Mechanism of osmotic flow in a periodic fiber array

The classic analysis by Anderson and Malone (Biophys J 14: 957-982, 1974) of the osmotic flow across membranes with long circular cylindrical pores is extended to a fiber matrix layer wherein the confining boundaries are the fibers themselves. The equivalent of the well-known result for the reflection coefficient sigma0 = (1 - phi)2, where phi is the partition coefficient, is derived for a periodic fiber array of hexagonally ordered core proteins. The boundary value problem for the potential energy function describing the solute distribution surrounding each fiber is solved by defining an equivalent fluid annulus in which the pressures and osmotic forces are determined. This model is of special interest in the osmotic flow of water across a capillary wall, where recent experimental studies suggest that the endothelial glycocalyx is a quasiperiodic fiber array that serves as the primary molecular sieve for plasma proteins. Results for the reflection coefficient are presented in terms of two dimensionless numbers, alpha = a/R and beta = b/R, where a and b are the solute and fiber radii, respectively, and R is the outer radius of the fluid annulus. In general, the results differ substantially from the classic expression for a circular pore because of the large difference in the shape of the boundary along which the osmotic force is generated. However, as in circular pore theory, one finds that the reflection coefficients for osmosis and filtration are the same.     

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

Configurational effect on the reflection coefficient for rigid solutes in capillary pores

Osmosis-driven flow through a leaky porous membrane is analyzed by combining the relevant equations describing spatial and orientational distributions of rigid non-spherical solute particles with the equations of fluid flow in a single capillary which is very narrow compared to its length. The capillary cross-section is either circular or rectangular and connects two bulk solution reservoirs having equal pressures but unequal concentrations of solute (osmotic pressure). The objective of this analysis is to study the effect of particle and pore shape on the reflection coefficient (σ₀). The most significant result is that for solute particles of any eccentricity from one (sphere) to infinity (needle) in either the circular or rectangular pores, σ₀ ≈ (1?K)², where K is the pore-bulk equilibrium partition coefficient. A corollary of this result is that, comparing solute particles of equal volume, the more elongated a solute is the higher is its reflection coefficient; furthermore, for a given solute, the reflection coefficient is higher for pores that are more eccentric compared to a circle of equal area.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25 mM glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption, Jv, and to measure the coefficient of osmotic flow, Lp. The clearances from the perfusion fluid of all other test solutes were approximately proportional to Jv. From Lp and rates of clearances as a function of Jv and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 A) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function of Jv. From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any given Jv and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.     

Osmosis: a bimodal theory with implications for symmetry

A theory is advanced that volume transfer across a membrane pore during osmosis takes place in two modes: if solute is sterically excluded from the pore a pressure gradient is set up and viscous flow of solvent results; if solute can enter the pore then osmotic flow is a diffusive phenomenon, and there is no pressure gradient in any part of the pore to which solute has access, even at low concentration due to a repulsive wall field. As a consequence the reflexion coefficients sigma s and sigma f for osmosis and ultrafiltration are not equal, although equality is usually assumed to result from an underlying thermodynamic reciprocity; instead, the two coefficients represent essentially different processes. These results follow from three basic thermodynamic considerations which have usually been overlooked: (i) there is a qualitative difference between a permeable pore and an impermeable one, the latter having a discontinuity of solute activity at the mouth, which the former does not; (ii) the osmotic pressure within the pore is determined by the activity of solute not the concentration; (iii) the effective resistance to flow through a channel depends upon the nature of the régime, being different for diffusive and viscous flow. An expression for sigma s is derived and shown to be compatible with experimental data on polymer membranes and homoporous bilayers.     

Single Water Channels of Aquaporin-1 Do not Obey the Kedem-Katchalsky Equations

The Kedem-Katchalsky (KK) equations are often used to obtain information about the osmotic properties and conductance of channels to water. Using human red cell membranes, in which the osmotic flow is dominated by Aquaporin-1, we show here that compared to NaCl the reflexion coefficient of the channel for methylurea, when corrected for solute volume exchange and for the water permeability of the lipid membrane, is 0.54. The channels are impermeable to these two solutes which would seem to rule out flow interaction and require a reflexion coefficient close to 1.0 for both. Thus, two solutes can give very different osmotic flow rates through a semi-permeable pore, a result at variance with both classical theory and the KK formulation. The use of KK equations to analyze osmotic volume changes, which results in a single hybrid reflexion coefficient for each solute, may explain the discrepancy in the literature between such results and those where the equations have not been employed. Osmotic reflexion coefficients substantially different from 1.0 cannot be ascribed to the participation of other 'hidden' parallel aqueous channels consistently with known properties of the membrane. Furthermore, we show that this difference cannot be due to second-order effects, such as a solute-specific interaction with water in only part of the channel, because the osmosis is linear with driving force down to zero solute concentration, a finding which also rules out the involvement of unstirred-layer effects. Reflexion coefficients smaller than 1.0 do not necessitate water-solute flow interaction in permeable aqueous channels; rather, the osmotic behaviour of impermeable molecular-sized pores can be explained by differences in the fundamental nature of water flow in regions either accessible or inaccessible to solute, created by a varying cross-section of the channel.     

Permeability characteristics of the basement membrane (basal lamella) of the intestine of Ascaris suum

Permeability characteristics have been determined for isolated ribbons of the basement membrane of the intestine ofAscaris suum. The solute permeability coefficient (P_c) was measured for a series of hydrophobic, nonionic molecules of graded molecular size. The geometric pore area per unit path length (A_o/Δx) was estimated to be 24.0 cm from the diffusion rates for the various solute molecules. A filtration coefficient (L_p) of 18.1×10^?12 cm⁵/dyne-sec was determined by a method that employs osmotic pressure. The preceding values were used to calculate an average pore radius of 24.0 A for the membrane. The unstirred layer was estimated to be 30μm thick from measurements of the change in the rate of diffusion of water across the membrane with change in the rate of perfusion. The preceding values were used to calculate a reflection coefficien (σ), effective permeability coefficient (ω′), and a permeability coefficient (ω). The results support the view that this basement membrane functions as a filter and selective barrier to diffusion of constituents of the worm's body fluid.     

Permeability studies on red cell membranes of dog, cat, and beef

Water permeability coefficients of dog, cat, and beef red cell membranes have been measured under an osmotic pressure gradient. The measurements employed a rapid reaction stop flow apparatus with which cell shrinking was measured under a relative osmotic pressure gradient of 1.25 to 1.64 times the isosmolar concentration. For the dog red cell the osmotic permeability coefficient is 0.36 cm⁴/(sec, osmol). The water permeability coefficient for the dog red cell under a diffusion gradient was also measured (rate constant = 0.10/msec). The ratio between the two permeabilities was used to calculate an equivalent pore radius of 5.9 A. This value agrees welt with an equivalent pore radius of 6.2 A obtained from reflection coefficients of nonelectrolyte water-soluble molecules, and is consistent with data on the permeability of the dog red cell membrane to glucose. These data provide evidence supporting the existence of equivalent pores in single biological membranes.     

Osmotic flow equations for leaky porous membranes

A basic set of equations describing the flows of volume (Jv) and solute (Js) across a leaky porous membrane, coupled to the differences of osmotic and hydrostatic pressures d pi and dP has been derived by using general frictional theory. Denoting the mean pore concentration of solute by c*s and the hydraulic and diffusive conductances by Lp and Ps/RT the equations take the form Jv = LpdP + sigma sLp d pi Js = c*s(1 - sigma f)Jv + Ps d pi/RT sigma s = theta (1 - DsVs/DwVw - Ds/Dos) sigma f = 1 - theta DsVs/DwVw - Ds/Dos in which Dw and Ds are the diffusion coefficients for water and solute in the pore and Dos that for free solution. The relation between the reflection coefficients sigma s and sigma f for osmosis and ultrafiltration is then given by sigma s = sigma f - (1- theta)(1 - Ds/Dos), where theta is the diffusive-driven:pressure-driven flow ratio. These equations follow from the fact that in leaky pores osmosis occurs by diffusion alone and that there cannot be any Onsager symmetry leading to sigma s = sigma f. Symmetry holds in the limits where either the pore is small, when sigma s = sigma f = 1, or where the pore is large when sigma s = sigma f = 0.     

Finite element implementation of mechanochemical phenomena in neutral deformable porous media under finite deformation

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http:∕∕mrl.sci.utah.edu∕software).     

Water relations of the pine exine

BACKGROUND AND AIMS: Water adhesion forces, water absorption capacity and permeability of the pine exine were investigated to consider a possible function of sporopollenin coatings in the control of water transport. METHODS: The experiments were carried out with sporopollenin capsules obtained from pine pollen consisting of an empty central capsule and two sacci. Changes in the concentration of excluded dextran molecules in the medium were analysed to quantify water absorption by purified exine fragments and the osmotic volume flow out of the intact central capsule. KEY RESULTS: The contact angle of sporopollenin to water is higher than the one to ethanol and lower than the one to n-heptane. The water-filled pore space in pine sporopollenin amounts to only 20.6 % of the matrix volume. A monosaccharide was excluded from 15 % and a trisaccharide from about 38 % of this space. Shrinkage of the central capsule induced by permeable osmotica was transient, whereas that induced by sodium polyacrylate (2100 g mol(-1)) was stable. Values obtained for the hydraulic conductance L(P) of the exine (0.39-0.48 microm s(-1) MPa(-1)) are comparable in size to those of biomembranes. Sodium sulfate solutions induced a significant osmotic flow through the exine (reflection coefficient at least 0.6). The exine around the central capsule can be ruptured by equilibration of its lumen with a concentrated electrolyte solution and subsequent transfer to water. The denatured protoplast along with the intact intine was ejected when pollen grains were subjected to this osmotic shock treatment. CONCLUSIONS: The pine exine is easily wetted with water and does not represent a significant barrier to water exchange either liquid or gaseous. Through osmotic burst, it can be separated from the intine. The effect of salts and small solute molecules on water fluxes may be functionally significant for rehydration upon pollination.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

Summary The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25mm glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption,J _v , and to measure the coefficient of osmotic flow,L _p . The clearances from the perfusion fluid of all other test solutes were approximately proportional toJ _v . FromL _p and rates of clearances as a function ofJ _v and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 Å) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function ofJ _v . From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any givenJ _v and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.     

Effects of hypoproteinemia on lung microvascular protein sieving and lung lymph flow

Experiments were conducted on five chronically instrumented unanesthetized sheep to determine the effects of sustained hypoproteinemia on lung fluid balance. Plasma total protein concentration was decreased from a control value of 6.17 +/- 0.019 to 3.97 +/- 0.17 g/dl (mean +/- SE) by acute plasmapheresis and maintained at this level by chronic thoracic lymph duct drainage. We measured pulmonary arterial pressure, left atrial pressure, aortic pressure, central venous pressure, cardiac output, oncotic pressures of both plasma and lung lymph, lung lymph flow rate, and lung lymph-to-plasma ratio of total proteins and six protein fractions for both control base-line conditions and hypoproteinemia base-line conditions. Moreover, we estimated the average osmotic reflection coefficient for total proteins and the solvent drag reflection coefficients for the six protein fractions during hypoproteinemia. Hypoproteinemia caused significant decreases in lung lymph total protein concentration, lung lymph-to-plasma total protein concentration ratio, and oncotic pressures of plasma and lung lymph. There were no significant alterations in the vascular pressures, lung lymph flow rate, cardiac output, or oncotic pressure gradient. The osmotic reflection coefficient for total proteins was found to be 0.900 +/- 0.004 for hypoproteinemia conditions, which is equal to that found in a previous investigation for sheep with a normal plasma protein concentration. Our results suggest that hypoproteinemia does not alter the lung filtration coefficient nor the reflection coefficients for plasma proteins. Possible explanations for the reported increase in the lung filtration coefficient during hypoproteinemia by other investigators are also made.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. I. Inequality of reflection coefficients for volume flow and solute flow.

The Kirkwood formulation of the Stefan-Maxwell equations is used to develop the transport equations for a membrane bounded by nonideal, nondilute solutions. The reflection coefficients for volume flow and solute flow are not equal but are related by a simple expression that depends on the concentration of the bounding solutions. The ratio of the two coefficients is independent of heteroporous membrane structure and the thickness of adjacent boundary layers. Experimental measurements of these reflection coefficients for sucrose transport across Cuprophan verify this relationship; this indicates that the Onsager reciprocal relation, which is assumed by the theory, holds for nonideal, nondilute solutions. The two reflection coefficients may be made operationally identical by a simple redefination of the osmotic driving force.     

A mixture theory analysis for passive transport in osmotic loading of cells

The theory of mixtures is applied to the analysis of the passive response of cells to osmotic loading with neutrally charged solutes. The formulation, which is derived for multiple solute species, incorporates partition coefficients for the solutes in the cytoplasm relative to the external solution, and accounts for cell membrane tension. The mixture formulation provides an explicit dependence of the hydraulic conductivity of the cell membrane on the concentration of permeating solutes. The resulting equations are shown to reduce to the classical equations of Kedem and Katchalsky in the limit when the membrane tension is equal to zero and the solute partition coefficient in the cytoplasm is equal to unity. Numerical simulations demonstrate that the concentration-dependence of the hydraulic conductivity is not negligible; the volume response to osmotic loading is very sensitive to the partition coefficient of the solute in the cytoplasm, which controls the magnitude of cell volume recovery; and the volume response is sensitive to the magnitude of cell membrane tension. Deviations of the Boyle-van't Hoff response from a straight line under hypo-osmotic loading may be indicative of cell membrane tension.     

Osmotic Biosensors. How to Use a Characean Internode for Measuring the Alcohol Content of Beer

Isolated internodes of Chara corallina and Nitella flexilis have been used to determine the concentration of one passively permeating solute in the presence of non-permeating solutes. The technique was based on the fact that the shape of the peaks of the biphasic responses of cell turgor (as measured in a conventional way using the cell pressure probe) depended on the concentration and composition of the solution and on the permeability and reflection coefficients of the solutes. Peak sizes were proportional to the concentration of the permeating solute applied to the cell. Thus, using the selective properties of the cell membrane as the sensing element and changes of turgor pressure as the physical signal, plant cells have been used as a new type of biosensor based on osmotic principles. Upon applying osmotic solutions, the responses of cell turgor (P) exactly followed the P(t) curves predicted from the theory based on the linear force/flow relations of irreversible thermodynamics. The complete agreement between theory and experiment was demonstrated by comparing measured curves with those obtained by either numerically solving the differential equations for volume (water) and solute flow or by using an explicit solution of the equations. The explicit solution neglected the solvent drag which was shown to be negligible to a very good approximation. Different kinds of local beers (regular and de-alcoholized) were used as test solutions to apply the system for measuring concentrations of ethanol. The results showed a very good agreement between alcohol concentrations measured by the sensor technique and those obtained from conventional techniques (enzymatic determination using alcohol dehydrogenase or from measurement of the density and refraction index of beer). However, with beer as the test solution, the characean internodes did show irreversible changes of the transport properties of the membranes leading to a shift in the responses when cells were treated for longer than 1 h with diluted beer. The accuracy and sensitivity of the osmotic biosensor technique as well as its possible applications are discussed.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

Interstitial albumin concentration measured during growth of perivascular cuffs in liquid-filled rabbit lung.

The growth rate and albumin concentration of interstitial fluid cuffs were measured in isolated rabbit lungs inflated with albumin solution (3 g/dl) to constant airway (Paw) and vascular pressures for up to 10 h. Cuff size was measured from images of frozen lung sections, and cuff albumin concentration (Cc) was measured from the fluorescence of Evans blue labeled albumin that entered the cuffs from the alveolar space. At 5-cmH2O Paw, cuff size peaked at 1 h and then decreased by 75% in 2 h. The decreased cuff size was consistent with an osmotic absorption into the albumin solution that filled the vascular and alveolar spaces. At 15-cmH2O Paw, cuff size peaked at 0.25 h and then remained constant. Cc rose continuously at both pressures, but was greater at the higher pressure. The increasing Cc with a constant cuff size was modeled as diffusion through epithelial pores. Initial Cc-to-airway albumin concentration ratio was 0.1 at 5-cmH2O Paw and increased to 0.3 at 15 cmH2O, a behavior that indicated an increased permeability with lung inflation. Estimated epithelial reflection coefficient was 0.9 and 0.7, and equivalent epithelial pore radii were 4.5 and 6.1 nm at 5- and 15-cmH2O Paw, respectively. The initial cuff growth occurred against an albumin colloid osmotic pressure gradient because a high interstitial resistance reduced the overall epithelial-interstitial reflection coefficient to the low value of the interstitium.