Microvascular Permeability and the Exchange of Water and Solutes Across Microvascular Walls

Exchange through microvascular walls is both the initial and the final step of transport of materials by the circulation. In most tissues, microvascular exchange is a passive process, driven by differences in hydrostatic pressure and solute concentration between the circulating plasma and the interstitial fluid that flank microvessel walls. Lipophilic molecules and small water-soluble molecules and ions can exchange rapidly in most vascular beds, but microvascular walls are a barrier to macromolecules, severely impeding their exchange. The consequent differences in macromolecular concentration across microvascular walls are responsible for differences in osmotic pressure, which were identified over a century ago to play an essential role in the balance of fluid between the circulating blood and the tissues.


Exchange through microvascular walls is both the initial and the final step of transport of materials by the circulation. In most tissues, microvascular exchange is a passive process, driven by differences in hydrostatic pressure and solute concentration between the circulating plasma and the interstitial fluid that flank microvessel walls. Lipophilic molecules and small water-soluble molecules and ions can exchange rapidly in most vascular beds, but microvascular walls are a barrier to macromolecules, severely impeding their exchange. The consequent differences in macromolecular concentration across microvascular walls are responsible for differences in osmotic pressure, which were identified over a century ago to play an essential role in the balance of fluid between the circulating blood and the tissues.

Although small hydrophilic molecules can exchange rapidly between the blood and the tissues, it is wrong to assume that microvascular walls are no barrier to them. The rate at which changes of concentration of a solute in the blood can be reflected as changes in interstitial fluid (ISF) concentration depends both on the blood flow to the capillary beds, and on the permeability of the capillary walls to the solute. It is often assumed that for small molecules only blood flow is important, but once flow has exceeded a certain minimum range of values, the rate of equilibration of blood and ISF becomes limited by permeability.

Microvascular exchange and microvascular permeability are sometimes regarded as synonymous but this in incorrect and it is important to distinguish between them. Microvascular permeability to a substance is the conductivity of the microvessel wall and the permeability coefficients which describe permeability in functional terms are determined by the structure and properties of the pathways through which its molecules traverse the vessel wall. Microvascular exchange rates and net transport through microvascular walls for a particular substance are determined by microvascular permeability to that substance and also by the value and direction of net fluid flow through the vessel wall and by differences in concentration of the substance between plasma and ISF. The difference between microvascular exchange and microvascular permeability is important when interpreting methods that claim to demonstrate changes in permeability. Many of these methods involve the measurement of changes in net transport of macromolecules between blood and tissues, without controlling the transcapillary differences in hydrostatic pressure and macromolecular concentration. We shall consider the potential errors later in this chapter.

First, we consider microvascular permeability, and then microvascular exchange. Not included in this chapter is a consideration of transport through the walls of microvessels of the central nervous system. The low permeabilities of these vessels and the specialized transport mechanisms for certain solutes constituting the blood–brain barrier are atypical of other microvessels, and resemble those of tight epithelia.

Microvascular Permeability

Microvascular Ultrastructure

Capillary walls consist of a single layer of flattened endothelial cells, the endothelia, and these cells constitute the barrier between the blood and the ISF. Electron microscopy has revealed that endothelial cells in different tissues are of two distinct types: “continuous” and “fenestrated” ( Figure 9.1 ). Continuous endothelium is found in microvessels of skin, muscle, lung, and connective tissues. Here, the endothelial cells are joined together by tight junctions to form a continuous layer surrounded by a continuous basement membrane. The plasmalemmal membranes of the continuous endothelia retain their integrity; even in areas where the cells are flattened, reducing their thickness to less than 0.1 μm, the distinct luminal and abluminal membranes are separated by a thin layer of cytoplasm.

Figure 9.1

Diagrams showing the ultrastuctural features of microvascular walls in transverse section: (a) Vessel with continuous endothelium; (b) Vessel with fenestrated endothelium.

The basement membrane (BM) forms a continuous layer around the outside of both vessel types and the luminal surfaces of both endothelia are covered with a negatively charged glycocalyx (SL) (EC: endothelial cell; J: junction; F: fenestration (fenestra); N: endothelial cell nucleus).

Fenestrated endothelium is found in microvessels associated with secretory and absorptive epithelia, e.g., the capillaries of the intestinal mucosae, glomerular, and peri-tubular capillaries of the kidney. The walls of fenestrated microvessels are also made of a single continuous layer of endothelial cells joined by tight junctions and surrounded by a continuous basement membrane, but in these vessels attenuated areas of cells appear to be penetrated by circular openings 40 to 70 nm in diameter. These are the fenestrae (or fenestrations), and in most cases the fenestrations are closed by a thin electron-dense diaphragm, which appears to be arranged as a series of broad spokes with central “hub” ( Figure 9.2 ).

Figure 9.2

En face view of fenestrated endothelium of peritubular capillary of the kidney in a rapid freeze deep etch preparation.

Scale bar=0.1 μm.

(From ref. [ ].)

Covering the luminal surface of endothelial cells is a layer of glycoprotein called the glycocalyx or endocapillary layer (ECL). First identified by Luft in 1966 using ruthenium red staining, its importance has only come to be widely appreciated in the past 15 years. Although both continuous and fenestrated endothelia have been found to contain the various inclusions common to most cells (e.g., mitochondria, rough and smooth endoplasmic reticulum) the dominating ultrastructural feature seen in transmission electron micrographs is the large number of small endoplasmic vesicles ( Figure 9.3 ). The majority of vesicles are arranged in fused clusters that communicate with each other and with flask like pits on either the luminal or abluminal surfaces of the cells called the caveolae intracellulares. Chains of fused vesicles forming channels that pass through endothelial cells appear to be relatively rare occurrences in unstimulated endothelium, but are a feature of endothelium activated by certain mediators.

Figure 9.3

Electron micrograph of microvascular endothelium of frog.

There are three mitochondria in the central part of the cell and large numbers of plasmalemmel vesicles. Scale bar=0.2 μm.

(Electron micrograph by H.Moffitt.)

The intercellular clefts of continuous endothelia, the fenestrae of fenestrated endothelia, and the small vesicles have all been implicated as pathways through the endothelia as a result of experiments using electron-dense tracers. Controversy surrounded the interpretation of many of these experiments, but progress has been made over the past 20 years as physiological evidence clarified their interpretation. For this reason, the ultrastructural basis of permeability is considered after we have defined the permeability coefficients by considering the principles of passive transport and have discussed their values in different endothelia to different types of molecules.

Passive Transport and Permeability Coefficients of Porous Membranes

The mechanisms of transport are convection and diffusion. Convection is equivalent to bulk flow of solutions and the solutes within them. Thus, if a solution flows from a reservoir A at a high pressure to a second reservoir, B, at a lower pressure, there is bulk flow of the solution and transport of the solutes by convection. If J V ml sec −1 is the rate at which the solution flows from A to B, it is proportional to the difference in hydrostatic pressure, ΔP , between A and B as follows:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='JV=KΔP’>??=???JV=KΔP
J V = K Δ P
where K is the conductance of the system between A and B.

If A and B are separated by a porous membrane, K is proportional to the area of the membrane, A m , through which fluid can flow. Thus:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='JV=LPAmΔP’>??=??????JV=LPAmΔP
J V = L P A m Δ P
<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='LP=(JV/AmΔP)’>??=(??/????)LP=(JV/AmΔP)
L P = ( J V / A m Δ P )

where L P is the hydraulic conductivity or hydraulic permeability of the membrane. L P is one of several membrane permeability coefficients. It describes the ease with which fluid flows through a unit area of membrane when driven by a unit difference in pressure. It can be thought of as describing the frictional interactions between the membrane molecules and the molecules of the solution (principally water), and like the other permeability coefficients its value depends on the structure of the membrane. If small water-filled pores penetrate the membrane, L P is proportional to the number of pores per unit area of membrane, to the fluid viscosity, and to a function of the dimensions of the pores. This function depends on the size and shape of the pores and the nature of flow through them.

Equation (9.2) describes the flow of a solution through a membrane only if the solute molecules can pass through the membrane as easily as the water molecules. If movement of solute is hindered to a greater extent than the water, filtration of the solution leads to the development of a solute concentration difference across the membrane as water enters compartment B faster than solute. The difference in solute concentration gives rise to a difference in osmotic pressure which opposes filtration of the solution across the membrane. The force driving solution through the membrane is no longer just ΔP , but ΔP minus the effective osmotic pressure between the solutions in A and B. The magnitude of this osmotic pressure difference is related not only to the concentration difference itself, but also to the degree to which the membrane hinders the movement of solute relative to water. This is described by a second membrane coefficient, σ d , referred to as the osmotic reflection coefficient. If the channels in the membrane are permeable to water but not solute molecules, filtration of a solution of this solute through the membrane will separate the solute from the water, with pure water leaving the membrane and concentration of the solution upstream. Since all the solute molecules are reflected at the membrane, σ d has a value of 1.0. The osmotic pressure exerted by differences in its concentration across this particular membrane should be close to that calculated from Van’t Hoff’s law, i.e., Δ Π = RTΔC , depending on the “ideality” of the solution. If, alternatively the solute molecules are able to pass through the membrane as easily as the water molecules, σ d has a value of 0, as none of the solute molecules are reflected. If the solute passes the membrane more easily than water, σ d has a negative value. If only a fraction of the solute molecules are “reflected” during ultrafiltration of the solution, σ d has a value between zero and one.

Only those molecules that are reflected at the membrane during ultrafiltration can exert an osmotic pressure across it. Thus, the osmotic pressure difference, ΔΠ, is related to the concentration difference, Δ C , through the universal gas constant, R , and the absolute temperature, T :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='ΔΠ=σdRTΔC’>??=??????ΔΠ=σdRTΔC
Δ Π = σ d R T Δ C
<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='σd=ΔΠRTΔC’>??=??????σd=ΔΠRTΔC
σ d = Δ Π R T Δ C

At microvascular walls, macromolecules such as plasma proteins have high values of σ d and σ f (0.8–0.999), whereas small ions (e.g., Na + , K + , Cl ) and small hydrophilic molecules (e.g., glucose, lactic acid, amino acids, urea) have values of σ less than 0.2 in most vessels.

Net fluid flow through microvascular walls carries dissolved solutes by convection. The rate of solute transport by convection from A to B depends on J V , and also upon the value of σ for the particular solute at the membrane. If σ has a value of zero, then J S is equal to J V C (in moles per second), where C is the solute concentration in the solution (in moles per ml), i.e., the solution flowing out of the membrane into B has the same concentration as that entering the membrane from A. If, however, σ has a value between zero and one, then the solution emerging from the membrane into B will have a lower solute concentration than that entering the membrane at A. Convective transport of solute through the membrane is now described by the relation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='JS=JV(1−σf)C’>??=??(1??)?JS=JV(1−σf)C
J S = J V ( 1 − σ f ) C

where C now refers to the concentration entering the membrane from A. Note that in Eq. (9.4) σ is written as σ f , whereas in describing the effective osmotic pressure σ is written as σ d . For “an ideal solute” σ f = σ d , but solutions of macromolecules deviate from “ideal” behavior and σ d is often measurably greater than σ f . Rearrangement of Eq. (9.3) provides a definition of σ f :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='σf=1−JSJVC’>??=1?????σf=1−JSJVC
σ f = 1 − J S J V C

If the only pathway for both water and solutes through the membrane is a population of equally sized channels, σ d and σ f are determined only by the ratio of the dimensions of the solute molecules to those of the channels, and are independent of the number of channels per unit area of membrane.

A second mechanism of transport through porous membranes is diffusion. This is most important for the transport of small molecules across microvascular walls. In contrast to the stately progression of molecules by convection, diffusion results from the random jostling of all molecules in a solution that represents their thermal energy. Diffusion is a mixing process, and where there are differences in concentration in a solution diffusion is responsible for the spontaneous net transport of solute from regions of high to regions of low concentration. On a macroscopic scale, Fick’s first law of diffusion describes net transport of solute by diffusion:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='JS=DA(−dCdx)’>??=??(????)JS=DA(−dCdx)
J S = D A ( − d C d x )

where D is the diffusion coefficient of the solute in the solution, A is the area through which diffusion occurs, and the derivative (− dC/dx ) is the concentration gradient of solute down which diffusion occurs. The negative sign of the derivative is to indicate that diffusion occurs from a region of high concentration (low value of x) to a region of lower concentration (higher value of x), i.e., the diffusion of a solute is directed down its concentration gradient.

Diffusion coefficients of solutes in aqueous solutions reflect the ability of solute molecules to slip past adjacent molecules of water. They are measured and defined in terms of net movements of solute under conditions in which there is no overall movement of the solution. Thus, diffusion in solution is a displacement process whereby the displacement of a solute molecule in one direction is accompanied by the displacement of an equal volume of water in the opposite direction. Because the rate at which displacement occurs is dependent on the thermal energy of the solution, the diffusion coefficient is directly proportional to temperature. It is also inversely proportional to the frictional interactions between the solute and water molecules.

When diffusion of a solute occurs through a thin porous membrane, the diffusional permeability of the membrane to the solute, P d , is defined in terms of the net solute flux, J S , the solute concentration difference across the membrane, ΔC , and the membrane area, A m , under conditions where there is no volume flow through the membrane. Thus:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='Pd=(JSAmΔC)JV=0′>??=(??????)??=0Pd=(JSAmΔC)JV=0
P d = ( J S A m Δ C ) J V = 0

P d has units of velocity (cm sec −1 ), and like L P and σ f , it has meaning in terms of the interactions between the solute molecules, the molecules of the membrane, and the water within the membrane. Such interactions depend critically upon the ultrastructure of the pathways for solute and water through the membrane, particularly when the width of the pathways is comparable to the diameter of the diffusing molecules.

Diffusional permeability coefficients are defined under conditions where there is no net volume flow through the membrane. In measuring P d of microvascular walls, it is often convenient to use radioactive isotopes or fluorescent tracers, because their fluxes can be detected when their concentration differences are in the micromolar range. Larger differences in concentration may set up significant differences in osmotic pressure, which may complicate the estimation of P d by giving rise to net fluid flows in the opposite direction to those of the diffusing molecules.

Permeability to Lipophilic Solutes

Solutes that can dissolve to a significant extent in lipids have high cell membrane permeabilities, and very high microvascular permeabilities. It is assumed that these molecules diffuse directly through the entire microvascular wall. This group of solutes includes gas molecules, including O 2 and CO 2 , as well as N 2 , the inert gases, and molecules of general anesthetics, although recent evidence suggests CO 2 and NH 3 may cross membranes additionally through specialized channels.

So rapidly can small lipophilic solutes cross microvascular walls that, under physiological conditions, their transport between the blood and the tissues is always limited by their rate of delivery or clearance by blood flow through the microcirculation, and it has been impossible to estimate their microvascular permeability coefficients with accuracy with values for some greater than 10 −2 cm.sec −1 .

Microvascular permeability to lipophilic molecules is, however, sensitive to temperature. Renkin showed that antipyrene, which is fat-soluble at body temperature, could exert substantial osmotic pressures across the walls of capillaries in cat hind limbs when the tissue was cooled to 15°C, but not when the tissue was at 37°C. A similar phenomenon has been demonstrated by Curry in single mesenteric capillaries.

Permeability Coefficients to Small Hydrophilic Molecules

Microvascular permeability to macromolecules is usually considered separately from permeability to hydrophilic molecules smaller than serum albumin, as different mechanisms of transport appear to be involved. Evidence for this emerged in 1956 from studies on the passage of a range of dextran polymers between plasma and lymph. Some of the original data are shown in Figure 9.4 , where it is seen that the steady-state concentrations of the smaller dextrans in the lymph draining hind limb tissues of anesthetized dogs relative to the plasma levels fall rapidly as their molecular radii increase up to 4–5 nm; for the larger molecules the decline of lymph concentration with molecular size is so small as to appear barely significant in these data.

Figure 9.4

Relations between permeability (P) of dog hind limb microvessels to hydrophilic solutes and the molecular diameter of the solutes.

The endothelium of these vessels is continuous and P has been calculated assuming they have a surface area for exchange of 7000 cm 2 100g− 1 of tissue. Note that P, which has been plotted on a logarithmic scale, declines sharply as molecular diameter increases up to 70 Å (7 nm), which is approximately the diameter of serum albumin. A less steep relation is seen for larger molecules.

(From ref. [ ]. With permission)

This two-component relation between P d and molecular diameter is seen in nearly all microvascular beds, suggesting that small molecules use different mechanisms or pathways to cross microvascular walls from those used by macromolecules.

Permeability Coefficients to Small Hydrophilic Molecules

In Figure 9.5 , the values of P d measured in microvascular beds of skeletal muscle and single mesenteric microvessels to some small water soluble solutes have been plotted against solute molecular radius. In mesenteric capillaries, values for P d to the smallest molecules and ions (e.g., Na + , K + , urea) are ten times greater than values of P d for the same solutes in muscle capillaries. To make the comparison easier, both the P d values and values for molecular radius are shown on logarithmic scales. The decline of P d with molecular radius for both types of microvessel is much greater than the decline of diffusion coefficient ( D ) for the same molecules in open aqueous solution. The more rapid decline of P d can be accounted for if molecules were diffusing through water-filled channels whose widths were comparable to their own diameters. The smooth curves, which have been fitted to the data, converge as molecular radius increases. If the channels were cylindrical pores, the convergence implies that the radii of the pores is very similar in mesenteric and muscle capillaries, but there are ten times more pores penetrating per unit area of the walls of mesenteric capillaries than of muscle capillaries. The value of molecular radius at which the curves intersect provides an estimate of the pore radius – in this case between 3.5 and 4 nm.

Figure 9.5

Relations between the logarithms of P d and molecular radius for small to intermediate sized hydrophilic solutes in capillaries of frog mesentery (filled circles) and cat skeletal muscle (filled triangles).

Data for frog obtained from measurements made in single perfused microvessels in situ. Data from cat based on measurements on perfused vascular bed. Both types of vessel have continuous endothelium. Note whereas P d for the smallest solutes is 10 times greater in mesentery than in muscle (1 log 10 unit=10×), values for P d converge as molecular size increases.

This pattern of declining P d to small hydrophilic solutes with increasing molecular diameter is seen in all microvessels where it has been sought, and curves based on the theory of diffusion through pores of radii between 3.5 nm–5 nm can be fitted to these data.

The values of P d to a particular small hydrophilic solute (e.g., Na + , K + , sucrose, and inulin) in different microvascular beds correlate with the values of hydraulic permeability ( L P ). This is shown in Figure 9.6 , where each point represents the mean value of L P plotted against the mean value of P d to Na + or K + in the same microvessel or microvascular bed, different points representing values for vessels in different tissues. The data have been plotted on logarithmic scales so that values covering two orders of magnitude can be compared. The slope that has been drawn through the points has been given a value of unity, to indicate that direct proportionality is a reasonable description of the relationship. The correlation is strong circumstantial evidence for believing that the same pathways through the endothelium serve both for the rapid exchange of small hydrophilic solutes, and for most net fluid movements. Furthermore, because Na + ions are likely to follow an extracellular route, it seems likely that this shared pathway is extracellular. This line of reasoning is greatly strengthened by the demonstration of similar linear correlations between L P and P d values for other extracellular solutes, such as sucrose and inulin in different microvascular beds.

Figure 9.6

Variations in L P and P d to small ions (Na + and K + ) in different microvascular beds.

The scales are logarithmic to include values covering two orders of magnitude, and the line has a slope of 1.0, indicating direct proportionality. Each point represents the value for L P and P d for one vascular bed; where several values of P d are available the largest has been used to minimize errors resulting from flow-limited transport. ○, frog mesentery; ∇, frog muscle; ●, mammalian skeletal muscle; ϒ, mammalian heart muscle; ▴, dog lung; ■, cat salivary gland.

(From ref. [ ]. With permission)

Although the exchange of small hydrophilic molecules occurs through the same channels that account for most of L P , some water may also cross microvascular walls of continuous endothelium by channels not available to solutes. This additional route has been identified by Pallone et al. as channels formed by the membrane protein aquaporin-1, AQP-1. The first real evidence for a “water only” pathway was indicated by Yudilevich and Alvarez from measurements of the rates of diffusion of triated water and Na + through dog heart capillaries. From measurements of σ to small hydrophilic solutes, Curry and colleagues estimated that in single perfused capillaries between 5 and 10% of the pathways responsible for L P were available only to water, and not to small solutes. More recently, Turner and Pallone have shown that “water only” channels account for a similar proportion of the L P of descending vasa recta of rat kidney. It is worth emphasizing that although fluid movements through AQP-1 channels of the descending vasa recta are of physiological importance, the channels contribute no more than 5 to 10% to the total L P of these vessels. Although it has been suggested that AQP-1 channels might contribute to as much as 30% of the L P of skeletal muscle capillaries, the strong correlation between P d and L P shown in Figure 9.6 indicates that the contribution of AQP-1 channels to the L P of most exchange vessels is small.

Although absolute values of L P and P d to small hydrophilic solutes vary greatly from one microvascular bed to another, the reflection coefficient to large molecules are remarkably similar in different vessels when the tissues are undamaged (or unstimulated). This is shown in Figure 9.7 , where the mean values of σ to serum albumin have been plotted against the mean value of L P for various tissues. Whereas L P varies over three orders of magnitude, σ to albumin is usually in the range of 0.8 to 1.0. There is no trend in the relation between σ albumin and L P . Vessels with high values of L P have mean values of σ albumin that are as high, if not higher, than in vessels with low values of L P . This means that the channels or pores that are largely responsible for the L P of vessels in different tissues all restrict the passage of albumin to a similar extent. Thus, both the variations of P d with molecular size and the variations in σ albumin and L P in different capillary beds lead to the same conclusion: individual channels for exchange of water and small hydrophilic solutes are similar in different capillary types, but the density of these channels in vessel walls varies considerably.

Figure 9.7

Relation between the reflection coefficient to serum albumin (σ) and the L P in different microvascular beds.

Each point represents a mean value for one vascular bed: * dog paw; □ dog skeletal muscle; ■ rat skeletal muscle; ▵ dog lung; ▾ rabbit heart muscle; rat mesentery; □ frog mesentery; ○ cat vary gland; ▴ rat descending vasa recta; cat small intestine; ● rabbit synovium; ▿ rat ascending vasa recta; dog renal glomerulus; rat renal glomerulus.

(With permission from ref. [ ].)

Permeability Coefficients to Macromolecules

Apart from the sinusoids of the liver and spleen, microvascular walls have high reflection coefficients and low permeabilities to macromolecules. These permeability properties are essential if the circulating blood is to be retained within the vascular system. Although their permeabilities are low, macromolecules do cross the walls of all microvessels at slow but finite rates. Table 9.1 compares estimates of σ and P d made from the transport of macromolecules between blood and lymph in the dog paw and the cat intestine. Although it is possible that the values given in this table are actually overestimates of the permeability coefficient of macromolecules, there are three important points to note here. First, the values of P d for serum albumin are more than 3000 times less than the permeabilities of the same vessels to Na + and urea. The diffusion coefficient of albumin in aqueous solutions is only 20 times less than those of Na + and urea. This means that the diffusion of albumin molecules through microvascular walls is hindered 150 times more than the diffusion of Na + ions or urea molecules. Second, compared with the changes seen for small molecules, there is a relatively small decrease in P d and rise in σ with increases in molecular size. The third point is the similarity of the values of P d to the same macromolecule at the predominantly continuous endothelium of the dog paw capillaries, and also at the predominantly fenestrated endothelium of vessels in the small intestine. The values of L P and P d to small hydrophilic solutes in these two microvascular beds differ by nearly two orders of magnitude. This would seem to be further evidence supporting the belief that the transport pathways through microvascular walls are different for macromolecules from those responsible for water small hydrophilic solutes.

Table 9.1

Reflection Coefficients (σ) and Permeability Coefficients ( P d ) to Macromolecules of Selected Molecular Radii (a ES , nm) in Microvascular Beds of Dog Paw and Cat Ileum

Dog Paw Cat Ileum
Molecule a ES (nm) σ P d ×10 8 (cm sec −1 ) σ P d × 10 8 (cm sec −1 )
Serum albumin 3.55 0.89 1.0–4.7 0.9 3.0
Transferrin 4.3 0.89 6.3
Haptoglobin 4.6 0.91 3.1 1.4
Immunoglobulin 5.6 0.91 3.3 0.95
Fibrinogen 10.0 0.94 1.6 0.98 0.7

Renkin, E. M. (1988). Transport pathways and processes. In “Endothelial Cell Biology,” 51–68, Simionescu, N., and Simionescu, M., (eds.) Plenum Publishing, New York.

It is possible that some of the values for P d in Table 9.1 are overestimates and those for σ are underestimates because, in calculating vascular permeability coefficients from plasma to lymph transport, it is assumed that a steady-state has been established between the newly formed filtrate surrounding the microvessels and the ISF entering the lymph. Simple calculations suggest that in some tissues the time taken to reach a steady-state after a change in microvascular filtration rate can be many hours. This can be understood by considering the events that follow an increase in microvascular filtration. A rise in filtration rate is accompanied by a rise in lymph flow and a fall in the concentrations of macromolecules in the newly formed interstitial fluid. It may, however, take several hours before the lymph has the same composition as this new filtrate, and if the lymph is sampled prematurely its concentration of macromolecules will be greater than that in the ultrafiltrate. The lymph flow, however, may reach its new steady-state level before the lymph concentration of macromolecules, and if flux of macromolecules is estimated from values for the product of lymph flow and lymph concentration of macromolecules at this stage, its value will exceed the real rate of transport into the tissue. Not only is macromolecular transport overestimated, but the mean concentration differences across the microvascular walls are also underestimated.

Since 1990, much work has been conducted on the passage of macromolecules through monolayers of culture endothelial cells. In many of these studies, changes in permeability to macromolecules have been investigated, and relative rather than absolute values of permeability coefficients have been reported. In most but not all studies, absolute values for P d of monolayers of cultured endothelial cells to albumin lie in the range of 10 −6 cm sec −1 , about 100 times greater than the values of P d to albumin at microvascular walls in situ . In a few laboratories, values in the range of 10 −7 to 10 −6 cm sec −1 have been reported, but even these values are at the very high end of the range found in microvessel walls in vivo . The reasons for this difference are not understood at present. Although studies on cultured endothelial cells have provided essential information of intracellular processes, conclusions from them relating to macromolecular permeability should be viewed with caution.

Like smaller hydrophilic molecules, the microvascular permeability coefficients to macromolecules decrease as molecular size increases, although the decline is considerably less steep. Molecular charge is also more important as molecular size increases. Evidence for the charge-selective nature of ultrafiltration in the renal glomerular capillaries is well-known, but in other microvessels, charge selectivity has been investigated in less detail. Areekul first provided evidence for charge selectivity in systemic capillaries. Working on the isolated perfused rabbit ear, he showed that σ d to sulfated dextran (which is negatively charged) was always greater than σ d to neutral dextran of the same molecular weight. Work on single perfused capillaries and on microvascular beds in rat hind limbs also supported the view of microvascular walls as a negatively-charged barrier.

This picture was temporarily confused by studies on the transport of charged macromolecules between plasma and lymph. Negatively-charged macromolecules appeared more rapidly in the lymph and at higher concentration than positively-charged molecules, suggesting a positively-charged barrier. It was then appreciated that the large number of fixed anionic sites in the interstitium (see ) would reduce the volume of distribution of the negatively-charged molecules relative to cationic or neutral molecules of the same molecular size. Parker and co-workers showed that the greater volume of distribution of neutral and cationic molecules increased the time for these molecules to reach a steady-state concentration in the ISF. This delay accounted for the apparently more rapid transport of the anionic molecules, a conclusion reinforced by the recent study of Gyenge and her co-workers on albumin distribution in skin and muscle tissue. With this point clarified, the evidence once again supports the concept of a negatively-charged barrier at microvascular walls hindering the transport of negatively-charged macromolecules greater than 3.0 nm in diameter.

The decline of P d (and an increase in σ) with an increase in molecular size led to the suggestion that macromolecules cross the endothelium through a system of large pores with radii in the range of 20–40 nm. These pores would be few in number compared with the small pores that act as a pathway for small hydrophilic solutes. Calculations suggest that individual capillaries in skeletal muscle may have an average of only three large pores and with the usual variation between microvessels this indicates that many vessels will have no large pores at all. In a comprehensive review, Taylor and Granger showed that microvascular permeability to macromolecules in different tissues could be described by transport through a population of small pores (radii 3.5–5 nm) and a set of large pores (15–30 nm radii). If large pores do exist, then transport of macromolecules through them will be largely convective, sensitive to microvascular pressure, and increase with fluid filtration rate. Experiments by Rippe and his colleagues showed that this is the case for the transport of labelled albumin from capillaries in skeletal muscle of an isolated perfused rat limb preparation. Defining the clearance of tracer from the blood into the tissue as the rate of its accumulation divided by the perfusate concentration, they not only showed that clearance of albumin increased linearly with fluid filtration into the tissues, but also that cooling the tissue from 36° to 14°C reduced albumin clearance by only 40%. This was similar to the reduction of the apparent hydraulic permeability of the microvessels. The results of this classic experiment are shown in Figure 9.8 . A 40% reduction in L P would be expected because the filtrate flow through the water-filled channels through the vessel walls is inversely proportional to fluid viscosity, and the viscosity of water at 36°C is approximately 60% of that at 14°C. Because albumin transported is proportional to filtration rate and is reduced in parallel to J V as the viscosity of water is increased, Rippe and his colleagues concluded that albumin is transport through water-filled channels in the microvascular walls. Figure 9.8 shows that the clearance of albumin from plasma to tissue is significant when fluid filtration is zero. Rippe and his colleagues accounted for this by pointing out that, because the hydrostatic pressure difference across microvascular walls is greater than zero under these conditions, there would still be fluid filtration through the large pores, and consequent transport of albumin because σ d to plasma proteins here is low. This filtration through the large pores would not be detected in whole tissue, because it would be balanced by an equal and opposite uptake of fluid through the “small pores” where σ d to plasma proteins is high. As we shall see, the steady uptake of fluid from tissues into capillary blood may peter out and become a low level of filtration in tissues such as muscle.

Figure 9.8

The clearance of serum albumin from perfusate into tissues of rat skeletal muscle at different filtration rates in experiments conducted at 36°C and 13–15°C.

β is the slope of the relation.

(From ref. [ ]. With permission.)

Ultrastructural Basis of Permeability

Small Hydrophilic Solutes and Water

If the molecular sieving properties of microvascular endothelia are determined by pores or channels of similar dimensions, one might expect to find common structural features in all endothelia that are more frequent in the more permeable vessels. Unfortunately, electron micrographs of endothelia do not reveal an obvious structure that might fill this role.

The endothelia of the vessels with the four highest values of L P in Figure 9.9 are fenestrated, while those with the seven lowest L P values are continuous. In some others (e.g., small intestine) values of L P and σ represent those of a microvascular bed where there are both fenestrated and non-fenestrated vessels. In a quantitative analysis of permeability of fenestrated vessels, Levick and Smaje found that variations in L P and P d to small hydrophilic solutes in fenestrated vessels can be correlated with the number of fenestrations per unit area of endothelium. From their analysis they estimated the mean hydraulic conductance per unit increment of area for fenestrations in a variety of microvascular beds as 0.38 µm.sec −1 mmHg −1 (2.8×10 −5 cm.sec −1 cmH 2 O −1 ). This means that the addition of a single fenestration (diameter=60 nm) to one µm of the endothelium of a skeletal muscle microvessel increases the L P of that area approximately 2.6 times. Although fenestrations appear as large pores passing through the endothelium, the fenestrations themselves are much too large to account for molecular sieving and their high reflection coefficients to macromolecules. Molecular sieving is now thought to be achieved by the endothelial glycocalyx, with significant contributions to the hydraulic resistance from the fenestral diaphragms and the basement membrane.

Figure 9.9

Diagram of the ultra-structure of an intercellular cleft based on reconstructions from serial ultrathin sections (A&M).

Part of the cell in the foreground has been removed to expose the interior of the cleft showing the junctional strands (heavy lines), which correspond to points of close apposition between the cells (tight junctions) in single sections. Lanthanum ions cannot diffuse through the junctional strands, but pass through breaks in the strands. Because there is usually only one continuous strand in the junctions of mesenteric microvessels, each break provides a direct pathway through the cleft.

The luminal glycocalyx was proposed by Curry and Michel as the structure responsible for molecular sieving in microvessels with continuous endothelia. Its wide acceptance came after direct observations of the exclusion of macromolecules from the luminal surface of living microvessels had been demonstrated 16 years later by Vink and Duling. Whereas variations in L P of fenestrated vessels results from variations in the number of fenestrae per unit area of vessel wall, the variations in L P and P d to small hydrophilic molecules in vessels with continuous endothelia appears to correlate with the numbers of breaks and complexity of the junctional strands of the intercellular clefts. Although evidence for this concept was available in 1978 from the work of Wissig and Williams, progress was hindered by the beliefs that: (1) the molecular sieve consisted of pores or narrow openings in the tight junction strands; and (2) that the breaks forming a pathway through the junctional strands were too few in number to account for permeability to water and small hydrophilic solutes. Thus, Bundgaard reconstructed the intercellular clefts of rat heart capillaries from ultrathin serial sections and confirmed the presence of a tortuous pathway through the cleft, but rejected this as the route taken by water and small hydrophilic solutes on the grounds that the dimensions of the openings through the junctional strands were too great to filter plasma proteins, and the number of breaks per unit length of junction were too few to account for water and small solute permeabilities.

The question was clarified by Adamson and Michel. Working on frog mesenteric capillaries in situ , they perfused single capillaries briefly with solutions containing lanthanum ions, before the tissues were fixed for electron microscopy. Micrographs of serial sections of the walls of the perfused vessels demonstrated that lanthanum ions were only able to pass through the intercellular clefts at breaks in the junctional strands. In a second series of experiments, they measured L P in individual capillaries in situ before fixing the tissue for electron microscopy (EM). The three-dimensional structures of the intercellular clefts of that capillary were then reconstructed from long runs of ultrathin sections of the vessel. Although the breaks only represented 3–10% of the length of the strands, Adamson and Michel used a mathematical model of Parker and colleagues to show that this was more than sufficient to account for permeabilities that were three times greater than those they had measured. The mathematical model provided a rigorous argument for believing that a small break in the junctional strands has a much greater effect upon L P than its size might suggest. The pressure gradient driving fluid flow through the intercellular cleft is steepest across the tiny distance through the break in the strand, and is much greater than that calculated for the entire cleft. More detailed mathematical models have been developed by Weinbaum and his colleagues and more recently, Adamson et al. have shown that the fine structure of the tight junction in intercellular clefts of rat mesenteric venules is very similar to that seen in frog vessels.

The L P of mesenteric vessels is approximately three times greater than the L P of heart muscle capillaries, which is approximately three times greater than the L P of capillaries in skeletal muscle. These differences in permeability appear to correlate with the complexity of the pathway through the tight junction in these different types of capillary. This is illustrated in Figure 9.10 for pathways through the intercellular clefts of mesenteric, cardiac, and skeletal muscle capillaries. It seems most probable that the wide variations in permeability to fluid and small hydrophilic solutes that is found in microvessels with continuous endothelium are determined by the complexity of the tight junctional architecture within the intercellular clefts.

Figure 9.10

Variations in the complexity of arrangement of junctional strands in intercellular clefts of microvessels with different hydraulic permeabilities.

he dashed lines with arrows indicate potential pathways through the breaks in the strands. (a) Mesenteric capillary (based on ); (b) Cardiac muscle capillary (based on ); (c) Skeletal muscle capillary (based on ).

As mentioned earlier, the glycocalyx on the luminal surface of the endothelium that covers the entrances to intercellular clefts and fenestrae is now considered to be the barrier to macromolecules. When this was first proposed there was indirect evidence to support it, and more evidence of this kind accumulated during the 1980s. In 1990, Adamson showed that the L P of single vessels was doubled by brief perfusions of pronase that disrupt the glycocalyx without having any other detectable effects on endothelial ultrastructure when electron micrographs of the same vessels were inspected. General recognition of the concept of the glycocalyx barrier resulted from some remarkable in vivo observations of Vink, Duling, and their colleagues. Using confocal microscopy to visualize capillaries in rat cremaster muscle, these authors observed that FITC dextrans were excluded from the endothelial cell membranes by a distance of 0.5 µm. The exclusion layer was diminished or even abolished by prolonged exposure to UV light and after perfusion with hyaluronidase. Observations of this kind continue to bolster the view of the glycocalyx as a barrier.

Direct evidence for how its structure acts as a molecular filter comes from the analysis of electron micrographs of glycocalyx. Examining very differently prepared specimens, including some made by the rapid freeze-deep etch technique in the absence of chemical fixatives, Squire et al. have concluded that the glycocalyx may be regarded as a regular cubic lattice with side length of 20 nm and a cubic internal space of side length 8 nm (see Figure 9.11 ). Since serum albumin molecules have diameter of 7–7.2 nm, the dimensions of this internal space are consistent with the glycocalyx acting as the molecular filter in microvascular walls. The initial observations were all made on the glycocalyx of continuous endothelia of the frog, but more recent work has revealed very similar structural features to the glycocalyx covering both continuous and fenestrated endothelia, including that over fenestrae in mammalian microvessels in a wide range of tissues.

Figure 9.11

Models of glycocalyx based on image analysis of electron micrographs. (a) An autocorrelation function of the glycocalyx indicating the underlying regularity of structure with a periodicity of approximately 20 nm both parallel and perpendicular to the cell membrane. (b) A molecular interpretation of (a). It consists of clusters of fibrous strands projecting perpendicular to the luminal cell membrane with periodicity along the strand provided by equally spaced globular proteins. It is suggested that adjacent clusters are separated by approximately 100 nm (consistent with a longer range periodicity) where they linked to the cortical cytoskeleton of the cell. Figures 9.11(c) and (d) show luminal surface and saggital views of the proposed structure.

(From ref. [ ].)

In summary, the main permeability pathways through microvascular walls to water and small hydrophilic solutes are located in the fenestrations of fenestrated endothelium, and through the intercellular clefts in vessels with continuous endothelium. In both types of endothelia, the molecular filter that forms the barrier to macromolecules at most microvascular walls is in the luminal glycocalyx of the endothelial cells.


Just how macromolecules cross the walls of small blood vessels remains a controversial subject. Two apparently conflicting hypotheses emerged from very different lines of evidence more than 40 years ago, and the question of which is more correct has not been finally resolved. As summarized earlier, a purely functional approach has led to the proposal that microvascular walls were penetrated by a small number of “large pores” (30–80 nm in diameter) through which macromolecules pass from plasma to interstitial fluid (ISF). The large pores are estimated to occur so infrequently that their contribution to the P d of small hydrophilic solutes would be negligible, although they might make a 5 to 10% contribution to L P . The large pores, however, would be entirely responsible for the permeability of macromolecules, and transport through them would be largely by convection.

The alternative arises from electron microscopy, and proposes that macromolecules cross endothelial cells by transcytosis via the small vesicles. After their injection into the blood, electron-dense macromolecules have been found labeling caveolae and small vesicles of the endothelia. Initially it was suggested that the vesicles acted as ferries, equilibrating with plasma when they opened as caveolae at the luminal surface, then budding off as small vesicles to travel across the cell where they fused with the abluminal surface of the endothelium and equilibrated with the ISF. In the absence of evidence for active transport of macromolecules through microvascular walls, it was suggested that equal fluxes of vesicles occurred in opposite directions across the cells, and the vesicles moved as a result of Brownian motion. The size dependence of macromolecular permeability arises in vesicular transport from volume exclusion of the macromolecules by the walls of the vesicles. The exclusion effect is considerably enhanced if the caveolae and small vesicles are lined with glycocalyx.

A detailed examination of the labeling of vesicles with ferritin molecules led to a more complicated model, in which neighboring vesicles periodically fused transiently for long enough for their contents to equilibrate. It was also shown that cooling the tissue inhibited the labeling of vesicles with ferritin. This fusion–fission hypothesis was consistent with the detailed structural analysis showing the vesicles to be arranged in fused clusters communicating with caveolae at either the luminal or the abluminal cell membranes. One extreme form of the fusion–fission hypothesis is for the joined vesicles to form channels through the endothelium. Evidence for such vesicular channels has been reported, and these could act as large pores.

Direct evidence for transport by vesicles through normal endothelium has been reported by Wagner and Chen, who demonstrated caveolae emptying terbium label at the abluminal endothelial surface at points distant from intercellular clefts. The demonstration of membrane binding sites for transferrin, insulin, ceruloplasmin, and albumin on endothelia suggested that the vesicle pathway might be involved in receptor mediated transport. A series of papers by Schnitzer and colleagues seemed to bolster the idea of vesicular shuttling or fusion–fission as an important mechanism of macromolecular transport through endothelium. The cholesterol scavenger, filipin, removes caveolae in cultured endothelial cells and in rat lung microvessels, and was also reported to reduce the clearance of albumin from perfusate to tissue in the isolated perfused rat lung. It was also reported that N-ethylmaleimide (NEM), which inhibits fusion processes of vesicles and vacuoles in yeast, in synaptic vesicles, and in transport vesicles operating between the Golgi stacks and the endoplasmic reticulum, inhibited transendothelial transport of macromolecules in microvessels of mouse heart and rat lung. Schnitzer and colleagues have reported that endothelial caveolae from rat lung capillaries can bud away from their anchorage in the presence of GTP and extracts of cytosol. Critical studies by Rippe and his colleagues, however, have cast serious doubt on the relevance of these findings to macromolecular permeability. They found that both filipin and NEM increased albumin transport in the isolated perfused rat lung. NEM was found to reduce σ to albumin. Reducing the tissue temperature from 35° to 22°C, however, lowered both albumin clearance and L P S in rough proportion to increased water viscosity. NEM also increased both albumin clearance and L P S in the microcirculation of rat muscle, and increased pre-capillary vascular resistance in both rat lung and rat muscle. The authors suggested that increased resistance would reduce microvascular perfusion, and this could account for the earlier studies where NEM appeared to reduce albumin clearance. Rippe and colleagues have recently reviewed the controversy, and provided further less direct evidence against endothelial transcytosis of macromolecules from studies of peritoneal dialysis.

Rippe’s arguments for convective transport of macromolecules via large pores are convincing. At present it seems that whereas there is strong evidence favoring convective transport of macromolecules (i.e., the large pore hypothesis), evidence that transcytosis makes a significant contribution to transendothelial transport of macromolecules is lacking. It is possible that the caveolae/small vesicle system is important for the transport of specific molecules. The blood–tissue transport of insulin, for example, appears to be anomalous for a protein of its size, and is more consistent with receptor-mediated transport. As mentioned already, the large pores carrying most macromolecules could be trans-endothelial channels formed by the fusion of vesicles. At normal tissue temperatures they might be continually forming and re-forming, accounting for the progressive labeling of the vesicle system with tracer macromolecules. On cooling the tissues, the open channels would remain open, but no new channels would form, consistent with both the effects of cooling on albumin transport, and the reduced vesicle labeling reported by electron microscopists.

The question of whether macromolecules are transported mainly by convection through large pores in the walls of microvessels in normal healthy tissue has implications for our understanding of fluid exchange between the blood and the tissues.

The Exchange of Fluid and Solutes by Convection and Diffusion through Microvascular Walls

Coupling of Fluid and Solute Transport during Ultrafiltration

In most tissues, ISF is formed by the ultrafiltration of plasma, a process that is driven by the greater hydrostatic pressure inside the microvessels than in the surrounding tissues. As fluid begins to be filtered through the vessel walls, its composition is determined by the rates at which the different plasma solutes can move with the filtrate by convection and diffusion. If one considers the transport of a solute past a point at a distance x cm along a pathway within the microvascular wall, and of cross-sectional area, A , the net flux of solute, J S , can be described by adding together the contributions of convection and diffusion. Thus from Eqs. (9.4)–(9.6) :

Total transport=Convective transport + Diffusive transport

<SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='JS=JV(1−σf)C+D′A(−dC/dx)’>??=??(1??)?+??(??/??)JS=JV(1−σf)C+D′A(−dC/dx)
J S = J V ( 1 − σ f ) C + D ′ A ( − d C / d x )

where C is the solute concentration of the solute at x , D ′ is solute diffusion coefficient, and (−) is the direction of the concentration gradient (from plasma to ISF). The first term on the right hand side of Eq. (9.8) is the convective component of transport, and the second term is the diffusive component. The concentration gradient that is responsible for net transport by diffusion is equal to the solute concentration difference between the plasma and the ISF, divided by the length of the pathway through the wall only when fluid filtration is zero and there is no convection of solute. When net fluid movements are present they distort the concentration gradients in the channels within the vessel walls. Once a steady-state is established so the solute flux, J S , is the same at all points along the diffusion pathway (i.e., the rate of solute entry equals the rate of its exit from the channels), then the extent of the distortion can be inferred by integrating Eq. (9.8) . This leads to a form of the Patlak expression which here relates J S through an area of vessel wall, A m , to the plasma concentration of solute, C p , and the concentration emerging from the vessel walls into the peri-capillary ISF, C i :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='JSAm=JVAm(1−σf)(Cp−Cie−Pe)(1−e−Pe)’>????=????(1??)(???????)(1???)JSAm=JVAm(1−σf)(Cp−Cie−Pe)(1−e−Pe)
J S A m = J V A m ( 1 − σ f ) ( C p − C i e − P e ) ( 1 − e − P e )
<SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='Pe=JV(1−σf)PdAm’>??=??(1??)????Pe=JV(1−σf)PdAm
P e = J V ( 1 − σ f ) P d A m

Pe is a dimensionless number, called the Péclet number, which expresses the ratio of solute velocities by convection and diffusion, P d being the diffusional permeability coefficient. Curry has recast Eq. (9.9) in a form that allows the convective and diffusive components of transport to be recognized:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-13-Frame class=MathJax style="POSITION: relative" data-mathml='JSAm=JVAm(1−σf)Cp+Pd(Cp−Ci)(PeePe−1)’>????=????(1??)??+??(????)(?????1)JSAm=JVAm(1−σf)Cp+Pd(Cp−Ci)(PeePe−1)
J S A m = J V A m ( 1 − σ f ) C p + P d ( C p − C i ) ( P e e P e − 1 )

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Jun 6, 2019 | Posted by in NEPHROLOGY | Comments Off on Microvascular Permeability and the Exchange of Water and Solutes Across Microvascular Walls

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