Microvascular Permeability to Solutes

Lipophilic versus Hydrophilic Solutes and the Importance of Flow Limitation

The solute permeability (Ps) of the capillary wall is dependent on the oil:water partition coefficient, the diffusion coefficient of the solute, Ax, the radius of the solute relative to the pore, and the pore area. Fat-soluble molecules are therefore very permeable across the capillary wall (Ps for oxygen is 1-10 x 10-3cms-1). The concentration gradient across the capillary wall can only be maintained by relatively high blood flows. Highly permeable solutes are therefore flow limited rather than diffusion limited. Small hydrophilic molecules are also flow limited, even though their transport is predominantly through extracellular pathways. Larger molecules such as plasma proteins have a Ps that is normally so low that the concentration gradient along the vessel is maintained independently of the rate of flow for most perfused vessels, and is therefore diffusion limited. Intermediate-sized solutes such as glucose move from flow limitation to diffusion limitation as the Ps of the vessel changes.

The Sites of Solute Permeability

In continuous capillaries the location of the barrier to solute movement is in the endothelial cell cleft. There are at least three possible barriers to solute flux—the glycocalyx, the tight junctional strands, and the adherens junctions of the cleft. There is still some support for the concept of transcel-lular movement of protein and other large solutes through the vesicular system of endothelial cells. Fused vesicle clusters attached to the lumen have been seen to cross the entire width of the cell and fuse with vesicle clusters attached to the abluminal side of the cell, thereby providing a potential route for solute movement.

Measurement of Permeability to Water-Soluble Solutes

Problems Common to Methods of Solute Permeability Measurement

Ps can be determined by measuring the solute flux across the vascular wall and calculating Ps based on known driving forces for solute flux, in a manner analogous to that for L The Ps of a membrane to a particular solute is set by Fick's law—the rate of diffusive flux per unit concentration difference per unit surface area. However, the total solute flux across the vascular wall depends upon diffusive and con-vective fluxes—that is, the rate of solute movement carried along in the flow of fluid that is also crossing the vessel wall. Furthermore, the concentration gradient across the vessel wall is also set by the balance of the diffusive and con-vective solute fluxes. The interstitial solute concentration depends upon solute flux relative to water flux. This ratio of diffusive to convective solute flux must be used to calculate the true driving force for diffusive solute movement. it is only possible to use the measurement of solute flux to accurately calculate Ps when all these parameters are known. Ps has been measured in cell culture models, in whole organs, and in single vessels. Most methods for measuring Ps use labeled solutes. These include radiolabeled (e.g., 125I-albumin, 57Cr-EDTA), or fluorescently labeled molecules (e.g., FITC-albumin), or dyes that bind to specific molecules (e.g., Evans blue, which binds albumin). All these methods suffer from two potential problems—dissociation of the marker from the test molecule and alteration of the test molecule by the marker.

1. Tracer dissociation. This can lead to a marked overesti-mation of Ps. For instance, Evans blue has a molecular weight of 960, albumin 66,000. Therefore for every molecule of EB that dissociates, Ps is 69-fold overesti-mated—if 1 percent of the EB dissociates, then 69 percent of the Ps will be that of EB, not that of albumin. Moreover, free EB is flow limited rather than diffusion limited. Therefore changes in EB transport occur far more easily by changing blood flow. This is also true for FITC and radiolabeled molecules that undergo radiolysis—125I-albumin usually has 0.01 to 2.5 percent dissociated 125I. This can be avoided by the use of tracers that do not readily dissociate, such as TRITC, or by nonnative tracers that are themselves detectable, such as green fluorescent protein or fluorescent dextrans.

2. Alteration of the test molecule. The process of labeling molecules may also alter their characteristics. Albumin is denatured when labeled with FITC, resulting in a change of charge and pH, and it has a different Ps than when it is labeled with other fluorescent molecules. Although this may have a small effect on Ps under normal conditions, it may be highly significant in conditions where albumin is endogenously modified (e.g., diabetes).

Cell-Culture Models

There are numerous problems measuring Ps of endothe-lial monolayers in cell culture. These include those outlined earlier concerning measurement of L Because Ps of the monolayer is so much higher than in vivo, basement membrane can significantly contribute in vitro. This can be controlled by measuring Ps after removal of endothelial cells. since cells are grown on a synthetic insert, the path length between the junction and the nearest pore in the membrane can also change. The average endothelial cell surface area and shape can be determined to eliminate this possibility. It is also necessary to ensure that there is not a significant decrease in the solute concentration difference between the endothelial cell and the pore, or the endothelial cell and the lower chamber. Calculation of true Ps (in cms-1) should be carried out rather than solute flux (mgs-1).

Measurement of Solute Permeability in Single Vessels

Ps can accurately and effectively be measured in individual microvessels by determining solute flux under known conditions of diffusive and convective driving forces. A vessel is cannulated with a pipette divided by a septum. The two halves are perfused at separate pressures and one side filled with a fluorescent tracer. The perfusate is switched rapidly to the fluorescently labeled one, thereby giving a known concentration difference. The total fluorescence of and around the vessel is measured. With small molecular weight solutes (convective flux being negligible) the rate of increase of fluorescence can be used to calculate solute flux per unit concentration gradient per unit area—Ps. For larger solutes (or for small solutes in very tight vessels such as the blood-brain barrier), solute flux can be measured at a variety of pressures such that convective flux can be measured.

Measurement of Solute Permeability in Whole Tissues

Permeability-surface area product (PS) is usually measured in whole tissues, since it is difficult to measure the surface area. PS can be measured using radiolabeled, colorimetric, or fluorescent tracers—bearing in mind the measurement problems discussed earlier. Assuming that the tracers are effectively labeled, do not dissociate, and do not denature the compound, PS can be accurately assessed using a double-labeled tracer technique. This involves perfusing animals for increasing amounts of time with a tissue tracer (e.g., 125I-albumin), followed by injection of a second reference tracer (e.g., 131I-albumin) for 1 minute to allow circulation. The animal is then killed, a blood sample is taken, and the tissue is excised and weighed. The lungs are then dried completely and water content determined. The reference tracer (Vr) distribution volume is calculated from the plasma concentration and the reference tracer tissue counts. Tissue distribution volume (Vt) is calculated from the tissue tracer counts and the blood. The albumin distribution volume (Va) can be calculated from Vr and Vt. Va will increase over time as solute moves from vascular to tissue so the time experiments are used to calculate initial solute flux. Va is measured under normal conditions and during increased filtration rate. The relationship between filtration rate and solute flux can be used to calculate the PS. A common mistake in this method is to divide rather than subtract the first tracer from the second. This results in the calculation of a meaningless ratio dependent on blood flow rather than PS.

Reflection Coefficient (a)

The reflection coefficient of a membrane to a solute is the osmotic pressure exerted by that solute across the membrane as a fraction of the osmotic pressure across an ideal membrane (it is a function of the mean pore area relative to the mean cross-sectional area of the solute). a for albumin, for instance, in normal capillaries is close to 1: It exerts almost its full osmotic pressure. An increase in the pore diameter (which would also increase solute Ps) would drastically reduce a to albumin.

Measurement of a in Single Microvessels

Reflection coefficient to macromolecules can be measured using the Landis-Michel technique [1]. A single vessel is cannulated and perfused as described for Lp. a can be calculated as the root of the ratio of the pressure required to balance filtration to that of the colloid osmotic pressure determined across an ideal membrane by a colloid osmome-ter. a has been determined in a number of capillary beds using these techniques.

Measurement of a in Whole Organs under conditions of high filtration rates the interstitial protein concentration, when expressed as a fraction of the plasma protein concentration, approximates to the permitted fraction, or 1 - a. Thus if filtration rate is raised and interstitial fluid can be sampled, a can be estimated. one way of doing this is to cannulate a lymphatic draining the tissue and measure the protein concentration under conditions of high filtration rate, after equilibration.

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