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Biophysics of Glomerular Filtration

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Abstract

Enlightened by William Bowman's depiction of the anatomy in 1842, Carl Ludwig immediately proposed glomerular filtration as a physical process. Nuances of this process have come to light in a rather orderly progression over the past 150 years with essential contributions from clearance methods, renal micropuncture, physical theories of nonequilibrium thermodynamics and electrical double layers, morphometry, and mathematics. Herein, we describe that progression of knowledge. Ongoing work pertains to the nature, location, and efficiency of the barrier to protein sieving, induction of endothelial fenestrae by growth factors from the podocyte, and potential resistance faced by filtrate exiting the subpodocyte space. Published 2012. Compr Physiol 2:1671‐1699, 2012.

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Figure 1. Figure 1.

William Bowman's drawings of blood supply, Malpighian corpuscle, and renal tubule in various species. [Adapted from, reference (), with permission].

Figure 2. Figure 2.

Oncometer devised by EH starling. A, colloid test solution; C, isotonic saline; M, mercury manometer; X, pivot point for rocking; B, tube with gelatin between two layers of peritoneal membrane supported on silver gauze and wrapped in thread. [Adapted from, reference (), with permission].

Figure 3. Figure 3.

The “unitary glomerulus” illustrating filtration equilibrium due to declining pressure along the glomerular capillary. [Adapted from, reference (), with permission].

Figure 4. Figure 4.

Experimental design for measuring intratubular stop‐flow pressure in individual nephrons of the rat kidney. [Adapted from, reference (), with permission].

Figure 5. Figure 5.

The glomerulus represented by as right circular cylinder with unit length and surface area. Q, plasma flow; Jv, filtration flux; x, axial position; SNGFR, single nephron GFR. [Adapted from, reference (), with permission].

Figure 6. Figure 6.

Pressure (left) and total flux (right) along the length of the glomerular capillary. In left panel, solid curves represent that rises due to removal of water while dashed line represents ΔP, which declines by 1 mmHg along the capillary due to flow resistance. SNGFR is the total amount filtered at position = 1. Other inputs include systemic plasma protein concentration 5.8 g/dL and LpA = 0.08 nL/s/mmHg. Filtration equilibrium occurs when ΔP = 0. Filtration equilibrium arises earlier along the capillary when nephron plasma flow (Q0) is low. SNGFR is the amount filtered at axial position = 1.

Figure 7. Figure 7.

SNGFR as a function of pairwise changes in its four determinants. Unless otherwise stated, g/dL, ΔP = 35 mmHg, nL/min, LpA = 0.05 nL/s/mmHg. SNGFR is insensitive to LpA when there is filtration equilibrium, which arises when Q0 is low (A), C0 is high (F), and as LpA is high (A, D, and F). Increasing ΔP does not prevent filtration equilibrium from arising as LpA increases (D). The effects of C0 shown in E are not observed in vivo, where changes in C0 and ΔP tend to be correlated (discussed in text). Likewise, the effects in F are not observed in vivo due to negative correlation between C0 and LpA.

Figure 8. Figure 8.

Isolated effects of efferent arteriole resistance (RE) on nephron plasma flow (Q0), glomerular capillary pressure (PGC), and single nephron GFR (SNGFR) for mean arterial blood pressure 100 mmHg, afferent resistance 25 mmHg/nL/min and plasma protein concentration 6 g/dL. Curves shown for ultrafiltration coefficient (LpA) from 0.04 to 0.08 nL/s/mmHg. Curvilinear shapes of Q0 and PGC result as glomerular filtration reduces blood flow in the efferent arteriole. The relationship of SNGFR to RE is biphasic with the peak value of SNGFR occurring in the normal physiologic range. Hence, circumstances arise in vivo where dilating the efferent arteriole may cause SNGFR to increase, decrease, or remain the same. Increasing afferent resistance will shift the SNGFR curve rightward (not shown).

Figure 9. Figure 9.

Results of 78 micropuncture experiments from two laboratories in which eight different protocols were employed to manipulate the systemic plasma oncotic pressure to assess the effect of oncotic pressure on glomerular hemodynamics. Squares refer to protocols without volume expansion. Multivariate regression on the pooled data reveals a strong dependence of ΔP on both Π0 and LpA, but no dependence on Q0. Circles refer to protocols where there was ; ; some form of volume expansion. The relationship between ΔP and Π0 is shown in the figure, where ΔP has been adjusted for effects of the covariate, log(LpA). For every 1 mmHg increment in Π0 there is a 0.9‐mmHg increment in ΔP, which minimizes the impact of manipulating Π0 on ultrafiltration pressure (P ≤ 0.00001).

Figure 10. Figure 10.

Albumin and low molecular weight protein in proximal tubular fluid obtained by micropuncture. TF/P inulin of unity corresponds to Bowman's space. By linear extrapolation, the sieving coefficient for albumin was estimated at 0.0006. [Adapted from, reference (), with permission].

Figure 11. Figure 11.

Hindered transport of a spherical molecule (radius a) traveling at velocity u in cylindrical pore (radius r) where bulk fluid velocity is v. The ratio of effective (Aeff) pore area to geometric pore area (Ap) is shown as a function of a/r. Note that a/r need only reach 0.4 for Aeff to decline by 90%. Curves for different values of are derived from published drag coefficients (). The curve denoted “Landis” was derived by the method of Landis and Pappenheimer (). [Adapted from, reference (), with permission].

Figure 12. Figure 12.

Sieving coefficient as a function of Stokes‐Einstein radius for molecules with different deformability where dextrans are most, and “proteins” are least, deformable. [Adapted from, reference (), with permission].

Figure 13. Figure 13.

Transmission electron micrograph showing three layers of the glomerular capillary wall. GenC, endothelial cell; GBM, basement membrane; Pod, visceral epithelial foot process; *, filtration slit between foot processes.

Adapted from, reference (), with permission, © the Biochemical Society.
Figure 14. Figure 14.

Sieving coefficients for a filtration barrier consisting of two layers displayed in semilog fashion over a reasonable range of Peclet number. The upstream and downstream layers are designated 1 and 2, respectively. Each layer has its own inherent reflection coefficient, σ. Cplasma, Cfiltrate, and CB are the respective solute concentrations in plasma, filtrate, and a the boundary between the two layers. When the Peclet number is zero, there is no bulk flow and the system comes to diffusion equilibrium with equal solute concentrations everywhere (all sieving coefficients = unity). (A) One layer has σ = 0.99 and the other has σ = 0.90. The overall efficiency as a filtration barrier is markedly diminished when the less restrictive layer is placed upstream of the more restrictive layer. (B) Placing a permeable layer (σ = 0) upstream of a restrictive layer yields a barrier that is less efficient than the restrictive layer alone. (C) The sieving coefficient of the upstream layer (CB/Cplasma) is strongly influenced by the reflection coefficient of the downstream layer. Remarkably, when the downstream layer is only 10% more restrictive than the upstream layer, the upstream sieving coefficient can exceed unity by several‐fold. In other words, there is concentration polarization in the upstream layer. This acts like a body force for diffusion through the downstream layer and explains the separation of the two curves in panel (A).

Figure 15. Figure 15.

Model predictions for charge‐selective sieving of dextrans. Circles are sieving data in the rat. The curve is a fit to the model for membrane fixed charge density of 160 mmol/L. [Adapted from, reference (), with permission].

Figure 16. Figure 16.

Schematic representation of model for charge‐selective glomerular sieving based on Donnan equilibrium at both sides of the barrier. [Adapted from, reference (), with permission].

Figure 17. Figure 17.

Reflection coefficient predicted for albumin as function of surface charge densities on albumin (Qs) and glycocalyx (Qf). [Modified from, reference (), with permission].

Figure 18. Figure 18.

Structure‐based model of the filtration barrier. (Left) Filtration unit consisting of a single filtration slit and several fenestrae. (Right) Filtration slit with slit diaphragm. [Adapted from, reference (), with permission].

Figure 19. Figure 19.

Flow across the glomerular filtration barrier and through the subpodocyte space (SPS). Resistance depends on height of subpodocyte space (h), the path length (a), and the area draining into SPS (). [Adapted from, reference (), with permission].



Figure 1.

William Bowman's drawings of blood supply, Malpighian corpuscle, and renal tubule in various species. [Adapted from, reference (), with permission].



Figure 2.

Oncometer devised by EH starling. A, colloid test solution; C, isotonic saline; M, mercury manometer; X, pivot point for rocking; B, tube with gelatin between two layers of peritoneal membrane supported on silver gauze and wrapped in thread. [Adapted from, reference (), with permission].



Figure 3.

The “unitary glomerulus” illustrating filtration equilibrium due to declining pressure along the glomerular capillary. [Adapted from, reference (), with permission].



Figure 4.

Experimental design for measuring intratubular stop‐flow pressure in individual nephrons of the rat kidney. [Adapted from, reference (), with permission].



Figure 5.

The glomerulus represented by as right circular cylinder with unit length and surface area. Q, plasma flow; Jv, filtration flux; x, axial position; SNGFR, single nephron GFR. [Adapted from, reference (), with permission].



Figure 6.

Pressure (left) and total flux (right) along the length of the glomerular capillary. In left panel, solid curves represent that rises due to removal of water while dashed line represents ΔP, which declines by 1 mmHg along the capillary due to flow resistance. SNGFR is the total amount filtered at position = 1. Other inputs include systemic plasma protein concentration 5.8 g/dL and LpA = 0.08 nL/s/mmHg. Filtration equilibrium occurs when ΔP = 0. Filtration equilibrium arises earlier along the capillary when nephron plasma flow (Q0) is low. SNGFR is the amount filtered at axial position = 1.



Figure 7.

SNGFR as a function of pairwise changes in its four determinants. Unless otherwise stated, g/dL, ΔP = 35 mmHg, nL/min, LpA = 0.05 nL/s/mmHg. SNGFR is insensitive to LpA when there is filtration equilibrium, which arises when Q0 is low (A), C0 is high (F), and as LpA is high (A, D, and F). Increasing ΔP does not prevent filtration equilibrium from arising as LpA increases (D). The effects of C0 shown in E are not observed in vivo, where changes in C0 and ΔP tend to be correlated (discussed in text). Likewise, the effects in F are not observed in vivo due to negative correlation between C0 and LpA.



Figure 8.

Isolated effects of efferent arteriole resistance (RE) on nephron plasma flow (Q0), glomerular capillary pressure (PGC), and single nephron GFR (SNGFR) for mean arterial blood pressure 100 mmHg, afferent resistance 25 mmHg/nL/min and plasma protein concentration 6 g/dL. Curves shown for ultrafiltration coefficient (LpA) from 0.04 to 0.08 nL/s/mmHg. Curvilinear shapes of Q0 and PGC result as glomerular filtration reduces blood flow in the efferent arteriole. The relationship of SNGFR to RE is biphasic with the peak value of SNGFR occurring in the normal physiologic range. Hence, circumstances arise in vivo where dilating the efferent arteriole may cause SNGFR to increase, decrease, or remain the same. Increasing afferent resistance will shift the SNGFR curve rightward (not shown).



Figure 9.

Results of 78 micropuncture experiments from two laboratories in which eight different protocols were employed to manipulate the systemic plasma oncotic pressure to assess the effect of oncotic pressure on glomerular hemodynamics. Squares refer to protocols without volume expansion. Multivariate regression on the pooled data reveals a strong dependence of ΔP on both Π0 and LpA, but no dependence on Q0. Circles refer to protocols where there was ; ; some form of volume expansion. The relationship between ΔP and Π0 is shown in the figure, where ΔP has been adjusted for effects of the covariate, log(LpA). For every 1 mmHg increment in Π0 there is a 0.9‐mmHg increment in ΔP, which minimizes the impact of manipulating Π0 on ultrafiltration pressure (P ≤ 0.00001).



Figure 10.

Albumin and low molecular weight protein in proximal tubular fluid obtained by micropuncture. TF/P inulin of unity corresponds to Bowman's space. By linear extrapolation, the sieving coefficient for albumin was estimated at 0.0006. [Adapted from, reference (), with permission].



Figure 11.

Hindered transport of a spherical molecule (radius a) traveling at velocity u in cylindrical pore (radius r) where bulk fluid velocity is v. The ratio of effective (Aeff) pore area to geometric pore area (Ap) is shown as a function of a/r. Note that a/r need only reach 0.4 for Aeff to decline by 90%. Curves for different values of are derived from published drag coefficients (). The curve denoted “Landis” was derived by the method of Landis and Pappenheimer (). [Adapted from, reference (), with permission].



Figure 12.

Sieving coefficient as a function of Stokes‐Einstein radius for molecules with different deformability where dextrans are most, and “proteins” are least, deformable. [Adapted from, reference (), with permission].



Figure 13.

Transmission electron micrograph showing three layers of the glomerular capillary wall. GenC, endothelial cell; GBM, basement membrane; Pod, visceral epithelial foot process; *, filtration slit between foot processes.

Adapted from, reference (), with permission, © the Biochemical Society.


Figure 14.

Sieving coefficients for a filtration barrier consisting of two layers displayed in semilog fashion over a reasonable range of Peclet number. The upstream and downstream layers are designated 1 and 2, respectively. Each layer has its own inherent reflection coefficient, σ. Cplasma, Cfiltrate, and CB are the respective solute concentrations in plasma, filtrate, and a the boundary between the two layers. When the Peclet number is zero, there is no bulk flow and the system comes to diffusion equilibrium with equal solute concentrations everywhere (all sieving coefficients = unity). (A) One layer has σ = 0.99 and the other has σ = 0.90. The overall efficiency as a filtration barrier is markedly diminished when the less restrictive layer is placed upstream of the more restrictive layer. (B) Placing a permeable layer (σ = 0) upstream of a restrictive layer yields a barrier that is less efficient than the restrictive layer alone. (C) The sieving coefficient of the upstream layer (CB/Cplasma) is strongly influenced by the reflection coefficient of the downstream layer. Remarkably, when the downstream layer is only 10% more restrictive than the upstream layer, the upstream sieving coefficient can exceed unity by several‐fold. In other words, there is concentration polarization in the upstream layer. This acts like a body force for diffusion through the downstream layer and explains the separation of the two curves in panel (A).



Figure 15.

Model predictions for charge‐selective sieving of dextrans. Circles are sieving data in the rat. The curve is a fit to the model for membrane fixed charge density of 160 mmol/L. [Adapted from, reference (), with permission].



Figure 16.

Schematic representation of model for charge‐selective glomerular sieving based on Donnan equilibrium at both sides of the barrier. [Adapted from, reference (), with permission].



Figure 17.

Reflection coefficient predicted for albumin as function of surface charge densities on albumin (Qs) and glycocalyx (Qf). [Modified from, reference (), with permission].



Figure 18.

Structure‐based model of the filtration barrier. (Left) Filtration unit consisting of a single filtration slit and several fenestrae. (Right) Filtration slit with slit diaphragm. [Adapted from, reference (), with permission].



Figure 19.

Flow across the glomerular filtration barrier and through the subpodocyte space (SPS). Resistance depends on height of subpodocyte space (h), the path length (a), and the area draining into SPS (). [Adapted from, reference (), with permission].

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Further Reading
 1. Haraldsson B, Nyström J, Deen WM. Properties of the glomerular barrier and mechanisms of proteinuria. Physiol Rev 88(2): 451‐487, 2008.

Further Reading

Haraldsson B, Nyström J, Deen WM. Properties of the glomerular barrier and mechanisms of proteinuria. Physiol Rev. 88(2):451-87, 2008.


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Scott C. Thomson, Roland C. Blantz. Biophysics of Glomerular Filtration. Compr Physiol 2012, 2: 1671-1699. doi: 10.1002/cphy.c100089