ANNUAL REVIEWS

Further

Quick links to online content RENAL PHYSIOLOGY

9

DETERMINANTS OF GLOMERULAR FILTRATION RATE

Barry M Brenner Kidney Research Laboratory, Veterans Administration Hospital, San Francisco, California

94121, the Departments of Medicine and Physiology,

and the Cardiovascular Research Institute of the University of California,

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

San Francisco, California

94143

William M Deen Kidney Research Laboratory, Veterans Administration Hospital, San Francisco, California

94121 and the Departments of Medicine and Physiology, 94143

University of California, San Francisco, California

Channing R. Robertson Department of Chemical Engineering, Stanford University, Stanford, California

94305

Introduction In mammals, about one fifth to one th�d of the large volume of blood plasma entering the renal glomerulus normally passes through the walls of its capillaries. By use of micropuncture techniques, the composition of this fluid has been found to conform to that of a nearly ideal ultrafiltrate, closely resembling plasma water: with respect to low molecular weight solute concentrations molecular weights greater than approximately

5000,

(14). For solutes with

however, transport becomes

restricted; the extent of restriction is almost complete for molecules the size of serum albumin or larger

(22).

The rate of ultrafiltrate formation is governed by the same driving force governing fluid movement across other capillary membranes, that is, the imbalance between transcapillary hydraulic and colloid osmotic pressures. At any point along a glomerular capillary, this relationship may be expressed as J.

= =

k (I1P - 111f) k[(PGC - PT) - (1fGC

-

1.

1fT)],

k is the effective hydraulic permeability

where J. is' the local rate of ultrafiltration, of the capillary wall, and

I1P and

111f are the transcapillary hydraulic and colloid

osmotic pressure differences, respectively.

PGC

and

1f GC

are the hydraulic and

colloid osmotic pressures in the glomerular capillary, and P T and

1f T

are the

corresponding pressures in Bowman's space. As the protein concentration in glomerular ultrafiltrate is extremely small

(13),

1f T

may be regarded as negligible.

Although it has been possible for some time to provide reasonably accurate esti­ mates in mammals of several of the terms shown in equation 1, namely,

1f

at afferent

10

BRENNER. DEEN

&

ROBERTSON

and efferent ends of the glomerular capillary. and PT. a meaningful description of the overall dynamics of glomerular ultrafiltration has been lacking until recently

because of the inability to obtain direct measurements of P GC. This is so because

glomeruli are not generally present as surface structures accessible to micropuncture in the mammal. This restriction has been overcome in the past few years. however. a result primarily of the discovery of a mutant strain of Wistar rats possessing glomeruli on the surface of the renal cortex. thereby making possible the direct

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

measurement of

PGC

in this mammalian species. Using the servonull pressure­

measuring technique of Wiederhielm et al found

PGC in

(26). Brenner. Troy & Daugharty (3)

these rats to average approximately 45 mm Hg, or some 40% of the

mean aortic pressure. Essentially the same findings have since been obtained in other laboratories

(1, 2). Mpreover, in the squirrel monkey, a small primate that also 45 mm Hg

possesses surface glomeruli, P GC has again been found to average some

(20). Normal Glomerular Dynamics From these measurements of

P GC'

together with the other measured pressures, it

is possible to evaluate the net driving force for ultrafiltration at the afferent and efferent ends of the glomerular capillary network. As shown for the rat in Table I, the value of P GC of

45

mm Hg is taken to be the same at the afferent and efferent

ends of the network, since the axial pressure drop along the network due to flow

(4).1 Proximal tubule pressure, PT, is normally 10 mm Hg. Measurements of afferent and efferent arteriolar plasma protein

has been found to be quite small about

concentrations indicate that the colloid osmotic pressure,

1T GC'

increases from about

20 mm Hg at the afferent end to 35 mm Hg at the efferent end of the glomerular Table 1

Glom eru lar capillary hydraulic and oncotic pressures (in mm Hg)a

Pee

Glomerular Capillary Site

10 10

45 45

Afferent end Efferent end

20 35

15 o

aAbbreviations: P

ee and PT, local glomerular capillary and Bowman's space (or early

proximal) hydraulic pressures, respectively; 1lee' local glomerular capillary plasma colloid

osmotic pressure; P

UF' local net ultrafiltration pressure.

'Some axial pressure drop must exist in order for blood to flow through the capillary. That

thi s pressure drop is small is giv en by the finding that the sum of the pressures opposing filtration at the efferent end of the glomerular capillary (as inferred from the sum of efe f rent arteriolar oncotic pressure,

'Tr E,

plus proximal tubule hydraulic pressure, P T) reaches a value

which, on average, balances P GC. Since P GC is measured at statistically random sites along the glomerular capillary. th e finding that 'Tr E + P T

=

P GC indicates that P GC changes little along

capillary segments at this level of the renal vascular circuit. The sensitivity of the methods used to determine

'TrE,

Pro and PGC makes it likely that this pressure drop is no greater than 2-3

mm Hg. Th us, the measured value of P GC is essentially the same as the value of P GC av e raged over the length of the glomerular capillary. denoted as

PGc·

RENAL PHYSIOLOGY capillary because of the largely protein-free nature of the ultrafiltrate

II

(2-4, 6, 21,

23). P UF, the local net ultrafiltration pressure (as given in Table I) thus declines from

a maximum value of about 15 mm Hg at the afferent end essentially to zero by the efferent end. In other words, it has been shown that by the eJferent end of the

capillary network t:.:rr rises to a value that, on the average, exactly equals

AP

(2- 4, 6, 21, 23). This equality of A P and A 7r is referred to as filtration pressure equilibrium. Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

These relationships are summarized graphically in Figure I, in which the abscissa

represents the normalized distance along an idealized glomerular capillary; 0 is the

AP, the difference between PT of 10, or 35 mm Hg, is essentially constant along the length of A7r, equal to 7r GC, as 7r T is negligible, increases from 20 to 35 mm

afferent end and 1 the efferent end. As already indicated,

PGC of 45

and

the capillary.

Hg along the capillary. Accordingly, the decline in

PUF from a

maximum value of

15 mm Hg essentially to zero is the consequence, not of an appreciable decline in

AP, but rather of a progressive increase in A7T. Because the measurements of 7T can only be performed on samples of systemic blood (taken as representative of blood at the afferent end of the glomerular capillary) and blood from efferent arterioles, the exact profile of the change in determined directly. The

A 7r

7r

with distance along the capillary cannot be

profile in Figure 1 is one of an infinite number of

profiles consistent with the measurements of point along the capillary at which

7rA

P UF = 0

and

.7r E

in hydropenia: hence the

cannot be determined from these

measurements alone. The rate of glomerular ultrafiltration may be expressed as SNGFR

=

KrPuF = koS[AP - A7r),

2.

where SNGFR, the single nephron glomerular filtration rate, is the product of the

ultrafiltration coefficient, Kf> and the net driving pressure averaged over the length

of the capillary,

PUFo PUF is the difference between the mean transcapillary hydrau­

lic and oncotic pressure differences,

AP and A7T,

respectively, equal to the shaded

60 PRESSURE

(mmHg)

40 ��=---t 20 O+-------.J o

DIMENSIONLESS DISTANCE ALONG IDEALIZED GLOMERULAR

CAPILLARY

Figure 1 Hydraulic and colloid osmotic pressure profiles among an idealized glomerular capillary in the rat. A.P = PGC - PT and A. 7T = 7T GC - 7T T, where P GC and PT are the hydraulic pressures in the glomerular capillary and Bowman's s pace, respectively . and 7T GC and 7T T are the corresponding colloid osmotic pressures.

BRENNER, DEEN & ROBERTSON

12

area between the!:J.P and!:J.rr curves in Figure 1. Kfis the product of the effective hydraulic permeability of the capillary wall (k) and the surface area available for filtration (S). As mentioned above, under conditions of filtration pressure equilib­ rium it is impossible to estimate PUF due to the uncertainty in determining the exact !:J.rr profile. Since the local rate of ultrafiltration is proportional to the local value of !:J.P !:J.rr, !:J.rr will tend to increase most rapidly near the afferent end of the capillary, so that any !:J.rr profile at equilibrium must, as shown in Figure 1, be highly nonlinear (8). A mUltiplicity of !:J.rr curves, including the one shown in Figure I, satisfy the requirement that the net driving pressure, !:J.P - !:J.rr, decline from a maximum value at the afferent end of the capillary to zero by the efferent end. Because PuFis equal to the area between the!:J.P and!:J.rr curves, PUF, and therefore Kf'

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

-

Mathematical Model of Glomerular Filtration Uncertainty in the determination of !:J.rr profiles has provided the incentive for the development of a mathematical model of glomerular ultrafiltration (8). In this model, conservation of mass and the Starling hypothesis (equation I) are used to derive a differential equation giving the rate of change of protein concentration with distance along the glomerular capillary. This formulation makes possible the calcu­ lation of !:J.rr profiles along the capillary, which, together with measured values of !:J.P, rrA, rr E' and SNGFR, permit determination of PUFo and hence Kfo under a variety of conditions discussed below. This approach has the additional advantage of enabling one to examine the effects of selective perturbations in rr A, !:J.P, Kf' and glomerular plasma flow rate (QA) on SNGFR. In this model, the glomerular capillary network is simplified to be a single tube of equivalent total surface area (S), with local plasma flow rate (Q) and protein concentration (C) functions only of the length coordinate (�). The latter is normal­ ized so that 0 < .Q < 1. Conservation of volume and protein requires that the following differential equations be satisfied: dQ/d.Q

=

-1.S, Q

=

QA at � = 0

3.

and d(QC)/d�

=

0, QC

=

QACA at .Q

=

4.

0,

where QA is the initial glomerular plasma flow rate and CA is the afferent arteriolar or systemic protein concentration. Equations 1, 3, and 4 may be combined to yield a single differential equation giving the rate of change of C (and hence !:J.rr)2 with distance along the glomerular capillary: Z/j,rr increases in /j,7I'

=

a

nonlinear fashion with increases in C:

alC + azCZ.

For protein concentrations in the range 4 S C < 10 g/iOO ml, and normal albumin to

globulin concentration ratio of unity, al Hg/(g/lOO mW

=

1.63

mm Hg/(g/l00 mI) and az

=

0.294 mm

RENAL PHYSIOLOGY 1\

"

dCldx

1\

=

_

=

I,

5.

where t CIC,4 and F K.rdP1Q,4. Since ll.P normally declines by no more than "'1-2 mm Hg with distance along the capillary (4), ,jp differs from ll.P by no more than 6 % A more detailed discussion of this and other features of the model, together with the method of solution of equation 5, is given elsewhere (8). For measured or assumed values of F, solution of equation 5 yields protein concentra­ tion and oncotic pressure profiles along a glomerular capillary, information that cannot yet be obtained from direct measurement. The value of K/ is an important determinant of ll.1T profiles, as the parameter F is proportional to K/" The difficulty in calculating K/ from experimental data is illustrated once again by Figure 2, which shows ll.1T profiles corresponding to several values of the dimensionless parameter F, In this figure, consider ll.P to be constant so that changes in F are proportional to changes in the ratio K/QA. Note that filtration pressure equilibrium, the previously discussed equality of dP and 1T E achieved in the normally hydrated rat and monkey (2-4, 6, 21, 23), is obtained in this illustration for values of F greater than "'3. It is clear that for a given value of dP at equilibrium, d1T rises to the same value at the efferent end of the capillary, irrespective of the value of K/" In other words, so long as Kf is sufficiently large to yield equilibrium, further increases in Kf will only shift the point at which equilibrium is achieved further toward the afferent end of the capillary. Thus, from measurements of d1T at the afferent and efferent ends of the glomerular capillary, it is not possible to distinguish among the many ll.1T profiles consistent with equilib­ rium; only a minimum value of Kf can be estimated. On the other hand, Figure 2 also suggests that if Kf and ll.P remain relatively constant, large values of QA' corresponding to lower values of F. should prevent achievement of filtration pres­ sure equilibrium. Of importance in this case, only one ll.1T profile can connect measured values of 1T at afferent and efferent ends of the capillary. The value of F corresponding to this unique d 1T profile, together with measured values of dPand QA' yields the value of K/" This approach has been used by Deen et al to estimate the value of K f in the normal rat (12). Intravenous infusion of a volume of isoncotic rat plasma equal to =

"'

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

1\

FC2[(dP - d1T)/dPJ, C(O)

13

=

.

tf z i;!

ti5

O.

� I�

� 0 .. � '" III



�.. �







6P

10

eo

0.8 0.7 o.� 0.6

02 AIT 0

0.1

02

0.3

0.4

05

06

0.1

0.8

0.9

1.0

X-, DIMENSIONLESS DISTANCE ALONG CAPILLARY

Figure 2 Transmembrane colloid osmotic pressure profiles as a function of the dimensionless parameter, F. Reprinted from Fed. Proc. 33:14-20, 1974.

14

BRENNER, DEEN & ROBERTSON

"'5% of body weight was found to increase QA to some 200 nl/min, approximately 75 nl/min, and sufficiently high to give disequilibrium. The yalue of KI was found to average about 4.8 nl!(minomm Hg).

three times the normal hydropenic value of

Of interest, KI was found to remain essentially unchanged within a twofold range QA' strongly suggesting that Klis independent of QA (12). In addition,

of changes in

it was confirmed that this value of K I is sufficiently large to permit attainment of

equilibrium at the lower values of

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

rat

QA

characteristic of hydropenia in the normal

(12).

SNGFR, it follows that PUF, attains a value of approximately 4--6 mm Hg (2--4, 6, 21, 23) and increases to roughly 10 mm Hg

Taking this value of Kftogether with measured values for the mean ultrafiltration pressure, in the normal hydropenic rat

under conditions of marked plasma volume expansion, thereby accounting for the large rise in SNGFR observed experimentally

(4, 7, II, 12, 21).

Effective Hydraulic Permeability of the Glomerular Capillary Wall Since KI

=

kS

(equation

2),

the effective hydraulic permeability3

(k)

of the

glomerular capillary can be estimated from Kf and the surface area available for

ultrafiltration (S). Taking Kf rat glomerulus (15 ), k

=

2.5

=

4.8 nl!(minomm Hg) and S = 0.0019 cm2for the

fJ.1!(minomm Hgocm2). This permeability is approxi­

mately

1-2 orders of magnitude greater than that reported for capillaries in other (5, 16, 17), rat skeletal muscle (24), rat peritubular capillaries (9), and rabbit omentum (18, 27). Thus the tissues in a variety of species, including frog mesen.tery

relatively high permeability of the glomerular capillaries enables glomerular ultrafil­ tration to proceed at a rapid rate despite a mean driving pressure of normally only about

5 mm Hg.

The Effects of Selective Alterations in the Determinants of Glomerular Filtration Rate As discussed above, the model of glomerular filtration provides the opportunity to examine the effects on glomerular filtration rate of selected perturbations in the four determinants of ultrafiltration, namely,

SNGFR

Q A,

Kf' AP, and

7T A'

In the present context,

is best expressed as

SNGFR

=

SNFFoQA,

6.

lConcentration pol�rization, the accumulation of retained solute next to an ultrafiltering membrane, elevates osmotic pressure above that which would exist in the absence of polariza­ tion. For ultrafiltration in a cylindrical tube, use of the radially averaged solute concentration

results in an underestimate of osmotic pressure, yielding an effective hydraulic permeability (k) less than the actual membrane hydraulic permeability (km). The extent to which k and k m might differ in an ultrafiltering capillary has been examined theoretically by solution of the momentum and species transport equations for idealized capillaries with and without erythrocytes (10). For diameters, flow velocities, protein concentrations and diffusivities, and ultrafiltration pressures representative of the rat glomerular capillary network, results indicate that the effects of polarization are substantial without erythrocytes (k/ k = 0.7) and persist, but to a lesser extent, with erythrocytes (kl k m = 0.9); the reduction in polarization in the latter case is due to enhanced plasma mixing. m

RENAL PHYSIOLOGY

15

where SNFF is the single-nephron filtration fraction. Because only a negligible amount of protein appears in glomerular filtrate, conservation of protein requires that

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

7. where C E is the efferent protein concentration and the other terms are as defined above. When equation 7 is rearranged and compared with equation 6, SNFF is related to CA and CE: 8.

It is clear from Figure 2 that, for given values of C A (hence 7TA), KI' and tlP, C E (hence 7T E) will be unaffected by changes in QA so long as equilibrium is maintained. Under these conditions, SNFF will remain constant. Further increases in QA' which cause disequilibrium, lead to progressively lower values of CEo Thus, for given values of KI, llP. and CA at disequilibrium, it is evident from equation 8 that SNFF must decrease with increasing QA' The theoretical interrelationships among SNFF, SNGFR, and QA are shown in Figure 3, calculated for values of KI' CA, and tlP representative of the normal hydropenic rat. It follows from Equation 6 that as long as SNFF remains constant, SNGFR will vary in a linear manner with QA' as shown for values of QA up to "'100 nllmin. This linear relationship at equilibrium, indicating that SNGFR is highly plasma-flow depen­ dent,has been observed experimentally (4,6,21,23). For higher values of QA' where disequilibrium occurs and SNFF decreases, SNGFR increases less than in propor­ tion to increases in QA (7, 12, 21), hence the departure from the dashed line in Figure 3, the latter denoting a constant filtration fraction of 0.33. Even at disequilib­ rium SNGFR will be highly plasma-flow dependent, but to a lesser extent than when equilibrium obtains. In the absence of experimental measurements of tlP and Kfin larger mammals, including man, it is not yet possible to quantify the interrelation­ ships among SNFF, SNGFR, and QA in the same detail as that shown for the rat in Figure 3. Nevertheless, it has been shown in both man and dog that SNFF tends to vary inversely with changes in renal plasma flow (25). 80 60 SNGfR 4 (nl/min) 0

100 200 300 QA. nl/min Figure 3 =

35

SNGFR

500

The effects

K,AP. and AP

400

7T of

typical of the normal hydropenic rat, that is, K,

mm Hg, and =

O.33QA'

7T of

=

19 mm Hg

(Cof

=

=

4.8 nl/ (min.mm Hg),

5.7 g /l00 ml). The dashed line is given by

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

16

BRENNER, DEEN & ROBERTSON

To understand the theoretical relationship between SNGFR and Kf, it is impor­ tant to recognize that low values of Kf lead to disequilibrium, and hence to low values of SNFF. For a given value of QA, SNGFR will vary in direct proportion toSNFF (equation 6); thus the dependence ofSNGFR on Kf will follow the pattern shown in Figure 4, where values of QA' CA' and AP are again chosen to be representative of the normal hydropenic rat. It can be seen in Figure 4 that once Kfachieves a value large enough to yield filtration pressure equilibrium, "'4 nl/(min ·mm Hg), further increases in Kf will fail to affect the value of SNGFR. In the normal rat, where Kf averages "'4.8 nIl(min.mm Hg), a reduction in Kf of at least 50% would be required to effect a 20% reduction in SNGFR. Accordingly, it is unlikely that Kfwill be an important determinant ofSNGFR except in pathological states in which capillary hydraulic permeability and/or surface area are reduced markedly. This has indeed been shown to be the case in a recent study of experimen­ tal glomerulonephritis in the rat (19). The changes inSNGFR expected from changes in AP alone are shown in Figure 5. Ultrafiltration of fluid across the walls of the glomerular capillary network occurs when ;s;P exceeds A7T (equation 2). Since 7TA in the rat is approximately 19 mm Hg (3, 4, 6), filtrate is formed only when KP exceeds this value. As AP is elevated, SNFF and SNGFR increase in parallel. Of interest is the prediction in Figure 5 that the rate of increase in SNGFR diminishes for larger values of KP. These nonlinear BO 60 SNGFR 40 (nl/mln)

KI.

4.0 6.0 B.O nl/(min.mm Hg)

10.0

Figure 4 The effects on SNGFR of selective alterations in Kf· QA is now taken as 75 nllmin and I::.P and 1TA are as defined in the legend to Figure 3. 60

SNGFR

(nl/min)

20 0

.... ' f:-�/ L�,' :::!I �..../ "

I

40

10

I I 20

30

40

bP, mm Hg

50

60

Figure 5 The effects on SNGFR of selective changes in I::.p. All other determinants assumed constant at values given in the legends to Figures 3 and 4. The dashed line is given by SNGFR Kf(I::. P - 1T A)' =

Annu. Rev. Physiol. 1976.38:9-19. Downloaded from www.annualreviews.org Access provided by Washington State University on 02/01/15. For personal use only.

RENAL PHYSIOLOGY

17

relationships result from the fact that as llP is increased, the resulting increase in the rate of ultrafiltration leads to a concurrent, but lesser increase in ll1T'. Were this increase in ll1T' not to occur, SNGFR would increase in a linear fashion with increases in llP, as in the dashed line in Figure 5. As evident from equation 2, the slope of this line is KJOnly in the mutant Wistar rat has it been possible to examine the extent to which llP varies in response to experimental maneuvers designed to produce large changes in SNGFR (2,4,6,7, 12,21,23). In these studies, llP rarely changes by more than

Determinants of glomerular filtration rate.

ANNUAL REVIEWS Further Quick links to online content RENAL PHYSIOLOGY 9 DETERMINANTS OF GLOMERULAR FILTRATION RATE Barry M Brenner Kidney Researc...
690KB Sizes 0 Downloads 0 Views