Biophysical Basis of Glomerular Filtration

Marcello Malpighi (1628–1694) discovered the renal corpuscle and proposed that each glomerular body embraces the ampullar extremity of a tubule to form a “glandular follicle”. Thereafter, progress toward understanding the structure and function of the nephron stalled for two centuries, until William Bowman finally established the proper anatomic relationship between the glomerular arterioles, capillary tuft, and uriniferous tubule in 1842. In that same year, Carl Ludwig, in his Habilitations thesis, addressed the driving force that separates the watery and crystalloid constituents of the plasma from its “proteid” constituents. He dismissed both the “nonexistent” vital force and chemical theories for converting blood to urine, and deduced from geometric considerations that local hydraulic forces drive filtration of blood plasma through porous glomerular capillary walls. Ludwig’s theory was not universally accepted at the time and other influential figures, such as Heidenhain, continued to advocate the secretory formation of urine. Ludwig also had the foresight to envision that the hyperproteinemia resulting from glomerular filtration causes concentration of the urine by endosmosis into the peritubular capillaries. Several decades later, vant Hoff and others began to describe osmosis in terms of pressure using thermodynamic principles, which inspired Ernest Henry Starling to contemplate a role for the osmotic pressure of the plasma colloids in glomerular filtration. Starling wondered whether the minimum blood pressure below which formation of urine ceases might equal the osmotic pressure of the plasma colloids that oppose filtration. In 1897, he tested this hypothesis using a colloid osmometer of his own design with which he estimated the osmotic pressure of the blood plasma protein to be 25–30 mmHg or about 0.4 mmHg-gram ⁻¹ /liter ⁻¹ . Then he observed that raising the ureteral pressure to within 30–45 mmHg of the arterial blood pressure would stop the flow of urine in a dog undergoing diuresis. Thus, the hydraulic pressure across the glomerular epithelium must exceed the plasma colloid osmotic pressure by some small amount in order for urine to form. On this basis, Ludwig’s filtration hypothesis was deemed credible. Further evidence for glomerular filtration was published in 1924 by Wearn and Richards, who directly visualized the passage of indigo carmine into Bowman’s space from the blood in the course of performing the first-ever micropuncture experiments. Wearn and Richards interpreted their own findings as “indirect evidence that the process in the glomerulus is physical”.

Introduction

Marcello Malpighi (1628–1694) discovered the renal corpuscle and proposed that each glomerular body embraces the ampullar extremity of a tubule to form a “glandular follicle”. Thereafter, progress toward understanding the structure and function of the nephron stalled for two centuries, until William Bowman finally established the proper anatomic relationship between the glomerular arterioles, capillary tuft, and uriniferous tubule in 1842. In that same year, Carl Ludwig, in his Habilitations thesis, addressed the driving force that separates the watery and crystalloid constituents of the plasma from its “proteid” constituents. He dismissed both the “nonexistent” vital force and chemical theories for converting blood to urine, and deduced from geometric considerations that local hydraulic forces drive filtration of blood plasma through porous glomerular capillary walls ( Figure 21.1 ). Ludwig’s theory was not universally accepted at the time and other influential figures, such as Heidenhain, continued to advocate the secretory formation of urine. Ludwig also had the foresight to envision that the hyperproteinemia resulting from glomerular filtration causes concentration of the urine by endosmosis into the peritubular capillaries. Several decades later, vant Hoff and others began to describe osmosis in terms of pressure using thermodynamic principles, which inspired Ernest Henry Starling to contemplate a role for the osmotic pressure of the plasma colloids in glomerular filtration. Starling wondered whether the minimum blood pressure below which formation of urine ceases might equal the osmotic pressure of the plasma colloids that oppose filtration. In 1897, he tested this hypothesis using a colloid osmometer of his own design with which he estimated the osmotic pressure of the blood plasma protein to be 25–30 mmHg or about 0.4 mmHg-gram ⁻¹ /liter ⁻¹ . Then he observed that raising the ureteral pressure to within 30–45 mmHg of the arterial blood pressure would stop the flow of urine in a dog undergoing diuresis. Thus, the hydraulic pressure across the glomerular epithelium must exceed the plasma colloid osmotic pressure by some small amount in order for urine to form. On this basis, Ludwig’s filtration hypothesis was deemed credible. Further evidence for glomerular filtration was published in 1924 by Wearn and Richards, who directly visualized the passage of indigo carmine into Bowman’s space from the blood in the course of performing the first-ever micropuncture experiments. Wearn and Richards interpreted their own findings as “indirect evidence that the process in the glomerulus is physical”.

Figure 21.1, Ludwig’s representation of renal microvasculature (a) and (b) pressure profiles along the glomerular capillary

Glomerular filtration eventually received theoretical consideration as a case of coupled transport, subject to the basic rules of non-equilibrium thermodynamics, which were articulated by Onsager in 1931 and adapted to describe the permeability of biological membranes by several investigators in the 1950s. Prior to the 1950s, the conventional description of transport through membranes simply combined Fick’s diffusion equation for solute flux with Darcy’s equation for water flux, such that the function of a membrane which is to “prescribe the road along which the system strives toward equilibrium”, was defined by two permeability coefficients, one for diffusion of solute and one for bulk flow of water. By the 1950s it had become clear that these “conventional” permeability equations for solute and volume flow could not fully describe the physical behavior of membranes, so attempts were made to supplement them. The most cited contribution in this area came from Kedem and Katchalsky, who pointed out that the prior approach was incomplete due to the fact that it included only two coefficients, whereas Onsager’s theory calls for exactly three coefficients to characterize permeability for a solute–solvent system. Qualitatively, the hydrodynamic resistance to free diffusion is due to friction between solute and solvent alone, and is determined by a single diffusion coefficient. But passage through a membrane involves two additional factors, namely, the friction between solute and membrane, and the friction between solvent and membrane. Hence, three processes are at play, and three coefficients are required to account for them all. Kedem and Katchalsky then proceeded with a formal argument, starting from the rate of entropy production and invoking Onsager’s theory for a solute–solvent system which is paraphrased as follows:

For present purposes, we are interested in the transmembrane flux of a two-component system consisting of a water (w) and a non-electrolyte solute (s). Each of these components is driven by a conjugate force equivalent to its difference in free energy across the membrane. The conjugate forces for water and non-electrolyte solute are:

Δ μ_{w} = V_{w} Δ P + R T Δ {\ln γ}_{w} X_{w}

$Δ μ_{w} = V_{w} Δ P + R T Δ {\ln γ}_{w} X_{w}$

Δ μ_{s} = V_{s} Δ P + R T Δ {\ln γ}_{s} X_{s}

$Δ μ_{s} = V_{s} Δ P + R T Δ {\ln γ}_{s} X_{s}$

where V is a partial molar volume, Δ P is the pressure difference, X is the mole fraction, and γ is an activity function, empirically derived as a function of X . Since water flux affects X _s and solute flux affects X _w , the two conjugate forces and fluxes are coupled. For a small deviation from equilibrium this coupling can be taken into account by the following linear flux equations:

J_{w} = L_{11} Δ μ_{w} + L_{12} Δ μ_{s}

$J_{w} = L_{11} Δ μ_{w} + L_{12} Δ μ_{s}$

J_{s} = L_{21} Δ μ_{w} + L_{22} Δ μ_{s}

$J_{s} = L_{21} Δ μ_{w} + L_{22} Δ μ_{s}$

where Lxy are the so-called phenomenological constants. Onsager’s theory says that L ₂₁ =L ₁₂ . Therefore, if the three coefficients, L ₁₁ , L ₂₂ , and L ₂₁ =L ₁₂ are known, along with baseline values of J _w and J _s , then one can predict the changes in J _w and J _s that will arise from any alteration in Δ μ _w or Δ μ _s . However, the physical meanings of the phenomenological constants are difficult to appreciate, and a more familiar form of the Onsager equations was provided in 1958 by Kedem and Katchalsky to describe transport across biological membranes :

J_{v} = L_{P} \cdot (Δ P - σ_{s} Δ Π)

$J_{v} = L_{P} \cdot (Δ P - σ_{s} Δ Π)$

J_{s} = P_{s} \cdot Δ C_{s} + J_{V} (1 - σ_{s}) \cdot \bar{C_{s}}

$J_{s} = P_{s} \cdot Δ C_{s} + J_{V} (1 - σ_{s}) \cdot \bar{C_{s}}$

When applied to movement across a capillary wall, J _v and J _s denote respectively the flux of volume (substituting volume for water is allowable for dilute solutions) and solute; Δ P , Δ Π , and Δ C are differences in hydrostatic pressure, osmotic pressure, and concentration integrated across the membrane; σ _s is the reflection coefficient of the membrane for s ; L _p is the hydraulic permeability per unit area of membrane; and P _s is the diffusive permeability of the membrane to s ; $\bar{C_{s}}$ $\bar{C_{s}}$ is the mean concentration of s within the membrane. Π is a function of C . σ _s assumes a value between zero and one. Three of these parameters, L _p , P _s , and σ _s , are characteristics of the membrane, in keeping with the Onsager theory which requires exactly three coefficients to describe the coupled transport of the two entities, v and s . Equation (21.3a) is often referred to as the “Starling equation.” Equation (21.3b) expresses J _s as the sum of diffusive and convective components. Equations (21.3a) and (21.3b) are coupled. J _s explicitly depends on J _v . J _v depends on J _s because J _s affects Δ Π .

There are limitations to irreversible thermodynamics and to the simplified equations, beginning with the assumption of a linear relationship between fluxes and forces. For example, one can imagine how increasing Δ P might cause a capillary wall to stretch, thereby changing the geometry of its pores and altering L _p . Also, $\bar{C_{s}}$ $\bar{C_{s}}$ can take a variety of forms, depending on whether σ is taken to be active throughout the membrane or to be a membrane entrance phenomenon, and this will affect how J _s is parsed into its diffusive and convective components. Finally, protein accumulates near the capillary wall during filtration, which could raise the local colloid osmotic pressure at the wall and cause L _p to be underestimated when calculated based on Π for the bulk plasma. Nonetheless, these equations remain the basis for all current understanding of the physical factors that determine transport of water and solutes between the glomerular capillary plasma and the urinary space.

Depending on the context, different simplifying assumptions are made that streamline the description of capillary flux in the glomerulus. For example, when considering J _v (i.e., glomerular filtration), the solutes are divided into two groups, large and small. Large solutes are the colloids, and it is assumed that P _s for these is zero and σ _s is unity. All other solutes are assumed to be small, and it is assumed that σ _s (and Δ C ) for these is zero. Solutes with intermediate permeability are ignored. Therefore, Δ Π can be substituted by the colloid osmotic pressure of the glomerular plasma, and a full description of J _v is provided by Eq. (21.3a) . This obviates the need to consider coupled transport. Although the contribution of filtered macromolecules to the transcapillary oncotic pressure may be negligible, there are times when it is critical to understand the sieving properties of the glomerulus for large molecules. In such cases, simplifying assumptions are made regarding the geometry of the filtration barrier and the shape of the solute molecules, so that the process can be conveniently described using hydrodynamic theory.

The Magnitude of Renal Blood Flow and Glomerular Filtration

In humans, the kidneys constitute 0.5% of the body weight, but receive 20% of the cardiac output. The low resistance to renal blood flow is owing to the large number of parallel conductances, with each human kidney containing about 1 million glomeruli. Approximately 8000 liters per day of blood plasma transits the extrarenal organs, of which about 20 liters is filtered into interstitial spaces and returned to the blood as lymph. In contrast, the kidneys form 180 liters per day of glomerular filtrate from 900 liters of blood plasma. The high rate of filtration by the kidney relative to other organs is due to a greater ultrafiltration coefficient, not to greater Starling force. The surface area available for filtration in the human kidney is in the order of 1.2 m ² overall or 0.6 mm ² per glomerulus. A meaningful number is difficult to assign to the capillary surface area in other major organs where the number of capillaries perfused at any given moment is highly variable. The hydraulic permeability L _p of fenestrated glomerular capillaries has been estimated from 2.5–4.0 μl/min/mmHg/cm ² in rats and humans, which is 50-fold higher than L _p for non-fenestrated skeletal muscle.

Glomerular Hemodynamics by Inference

Having first identified inulin and PAH as a markers of GFR renal plasma flow (RPF), Homer Smith and colleagues used clearance of these markers to make logical judgments about the regulation of GFR. Smith observed a reciprocal relationship between RPF and filtration fraction in human subjects injected with pyrogens, and recognized that this is contrary to what should occur if the changes in RPF were mediated by a preglomerular resistance. He used equations to argue that the renal resistance changed in these experiments due to dilation and constriction of the efferent arteriole. His formulation required a strong inverse effect of efferent resistance on filtration fraction, which could be achieved by assuming that the net ultrafiltration pressure vanishes at some point along the capillary, as hydrostatic pressure declines and plasma oncotic pressure increases. Based on knowledge that this occurs in the mesenteric circulation, Smith was willing to assume that this also happens in the kidney, and coined the term “filtration pressure equilibrium” in reference to the phenomenon (see Figure 21.2 ). Smith later recanted his notion of filtration pressure equilibrium in the glomerular capillary, arguing on teleologic grounds that the hydrostatic null point should occur in the proximal portion of the efferent arteriole in order to promote maximal GFR and maximal reabsorption in the peritubular capillary. His revised thinking was likely influenced by the contemplations of Gomez.

Figure 21.2, Filtration equilibrium illustrated in the glomerulus

Glomerular Hemodynamics and Micropuncture

A full and direct assessment of the filtration forces and hydraulic permeability in a mammalian glomerulus was first published by Brenner et al. in 1971. Three developments made this possible. First, a mutant rat strain (Munich Wistar) was discovered with glomeruli on the kidney surface making them accessible for glomerular micropuncture. Second, a servo-null device was invented that enabled accurate and rapid pressure measurements in capillaries and tubules. Third, a microadaptation of the Lowry method was developed for measuring the protein concentration in a few nanoliters of plasma which could be obtained by micropuncture from a postglomerular arteriole.

Given values for the pressure in the glomerular capillary P _GC and Bowman’s space P _BS , pre- and postglomerular plasma protein concentrations c ₀ and c ₁ , single nephron ³ H-inulin clearance SNGFR , and a simple mathematical model for computing changes in the ultrafiltration pressure P _UF along the glomerular capillary, it is possible to obtain values for the glomerular plasma flow Q ₀ and ultrafiltration coefficient LpA . LpA is the product of the hydraulic permeability Lp (see Eq. (21.3a) ) and the filtration surface area A .

The mathematical model for computing the physical determinants of SNGFR from micropuncture data was developed by Deen, Robertson, and Brenner in 1972. This model treats the glomerular capillary as a circular cylinder of unit length and surface area, uniform permeability to water and small solutes, and zero permeability to protein (see Figure 21.3 ). As in Eq. (21.3a) , the filtration flux at any point along the capillary is equal to the product of the Starling force, Δ P −ΔΠ, and the hydraulic permeability, Lp . SNGFR is obtained by integrating the flux along the capillary length:

\begin{matrix} S N G F R & = \int_{0}^{1} J v \cdot d x \\ = L p A \int_{0}^{1} (Δ P - Δ Π) d x \\ = L p A ⟨ P_{U F} ⟩ \end{matrix}

$\begin{matrix} S N G F R & = \int_{0}^{1} J v \cdot d x \\ = L p A \int_{0}^{1} (Δ P - Δ Π) d x \\ = L p A ⟨ P_{U F} ⟩ \end{matrix}$

where Δ P = P _GC − P _BS , ΔΠ+Π _GC −Π _BS and ⟨ P _UF ⟩ is the mean ultrafiltration pressure. The term LpA represents the product of the hydraulic permeability Lp and filtration surface area A . For the non-dimensionalized capillary, A equals unity. For the real capillary, micropuncture data do not distinguish between changes in Lp and changes in A .

Figure 21.3, Glomerular capillary represented by a homogerous circular circular cylinder with unit length and surface area (Q: Plasma flow; Jv: Filtration water flux; X: Axial position along the capillary).

To perform the integration in Eq. (21. 4) it is necessary to know how the integrand varies along the capillary. In theory, both Δ P and Δ Π should change along the capillary, since P _GC must decline due to axial flow resistance and Π _GC must rise as water moves from the plasma into Bowman’s space. It has always been assumed that the decline in P _GC along the capillary is small relative to the increase in Π _GC . This assumption was eventually justified by a three-dimensional reconstruction of the rat glomerulus submitted to computational analysis. It is our custom to ignore the small axial pressure drop and represent Δ P as a constant, since including a 1–2 mmHg axial pressure drop in the model has a minimal effect on ⟨ P _UF ⟩. However, to better illustrate certain principles in this chapter, we have incorporated a 1 mmHg decline in P _GC from the beginning to the end of the glomerular capillary.

For the purposes of determining Δ Π it is assumed that all solutes in the system are either completely impermeant plasma proteins that exert their full osmotic potential ( σ =1, Ps =0) and reside solely in the plasma or small molecules that are freely filtered ( σ =0) and contribute nothing to Δ Π. Thus, Δ Π is reduced to the plasma oncotic pressure, Π _GC . The oncotic pressure in a plasma sample is determined from the protein concentration c , according to an empiric relationship developed by Landis and Pappenheimer:

Π = α_{1} c + α_{2} c^{2}

$Π = α_{1} c + α_{2} c^{2}$

The values of α ₁ and α ₂ in Eq. (21.5) vary according to the ratio of albumin to globulin in the plasma. When Π is expressed in mmHg and c in grams per 100 ml, for rat plasma, α ₁ and α ₂ are 1.73 and 0.28, respectively. According to Eq. (21.5) , Π _GC will increase from 18 to 35 mmHg along the length of a glomerular capillary if the systemic plasma contains 6 g/dl of protein and the nephron filtration fraction is 0.29. Such values are typical of the rat.

LpA is computed from SNGFR and ⟨ P _UF ⟩, according to Eq. (21.4) . To obtain ⟨ P _UF ⟩ it is necessary to know the profile for Π _GC along the capillary. This profile is computed from the following mass balance considerations for protein and water. First are three conservation of mass equations:

Q_{0} = S N G F R (\frac{c_{1}}{c_{1} - c_{0}})

$Q_{0} = S N G F R (\frac{c_{1}}{c_{1} - c_{0}})$

c Q = c_{0} Q_{0}

$c Q = c_{0} Q_{0}$

J_{v} = - \frac{d Q}{d x}

$J_{v} = - \frac{d Q}{d x}$

where Q ₀ is the nephron plasma flow and c ₀ and c ₁ are the pre- and post-capillary plasma protein concentrations. Differentiating Eq. (21.6b) and substituting Eqs. (21.6c), (21.5), and (21.3a) :

\frac{d c}{d x} = \frac{c^{2}}{c_{0} Q_{0}} J_{v}

$\frac{d c}{d x} = \frac{c^{2}}{c_{0} Q_{0}} J_{v}$

= \frac{L p \cdot c^{2}}{c_{0} Q_{0}} (Δ P - (α_{1} c + α_{2} c^{2}))

$= \frac{L p \cdot c^{2}}{c_{0} Q_{0}} (Δ P - (α_{1} c + α_{2} c^{2}))$

A standard root-finding algorithm is used to obtain a value for LpA by numerical integration of Eq. (21.7) along the entire capillary to obtain an estimate for the plasma protein concentration at the end of the capillary ( c ₁ *) and adjust the value of LpA until c ₁ * is arbitrarily close to the measured value of c ₁ .

c_{1}^{*} = c_{0} + \frac{L P A}{c_{0} Q_{0}} \int_{0}^{1} c^{2} (Δ P - (α_{1} c + α_{2} c^{2})) \cdot d x

$c_{1}^{*} = c_{0} + \frac{L P A}{c_{0} Q_{0}} \int_{0}^{1} c^{2} (Δ P - (α_{1} c + α_{2} c^{2})) \cdot d x$

In a typical experiment, SNGFR , Δ P , and c ₁ are measured in several nephrons. Most often, these parameters are not obtained from the same nephrons. The mean values for an experiment are inserted into the model to calculate the determinants of SNGFR for an idealized nephron.

From the foregoing description, we see that SNGFR is fully determined by Δ P , Q ₀ , c ₀ , and LpA . Typical values for these parameters are shown in Table 21.1 for Munich Wistar rats from two different breeding colonies under different volume states. Conceptually, SNGFR can be made to increase by raising Δ P , Q ₀ or LpA or by reducing c ₀ . But the magnitude of the dependence on each of the four determinants depends on the values of the other three. Some of these interactions are shown in Figures 21.4–21.7 and discussed below.

Table 21.1

Representative Micropuncture Data in Munich Wistar Rats from the Blantz Lab in San Diego and Brenner Lab in Boston.

Laboratory	State of Hydration	SNGFR (nl/min)	Δ P (mmHg)	Π ₀ (mmHg)	Q ₀ (nl/min)	LpA (nl/s/mmHg)	Filtration Pressure Equilibrium
Blantz	Hydropenia	30	30.5	18.3	86	0.08 *	Yes
	Euvolemia	31	37.2	19.7	121	0.06	No
	Acute 2.5% plasma volume expansion	45	42.2	18.2	177	0.05	No
Brenner	Hydropenia	21	35.3	19.4	65	0.08 *	Yes
	Euvolemia	32	33.4	19.4	114	0.08 *	Yes
	Acute 5% plasma volume expansion	50	41.2	22.9	201	0.08	No

* Minimum estimate due to filtration pressure equilibrium. LpA values that show differently from the original papers were originally calculated based on a linear estimate of the oncotic pressure profile and are recalculated here using the non-linear model.

Figure 21.4, Pressure (left) and total flux (right) along the length of the glomerular capillary.

Figure 21.5, Δ P (lines) and Π GC (curves) along the length of a glomerular capillary for three different values of Δ P .

$Figure 21.6, SNGFR , filtration fraction or mean ultra-filtration pressure (P UF ) as a function of nephron plasma flow, Q 0 .$

Figure 21.7, Effects of efferent arteriolar resistance ( R E ) on SNGFR , nephron plasma flow ( Q 0 ), and glomerular capillary pressure ( P GC ).

Ultrafiltration Coefficient, LpA , and Filtration Pressure Equilibrium

If the ratio of LpA to Q ₀ is great enough, then Π _GC will rise to become arbitrarily near to Δ P at some point along the glomerular capillary, resulting in filtration pressure equilibrium. The remaining capillary surface downstream from the equilibration point will not contribute to the flux. It is possible to infer the presence of filtration equilibrium from micropuncture data, but it is not possible to know at what point along the length of the capillary equilibrium occurs. Therefore, it is not possible to compute actual values for ⟨ P _UF ⟩ or LpA for nephrons in filtration equilibrium. When Eqs. (21.4)–(21.8) are applied to data from a nephron in filtration pressure equilibrium, the values generated for LpA and ⟨ P _UF ⟩ are respective minimum and maximum estimates for actual LpA and ⟨ P _UF ⟩. If a change in LpA occurs while a nephron remains in filtration pressure equilibrium, the equilibrium point will shift along the capillary, but SNGFR will not be affected. In order for SNGFR to be affected by a change in LpA , the nephron must not be in filtration equilibrium.

A debate over whether filtration pressure equilibrium occurs dates back to Homer Smith, who used conjecture and teleology to argue both sides of the issue at different points in his career ( vide supra ). Brenner and colleagues found filtration equilibrium in each of 12 consecutive published series, suggesting that filtration equilibrium is universal for hydropenic or euvolemic Munich Wistar rats. However, contrary data were generated by other micropuncture laboratories. At one point, this led to consternation. The issue was resolved after experiments done with rats exchanged between different laboratories led to the conclusion that filtration equilibrium prevails in some rat strains or breeding colonies but not in others, and that the difference is attributable to differences in LpA . This finding detracts somewhat from teleologic arguments for or against filtration pressure equilibrium.

Nephron Plasma Flow, Q ₀

Q ₀ does not appear in the Starling equation for water flux ( Eq. (21.3a) ) or in the flux integral that defines SNGFR ( Eq. (21.4) ). Nonetheless, Q ₀ is an important determinant of SNGFR . In fact, increased renal plasma flow underlies many of the physiologic increases in GFR that occur in the normal course of life, such as during pregnancy or after protein feeding. SNGFR is the simple product of LpA and ⟨ P _UF ⟩ ( Eq. (21.4) ). ⟨ P _UF ⟩ becomes greater if the average plasma oncotic pressure along the capillary is less. Removing a given amount of water from the plasma will cause a lesser increase in the plasma oncotic pressure if that water is subtracted from a larger initial plasma volume. Hence, increasing Q ₀ will cause oncotic pressure to rise more slowly along the capillary. Therefore, increasing Q ₀ causes ⟨ P _UF ⟩ to increase. The precise effect of Q ₀ on the rate of rise in plasma protein concentration along the nephron is described mathematically in Eq. (21.7). SNGFR will be most sensitive to changes in Q ₀ under conditions of filtration pressure equilibrium where the filtration fraction remains constant as Q ₀ increases. In filtration disequilibrium, c ₁ , ergo filtration fraction, will decline with increasing Q ₀ to reduce the impact of Q ₀ on SNGFR . Homer Smith recognized that renal plasma flow should affect GFR by this mechanism, and that his experiments ( vide supra ) failed to confirm a plasma flow dependence of GFR only because the particular tools that he employed to manipulate the renal blood flow were confounded by offsetting effects on P _GC .

Systemic Plasma Protein Concentration, c ₀

In the idealized glomerulus, an isolated change in c ₀ will cause opposite changes in ⟨ P _UF ⟩ and, therefore, SNGFR . However, it is difficult to demonstrate this experimentally because it is nearly impossible to manipulate oncotic pressure of the arterial plasma without affecting the neurohumoral milieu of the entire body, thereby altering other determinants of SNGFR . In fact, the circumstances associated with low oncotic pressure in real life (e.g., generalized capillary leak, sepsis, malnutrition or nephrosis) are generally associated with a low GFR. When c ₀ is manipulated by whatever means, changes in other determinants occur to offset the impact on SNGFR . These changes are discussed below under “Interactions Among the Determinants of SNGFR.”

Hydrostatic Pressure, P _GC , and Δ P

Whereas SNGFR is insensitive to LpA when Q ₀ is low and insensitive to Q ₀ when LpA is low, SNGFR will always be sensitive to an isolated change in Δ P unless Δ P is so low as to be exceeded by the incoming plasma oncotic pressure, in which case SNGFR will be zero. This is true because the proportional increase in ⟨ P _UF ⟩ brought about by any increment in Δ P−Π ₀ is relatively insensitive to the other determinants of SNGFR. This is illustrated in Figure 21.5 and in the lower half of Figure 21.6 .

The interposition of the efferent arteriole between the glomerulus and peritubular capillary provides a simple mechanism for regulating Δ P independently of Q ₀ . Furthermore, this arrangement provides an opportunity to elicit reciprocal changes in P _GC and pressure in the downstream peritubular capillary P _PTC . Tying an increase in P _GC to a decrease in P _PTC has teleologic appeal, as this will facilitate homeostasis of the effective circulating blood volume while stabilizing GFR. If the efferent arteriole reacts to sustain P _GC and reduce P _PTC during a decline in renal perfusion pressure or effective circulating blood volume, then GFR will be relatively spared from declining while filtration fraction will increase, thus affecting both the hydraulic and oncotic components of the Starling force that drives reabsorption by the peritubular capillary.

Regulating the efferent arteriole in this way is largely the purview of the renin–angiotensin system, which figures prominently among the myriad neurohumoral mechanisms contained in models of blood pressure and salt homeostasis. Angiotensin II is antinatriuretic and constricts arterioles throughout the body but, on balance, its effect on the glomerulus is always to elevate Δ P . Thus, in spite of being a renal vasoconstrictor, angiotensin II protects GFR from total decline when the arterial blood pressure is low or when the preglomerular resistance is high.

While unduly low P _GC must impair glomerular filtration, P _GC and SNGFR are poorly correlated under normal circumstances, as are P _GC and arterial blood pressure. This implies that the kidney generally protects P _GC against the influence of arterial blood pressure and employs determinants other than Δ P to effect physiologically those changes in SNGFR that normally occur throughout life. Furthermore, it has recently been demonstrated that the preglomerular myogenic elements, long associated with static renal blood flow autoregulation, efficiently buffer the glomerular capillary against systolic pressure pulses delivered at the heart-rate frequency. Teleologic reasoning behind sheltering the glomerular capillary from high pressure is that high P _GC augments wall stress in the glomerular capillary, which elicits a trophic response. If unchecked, this response will ultimately sclerose and destroy the glomerulus. Therefore, high P _GC is always pathologic, and treating glomerular capillary hypertension has been a cornerstone of nephrology practice for more than two decades. Some examples of glomerular capillary hypertension include angiotensin II-mediated hypertension, experimental glomerulonephritis, and residual nephrons after subtotal nephrectomy. It has been asserted, and commonly accepted, that glomerular capillary hypertension also underlies glomerular hyperfiltration in early diabetes mellitus. However, there are more than 10 published micropuncture studies in which diabetic hyperfiltration occurred in the absence of glomerular capillary hypertension or in which glomerular capillary hypertension was treated with no mitigating effect on diabetic hyperfiltration. This does not detract from the salutary effect of therapy to reduce P _GC , which applies to all glomerular diseases.

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