The Microcirculation

The microcirculation serves both nutritional and non-nutritional roles

The primary function of the cardiovascular system is to maintain a suitable environment for the tissues. The microcirculation is the “business end” of the system. The capillary is the principal site for exchange of gases, water, nutrients, and waste products. In most tissues, capillary flow exclusively serves these nutritional needs. In a few tissues, however, a large portion of capillary flow is non-nutritional. For example, in the glomeruli of the kidneys, capillary flow forms the glomerular filtrate (see p. 739 ). Blood flow through the skin, some of which may shunt through arteriovenous anastomoses, plays a key role in temperature regulation (see pp. 1200–1201 ). Capillaries also serve other non-nutritional roles, such as signaling (e.g., delivery of hormones) and host defense (e.g., delivery of platelets). In the first part of this chapter, we discuss the nutritional role of capillaries and examine how gases, small water-soluble substances, macromolecules, and water pass across the endothelium. In the last two subchapters, we discuss lymphatics as well as the regulation of the microcirculation.

The morphology and local regulatory mechanisms of the microcirculation are designed to meet the particular needs of each tissue. Because these needs are different, the structure and function of the microcirculation may be quite different from one tissue to the next.

The microcirculation extends from the arterioles to the venules

The microcirculation is defined as the blood vessels from the first-order arteriole to the first-order venule. Although the details vary from organ to organ, the principal components of an idealized microcirculation include a single arteriole and venule, between which extends a network of true capillaries ( Fig. 20-1 ). Sometimes a metarteriole—somewhat larger than a capillary—provides a shortcut through the network. Both the arteriole and the venule have vascular smooth-muscle cells (VSMCs). Precapillary sphincters—at the transition between a capillary and either an arteriole or a metarteriole—control the access of blood to particular segments of the network. Sphincter closure or opening creates small local pressure differences that may reverse the direction of blood flow in some segments of the network.

Arteries consist of an inner layer of endothelium, an internal elastic lamina, and a surrounding sheath of at least two continuous layers of innervated VSMCs (see p. 453 ). The inner radius of terminal arteries (called feed arteries in muscle) may be as small as 25 µm. Arterioles (inner radius, 5 to 25 µm) are similar to arteries but have only a single continuous layer of VSMCs, which are innervated. Metarterioles are similar to arterioles, but of shorter length. Moreover, their VSMCs are discontinuous and are not usually innervated. The precapillary sphincter is a small cuff of smooth muscle that usually is not innervated but is very responsive to local tissue conditions. Relaxation or contraction of the precapillary sphincter may modulate tissue blood flow by an order of magnitude or more. Metarterioles and precapillary sphincters are not found in all tissues.

True capillaries (inner radius, 2 to 5 µm) consist of a single layer of endothelial cells surrounded by a basement membrane, a fine network of reticular collagen fibers, and—in some tissues—pericytes. The endothelial cells have a smooth surface and are extremely thin (as little as 200 to 300 nm in height), except at the nucleus. The thickness and density of the capillary basement membrane vary among organs. Where large transcapillary pressures occur or other large mechanical forces exist, the basement membrane is thickest. Some endothelial cells have, on both luminal and basal surfaces, numerous pits called caveolae (see pp. 42–43 ) that are involved in ligand binding. Fluid-phase and receptor-mediated endocytosis (see pp. 41–42 ) can result in 70-nm caveolin-coated vesicles. In addition, the cytoplasm of capillary endothelial cells is rich in other endocytotic (pinocytotic) vesicles that contribute to the transcytosis of water and water-soluble compounds across the endothelial wall. In some cases, the endocytotic vesicles are lined up in a string and even appear linked together to form a transendothelial channel.

Linking endothelial cells together are interendothelial junctions ( Fig. 20-2 ) where the two cell membranes are ~10 nm apart, although there may be constricted regions where the space or cleft between the two cells forms adhering junctions only ~4 nm wide. Tight junctions (see pp. 43–44 ) may also be present in which the apposed cell membranes appear to fuse, and claudins 1, 3, and 5 (CLDN1, CLDN3, CLDN5; see pp. 43–44 ) as well as occludin seal the gap. CLDN5 is quite specific for endothelial cells. Occludin is not found in all endothelia.

Some endothelial cells have membrane-lined, cylindrical conduits— fenestrations —that run completely through the cell, from the capillary lumen to the interstitial space. These fenestrations are 50 to 80 nm in diameter and are seen primarily in tissues with large fluid and solute fluxes across the capillary walls (e.g., intestine, choroid plexus, exocrine glands, and renal glomeruli). A thin diaphragm often closes the perforations of the fenestrae (e.g., in intestinal capillaries).

The endothelia of the sinusoidal capillaries in the liver, bone marrow, and spleen have very large fenestrations as well as gaps 100 to 1000 nm wide between adjacent cells. Vesicles, transendothelial channels, fenestrae, and gaps—as well as structures of intermediate appearance—are part of a spectrum of regulated permeation across the endothelial cells.

Capillaries fall into three groups, based on their degree of leakiness ( Fig. 20-3 ).

• 1

  Continuous capillary. This is the most common form of capillary, with interendothelial junctions 10 to 15 nm wide (e.g., skeletal muscle). However, these clefts are absent in the blood-brain barrier (see p. 284 ), whose capillaries have narrow tight junctions.

• 2

  Fenestrated capillary. In these capillaries, the endothelial cells are thin and perforated with fenestrations. These capillaries most often surround epithelia (e.g., small intestine, exocrine glands).

• 3

  Discontinuous capillary. In addition to fenestrae, these capillaries have large gaps. Discontinuous capillaries are found in sinusoids (e.g., liver).

At their distal ends, true capillaries merge into venules (inner radius, 5 to 25 µm), which carry blood back into low-pressure veins that return blood to the heart. Venules have a discontinuous layer of VSMCs and therefore can control local blood flow. Venules may also exchange some solutes across their walls.

The exchange of O ₂ and CO ₂ across capillaries depends on the diffusional properties of the surrounding tissue

Gases diffuse by a transcellular route across the two cell membranes and cytosol of the endothelial cells of the capillary with the same ease that they diffuse through the surrounding tissue. In this section, we focus primarily on the exchange of O ₂ . Very similar mechanisms exist for the exchange of CO ₂ , but they run in the opposite direction. Arterial blood has a relatively high O ₂ level. As blood traverses a systemic capillary, the principal site of gas exchange, O ₂ diffuses across the capillary wall and into the tissue space, which includes the interstitial fluid and the neighboring cells.

The most frequently used model of gas exchange is August Krogh's tissue cylinder, a volume of tissue that a single capillary supplies with O ₂ ( Fig. 20-4 A ). The cylinder of tissue surrounds a single capillary. According to this model, the properties of the tissue cylinder govern the rate of diffusion of both O ₂ and CO ₂ . The radius of a tissue cylinder in an organ is typically half the average spacing from one capillary to the next, that is, half the mean intercapillary distance. Capillary density and therefore mean intercapillary distance vary greatly among tissues. Among systemic tissues, capillary density is highest in tissues with high O ₂ consumption (e.g., myocardium) and lowest in tissues consuming little O ₂ (e.g., joint cartilage). Capillary density is extraordinarily high in the lungs (see p. 684 ).

The Krogh model predicts how the concentration or partial pressure of oxygen ( ) within the capillary lumen falls along the length of the capillary as O ₂ exits for the surrounding tissues (see Fig. 20-4 A ). The within the capillary at any site along the length of the capillary depends on several factors:

• 1

  The concentration of free O ₂ in the arteriolar blood that feeds the capillary. This dissolved [O ₂ ], which is the same in the plasma and the cytoplasm of the red blood cells (RBCs), is proportional to the partial pressure of O ₂ (see p. 647 ) in the arterioles.

• 2

  The O ₂ content of the blood. Less than 2% of the total O ₂ in arterial blood is dissolved; the rest is bound to hemoglobin inside the RBCs. Each 100 mL of arterial blood contains ~20 mL of O ₂ gas, or 20 volume%—the O ₂ content (see Table 29-3 ).

• 3

  The capillary blood flow (F).

• 4

  The radial diffusion coefficient ( D _r ), which governs the diffusion of O ₂ out of the capillary lumen. For simplicity, we assume that D _r is the same within the blood, the capillary wall, and the surrounding tissue and that it is the same along the entire length of the capillary.

• 5

  The capillary radius ( r _c ).

• 6

  The radius of tissue cylinder ( r _t ) that the capillary is supplying with O ₂ .

• 7

  The O ₂ consumption by the surrounding tissues ( ).

• 8

  The axial distance (x) along the capillary.

The combination of all these factors accounts for the shape of the concentration profiles within the vessel and the tissue. Although this model appears complicated, it is actually based on many simplifying assumptions. N20-1

The O ₂ extraction ratio of a whole organ depends primarily on blood flow and metabolic demand

In principle, beginning with a model like Krogh's but more complete, one could sum up the predictions for a single capillary segment and then calculate gas exchange in an entire tissue. However, it is more convenient to pool all the capillaries in an organ and to focus on a single arterial inflow and single venous outflow. The difference in concentration of a substance in the arterial inflow and venous outflow of that organ is the arteriovenous (a-v) difference of that substance. For example, if the arterial O ₂ content ([O ₂ ] _a ) entering the tissue is 20 mL O ₂ /dL blood and the venous O ₂ content leaving it ([O ₂ ] _v ) is 15 mL O ₂ /dL blood, the O ₂ a-v difference for that tissue is 5 mL O ₂ gas/dL blood.

For a substance like O ₂ , which exits the capillaries, another way of expressing the amount that the tissues remove is the extraction ratio. This parameter is merely the a-v difference normalized to the arterial content of the substance. Thus, the extraction ratio of oxygen ( ) is

Thus, in our example,

In other words, the muscle in this example removes (and burns) 25% of the O ₂ presented to it by the arterial blood.

What are the factors that determine O ₂ extraction? To answer this question, we return to the hypothetical Krogh cylinder. The same eight factors that influence the profiles in Figure 20-4 A also determine the whole-organ O ₂ extraction. Of these factors, the two most important are capillary flow (item 3 in the list above) and metabolic demand (item 7). The O ₂ extraction ratio decreases with increased flow but increases with increased O ₂ consumption. These conclusions make intuitive sense. Greater flow supplies more O ₂ , so the tissue needs to extract a smaller fraction of the incoming O ₂ to satisfy its fixed needs. Conversely, increased metabolic demands require that the tissue extract more of the incoming O ₂ . These conclusions are merely a restatement of the Fick principle (see p. 423 ), which we can rewrite as

The term on the left is the a-v difference. The extraction ratio is merely the a-v difference normalized to [O ₂ ] _a . Thus, the Fick principle confirms our intuition that the extraction ratio should increase with increasing metabolic demand but decrease with increasing flow.

Another important factor that we have so far ignored is that not all of the capillaries in a tissue may be active at any one time. For example, skeletal muscle contains roughly a half million capillaries per gram of tissue. However, only ~20% are perfused at rest (see Fig. 20-4 B ). During exercise, when the O ₂ consumption of the muscle increases, the resistance vessels and precapillary sphincters dilate to meet the increased demand. This vasodilation increases muscle blood flow and the density of perfused capillaries (see Fig. 20-4 C ). This response is equivalent to decreasing the tissue radius of Krogh's cylinder because each perfused capillary now supplies a smaller region. Other things being equal, reduced diffusion distances cause in the tissue to increase.

The velocity of blood flow in the capillaries also increases during exercise. All things being equal, this increased velocity would cause to fall less steeply along the capillary lumen. For example, if the velocity were infinite, would not fall at all! In fact, because O ₂ consumption rises during exercise, actually falls more steeply along the capillary.

According to Fick's law, the diffusion of small water-soluble solutes across a capillary wall depends on both the permeability and the concentration gradient

Although the endothelial cell is freely permeable to O ₂ and CO ₂ , it offers a significant barrier to the exchange of lipid-insoluble substances. Hydrophilic solutes that are smaller than albumin can traverse the capillary wall by diffusion via a paracellular route (i.e., through the clefts and interendothelial junctions as well as gaps and fenestrae, if these are present).

The amount of solute that crosses a particular surface area of a capillary per unit time is called a flux. It seems intuitive that the flux ought to be proportional to the magnitude of the concentration difference across the capillary wall and that it ought to be bigger in leakier capillaries ( Fig. 20-5 ). These ideas are embodied in a form of Fick's law: N20-2

N20-2

Fick's Law

The passive movement of a small solute (X) across any surface can be described by Fick's law:

where J _X is the flux of solute ( units: moles · cm ⁻² · s ⁻¹ ), assuming a positive J _X in the direction of increasing distance z. D is the diffusion coefficient in cm ² · s ⁻¹ , and ∂[X]/∂ z is the concentration gradient of X ( units: moles · cm ⁻³ · cm ⁻¹ ) along the z axis. In the case of a solute crossing a capillary wall (see Fig. 20-5 ), we assume that the concentration of the solute in the bulk phase of the capillary ([X] _c ), as well as in the bulk phase of the interstitial fluid ([X] _if ), is constant and uniform. We also assume that the diffusion distance along the axis of diffusion (z) is equal to the thickness of the capillary wall (a). We can then rewrite Fick's law as

Because the wall thickness (a) is hard to determine, one often combines the terms D _X and a into a single permeability coefficient P ( units: cm · s ⁻¹ ), defined as P _X = D _X / a . The permeability coefficient is an expression of the ease with which a solute crosses a membrane, driven by the concentration difference. Therefore, the flux of a solute becomes

Equation NE 20-3 is the same as Equation 20-4 .

In Figure 20-5 and Equation 20-4 , J _X is the flux of the solute X ( units: moles/[cm ² s]), assuming a positive J _X with flow out of the capillary, into the interstitial fluid. [X] _c and [X] _if are the dissolved concentrations of the solute in the capillary and interstitial fluid, respectively. Because the capillary wall thickness a ( units: cm) is difficult to determine, we combined the diffusion coefficient D _X ( units: cm ² /s) and wall thickness into a single term ( D _X / a ) called P _X , the permeability coefficient ( units: cm/s). Thus, P _X expresses the ease with which the solute crosses a capillary by diffusion.

Because, in practice, the surface area (S) of the capillary is often unknown, it is impossible to compute the flux of a solute, which is expressed per unit area. Rather, it is more common to compute the mass flow ( ), which is simply the amount of solute transferred per unit time ( units: moles/s):

The whole-organ extraction ratio for small hydrophilic solutes provides an estimate of the solute permeability of capillaries

How could we estimate the permeability coefficient for a solute in different capillaries or for different solutes in the same capillary? Unfortunately, it is difficult to determine permeability coefficients in single capillaries. Therefore, investigators use an indirect approach that begins with measurement of the whole-organ extraction ratio for the solute X. As we have already seen for O ₂ (see Equation 20-1 ), the extraction ratio ( E _X ) is a normalized a-v difference for X:

Thus, E _X describes the degree to which an organ removes a solute from the circulation. Unlike the situation for O ₂ , the extraction ratio for small hydrophilic solutes depends not only on total organ blood flow (F) but also on the overall “exchange properties” of all of its capillaries, expressed by the product of permeability and total capillary area ( P _X · S ). The dependence of E _X on the P _X · S product and F is described by the following equation:

Therefore, by knowing the whole-organ extraction ratio for a solute and blood flow through the organ, we can calculate the product P _X · S. The second column of Table 20-1 lists the P _X · S products for a single solute (inulin), determined from Equation 20-7 , for a number of different organs. Armed with independent estimates of the capillary surface area (see Table 20-1 , column 3), we can compute P _X (column 4). P _X increases by a factor of ~4 from resting skeletal muscle to heart, which reflects a difference in the density of fluid-filled interendothelial clefts. Because a much greater fraction of the capillaries in the heart are open to blood flow (i.e., S is ~10-fold larger), the P _X · S product for heart is ~40-fold higher than that for resting skeletal muscle.

The cerebral vessels have unique characteristics that constitute the basis of the blood-brain barrier (see p. 284 ). The tight junctions of most brain capillaries do not permit any paracellular flow of hydrophilic solutes; therefore, they exhibit a very low permeability to sucrose or inulin, probably because of the abundant presence of CLDN5 and occludin. In contrast, the water permeability of cerebral vessels is similar to that of other organs. Therefore, a large fraction of water exchange in cerebral vessels must occur through the endothelial cells.

Whole-organ P _X · S values are not constant. First, arterioles and precapillary sphincters control the number of capillaries being perfused and thus the available surface area (S). Second, in response to a variety of signaling molecules (e.g., cytokines), endothelial cells can reorganize their cytoskeleton, thereby changing their shape. This deformation widens interendothelial clefts and increases P _X . One example is the increased leakiness that develops during inflammation in response to the secretion of histamine by mast cells and basophilic granulocytes. N20-3

Small polar molecules have a relatively low permeability because they can traverse the capillary wall only by diffusing through water-filled pores (small-pore effect)

Having compared the permeabilities of a single hydrophilic solute (inulin) in several capillary beds, we can address the selectivity of a single capillary wall to several solutes. Table 20-2 shows that the permeability coefficient falls as molecular radius rises. For lipid-soluble substances such as CO ₂ and O ₂ , which can diffuse through the entire capillary endothelial cell and not just the water-filled pathways, the permeability is much larger than for the solutes in Table 20-2 . Early physiologists had modeled endothelial permeability for hydrophilic solutes on the basis of two sets of pores: N20-4 large pores with a diameter of ~10 nm or more and a larger number of small pores with an equivalent radius of 3 nm. Small water-soluble, polar molecules have a relatively low permeability because they can diffuse only by a paracellular path through interendothelial clefts or other water-filled pathways, which constitute only a fraction of the total capillary area. Discontinuities or gaps in tight-junction strands could form the basis for the small pores. Alternatively, the molecular sieving properties of the small pores may reside in a fiber matrix ( Fig. 20-6 ) that consists of either a meshwork of glycoproteins in the paracellular clefts (on the abluminal side of the tight junctions) or the glycocalyx on the surface of the endothelial cell (on the luminal side of the tight junctions). The endothelium-specific, calcium-dependent adhesion molecule VE-cadherin (CDH5; see p. 17 ) and platelet/endothelial cell adhesion molecule 1 ( PECAM1, or CD31 antigen) are important glycoprotein components of the postulated fiber matrix in the paracellular clefts. In fact, the small-pore effect is best explained by an arrangement of discontinuities in the tight junctional strands in series with a fiber matrix on either side of the tight junction.

Interendothelial clefts are wider—and fenestrae are more common—at the venular end of the capillary than at its arteriolar end, so that P _X increases along the capillary. Therefore, if the transcapillary concentration difference ([X] _c − [X] _if ) were the same, the solute flux would actually be larger at the venous end of the microcirculation.

Small proteins can also diffuse across interendothelial clefts or through fenestrae. In addition to molecular size, the electrical charge of proteins and other macromolecules is a major determinant of their apparent permeability coefficient. In general, the flux of negatively charged proteins is much smaller than that of neutral macromolecules of equivalent size, whereas positively charged macromolecules have the highest apparent permeability coefficient. Fixed negative charges in the endothelial glycocalyx exclude macromolecules with negative charge and favor the transit of macromolecules with positive charge. Selective permeability based on the electrical charge of the solute is a striking feature of the filtration of proteins across the glomerular barrier of the nephron (see pp. 742–743 ).

The diffusive movement of solutes is the dominant mode of transcapillary exchange. However, the convective movement of water can also carry solutes. This solvent drag is the flux of a dissolved solute that is swept along by the bulk movement of the solvent. Compared with the diffusive flux of a small solute with a high permeability coefficient (e.g., glucose), the contribution of solvent drag is minor.

The exchange of macromolecules across capillaries can occur by transcytosis (large-pore effect)

Macromolecules with a radius >1 nm (e.g., plasma proteins) can cross the capillary, at a low rate, through wide intercellular clefts, fenestrations, and gaps—when these are present. However, it is caveolae (see p. 461 ) that are predominantly responsible for the large-pore effect that allows transcellular translocation of macromolecules. The transcytosis of very large macromolecules by vesicular transport involves (1) equilibration of dissolved macromolecules in the capillary lumen with the fluid phase inside the open vesicle; (2) pinching off of the vesicle; (3) vesicle shuttling to the cytoplasm and probably transient fusion with other vesicles within the cytoplasm, allowing intermixing of the vesicular content; (4) fusion of vesicles with the opposite plasma membrane; and (5) equilibration with the opposite extracellular fluid phase.

Although one can express the transcytotic movement of macromolecules as a flux, the laws of diffusion (see Equation 20-4 ) do not govern transcytosis. Nevertheless, investigators have calculated the “apparent permeability” of typical capillaries to macromolecules ( Table 20-3 ). The resulting “permeability”—which reflects the total movement of the macromolecule, regardless of the pathway—falls off steeply with increases in molecular radius, a feature called sieving. This sieving may be the result of steric hindrance when large macromolecules equilibrate across the neck of nascent vesicles or when a network of glycoproteins in the glycocalyx above the vesicle excludes the large macromolecules. In addition, sieving of macromolecules according to molecular size could occur as macromolecules diffuse through infrequent chains of fused vesicles that span the full width of the endothelial cell. N20-5

Transcytosis is not as simple as the luminal loading and basal unloading of ferryboats—the cell may process some of the cargo. Although the luminal surface of endothelial cells avidly takes up ferritin (750 kDa), only a tiny portion of endocytosed ferritin translocates to the opposite side of the cell (see Table 20-3 ). The remainder stays for a time in intracellular compartments, where it is finally broken down.

Both transcytosis and chains of fused vesicles are less prominent in brain capillaries. The presence of continuous tight junctions and the low level of transcytosis account for the blood-brain barrier's much lower apparent permeability to macromolecules.

Fluid transfer across capillaries is convective and depends on net hydrostatic and osmotic forces (i.e., Starling forces)

The pathway for fluid movement across the capillary wall is a combination of transcellular and paracellular pathways. Endothelial cell membranes express constitutively active aquaporin 1 (AQP1) water channels (see p. 110 ). It is likely that AQP1 constitutes the principal transcellular pathway for water movement. The interendothelial clefts, fenestrae, or gaps may be the anatomical substrate of the paracellular pathway.

Whereas the main mechanism for the transfer of gases and other solutes is diffusion, the main mechanism for the net transfer of fluid across the capillary membrane is convection. As first outlined in 1896 by Ernest Starling, N20-6 the two driving forces for the convection of fluid—or bulk water movement—across the capillary wall are the transcapillary hydrostatic pressure difference and effective osmotic pressure difference, also known as the colloid osmotic pressure or oncotic pressure difference (see p. 128 ).

The hydrostatic pressure difference (Δ P ) across the capillary wall is the difference between the intravascular pressure (i.e., capillary hydrostatic pressure, P _c ) and the extravascular pressure (i.e., interstitial fluid hydrostatic pressure, P _if ). Note that the term hydrostatic includes all sources of intravascular pressure, not only that derived from gravity; we use it here in opposition to osmotic .

The colloid osmotic pressure difference (Δπ) across the capillary wall is the difference between the intravascular colloid osmotic pressure caused by plasma proteins (π _c ) and the extravascular colloid osmotic pressure caused by interstitial proteins and proteoglycans (π _if ). A positive Δ P tends to drive water out of the capillary lumen, whereas a positive Δπ attracts water into the capillary lumen.

Starling's hypothesis to describe the volume flow ( F ) or volume flux ( J _V ) of fluid across the capillary wall is embodied in the following equation, which is similar to Equation 5-26 :

Table 20-4 describes the terms in this equation. The equation is written so that the flux of water leaving the capillary is positive and that of fluid entering the capillary is negative.

The hydraulic conductivity ( L _p ) N20-7 is the proportionality constant that relates the net driving force to J _V and expresses the total permeability provided by the ensemble of AQP1 channels and the paracellular pathway.

N20-7

Hydraulic Conductivity Versus Water Permeability Coefficient

The hydraulic conductivity ( L _p ) is the coefficient that relates water flux J _V ( units: cm ³ · cm ⁻² · s ⁻¹ ) to the net driving force in units of pressure (Δ P or Δπ; units: mm Hg).

Thus, the units of L _p are cm · s ⁻¹ · (mm Hg) ⁻¹ . These are the terms used in Equation 20-8 and in Table 20-4 .

The water permeability coefficient or osmotic permeability coefficient or filtration coefficient ( P _f ) is the coefficient that relates water flux ( J _V ; units: moles · cm ⁻² · s ⁻¹ ) to the net driving force of water in units of concentration difference (Δ[X]; units: moles · cm ⁻³ ):

$J_V=P_f\Delta \left[X\right]$

Thus, the units of P _f are cm · s ⁻¹ .

What is the relationship between the two proportionality factors L _p and P _f ? It can be shown that

Here, R is the universal gas constant (0.082055 atm · L · mole ⁻¹ · K ⁻¹ ) = 62.4 mm Hg · L · mole ⁻¹ · K ⁻¹ ), T is the absolute temperature, and V _W is the partial molar volume of water (0.018 L · mole ⁻¹ ). Note that the P _f - L _p conversion factor depends on temperature. At 37°C,

Thus, at 37°C,

$P_f=(1,074,667\text{mm Hg})L_p$

This conversion makes sense because multiplying L _p , which is in units of cm · s ⁻¹ · (mm Hg) ⁻¹ by (mm Hg) yields cm · s ⁻¹ , which are the units of P _f .

According to van't Hoff's law, the theoretical colloid osmotic pressure difference (Δπ _theory ) is proportional to the protein concentration difference (Δ[X]):

However, because capillary walls exclude proteins imperfectly, the observed colloid osmotic pressure difference (Δπ _obs ) is less than the ideal. The ratio Δπ _obs /Δπ _theory is the reflection coefficient (σ) N20-8 that describes how a semipermeable barrier excludes or “reflects” solute X as water moves across the barrier, driven by hydrostatic or osmotic pressure gradients.

N20-8

Reflection Coefficient

Lest we forget … she is still here!

If a semipermeable membrane excludes a solute (X) perfectly, then a concentration difference of the solute X (Δ[X]) generates an osmotic pressure difference that is exactly the same as the theoretically predicted value (see Equation 20-9 , reproduced here):

Here, R is the gas constant (0.082055 atm · L · mole ⁻¹ · K ⁻¹ ) and T is the absolute temperature (K). Equation NE 20-9 is known as van't Hoff's law. Because RT at 37°C equals 25.4 atm · L · mole ⁻¹ or 19,332 mm Hg · L · mole ⁻¹ , an osmotic pressure difference of 1 mM should exert an ideal osmotic pressure (Δπ _theory ) of 19.3 mm Hg (see p. 128 ).

If, on the other hand, the membrane excludes the solute imperfectly, the observed osmotic pressure (Δπ _obs ) is less than the ideal. The reflection coefficient for solute X (σ) is the ratio of the observed to the predicted osmotic pressure:

The reflection coefficient is the property of a semipermeable membrane that causes the observed osmotic pressure (π _obs )—generated by a concentration difference Δ[X]—to be less than the theoretical osmotic pressure for an ideal membrane (π _theory ). The reflection coefficient is dimensionless and ranges between 0 and 1. When σ = 1, the membrane excludes the solute perfectly and is an ideal osmometer. When σ = 0, the membrane treats the solute the same as water, and the solute generates no osmotic pressure.

Because the capillary endothelium has multiple “permeability” pathways for macromolecules, and because the permeability is different for different macromolecules, the σ in Equation 20-8 (reproduced here)

is actually the average reflection coefficient of proteins by the capillary wall.

The value of σ can range from 0 to 1. When σ is zero, the moving water perfectly “entrains” the solute, which moves with the water and exerts no osmotic pressure across the barrier. When σ is 1, the barrier completely excludes the solute as the water passes through, and the solute exerts its full or ideal osmotic pressure. To the extent that σ exceeds zero, the membrane sieves out the solute. The σ for plasma proteins is nearly 1.

Because small solutes such as Na ⁺ and Cl ⁻ freely cross the endothelium, their σ is zero, and they are not included in the Starling equation for the capillary wall (see Equation 20-8 ). Thus, changing the intravascular or interstitial concentrations of such “crystalloids” does not create a net effective osmotic driving force across the capillary wall. (Conversely, because plasma membranes have an effective σ _NaCl = 1, NaCl gradients do shift water between the intracellular and interstitial compartments.)

The net driving force in the Starling equation (see Equation 20-8 ), [( P _c − P _if ) − σ (π _c − π _if )], has a special name, the net filtration pressure. Filtration of fluid from the capillary into the tissue space occurs when the net filtration pressure is positive. In the special case where σ for proteins is 1, the fluid leaving the capillary is protein free; this process is called ultrafiltration. Con­versely, absorption of fluid from the tissue space into the vascular space occurs when the net filtration pressure is negative. At the arterial end of the capillary, the net filtration pressure is generally positive, so that filtration occurs. At the venous end, the net filtration pressure is generally negative, so that absorption occurs. However, as is discussed below, some organs do not adhere to this general rule.

In the next four sections, we examine each of the four Starling forces that constitute the net filtration pressure: P _c , P _if , π _c , and π _if .

Capillary blood pressure ( P _c ) falls from ~35 mm Hg at the arteriolar end to ~15 mm Hg at the venular end

Capillary blood pressure is also loosely called the capillary hydrostatic pressure, to distinguish it from capillary colloid osmotic pressure. It is possible to record P _c only in an exposed organ, ideally in a thin tissue (e.g., a mesentery) that allows good transillumination. One impales the lumen of the capillary with a fine micropipette (tip diameter < 5 µm) filled with saline and heparin. The micropipette lumen connects to a manometer, which has a sidearm to a syringe. Immediately after the impalement, blood begins to rise slowly up the pipette. A pressure reading at this time would underestimate the actual P _c because pipette pressure is less than P _c . The syringe makes it possible to apply just enough pressure to the pipette lumen to reach true pressure equilibrium—when fluid flows neither from nor to the pipette. By use of this null-point approach, the recorded pressure is the true P _c . In the human skin, P _c is ~35 mm Hg at the arteriolar end and ~15 mm Hg at the venular end.

When the arteriolar pressure is 60 mm Hg and the venular pressure is 15 mm Hg, the midcapillary pressure is not the mean value of 37.5 mm Hg but only 25 mm Hg ( Table 20-5, top row). The explanation for the difference is that normally the precapillary upstream resistance exceeds the postcapillary downstream resistance ( R _post / R _pre is typically 0.3; see pp. 451–452 ). However, the midcapillary pressure is not a constant and uniform value. In the previous chapter, we saw that P _c varies with changes in R _pre and R _post (see Equation 19-3 ). P _c also varies with changes in four other parameters: (1) upstream and downstream pressure, (2) location, (3) time, and (4) gravity.