Medical Physiology, 3rd Edition

Capillary Exchange of Water

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, imageN20-6 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).

N20-6

Ernest Henry Starling

Contributed by Emile Boulpaep

Ernest Starling (1866–1927) was born in London and educated at Guy's Hospital Medical School (MB, 1889). Upon graduation, he became a demonstrator in physiology at Guy's. In 1890 he began part-time work at University College, London, where he soon began a lifelong association with Sir William M. Bayliss.

Starling was professor of physiology at University College, London, where he did pioneering work in two cardiovascular areas, the heart and the microcirculation. His name is attached to Starling's law of the heart, which describes the dependence of stroke volume on end-diastolic volume (see pp. 524–526) and the Starling equation, which describes the movement of fluid across the capillary wall (see pp. 467–468). In addition, Starling and Bayliss together introduced the concept of a hormone and coined the term as part of their discovery of secretin, the first hormone identified. He and Bayliss also showed that intestinal peristalsis is a ganglionic reflex.

Starling's textbook Principles of Human Physiology (1912; 14th edition with Sir Charles A. Evans, 1968) was a standard physiology textbook in the first half of the 20th century.

Reference

Whonamedit? Ernest Henry Starling.  http://www.whonamedit.com/doctor.cfm/1188.html [Accessed May 2015].

The hydrostatic pressure difference (ΔP) across the capillary wall is the difference between the intravascular pressure (i.e., capillary hydrostatic pressure, Pc) and the extravascular pressure (i.e., interstitial fluid hydrostatic pressure, Pif). 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 (πc) and the extravascular colloid osmotic pressure caused by interstitial proteins and proteoglycans (πif). A positive ΔP 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 (JV) of fluid across the capillary wall is embodied in the following equation, which is similar to Equation 5-26:

image

(20-8)

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.

TABLE 20-4

Terms in the Starling Equation

TERM

DEFINITION

UNITS

JV

Volume flux across the capillary wall

cm3 · cm−2 · s−1 or [cm3/(cm2 · s)]

Lp

Hydraulic conductivity*

cm · s−1 · (mm Hg)−1 or [cm/(s · mm Hg)]

Pc

Capillary hydrostatic pressure

mm Hg

Pif

Tissue (interstitial fluid) hydrostatic pressure

mm Hg

πc

Capillary colloid osmotic pressure caused by plasma proteins

mm Hg

πif

Tissue (interstitial fluid) colloid osmotic pressure caused by interstitial proteins and proteoglycans

mm Hg

σ

Average colloid osmotic reflection coefficient

(dimensionless, varies between 0 and 1)

F

Flow of fluid across the capillary wall

cm3/s

Sf

Functional surface area

cm2

*Alternatively, the leakiness of the capillary wall to water may be expressed in terms of water permeability (Pfunits: cm/s). imageN20-7 In this case, the hydrostatic and osmotic forces are given in the units of osmolality.

The hydraulic conductivity (Lp)imageN20-7 is the proportionality constant that relates the net driving force to JV and expresses the total permeability provided by the ensemble of AQP1 channels and the paracellular pathway.

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Hydraulic Conductivity Versus Water Permeability Coefficient

Contributed by Emile Boulpaep

The hydraulic conductivity (Lp) is the coefficient that relates water flux JV (units: cm3 · cm−2 · s−1) to the net driving force in units of pressure (ΔP or Δπ; units: mm Hg).

image

(NE 20-4)

Thus, the units of Lp 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 (Pf) is the coefficient that relates water flux (JVunits: moles · cm−2 · s−1) to the net driving force of water in units of concentration difference (Δ[X]; units: moles · cm−3):

image (NE 20-5)

Thus, the units of Pf are cm · s−1.

What is the relationship between the two proportionality factors Lp and Pf? It can be shown that

image

(NE 20-6)

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 VW is the partial molar volume of water (0.018 L · mole−1). Note that the Pf-Lp conversion factor depends on temperature. At 37°C,

image

(NE 20-7)

Thus, at 37°C,

image (NE 20-8)

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

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

image

(20-9)

However, because capillary walls exclude proteins imperfectly, the observed colloid osmotic pressure difference (Δπobs) is less than the ideal. The ratio Δπobs/Δπtheory is the reflection coefficient (σ)imageN20-8 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

Contributed by Emile Boulpaep

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):

image

(NE 20-9)

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 (Δπtheory) of 19.3 mm Hg (see p. 128).

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

image

(NE 20-10)

The reflection coefficient is the property of a semipermeable membrane that causes the observed osmotic pressure (πobs)—generated by a concentration difference Δ[X]—to be less than the theoretical osmotic pressure for an ideal membrane (πtheory). 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)

image

(NE 20-4)

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 σNaCl = 1, NaCl gradients do shift water between the intracellular and interstitial compartments.)

The net driving force in the Starling equation (see Equation 20-8), [(Pc − Pif) − σ (πc − πif)], 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: PcPif, πc, and πif.

Capillary blood pressure (Pc) 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 Pc 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 Pc because pipette pressure is less than Pc. 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 Pc. In the human skin, Pc 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 (Rpost/Rpre 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 Pc varies with changes in Rpre and Rpost (see Equation 19-3). Pc also varies with changes in four other parameters: (1) upstream and downstream pressure, (2) location, (3) time, and (4) gravity.

TABLE 20-5

Effect of Upstream and Downstream Pressure Changes on Capillary Pressure*

 

Pa (mm Hg)

Pc (mm Hg)

Pv (mm Hg)

Control

60

25

15

Increased arteriolar pressure

70

27

15

Increased venular pressure

60

33

25

*Constant Rpost/Rpre = 0.3.

Arteriolar (Pa) and Venular (Pv) Pressure

Because Rpost is less than RprePc follows Pv more closely than Pa (see p. 451). Thus, increasing Pa by 10 mm Hg—at a constant Rpost/Rpre of 0.3—causes Pc to rise by only 2 mm Hg (see Table 20-5, middle row). On the other hand, increasing Pv by 10 mm Hg causes Pc to rise by 8 mm Hg (see Table 20-5, bottom row).

Location

Capillary pressure differs markedly among tissues. For example, the high Pc of glomerular capillaries in the kidney, ~50 mm Hg (see p. 744), is required for ultrafiltration. The retinal capillaries in the eye must also have a high Pc because they bathe in a vitreous humor that is under a pressure of ~20 mm Hg (see pp. 360–361). A higher Pc is needed to keep the capillaries patent in the face of the external compressing force. The pulmonary capillaries have unusually low Pc values, 5 to 15 mm Hg, which minimizes the ultrafiltration that otherwise would lead to the accumulation of edema fluid in the alveolar air spaces (see p. 684).

Time

Capillary blood pressure varies considerably from moment to moment at any given site, depending on the arteriolar diameter and tone of the precapillary sphincter (i.e., Rpre). In individual capillaries, these fluctuations lead to times of net filtration and other times of net fluid absorption.

Gravity

Finally, the effect of gravity on Pc is the same as that discussed for arterial and venous pressure. Thus, a capillary bed below the level of the heart has a higher Pc than a capillary bed at the level of the heart.

Interstitial fluid pressure (Pif) is slightly negative, except in encapsulated organs

The interstitium consists of both a solid and a liquid phase. The solid phase is made up of collagen fibers and proteoglycans. In the liquid phase, only a small fraction of interstitial water is totally “free” and capable of moving under the influence of convective forces. Most of the water is trapped in gels (e.g., proteoglycans), in which both water and small solutes move by diffusion. It was once thought that Pif in the liquid phase is slightly above barometric pressure throughout the interstitium, but more recent measurements indicate that Pif is subatmospheric in many tissues.

Estimation of Pif is very difficult because the probe used to make the measurement is far larger than the interstitial space; thus, the measurement itself can alter Pif. If one inserts a probe percutaneously and immediately uses a null-point method imageN20-9 to measure Pif (as outlined above for capillary pressure), the values are +1 to +2 mm Hg. However, during the next 4 to 5 hours, the measured value drops to −1 to −2 mm Hg. Arthur Guyton implanted a perforated, hollow plastic sphere under the skin to provide a long-term record of Pif (Fig. 20-7). After the wound has healed, the pressure inside the sphere may be as low as −2 to −10 mm Hg after 1 or 2 weeks. Another approach, the wick-in-needle technique, also yields subatmospheric values.

image

FIGURE 20-7 Long-term measurement of interstitial fluid pressure using an implanted capsule.

N20-9

Null-Point Technique for Measuring Interstitial Pressure

Contributed by Emile Boulpaep

As pointed out on pages 469–470, measuring interstitial pressure (Pif) is technically challenging. If one measures Pif by inserting a small needle percutaneously and immediately recording the pressure needed to force fluid out of the needle and into the interstitial fluid, one obtains values of +1 to +5 mm Hg. However, this approach suffers from some weaknesses. First, the very act of pushing fluid out of the needle distorts the narrow interstitial spaces during this brief measurement. Second, the interstitial fluid is actually in several microcompartments that are separated by connective tissue; the fluid injected cannot communicate freely among all of these microcompartments. As a result, one would have to wait a very long time for the distortions to dissipate.

A “null-point” method overcomes some of the aforementioned difficulties. In this case, the experimenter makes upward and downward adjustments to the pressure inside the probe in an effort to avoid any net movement of fluid into or out of the interstitial fluid (i.e., out of or into the needle). In brief experiments, this null-point method for measuring Pif (see p. 469), yields values of +1 to +2 mm Hg. However, during the next 4 to 5 hours, the measured value drops to −1 to −2 mm Hg. Thus, the short-term measurements of Pif—even those using a null-point method—are intrinsically flawed. As outlined in the text, Guyton overcame these shortcomings by obtaining a long-term record of Pif.

A value of −2 mm Hg is a reasonable average in loose tissues, such as the lung and subcutaneous tissue. Pif is slightly negative because of fluid removal by the lymphatics (see below). Inside rigid enclosed compartments, such as the bone marrow or brain, Pif is positive. It is also positive in encapsulated organs such as the kidney, where Pif is +1 to +3 mm Hg within the parenchyma. Expansion of high-pressure vessels in the kidney pushes the interstitial fluid against an unyielding fibrous capsule, raising Pif. The same principle applies to skeletal muscle, which is surrounded by layers of fascia. In some cases, it is not the interstitial fluid but another specialized compartment that provides the pressure around the capillaries. For renal glomerular capillaries, it is Bowman's space (see pp. 743–744)—filled with glomerular filtrate to a pressure of about +10 mm Hg—that is the relevant outside compartment. For pulmonary capillaries, the relevant outside compartment is the alveolus, the pressure of which varies during the respiratory cycle (see p. 622).

Pif is also sensitive to the addition of fluid to the interstitial compartment. When small amounts of fluid are added to the interstitial compartment, the interstitium behaves like a low-compliance system, so that Pif rises steeply for the small amount of added fluid. Adding more fluid disrupts the solid phase of collagen fibers and the gel of proteoglycans, so that large volumes can now accumulate with only small additional pressure increases. In this high-volume range, the interstitial compartment thus behaves like a high-compliance system. This high compliance is especially high in loose subcutaneous tissues, which can accommodate more edema fluid (Box 20-1) than can muscle.

Box 20-1

Interstitial Edema

Edema (from the Greek oidema [swelling]) is characterized by an excess of salt and water in the extracellular space, particularly in the interstitium. Edema may be associated with any disease leading to salt retention and expansion of the extracellular fluid volume—in particular, renal, cardiac, and hepatic disease (see p. 838). However, interstitial edema can also occur without overall salt and water retention because of microcirculatory alterations that affect the Starling forces. Regardless of the cause, the resulting edema can be either generalized (e.g., widespread swelling of subcutaneous tissue, often first evident in facial puffiness) or localized (e.g., limited to the dependent parts of the body). In this box, we focus on how edema can result from changes in parameters that are included in the Starling equation.

Hydrostatic Forces

When a person is standing for a sustained time, venous pressure and thus capillary pressure (Pc) in the legs increase because of gravity. The result is movement of fluid into the tissue space. In most cases, the lymphatic system can take up the extra interstitial fluid and return it to the vascular space, maintaining proper fluid balance. The return of fluid requires contractions of the leg muscles to compress the veins and lymphatics and to propel the fluid upward through the valves in these vessels and toward the heart (see pp. 474–476). If the standing person does not contract these muscles, the transudation of fluid can exceed the lymphatic return, causing interstitial edema.

An organ that is particularly sensitive to proper fluid balance is the lung. Slight increases in the hydrostatic pressure of the pulmonary capillaries (pulmonary hypertension) can lead to pulmonary edema. This condition decreases lung compliance (making lung inflation more difficult; see p. 610) and also may severely compromise gas exchange across the pulmonary capillary bed (see pp. 661–663). Left-sided heart failure causes blood to back up into the vessels of the lung, which raises pulmonary vascular pressures and causes pulmonary edema.

In right-sided heart failure, blood backs up into the systemic veins. As a result, there is a rise in central venous pressure (i.e., the pressure inside the large systemic veins leading to the right side of the heart), causing an increase in the Pc in the lower extremities and abdominal viscera. Fluid transudated from the hepatic and intestinal capillaries may leave the interstitial space and enter the peritoneal cavity, a condition called ascites.imageN20-18

Colloid Osmotic Forces

In nephrotic syndrome, a manifestation of a number of renal diseases, protein is lost in the urine. The result is a fall in plasma colloid osmotic pressure, a decrease in the ability of the capillaries to retain fluid, and generalized peripheral edema.

In pregnancy, synthesis of plasma proteins by the mother does not keep pace with the expanding plasma volume and nutritional demands of the fetus. As a result, maternal plasma protein levels fall. The same occurs in protein malnutrition. Although it is less severe than in nephrotic syndrome, the lower capillary colloid osmotic pressure nevertheless leads to edema in the extremities.

The opposite effect is seen in dehydration. A deficit of salt and water causes an increase in the plasma protein concentration, increasing the capillary colloid osmotic pressure and thus pulling fluid out of the interstitial space. The result is reduced turgor of the interstitial space. This effect is easily noticed by pinching the skin, which is unable to spring back to its usual firm position.

Properties of the Capillary Wall

Inflammation causes the release of vasodilators, such as histamine and cytokines, into the surrounding tissue. Vasodilation increases the number of open capillaries and therefore the functional surface area (Sf). Cytokines also cause widening of interendothelial clefts and a fall in the reflection coefficient (σ) for proteins. The net effect is enhanced filtration of fluid from capillary lumen to interstitium, so that tissue swelling is one of the hallmarks of inflammation.

Severe head injuries can result in cerebral edema, a result of the breakdown of the normally tight endothelial barrier of the cerebral vessels (see pp. 285–286). Because the rigid skull prevents expansion of the brain, cerebral edema can lead to occlusion of the cerebral microcirculation.

During ischemia—when blood flow to a tissue is severely reduced or completely stopped—blood vessels deteriorate, which causes hydraulic conductivity (Lp) to increase and reflection coefficient to decrease. Once blood flow is reestablished (reperfusion), these changes lead to local edema. If the increased leakiness is substantial, large quantities of plasma proteins freely move into the interstitial space, dissipating the colloid osmotic gradient across the capillary wall and aggravating the edema.

Lymphatic Drainage

Lymphatic drainage may become impaired after lymph nodes are removed in cancer surgery or when lymph nodes are obstructed by malignant neoplasms. The reduction in the lymphatic drainage leads to local edema upstream from the affected nodes.

N20-18

Transcapillary Refill

Contributed by Emile Boulpaep

The opposite of the changes responsible for interstitial edema occurs when there is significant hemorrhage. During severe hemorrhagic hypotension, capillary pressure drops and fluid moves from the tissue space into the vascular space, as discussed on pages 585–586. This fluid movement—known as transcapillary refill—helps replace the fluid lost in the hemorrhage and thereby serves as a compensatory mechanism for blood loss. The amount of fluid that can be replaced from the interstitium of the skeletal muscle is significant. Because this fluid is cell free, it lowers the hematocrit of the blood, a condition known as hemodilution.

Capillary colloid osmotic pressure (πc), which reflects the presence of plasma proteins, is ~25 mm Hg

The colloid osmotic pressure difference across the capillary endothelium is due solely to the plasma proteins, such as albumin, globulins, and fibrinogen. Total plasma protein concentration is ~7.0 g/dL, which corresponds to ~1.5 mM of protein. According to van't Hoff's law (see Equation 20-9), these proteins would exert an osmotic pressure of ~28 mm Hg if perfectly reflected by the capillary wall (σ = 1). The σ is indeed close to 1 for the principal plasma proteins—albumin (3.5 to 5.5 g/dL) and the globulins (2.0 to 3.5 g/dL)—so that the actual colloid osmotic pressure (σπc) in capillaries is ~25 mm Hg. This value is the same as if osmotically active solutes were present at ~1.3 mM. Note that because of the very definition of colloid osmotic pressure, we have ignored the osmotic effects of the small solutes in plasma, which have an osmolality of 290 mOsm (see p. 105). imageN20-10

N20-10

Total Osmotic Pressure versus Colloid Osmotic Pressure of Plasma

Contributed by Emile Boulpaep

The total osmotic pressure of blood plasma that contains ~290 milliosmoles/L of solutes can be computed from the van't Hoff equation (see Equation 20-9, reproduced here):

image

(NE 20-9)

As described in imageN20-8RT can be expressed as 19,332 mm Hg · L · mole−1. Thus, for a Δ[X] of 0.29 moles/L (i.e., 290 mOsm),

image

(NE 20-11)

This pressure of 5597 mm Hg corresponds to 7.4 atm. If distilled water were on the opposite side of the capillary endothelium, and if the capillary wall reflected all of the solutes in the blood plasma (i.e., if the wall were perfectly impermeable to all solutes, but permeable to water), then the osmotic pressure difference across the capillary wall would be 7.4 atm. However, these conditions are not valid. First, most of the solutes in blood plasma are also in the interstitial fluid at approximately the same concentrations. Second, even when small concentration differences exist across the capillary wall for these small solutes such as Na+ or Cl (sometimes called crystalloids), these solutes do not exert any effective osmotic pressure across the capillary wall because they pass with great ease through the capillary wall. That is, these crystalloids have a reflection coefficient (σ imageN20-8) of zero.

As stated in the text (see p. 470), the colloid osmotic pressure (πc) of blood plasma is only 25 mm Hg, which is minuscule compared to the total osmotic pressure (5597 mm Hg). The colloid osmotic pressure is generated solely by the concentration difference across the capillary wall of solutes with a reflection coefficient of ~1, that is, the proteins in the blood plasma. The concentration difference for these proteins is ~1.3 mM. Thus,

image

(NE 20-12)

πc does vary appreciably along the length of the capillary. Indeed, most capillary beds filter <1% of the fluid entering at the arteriolar end. Thus, the loss of protein-free fluid does not measurably concentrate plasma proteins along the capillary and does not appreciably raise πc.

Because clinical laboratories report plasma protein concentrations in grams per deciliter and not all proteins have the same molecular weight, a plasma protein concentration of 7 g/dL can produce different πcvalues, depending on the protein composition of the plasma. Because albumin has a much lower molecular weight than γ-globulin, replacement of 1 g of the heavier γ-globulin with 1 g of the lighter albumin raises πc. Whereas van't Hoff's law (see Equation 20-9) predicts a linear relationship between osmotic pressure and concentration, colloid osmotic pressure actually increases more steeply, even when the albumin/globulin ratio is held constant at 1.8 (Fig. 20-8, orange curve). imageN20-11 Obviously, the steepness of the curve varies from one plasma protein to the next because all have different molecular weights.

image

FIGURE 20-8 Dependence of colloid osmotic pressure on the concentration of plasma proteins. The point on the orange curve indicates that normal plasma, a mixture of proteins at a concentration of 7 g/dL, has a colloid osmotic pressure (πc) of 25 mm Hg.

N20-11

Effects of Changes in Plasma H2O on Colloid Osmotic Pressure

Contributed by Emile Boulpaep

The curves in Figure 20-8 show a nonlinear dependence of colloid osmotic pressure on the concentration of plasma proteins. The nonlinearity of the curves becomes clinically significant when a gain or loss of plasma water alters the plasma protein concentration. As expected, identical increases or decreases in plasma H2O—caused by gain or loss in extracellular fluid—exert changes in colloid osmotic pressure that are of opposite sign. However, the changes in colloid osmotic pressure are not identical in magnitude.

For instance, if we assume a normal plasma volume of 3000 mL and a plasma protein concentration of 7.0 g/dL, then a 300-mL loss of plasma H2O will increase plasma protein concentration to 7.78 g/dL (a gain of 0.78 g/dL), whereas a 300-mL gain of plasma H2O will decrease plasma protein concentration to 6.36 g/dL (a loss of 0.64 g/dL). These two identical changes in plasma H2O do not result in the same change in colloid osmotic pressure. First, the absolute change in plasma protein concentration is less for 300 mL of overhydration than for 300 mL of dehydration. Second, because the “Normal plasma” curve in Figure 20-8 is nonlinear, the change in colloid osmotic pressure is larger in the direction of increased protein concentration (i.e., during dehydration, when the curves in Fig. 20-8 are becoming steeper) than in the direction of decreased protein concentration (i.e., during an equivalent overhydration).

Not only does πc vary markedly with protein composition and concentration, the reflection coefficient for colloids also varies widely among organs. The lowest values for σ (i.e., greatest leakiness) are in discontinuous capillary beds (e.g., liver); intermediate values are in muscle capillaries; and the highest values (σ = 1) are in the tight, continuous capillary beds of the brain.

The plasma proteins do more than just act as osmotic agents. Because these proteins also carry negative charges, the Donnan effectimageN20-12 (see Fig. 5-15) causes an increase in both the concentrations of cations (see p. 104) and the colloid osmotic pressure in the capillary lumen.

N20-12

Donnan Effect Across the Capillary Wall

Contributed by Emile Boulpaep

Plasma proteins do more than act as osmotic agents. They also carry net negative charges. Thus, albumin and other plasma proteins can act as the counterbalancing anion for some of the cations in blood plasma. Because the endothelium is relatively impermeable to proteins, the protein concentration in the interstitial fluid is lower than that in the capillary. The result is a “Donnan effect” (see p. 104) across the endothelial wall, so that at equilibrium the composition of cations and anions in the interstitial fluid is not identical to that in the protein-free plasma of the capillary (see Table 5-2). If we make the simplifying assumption that the capillary wall excludes all proteins from the interstitial fluid, the equilibrium concentration ratios for monovalent cations and anions are as follows:

image

(NE 20-13)

Thus, the Donnan effect causes the capillary lumen to contain higher concentrations of cations and lower concentrations of anions than the protein-free solution of the interstitium.

As noted on page 129, it is a general property of a Gibbs-Donnan equilibrium that, after the permeant ions achieve the predicted electrochemical equilibrium across a barrier separating two compartments, the compartment containing the impermeant ions has a higher osmolality than the compartment from which the impermeant ions are excluded (see Fig. 5-15). Thus, just as the presence of impermeant proteins in the cytoplasm leads to cell swelling because of Donnan forces, the presence of impermeant anions in the capillary lumen leads to the movement of water from the interstitium into the capillary lumen.

Note that the water movement we have chosen to discuss so far is not due to the osmotic pressure exerted by the plasma proteins per se. Rather, we are considering the osmotic pressure difference that arises from the unequal distribution of Na+ and Cl between capillary lumen (c) and interstitial fluid (if). By analogy to the calculation shown in Equation 5-31, we can calculate the theoretically predicted osmotic force (Δπtheory) caused by the difference in the osmolalities of small, permeant ions (ΔOsm):

image (NE 20-14)

Of course, it was the Gibbs-Donnan equilibrium that set up this difference in total osmolality across the capillary wall. Because the major small ions on either side of the capillary wall are Na+ and Cl,

image

(NE 20-15)

Using the values in Table 5-2 for protein-free plasma and interstitial fluid, we have the following:

image

(NE 20-16)

Because RT at 37°C equals 19,332 mm Hg/M, an osmolality difference of 1 mM exerts an ideal osmotic pressure of 19.332 mm Hg. Thus, the Gibbs-Donnan equilibrium for Na+ and Cl causes a theoretical osmotic pressure difference of

image

(NE 20-17)

Physiologically, the osmotic difference of 38.7 mm Hg caused by the unequal distribution of small ions is of no consequence for water movement across the capillary wall because the capillary does not reflect Na+ or Cl (i.e., σNa = σCl = 0), and therefore these solutes generate no effective osmotic pressure. See imageN20-8 for a discussion of the reflection coefficient (σ).

As introduced on page 128 and discussed more fully on page 469, the only effective osmotic pressure difference across the capillary wall is that caused directly by the plasma proteins themselves, acting as solutes. This effective osmotic pressure difference is the colloid osmotic pressure, which tends to pull water into the capillary lumen.

image

(NE 20-18)

As shown in Table 20-6, the physiological force opposing the colloid osmotic pressure (Δπ) is the difference between the capillary hydrostatic pressure (Pc) and the interstitial hydrostatic fluid pressure (Pif).

In the preceding discussion, we saw that because the capillary wall is freely permeable to Na+ and Cl, the only transmural concentration differences that count are those for the colloids. What would happen if the capillary wall were an ideal osmotic membrane, permeable to water but not to any solutes (i.e., neither ions nor proteins)? In such a hypothetical case, the total osmotic pressure difference across the capillary wall would be the sum of the Δπsmall ions (or 38.7 mm Hg) caused by the small ions and the Δπ (or 25 mm Hg) caused by the colloids, which totals ~64 mm Hg. Of course, the hydrostatic pressure difference (Pc − Pif) would never be large enough to prevent the net movement of water into the lumen of the typical capillary.

Interstitial fluid colloid osmotic pressure (πif) varies between 0 and 10 mm Hg among different organs

It is difficult to measure the interstitial fluid colloid osmotic pressure because it is virtually impossible to obtain uncontaminated samples. As a first approximation, we generally assume that πif is the same as the colloid osmotic pressure of lymph. The protein content of lymph varies greatly from region to region; for example, it is 1 to 3 g/dL in the legs, 3 to 4 g/dL in the intestine, and 4 to 6 g/dL in the liver. Such lymph data predict that πif ranges from 3 to 15 mm Hg. However, the protein concentration in the interstitial fluid is probably somewhat higher than in the lymph. A total-body average value for πif is ~3 mm Hg, substantially less than the value of 25 mm Hg for πc in the capillary lumen.

The πif appears to increase along the axis of the capillary (Table 20-6). The lowest values are near the arteriolar end, where the interstitium receives protein-free fluid from the capillary as the result of filtration. The highest values are near the venular end, where the interstitium loses protein-free fluid to the capillary as the result of absorption.

TABLE 20-6

Typical Values of Transcapillary Driving Forces for Fluid Movement in Loose, Nonencapsulated Tissue

 

CAPILLARY BLOOD PRESSURE (Pc)

INTERSTITIAL FLUID PRESSURE (Pif)

EFFECTIVE CAPILLARY COLLOID OSMOTIC PRESSURE (σπc)

EFFECTIVE INTERSTITIAL FLUID COLLOID OSMOTIC PRESSURE (σπif)

NET FORCE

Arteriolar end

+35 mm Hg

−2 mm Hg

+25 mm Hg

+0.1 mm Hg*

+12 mm Hg

Venular end

+15 mm Hg

−2 mm Hg

+25 mm Hg

+3 mm Hg

−5 mm Hg

*The low effective colloid osmotic pressure prevails only in the subcalyx fluid compartment (see Fig. 20-10B).

The Starling principle predicts ultrafiltration at the arteriolar end and absorption at the venular end of most capillary beds

The idealized forces acting on fluid movement across a capillary are shown in Figure 20-9A. Using the Starling equation and the values in Table 20-6, we can calculate the net transfer of fluid (JV) at both the arteriolar and venular ends of a typical capillary:

image

(20-10)

image

FIGURE 20-9 Starling forces along a capillary. In A, the yellow lines are idealized profiles of capillary (Pc) and interstitial (Pif) hydrostatic pressures. The red lines are idealized capillary (πc) and interstitial (πif) colloid osmotic pressures. In B, the net filtration pressure is (Pc − Pif) − σ(πc − πif).

The net filtration pressure is thus positive (favoring filtration) at the arteriolar end, and it gradually makes the transition to negative (favoring absorption) at the venular end (see Fig. 20-9B). At the point where the filtration and reabsorptive forces balance each other, an equilibrium exists, and no net movement of water occurs across the capillary wall.

Net filtration pressure varies—sometimes considerably—among tissues. For example, in the intestinal mucosa, Pc is so much lower than πc that absorption occurs continually along the entire length of the capillary. On the other hand, in glomerular capillaries, Pc exceeds πc throughout most of the network, so that filtration may occur along the entire capillary (see pp. 745–746). Hydraulic conductivity also can affect the filtration/absorption profile along the capillary. Because the interendothelial clefts become larger toward the venular end of the capillary, Lp increases along the capillary from the arteriolar to the venular end.

Ignoring glomerular filtration in the kidney, Landis and Pappenheimer calculated a filtration of ~20 L/day at the arteriolar end of the capillary and an absorption of about 16 to 18 L/day at the venular end, for a net filtration of about 2 to 4 L/day from blood to interstitial fluid. This 2 to 4 L of net filtration does not occur uniformly in all capillary beds. The flow of fluid across a group of capillaries (F) is the product of the flux (JV) and the functional surface area (Sf): F = JV · Sf. Thus, net filtration of fluid in an organ depends not only on the net filtration pressure and the hydraulic conductivity of the capillary wall (terms that contribute to JV) but also on the surface area of capillaries that happen to be perfused. For example, exercise recruits additional open capillaries in muscle, raising Sf and thereby increasing filtration.

For continuous capillaries, the endothelial barrier for fluid exchange is more complex than considered by Starling

The contribution of Landis and Pappenheimer was to insert experimentally measured values into the Starling equation (see Equation 20-8) and to calculate the total-body filtration and absorption rates and, by difference, net filtration. Because the estimate of 2 to 4 L for the net filtration rate agreed so well with total lymph flow, the scientific public accepted the entire Landis-Pappenheimer analysis. However, for continuous capillaries, the Landis-Pappenheimer estimates of filtration and absorption are far higher than those indicated by the modern experimental data. Two major reasons for the discrepancy have emerged. First, Starling's assumptions about the nature of the capillary barrier were overly simplistic. Namely, he assumed that a single barrier separated two well-defined, uniform compartments (Fig. 20-10A). Thus, according to Equation 20-8, the dependence of JV on net filtration pressure ought to be linear, as indicated by the plot in the inset of Figure 20-10A. Second, Landis and Pappenheimer used (1) Pc values that are valid only at the level of the heart (i.e., ignoring gravity), (2) Pc values that are not subject to the vagaries of vasomotion, (3) unrealistically low values of πif (which would predict a greater absorption), and (4) Pifand πif values that are invariant. imageN20-13

image

FIGURE 20-10 Models of fluid exchange across continuous endothelia with interendothelial junctions. Pc, capillary hydrostatic pressure; Pif, interstitial fluid hydrostatic pressure; Psg, subglycocalyx hydrostatic pressure; πc, capillary colloid osmotic pressure; πif, interstitial fluid colloid osmotic pressure; πsg, subglycocalyx colloid osmotic pressure; JV, volume flux.

N20-13

Assumptions of Landis and Pappenheimer

Contributed by Emile Boulpaep

Direct measurements of the four parameters of the Starling equation (PcPif, πc , πif) in organs with low lymph flow such as skeletal muscle indicate that Pc > [Pif + σ (πc − πif)] throughout the length of the capillary. These values would predict unrealistically high net filtration rates that are incompatible with the observed low lymph flow.

Landis and Pappenheimer had estimated only 2 to 4 L of net total-body filtration (excluding renal glomerular filtration), which agreed well with total lymph flow, because of the particular values that they used in the classical Starling equation.

1. Landis and Pappenheimer used arterial and venous values of Pc that can be correct only at the level of the heart. As shown in Figure 17-8 on page 418, gravity can add 95 mm Hg to the transmural pressure in feed arteries of the dependent limb and can raise Pc to 90 to 100 mm Hg, which predicts filtration throughout the length of the capillary.

2. Landis and Pappenheimer ignored dynamic changes in Pc. Vasomotion causes Pc to cycle between high and low values, creating alternating periods of filtration and reabsorption.

3. Landis and Pappenheimer assumed low arterial values of πif.

4. Landis and Pappenheimer assumed that values of Pif and πif were clamped in time, whereas the rate of filtration itself determines Pif and πif. At high filtration rates, Pif tends to rise, opposing further filtration. At high filtration rates, πif tends to fall, also opposing further filtration.

In reality, as noted on page 472, net total-body filtration (excluding renal glomerular filtration) is even much less than the 2 to 4 L estimated by Landis and Pappenheimer because the endothelial barrier is not a single membrane separating two well-stirred clamped compartments and the barrier effectively exhibits osmotic asymmetry. Placing the protein osmotic barrier at the glycocalyx and considering a dynamic range of subglycocalyx colloid osmotic pressures (πsg) independent of bulk πif carries important implications. First, the net filtration pressure is far less than expected from the Starling equation, and this explains why actual lymph flows are less than the net filtration rates postulated from bulk values of PcPif , πc, and πif. Second, during reversal of flow (i.e., absorption), protein in the subcalyx fluid should quickly concentrate to prevent all absorption. Thus, overall fluid balance of the interstitium is primarily maintained not by venous absorption but by lymphatic function.

References

Landis EM. Capillary pressure in frog mesentery as determined by microinjection methods. Am J Physiol. 1925–1926;75:548–570.

Landis EM. The capillary blood pressure in mammalian mesentery as determined by the micro-injection method. Am J Physiol. 1930;93:353–362.

Landis EM, Pappenheimer JR. Exchange of substances through the capillary walls. American Physiological Society: Washington, DC; 1963:961–1034. Hamilton WF, Dow P. Handbook of Physiology, Section 2: Circulation. vol 2.

Levick JR. Revision of the Starling principle: New views of tissue fluid balance. J Physiol. 2004;557:704.

Pappenheimer JR, Soto-Rivera A. Effective osmotic pressure of the plasma proteins and other quantities associated with the capillary circulation in the hindlimbs of cats and dogs. Am J Physiol. 1948;152:471–491.

A revised model has emerged for fluid exchange across continuous endothelia (see p. 462) with interendothelial junctions (see p. 461) to account for discrepancies between the classical Starling predictions and the modern data. The revised model has two major features. First, the primary barrier for colloid osmotic pressure—that is, the semipermeable “membrane” that reflects proteins but lets water and small solutes pass—is not the entire capillary but only the luminal glycocalyx, in particular the glycocalyx overlying the paracellular clefts (see Fig. 20-10B). Second, the abluminal surface of the glycocalyx is not in direct contact with the bulk interstitial fluid but is bathed by the subglycocalyx fluid at the top of the long paracellular cleft—a third compartment. Thus, the flow across the glycocalyx barrier depends not on Pif and πifin the bulk interstitial fluid but on the comparable parameters in the subglycocalyx fluid (Psg and πsg):

image

(20-11)

Let us now examine the predictions of this equation for three states.

1. During ultrafiltration (i.e., JV is positive). Here, the hydrostatic pressure in the subglycocalyx fluid—that is, the fluid in direct contact with the abluminal surface of the glycocalyx—is higher than that in the bulk interstitial fluid (i.e., Psg > Pif in Fig. 20-10B). Thus, fluid moves from the subglycocalyx space, along the paracellular cleft, to the bulk interstitial fluid. Moreover, as long as protein-free ultrafiltrate enters the subglycocalyx space, the colloid osmotic pressure in the subglycocalyx fluid is low (πsg < πif). Both the rise in Psg and the fall in πsg tend to oppose filtration.
Because proteins enter the interstitium through the large-pore pathway (see p. 467), πif in the bulk interstitial compartment is about that of lymph. However, at high rates of ultrafiltration, this πif has no osmotic effect on the glycocalyx barrier because the protein cannot diffuse against the convective flow of fluid from lumen to interstitium. On the other hand, if the ultrafiltration rate is low, interstitial proteins can diffuse from the bulk interstitial space into the paracellular cleft, raising πsg and promoting more ultrafiltration.

2. When net flow falls to nearly zero (i.e., JV is ~0). Here, the parameters in the subglycocalyx fluid (i.e., Psg and πsg) should thus be very close to their values in the bulk interstitial fluid (i.e., Pif and πif), and the revised model simplifies to the classical Starling model (see Fig. 20-10A).

3. During absorption (i.e., reversal of flow, where JV is negative). Here, water and small solutes move from the subglycocalyx space to the capillary lumen, leaving behind and thereby concentrating the protein in the subglycocalyx space (see Fig. 20-10C). The resulting rise of πsg (see Equation 20-11) opposes further absorption and, indeed, can quickly bring it to a halt. This effect explains why the plot is nearly flat in the left lower quadrant of the inset between Figure 20-10B and C.

Thus, a more sophisticated understanding of the structure of the endothelial barrier for proteins correctly makes two predictions. First, the fluxes are smaller than predicted by Starling for bulk driving forces because the actual driving force across the glycocalyx barrier (see Equation 20-11) is smaller than the net driving force in the Starling equation (see Equation 20-8). Second, the magnitude of the flux for a given net driving force is greater for ultrafiltration than for absorption—osmotic asymmetry or rectification.