, 8 or 15.0 cmH2O by a continuous intra-articular saline infusion that matched the trans-synovial interstitial drainage rate.

RESULTS

At endogenous Pj the peri-articular Pif was subatmospheric (-1.9 +/- 0.3 cmH2O, n = 19). At raised Pj the Pif values became positive. Gradient dPif /dx was approximately 20 times steeper across synovium than subsynovium. Pif close to the synovium-subsynovium border (Pif*) increased as a non-linear function of Pj to 1.4 +/- 0.2 cmH2O (n = 23) at Pj = 4.3 +/- 0.1 cmH2O : 2.3 +/- 0.2 cmH2O (n = 17) at Pj = 7.6 +/- 0.2 cmH2O: and 3.0 +/- 0.4 cmH2O (n = 26) at Pj = 15 +/- 0.2 cmH2O (P = 0.03, anova).

CONCLUSIONS

Synovial resistivity is approximately 20x subsynovial resistivity. The increase in Pif*with Pj means that true synovial resistance d(Pj-Pif*)/dQs is overestimated 1.5x by dPj/dQs. This narrows but does not eliminate the gap between analysed glycosaminoglycan concentration, 4 mg ml(-1), and the net interstitial biopolymer concentration of 11.5 mg ml(-1) needed to generate the resistance.

Non-equilibrium thermodynamics of concentration polarization

Ultrafiltration is a membrane separation process with many applications, including the treatment of industrial wastes and the processing of milk and juices. Academics are also interested in ultrafiltration as a possible tool for measuring empirical coefficients such as the diffusion coefficient and the permeability. One particular region of an ultrafiltration system that is not yet fully understood, and is related to a decline in the efficiency, is the concentration polarization layer, which develops as the macromolecules retained by the membrane form a highly concentrated layer that attempts to diffuse back toward the bulk of the solution. Using the postulates of classical non-equilibrium thermodynamics, a complete model, which accounts for the fact that a concentration polarization layer may have properties of both a porous medium and a region undergoing Brownian diffusion, has been derived and applied to several systems from the literature.

Glycosaminoglycan concentration in synovium and other tissues of rabbit knee in relation to synovial hydraulic resistance

1. The hydraulic resistance of the synovial lining of a joint, a key coupling coefficient in synovial fluid turnover, is thought to depend on the concentration of biopolymers (glycosaminoglycans (GAGs) and collagen) in the synovial intercellular spaces, because these polymers create hydraulic drag. The primary aim of this study was to obtain microscopically separated, milligram samples of the very thin synovium from eight rabbit knees, and to analyse these quantitatively for GAGs (chondroitin sulphate, heparan sulphate and hyaluronan) and collagen to allow comparison with published hydraulic resistance data. Synovial fluid and femoral cartilage were also studied. 2. Synovium comprised 73 +/- 3% water by weight (mean +/- S.E.M.). Of the 270 mg solid per gram of wet tissue, protein formed 136 mg (by automated amino acid analysis), and of this 94 mg was collagen by hydroxyproline analysis. From the collagen mass and fibril volume fraction (0.153 of tissue by morphometry), fibrillar specific volume was calculated to be 1.43 ml per gram of molecular collagen, and fibril water content 47% by volume. 3. The concentration of chondroitin 4-sulphate (C4S) plus chondroitin 6-sulphate (C6S), measured by capillary zone electrophoresis was 0.55 mg per gram of synovium--much greater than in synovial fluid (0.04 mg g-1) and much less than in cartilage (27.8 mg g-1). The C4S/C6S ratio in synovium (7.3) differed from that in cartilage (0.7), indicating that different proteoglycans predominated in synovium. The heparan sulphate concentration, assayed by radioactive Ruthenium Red binding, was 0.92 mg per gram of synovium (synovial fluid, 0.08 mg g-1; cartilage, 0.72 mg g-1). 4. In contrast to sulphated GAGs, the hyaluronan concentration was highest in synovial fluid (3.53 mg g-1; biotinylated G1 domain binding assay). The concentration in synovial interstitium was only 0.56 mg g-1 (corrected for interstitial volume fraction, 0.66), even though there is open contact between synovial interstitium and synovial fluid. This may be due to exclusion or washout. 5. Total GAG mass was approximately 4 mg per gram of synovial interstitium. A model of trans-synovial flow indicated that a uniform GAG concentration of 4 mg g-1 is less than 1/3rd of that required to explain the experimental estimate of synovial hydraulic resistance. Errors in the resistance estimate do not appear to be large enough to resolve the problem. It is possible, therefore, that additional polymeric material in the interstitium, such as glycoproteins and proteoglycan core protein, may contribute to the hydraulic resistance.

Radial organization of interstitial exchange pathway and influence of collagen in synovium

The synovial intercellular space is the path by which water, nutrients, cytokines, and macromolecules enter and leave the joint cavity. In this study two structural factors influencing synovial permeability were quantified by morphometry (Delesse's principle) of synovial electronmicrographs (rabbit knee), namely interstitial volume fraction Vv.1 and the fraction of the interstitium obstructed by collagen fibrils. Mean Vv.1 across the full thickness was 0.66 +/- 0.03 SEM (n = 11); but Vv.1 actually varied systematically with depth normal to the surface, increasing nonlinearly from 0.40 +/- 0.04 (n = 5 joints) near the free surface to 0.92 +/- 0.02 near the subsynovial interface. Tending to offset this increase in transport space, however, the space "blocked" by collagen fibrils also increased nonlinearly with depth. Bundles of collagen fibrils occupied 13.6 +/- 2.4% of interstitial volume close to the free surface but 49 +/- 4.8% near the subsynovial surface (full-thickness average, 40.5 +/- 3.5%), with fibrils accounting for 48.6-57.1% of the bundle space. Because of the two counteracting compositional gradients, the space available for fibril-excluded transport (hydraulic flow and macromolecular diffusion) was relatively constant > 4 microns below the surface but constricted at the synovium-cavity interface. The space available to extracellular polymers was only 51-53% of tissue volume, raising their effective concentration and hence the lining's resistance to flow and ability to confine the synovial fluid.

Fluid movement across synovium in healthy joints: role of synovial fluid macromolecules

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A simple model for the function of proteoglycans and collagen in the response to compression of the intervertebral disc

The nucleus pulposus of the intervertebral disc exerts a pressure which enables it to support axial compression when contained by the annulus fibrosus. The disc was modelled as a thick-walled cylindrical pressure vessel in which the nucleus was contained radially by the annulus. As a result, the stress in the annulus had radial (compressive) as well as tangential (tensile) components. The radial stress at a given point in the annulus was considered to be balanced by the internal pressure which is expected to arise from the attraction of water by proteoglycans. There was a reasonable agreement between the calculated radial stress distribution and published results on the distribution of water within the annulus. As the internal pressure is expected to be isotropic, the annulus was expected to contribute to the axial resistance to compression of the disc; this contribution would be equal, in magnitude, to the radial stress. Predictions of the pressure distribution within the annulus were similar to published experimental measurements made in the radial and axial directions. The tangential stress within the annulus was considered to arise from the restoring stress in its strained collagen fibrils.