A high glomerular filtration rate is essential for maintaining stable and optimal extracellular levels of solutes and water
Qualitatively, the filtration of blood plasma by the renal glomeruli is the same as the filtration of blood plasma across capillaries in other vascular beds (see pp. 467–468). Glomerular ultrafiltration results in the formation of a fluid—the glomerular filtrate—with solute concentrations that are similar to those in plasma water. However, proteins, other high-molecular-weight compounds, and protein-bound solutes are present at reduced concentration. The glomerular filtrate, like filtrates formed across other body capillaries, is free of formed blood elements, such as red and white blood cells.
Quantitatively, the rate of filtration that occurs in the glomeruli greatly exceeds that in all the other capillaries of the circulation combined because of greater Starling forces (see pp. 467–468) and higher capillary permeability. Compared with other organs, the kidneys receive an extraordinarily large amount of blood flow—normalized to the mass of the organ—and filter an unusually high fraction of this blood flow. Under normal conditions, the glomerular filtration rate (GFR; see p. 732) of the two kidneys is 125 mL/min or 180 L/day. Such a large rate of filtrate formation is required to expose the entire extracellular fluid (ECF) frequently (>10 times a day) to the scrutiny of the renal-tubule epithelium. If it were not for such a high turnover of the ECF, only small volumes of blood would be “cleared” per unit time (see p. 731) of certain solutes and water. Such a low clearance would have two harmful consequences for the renal excretion of solutes that renal tubules cannot adequately secrete.
First, in the face of a sudden increase in the plasma level of a toxic material—originating either from metabolism or from food or fluid intake—the excretion of the material would be delayed. A high blood flow and a high GFR allow the kidneys to eliminate harmful materials rapidly by filtration.
A second consequence of low clearance would be that steady-state plasma levels would be very high for waste materials that depend on filtration for excretion. The following example by Robert Pitts, a major contributor to renal physiology, illustrates the importance of this concept. Consider two individuals consuming a diet that contains 70 g/day of protein, one with normal renal function (e.g., GFR of 180 L/day) and the other a renal patient with sharply reduced glomerular filtration (e.g., GFR of 18 L/day). Each individual produces 12 g/day of nitrogen in the form of urea (urea nitrogen) derived from dietary protein and must excrete this into the urine. However, these two individuals achieve urea balance at very different blood urea levels. We make the simplifying assumption that the tubules neither absorb nor secrete urea, so that only filtered urea can be excreted, and all filtered urea is excreted. The normal individual can excrete 12 g/day of urea nitrogen from 180 L of blood plasma having a [blood urea nitrogen] of 12 g/180 L, or 6.7 mg/dL. In the patient with end-stage renal disease (ESRD), whose GFR may be only 10% of normal, excreting 12 g/day of urea nitrogen requires that each of the 18 L of filtered blood plasma have a blood urea nitrogen level that is 10 times higher, or 67 mg/dL. Thus, excreting the same amount of urea nitrogen—to maintain a steady state—requires a much higher plasma blood urea nitrogen concentration in the ESRD patient than in the normal individual.
The clearance of inulin is a measure of GFR
The ideal glomerular marker for measuring GFR would be a substance X that has the same concentration in the glomerular filtrate as in plasma and that also is not reabsorbed, secreted, synthesized, broken down, or accumulated by the tubules (Table 34-1). In Equation 33-4, we saw that
(34-1)
P_{X} is the concentration of the solute in plasma, GFR is the sum of volume flow of filtrate from the plasma into all Bowman's spaces, U_{X} is the urine concentration of the solute, and is the urine flow. Rearranging this equation, we have
(34-2)
Note that Equation 34-2 has the same form as the clearance equation (see Equation 33-3) and is identical to Equation 33-5. Thus, the plasma clearance of a glomerular marker is the GFR. N34-1
TABLE 34-1
Criteria for Use of a Substance to Measure GFR
1. Substance must be freely filterable in the glomeruli. 2. Substance must be neither reabsorbed nor secreted by the renal tubules. 3. Substance must not be synthesized, broken down, or accumulated by the kidney. 4. Substance must be physiologically inert (not toxic and without effect on renal function). |
N34-1
Units of Clearance
Contributed by Erich Windhager, Gerhard Giebisch
Clearance values are conventionally given in milliliters of total plasma per minute, even though plasma consists of 93% “water” and 7% protein, with only the “plasma water”—that is, the protein-free plasma solution, including all solutes small enough to undergo filtration—undergoing glomerular filtration. As pointed out in Chapter 5 (see Table 5-2) the concentrations of plasma solutes can be expressed in millimoles per liter of total plasma, or millimoles per liter of protein-free plasma (i.e., plasma water). Customarily, clinical laboratories report values in millimoles (or milligrams) per deciliter of plasma, not plasma water. When we say that the GFR is 125 mL/min, we mean that each minute the kidney filters all ions and small solutes contained in 125 mL of plasma. However, because the glomerular capillary blood retains the proteins, only 0.93 × 125 mL = 116 mL of plasma water appear in Bowman's capsule. Nevertheless, GFR is defined in terms of volume of blood plasma filtered per minute rather than in terms of the volume of protein-free plasma solution that actually arrives in Bowman's space (i.e., the filtrate).
Inulin is an exogenous starch-like fructose polymer that is extracted from the Jerusalem artichoke and has a molecular weight of 5000 Da. Inulin is freely filtered at the glomerulus, but neither reabsorbed nor secreted by the renal tubules (Fig. 34-1A). Inulin also fulfills the additional requirements listed in Table 34-1 for an ideal glomerular marker.
FIGURE 34-1 Clearance of inulin.
Assuming that GFR does not change, three tests demonstrate that inulin clearance is an accurate marker of GFR. First, as shown in Figure 34-1B, the rate of inulin excretion () is directly proportional to the plasma inulin concentration (P_{In}), as implied by Equation 34-2. The slope in Figure 34-1B is the inulin clearance. Second, inulin clearance is independent of the plasma inulin concentration (see Fig. 34-1C). This conclusion was already implicit in Figure 34-1B, in which the slope (i.e., inulin clearance) does not vary with P_{In}. Third, inulin clearance is independent of urine flow (see Fig. 34-1D). Given a particular P_{In}, after the renal corpuscles filter the inulin, the total amount of inulin in the urine does not change. Thus, diluting this glomerular marker in a large amount of urine, or concentrating it in a small volume, does not affect the total amount of inulin excreted (). If the urine flow is high, the urine inulin concentration will be proportionally low, and vice versa. Because () is fixed, is also fixed.
Two lines of evidence provide direct proof that inulin clearance represents GFR. First, by collecting filtrate from single glomeruli, Richards and coworkers showed in 1941 that the concentration of inulin in Bowman's space of the mammalian kidney is the same as that in plasma. Thus, inulin is freely filtered. Second, by perfusing single tubules with known amounts of labeled inulin, Marsh and Frasier showed that the renal tubules neither secrete nor reabsorb inulin.
Although the inulin clearance is the most reliable method for measuring GFR, it is not practical for clinical use. One must administer inulin intravenously to achieve reasonably constant plasma inulin levels. Another deterrent is that the chemical analysis for determining inulin levels in plasma and urine is sufficiently demanding to render inulin unsuitable for routine use in a clinical laboratory.
The normal value for GFR in a 70-kg man is ~125 mL/min. Population studies show that GFR is proportional to body surface area. Because the surface area of an average 70-kg man is 1.73 m^{2}, the normal GFR in men is often reported as 125 mL/min per 1.73 m^{2} of body surface area. In women, this figure is 110 mL/min per 1.73 m^{2}. Age is a second variable. GFR is very low in the newborn, owing to incomplete development of functioning glomerular units. Beginning at ~2 years of age, GFR normalizes for body surface area and gradually falls off with age as a consequence of progressive loss of functioning nephrons.
The clearance of creatinine is a useful clinical index of GFR
Because inulin is not a convenient marker for routine clinical testing, nephrologists use other compounds that have clearances similar to those of inulin. The most commonly used compound in human studies is ^{125}I-iothalamate. However, even ^{125}I-iothalamate must be infused intravenously and is generally used only in clinical research studies rather than in routine patient care.
The problems of intravenous infusion of a GFR marker can be completely avoided by using an endogenous substance with inulin-like properties. Creatinine is such a substance, and creatinine clearance (C_{Cr}) is commonly used to estimate GFR in humans. Tubules, to a variable degree, secrete creatinine, which, by itself, would lead to a ~20% overestimation of GFR in humans. Moreover, when GFR falls to low levels with chronic kidney disease, the overestimation of GFR by C_{Cr} becomes more appreciable. In clinical practice, determining C_{Cr} is an easy and reliable means of assessing the GFR, and such determination avoids the need to inject anything into the patient. One merely obtains samples of venous blood and urine, analyzes them for creatinine concentration, and makes a simple calculation (see Equation 34-3 below). Although C_{Cr} may overestimate the absolute level of GFR, assessing changes in C_{Cr} is extremely useful for monitoring relative changes in GFR in patients.
The source of plasma creatinine is the normal metabolism of creatine phosphate in muscle. In men, this metabolism generates creatinine at the rate of 20 to 25 mg/kg body weight per day (i.e., ~1.5 g/day in a 70-kg man). In women, the value is 15 to 20 mg/kg body weight per day (i.e., ~1.2 g/day in a 70-kg woman), owing to a lower muscle mass. In the steady state, the rate of urinary creatinine excretion equals this rate of metabolic production. Because metabolic production of creatinine largely depends on muscle mass, the daily excretion of creatinine depends strongly not only on gender but also on age, because elderly patients tend to have lower muscle mass. For a C_{Cr} measurement, the patient generally collects urine over an entire 24-hour period, and the plasma sample is obtained by venipuncture at one time during the day based on the assumption that creatinine production and excretion are in a steady state.
Frequently, clinicians make a further simplification, using the endogenous plasma concentration of creatinine (P_{Cr}), normally 1 mg/dL, as an instant index of GFR. This use rests on the inverse relationship between P_{Cr} and C_{Cr}:
(34-3)
In the steady state, when metabolic production in muscle equals the urinary excretion rate () of creatinine, and both remain fairly constant, this equation predicts that a plot of P_{Cr} versus C_{Cr} (i.e., P_{Cr}versus GFR) is a rectangular hyperbola (Fig. 34-2). For example, in a healthy person whose GFR is 100 mL/min, plasma creatinine concentration is ~1 mg/dL. The product of GFR (100 mL/min) and P_{Cr} (1 mg/dL) is thus 1 mg/min, which is the rate both of creatinine production and of creatinine excretion. If GFR suddenly drops to 50 mL/min (Fig. 34-3, top), the kidneys will initially filter and excrete less creatinine (see Fig. 34-3, middle), although the production rate is unchanged. As a result, the plasma creatinine level will rise to a new steady state, which is reached at a P_{Cr} of 2 mg/dL (see Fig. 34-3, bottom). At this point, the product of the reduced GFR (50 mL/min) and the elevated P_{Cr} (2 mg/dL) will again equal 1 mg/min, the rate of endogenous production of creatinine. Similarly, if GFR were to fall to one fourth of normal, P_{Cr}would rise to 4 mg/dL. This concept is reflected in the right-rectangular hyperbola of Figure 34-2. N34-2
FIGURE 34-2 Dependence of plasma creatinine and blood urea nitrogen on the GFR. In the steady state, the amount of creatinine appearing in the urine per day () equals the production rate. Because all filtered creatinine (P_{Cr} · C_{Cr}) appears in the urine, (P_{Cr} · C_{Cr}) equals (), which is constant. Thus, P_{Cr} must increase as C_{Cr} (i.e., GFR) decreases, and vice versa. If we assume that the kidney handles urea in the same way that it handles inulin, then a plot of blood urea nitrogen versus GFR will have the same shape as that of creatinine concentration versus GFR.
FIGURE 34-3 Effect of suddenly decreasing the GFR on plasma creatinine concentration.
N34-2
Calculating Estimated Glomerular Filtration Rate
Contributed by Gerhard Giebisch, Peter Aronson, Walter Boron, Emile Boulpaep
Clinicians can use the plasma creatinine concentration (P_{Cr}) to calculate C_{Cr}—that is, the estimated GFR (eGFR)—without the necessity of collecting urine. Researches have derived empirical equations for calculating eGFR based on patient data, including not only P_{Cr}, but also parameters that include patient age, weight, gender, and race. In using these equations, we recognize that daily creatinine excretion depends on muscle mass, which in turn depends on age, weight, sex, and race. An example is the Modification of Diet in Renal Disease (MDRD) Study equation:
(NE 34-1)
Thus, the MDRD calculation takes into account P_{Cr}, age, sex, and—in the United States—whether or not the person is African American. Because MDRD is normalized to body surface area, it does not include body weight.
Improving upon the MDRD equation was the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) calculator for eGFR (http://www.qxmd.com/calculate-online/nephrology/ckd-epi-egfr):
(NE 34-2)
Here, k is 0.7 for females and 0.9 for males, and a is −0.329 for females and −0.411 for males. In the first bracketed term, we take the larger of (P_{Cr}/k) or 1, whereas in the second bracketed term, we take the smaller of (P_{Cr}/k) or 1. Like the MDRD calculation, the CKD-EPI eGFR is normalized to body surface area (i.e., it does not include body weight).
The Cockcroft-Gault calculator for eGFR,
(NE 34-3)
takes into account P_{Cr}, weight (ideally, lean body mass), sex, and age. For example, for a male aged 22 and weighing 60 kg, the Cockcroft-Gault calculator
(NE 34-4)
yields an eGFR of 122 mL/min.
The National Kidney Foundation (NKF) recommends that one calculate eGFR with each determination of P_{Cr}.
References
Cockcroft D, Gault MD. Prediction of creatinine clearance from serum creatinine. Nephron. 1976;16:31–41.
Levey AS, Stevens LA, Schmid CH, et al. for the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI): A new equation to estimate glomerular filtration rate. Ann Intern Med. 2009;150:604–612.
National Kidney Disease Education Program. GFR calculators. [Last updated April 25, 2012] http://nkdep.nih.gov/lab-evaluation/gfr-calculators.shtml.
National Kidney Disease Education Program. GFR MDRD calculator for adults (conventional units). [Last updated March 1, 2012] http://www.niddk.nih.gov/health-information/health-communication-programs/nkdep/lab-evaluation/gfr-calculators/Pages/gfr-calculators.aspx [Accessed October 2015].
National Kidney Foundation. Calculators for health care professionals. http://www.kidney.org/professionals/KDOQI/gfr_calculator [Accessed October 2015].
QxMD. CKD-EPI eGFR. http://www.qxmd.com/calculate-online/nephrology/ckd-epi-egfr [Accessed October 2015].
Molecular size and electrical charge determine the filterability of solutes across the glomerular filtration barrier
The glomerular filtration barrier consists of four elements (see p. 726): (1) the glycocalyx overlying the endothelial cells, (2) endothelial cells, (3) the glomerular basement membrane, and (4) epithelial podocytes. Layers 1, 3, and 4 are covered with negative charges from anionic proteoglycans. The gene mutations that cause excessive urinary excretion of albumin (nephrotic syndrome; see p. 727) generally affect slit diaphragm proteins, which suggests that the junctions between adjacent podocytes are the predominant barrier to filtration of macromolecules.
Table 34-2 summarizes the permselectivity of the glomerular barrier for different solutes, as estimated by the ratio of solute concentration in the ultrafiltrate versus the plasma (UF_{X}/P_{X}). The ratio UF_{X}/P_{X}, also known as the sieving coefficient for the solute X, depends on molecular weight and effective molecular radius. Investigators have used two approaches to estimate UF_{X}/P_{X}. The first, which is valid for all solutes, is the micropuncture technique (see Fig. 33-9A). Sampling fluid from Bowman's space yields a direct measurement of UF_{X}, from which we can compute UF_{X}/P_{X}. The second approach, which is valid only for solutes that the kidney neither absorbs nor secretes, is to compute the clearance ratio (see p. 733), N34-3 the ratio of the clearances of X (C_{X}) and inulin (C_{In}).
TABLE 34-2
Permselectivity of the Glomerular Barrier
SUBSTANCE |
MOLECULAR WEIGHT (Da) |
EFFECTIVE MOLECULAR RADIUS* (nm) |
RELATIVE CONCENTRATION IN FILTRATE (UF_{X}/P_{X}) |
Na^{+} |
23 |
0.10 |
1.0 |
K^{+} |
39 |
0.14 |
1.0 |
Cl^{–} |
35 |
0.18 |
1.0 |
H_{2}O |
18 |
0.15 |
1.0 |
Urea |
60 |
0.16 |
1.0 |
Glucose |
180 |
0.33 |
1.0 |
Sucrose |
342 |
0.44 |
1.0 |
Polyethylene glycol |
1,000 |
0.70 |
1.0 |
Inulin |
5,200 |
1.48 |
0.98 |
Lysozyme |
14,600 |
1.90 |
0.8 |
Myoglobin |
16,900 |
1.88 |
0.75 |
Lactoglobulin |
36,000 |
2.16 |
0.4 |
Egg albumin |
43,500 |
2.80 |
0.22 |
Bence Jones protein |
44,000 |
2.77 |
0.09 |
Hemoglobin |
68,000 |
3.25 |
0.03 |
Serum albumin |
69,000 |
3.55 |
<0.01 |
^{*}The effective molecular radius is the Einstein-Stokes radius, which is the radius of a sphere that diffuses at the same rate as the substance under study.
Data from Pitts RF: Physiology of the Kidney and Body Fluids, 3rd ed. Chicago, Year Book Medical Publishers, 1974.
N34-3
Clearance Ratio
Contributed by Erich Windhager, Gerhard Giebisch
The clearance ratio is the ratio of the clearances of X (C_{X}) and inulin (C_{In}):
(NE 34-5)
The symbols U, , and P have the same meanings as in Chapter 33: namely, U is urine concentration, is urine flow, P_{X} is the plasma concentration of the solute X, and P_{In} is the plasma concentration of inulin. We can now regroup the terms in the rightmost quotient to create the following expression:
(NE 34-6)
We will now show that—if the tubules transport neither X nor inulin—the numerator, U_{X}/(U_{In}/P_{In}), is in fact the concentration of X in Bowman's capsule, UF_{X}, where the symbol UF means ultrafiltrate. Between Bowman's capsule and the final urine, the reabsorption of water by the tubules should have concentrated both inulin and X to the same extent, provided neither inulin nor X is secreted or absorbed. The extent to which inulin has been concentrated is merely U_{In}/P_{In}. Therefore, if we know the concentration of X in the urine, we merely divide U_{X} by U_{In}/P_{In} to obtain the concentration of X in Bowman's capsule:
(NE 34-7)
Therefore, in Equation NE 34-6 we can replace the term U_{X}/(U_{In}/P_{In}) by UF_{X}:
(NE 34-8)
Thus, the ratio UF_{X}/P_{X} is the same as the clearance ratio, which is the value shown in the rightmost column of Table 34-2. The clearance ratio is an index of the sieving coefficient (UF_{X}/P_{X}) of the glomerular filtration barrier for solute X.
Inspection of Table 34-2 shows that substances of low molecular weight (<5500 Da) and small effective molecular radius (e.g., water, urea, glucose, and inulin) appear in the filtrate in the same concentration as in plasma (UF_{X}/P_{X} ≈ 1). In these instances, no sieving of the contents of the fluid moving through the glomerular “pores” occurs, so that the water moving through the filtration slits by convection carries the solutes with it. N34-4 As a result, the concentration of the solute in the filtrate is the same as that in bulk plasma. The situation is different for substances with a molecular weight that is greater than ~14 kDa, such as lysozyme. Larger and larger macromolecules are increasingly restricted from passage.
N34-4
Filtration of Solutes Through Water-Filled Pores
Contributed by Erich Windhager, Gerhard Giebisch
Filtration of solutes across the glomerular capillary barrier can be modeled as the movement of molecules through water-filled pores. The flux of a solute X (J_{X}) through such glomerular pores—the rate at which X crosses a unit area of the barrier—is the sum of the convective and the diffusional flux:
(NE 34-9)
In this equation, J_{V} is the flux of fluid volume through the barrier, which is proportional to GFR. P_{X} and UF_{X} are the solute concentrations in plasma and filtrate, respectively.* σ_{X} is the reflection coefficient for X (see p. 468). The reflection coefficient is a measure of how well the barrier restricts or “reflects” the movement of the solute X as water moves across the barrier by convective flow. σ_{X} varies between zero (when convective movement of X is unrestricted) and unity (when the solute cannot pass at all through the pore together with water). We use “permeability” here in the same sense as “permeability coefficient” on page 108 and in N5-6.
As we saw on page 742 and in Table 34-2, the filtrate/filtrand ratio (UF_{X}/P_{X})—also known as the sieving coefficient—is unity for small solutes, such as urea, glucose, sucrose, and inulin. For these solutes, filtration does not lead to the development of a concentration gradient across the glomerular barrier. In other words, (P_{X} − UF_{X}) is zero. Thus, the diffusional flux in Equation NE 34-9 disappears, and all the movement of these small molecules must occur by convection.
For larger molecules, both the convective and diffusional terms in Equation NE 34-9 contribute to the flux of the solute X. At a normal GFR, any restriction to the movement of X (i.e., σ_{X} > 0) will cause the concentration of X to be less in the filtrate than in the plasma (UF_{X} < P_{X}). As a result, there is a concentration gradient favoring the diffusion of X from plasma into Bowman's space, as described by Equation NE 34-9. Two factors will enhance the relative contribution of the diffusional component. First, the more restricted the solute by the barrier, the lower the concentration of X in the filtrate, and thus the greater the driving force for diffusion. Second, the greater and greater the GFR, the greater the flow of water into Bowman's space, the greater the dilution of X in Bowman's space, the lower the UF_{X}, and thus the greater the driving force for diffusion of X.
For partially restricted molecules, the greater the GFR, the lower the UF_{X}—as we just saw—and thus the lower the filtrate/filtrand ratio. In the extreme case is which GFR falls to zero, the filtrate/filtrand ratio approaches unity as even relatively large molecules ultimately reach diffusion equilibrium. On the other hand, if GFR increases to very high values, the convective flow of water carrying low concentrations of the partially restricted solute dominates, and the filtrate/filtrand concentration ratio drops. Because hemodynamic factors such as blood pressure affect GFR (see pp. 745–750), one must carefully control these factors—and thus GFR—in order to use clearance ratios of macromolecules to characterize glomerular permeability.
^{*}Caution! Do not confuse P_{X}, the permeability of X, with the concentration of X in the blood plasma, which is denoted by a nonitalicized P_{X}—an issue discussed in N33-6.
In addition to molecular weight and radius, electrical charge also makes a major contribution to the permselectivity of the glomerular barrier. Figure 34-4A is a plot of the clearance ratio for uncharged, positively charged, and negatively charged dextran molecules of varying molecular size. Two conclusions can be drawn from these data. First, neutral dextrans with an effective molecular radius of <2 nm pass readily across the glomerular barrier. For dextrans with a larger radius, the clearance ratio decreases with an increase in molecular size, so that passage ceases when the radius exceeds 4.2 nm. Second, anionic dextrans (e.g., dextran sulfates) are restricted from filtration, whereas cationic dextrans (e.g., diethylaminoethyl dextrans) pass more readily into the filtrate. For negatively charged dextrans, the relationship between charge and filterability is characterized by a left shift of the curve relating molecular size to clearance ratio, whereas the opposite is true for positively charged dextrans.
FIGURE 34-4 Clearance ratios of dextrans. (Data from Bohrer MP, Baylis C, Humes HD, et al: Permselectivity of the glomerular capillary wall: Facilitated filtration of circulating polycations. J Clin Invest 61:72–78, 1978.)
The previously discussed results suggest that the glomerular filtration barrier carries a net negative charge that restricts the movement of anions but enhances the movement of cations. In some experimental models of glomerulonephritis, in which the glomerular barrier loses its negative charge, the permeability of the barrier to negatively charged macromolecules is enhanced. Figure 34-4B compares clearance ratios of dextran sulfate in normal rats and in rats with nephrotoxic serum nephritis. Clearance ratios of dextran sulfate are uniformly greater in the animals with nephritis. Thus, the disease process destroys negative charges in the filtration barrier and accelerates the passage of negatively charged dextrans. The red curve in Figure 34-4A shows that a neutral dextran with the same effective radius as albumin (i.e., 3.5 nm) would have a clearance ratio of ~0.1, which would allow substantial filtration and excretion. However, because albumin is highly negatively charged, its clearance ratio is nearly zero, similar to that of anionic dextrans (see Fig. 34-4A, green curve), and it is restricted from filtration. Glomerular diseases causing loss of negative charge in the glomerular barrier lead to the development of albuminuria. Glomerular diseases causing high rates of albumin filtration can lead to a low plasma [albumin] and the development of edema (see Box 20-1), a clinical condition known as nephrotic syndrome. N34-5
N34-5
Effect of Molecular Shape on Permselectivity
Contributed by Gerhard Giebisch, Erich Windhager
In addition to molecular size (i.e., effective molecular radius) and electrical charge, the shape of macromolecules may also affect the permselectivity of the glomerular barrier. Thus, two molecules can diffuse at the same rate—and thus have the same effective molecular radius—but have different shapes. Rigid or globular molecules have lower clearance ratios (i.e., sieving coefficients) than molecules of a similar size (e.g., dextrans), which are highly deformable.
Hydrostatic pressure in glomerular capillaries favors glomerular ultrafiltration, whereas oncotic pressure in capillaries and hydrostatic pressure in Bowman's space oppose it
As is the case for filtration in other capillary beds (see pp. 467–468), glomerular ultrafiltration depends on the product of the ultrafiltration coefficient (K_{f}) and net Starling forces.
(34-4)
Figure 34-5A provides a schematic overview of the driving forces affecting ultrafiltration. Hydrostatic pressure in the glomerular capillary (P_{GC}) favors ultrafiltration. Hydrostatic pressure in Bowman's space (P_{BS}) opposes ultrafiltration. Oncotic pressure in the glomerular capillary (π_{GC}) opposes ultrafiltration. Oncotic pressure of the filtrate in Bowman's space (π_{BS}) favors ultrafiltration. Thus, two forces favor filtration (P_{GC} and π_{BS}), and two oppose it (P_{BS} and π_{GC}).
FIGURE 34-5 Glomerular ultrafiltration. In B, the oncotic pressure of the glomerular capillary (π_{GC}), which starts off at the value of normal arterial blood, rises as ultrafiltration removes fluid from the capillary. In C, P_{UF} is the net driving force favoring ultrafiltration. N34-9
N34-9
Starling Forces Along the Glomerular Capillary
Contributed by Walter Boron
The π_{GC} curve in Figure 34-5B is the result of a computer simulation that is based on Equation 34-4 (shown here as Equation NE 34-10):
(NE 34-10)
We recall from the text that, by definition, FF is related to GFR and RPF by Equation 34-6 (shown here as Equation NE 34-11):
(NE 34-11)
Thus,
(NE 34-12)
Note that is merely K_{f}/RPF.
Equation NE 34-10 is presented in textbooks—including ours—as if it applies to the macroscopic GFR (e.g., 125 mL/min) that the two kidneys together produce via the actions of all ~2,000,000 of their glomeruli. In reality, Equation NE 34-10 really applies only to a microscopic GFR, that is, a rate of filtration at a particular point along the glomerular capillary of a particular glomerulus.* The reasons are that (1) π_{GC}—and thus P_{UF}—change continuously along the glomerular capillary, and (2) K_{f} as well as this π_{GC} profile are not identical for all glomeruli. Thus, Equation NE 34-10 really is valid only at a particular point along a particular glomerular capillary, where π_{GC} has a particular value.^{†} The same is true for Equation NE 34-12. To make this point more clear, we will define the microscopic filtration fraction (ff) and its counterpart —relevant for a small stretch of a particular glomerular capillary—as we march down this capillary:
(NE 34-13)
We will now apply Equation NE 34-13 at multiple points along a theoretical monolithic capillary, arbitrarily dividing the capillary into 100 identical segments. For the first of these 100 segments, we assume that all the terms that determine P_{UF} have the values shown in Figure 34-5A at distance (x) = 0:
P_{GC} = 50 mm Hg
π_{GC} = 25 mm Hg
P_{BS} = 10 mm Hg
π_{BS} = 0 mm Hg
Thus, at x = 0, the forces favoring filtration are (P_{GC} + π_{BS}) = 50 mm Hg (green curve in Fig. 34-5C), whereas the forces opposing filtration are (P_{BS} + π_{GC}) = 35 mm Hg (red curve in Fig. 34-5C). The net ultrafiltration pressure (P_{UF}) at time = 0 is therefore 50 − 35 = 15 mm Hg (vertical distance between the green and red curves, colored gold in Fig. 34-5C).
We then apply Equation NE 34-13, multiplying this (P_{UF})_{Distance=0} by a preassigned value for . Recall that this value of has built into it not only the microscopic filtration coefficient per se, but also microscopic RPF, and it has the units (mm Hg)^{−1}. Thus, the product of and P_{UF} in our model is the fraction of the initial ECF volume (inside the glomerular capillary) lost in the first of the 100 segments of the capillary—the ff. Below, we will see that, for a normal RPF, has the value 0.0001765 (mm Hg)^{−1}. Thus, the fraction of ECF lost from the capillary in the first 1% of the capillary is
(NE 34-14)
That is, about 0.265% of the ECF originally in the capillary is lost (i.e., filtered) in the first 1% of the glomerular capillary. Stated differently, after the blood has passed the 1% mark, the ECF volume remaining in the glomerular capillary would be only 100% − 0.265% = 99.735% as large as it was at the outset.
Because the mass of proteins in the blood ECF is fixed (we assume no filtration of proteins), π_{GC} must rise by the fraction by which ECF falls. In our example, at the end of the first 1% of distance, π_{GC} would be (25 mm Hg)/0.99735 ≅ 25.0664 mm Hg. We will then use this new value of π_{GC} in the computation for the second iteration (i.e., for the second increment of 1%), and so on, for a total of 100 iterations; that is, for the entire 100% of the distance. At the end of 100 iterations, we can sum up the 100 microscopic ff values to arrive at the macroscopic FF.
What is a bit tricky is assigning the value for . We do it in the following way. First, we define a standard GFR value (which we take to be 125 mL/min) and a standard RPF value (600 mL/min). Next, we guess at a provisional value for the standard , insert it into the above equation, go through the 100 iterations, and then add up the 100 ff values to arrive at the macroscopic FF. From this FF value—as well as RPF—we compute GFR using Equation NE 34-11. If this provisional standard does not produce the desired GFR of 125 mL/min, we make another guess and repeat the process until we eventually arrive at the standard . In our case, this standard is 0.0001765 (mm Hg)^{−1}. Note that this value includes the standard RPF of 600 mL/min.
The π_{GC} curve in Figure 34-5B actually represents a “low” RPF of 70.6 mL/min versus the standard RPF of 600 mL/min. The ratio of these two values is 600/70.6 ≅ 8.5 … and in our model we achieve this low RPF by multiplying our standard by a factor of ~8.5, from 0.0001765 (mm Hg)^{−1} to 0.0015 (mm Hg)^{−1}.
Note that because π_{GC} exponentially rises from its initial value of 25 mm Hg to an asymptotic value of 40 mm Hg, P_{UF} exponentially decays from a maximal value of 15 mm Hg to zero, as shown by the vertical distance between the green and red curves (the gold area) in Figure 34-5C.
See also N34-11.
^{*}This principle also applies to the version of Fick's law that we use to describe the diffusion of gases from the alveolar air to the blood, or vice versa. See Equation 30-4, which is the simplified version of the equation (analogous to Equation NE 34-10 above) as well as the more precise Equation 30-9.
^{†}As in the text, we are assuming that the values of all the other parameters are fixed.
The net driving force favoring ultrafiltration (P_{UF}) at any point along the glomerular capillaries is the difference between the hydrostatic pressure difference and the oncotic pressure difference between the capillary and Bowman's space. Thus, GFR is proportional to the net hydrostatic force (P_{GC} − P_{BS}) minus the net oncotic force (π_{GC} − π_{BS}).
As far as the hydrostatic pressure difference is concerned, the unique arrangement in which afferent and efferent arterioles flank the glomerular capillary keeps the first term, P_{GC}, at ~50 mm Hg (see Fig. 34-5B), a value that is twice as high as that in most other capillaries (see pp. 467–468). Moreover, direct measurements of pressure in rodents show that P_{GC} decays little between the afferent and efferent ends of glomerular capillaries. The second term of the hydrostatic pressure difference, P_{BS}, is ~10 mm Hg and does not vary along the capillary.
As far as the oncotic driving forces are concerned, the first term, π_{BS}, is very small (see Fig. 34-5B). The second term, π_{GC} starts off at 25 mm Hg at the beginning of the capillary. As a consequence of the continuous production of a protein-free glomerular filtrate—and the resulting concentration of plasma proteins—the oncotic pressure of the fluid left behind in the glomerular capillary progressively rises along the capillary.
Figure 34-5C compares the two forces favoring ultrafiltration (P_{GC} + π_{BS}) with the two forces opposing ultrafiltration (P_{BS} + π_{GC}) and shows how they vary along the glomerular capillary. The rapid increase in the oncotic pressure of capillary blood (π_{GC}) is the major reason why the forces favoring and opposing filtration may balance each other at a point some distance before the end of the glomerular capillary. Beyond this point, P_{UF} is zero and the system is said to be in filtration equilibrium (i.e., no further filtration).
Note that K_{f} in Equation 34-4 is the product of the hydraulic conductivity of the capillary (L_{p}) and the effective surface area available for filtration (S_{f}), as defined in Table 20-4. We use K_{f} because it is experimentally difficult to assign values to either L_{p} or S_{f}. The value of K_{f} of the glomerular filtration barrier exceeds—by more than an order of magnitude—the K_{f} of all other systemic capillary beds combined. This difference in K_{f} values underlies the tremendous difference in filtration, ~180 L/day in the kidneys (which receive ~20% of the cardiac output) compared with ~20 L/day (see pp. 475–476) in the combined arteriolar ends of capillary beds in the rest of the body (which receive the other ~80%).
Alterations in the glomerular capillary surface area—owing to changes in mesangial-cell contractility (see p. 727)—can produce substantial changes in the S_{f} component of K_{f}. These cells respond to extrarenal hormones such as systemically circulating angiotensin II (ANG II), arginine vasopressin (AVP), and parathyroid hormone. Mesangial cells also produce several vasoactive agents, such as prostaglandins and ANG II.