AMERICAN JOURNAL OF PHYSIOLOGY Vol. 229, No. 3, September 1975. Printed in U.S.A.
Role
of luminal
tubular
fluid
hydrostatic reabsorption
pressure
in proximal
in the rat
ALAIN GRANDCHAMP, JEAN RAOUL SCHERRER, DIETER SCHOLER, AND JACQUELINE BORNAND Labora toire de NJphrologie Exphimen tale, Division de N@hrologie, D@artement de A&de&e, et Division d’hformatique Mdicale, Universiti de GenZve, Hb’pital Cantonal, CH 1211 Gentve 4, SzvitJs, andJL-
K/2
SCHOLER,
mm&
27.5 40.0 36.5 33.0 28.0 24.0 32.5 29.5 34.0 30.0 32.0
24.0 15.0 18.0 23.0 21 .o 11 .o 7.5 15.0 8.5 8.5
significant.
average of 2.2 pm within 1 min and did not change afterward. Saline reabsorption characteristics. The data calculated from the shrinkage observation of split drop A and B are shown in Table 4 and Fig. 7. In spite of the significant difference in tubular dilatation, net fluid reabsorption per unit of the tubular wall area (Js> was similar in split drop A and B: 2.72 =t 0.20 and 2.78 =t 0.33 10-S cm3 crnv2 s-l, respectively. The 2 70 difference between these values was below the level of significance. J L, X, and Tl,z varied to a larger extent, but below the 0.05 levei of significance. The changes in A, T1/2 , and JL in split drop A amounted, respectively, to - 17 %, +- ‘15 70, and +- ‘I 5 70 uf the corresponding va’lue:s in @zt & Dp B. In comparison with the data of the literature, reduced reabsorptive rates were found in the present study. The observed half-times of 26.7 and 30.6 s in both techniques are markedly different from the value of 10 s considered to be normal since the original publication of Gertz (9). This discrepancy is almost entirely explained by the previous investigators’ use of equation 2 without meniscus correction,’ as suggested by the recent publications of Nakajima et al. (18) and Gyory (15) (Fig. 5). In the absence of a meniscus
(minutes)
suddenly
occluded
by Fig.
l v/v, 5.
=
L/L,,
in place
of: V/V,
=
(L
+
2r)/(L,
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
+
2r).
See
INTRALUMINAL
PRESSURE
IN
SPLIT
817
DROPS
correction, the rate constant A is overestimated (15, 18). The influence of an absence of meniscus correction in split drop A and B is shown in Table 5. The uncorrected flow parameters of split drop A and B approach the original Gertz’s values. It was also demonstrated that in the absence of meniscus correction, the volume decrease of the saline droplet is not a single exponential function (15, 18), as it should be in theory (9). Lack of an exponential fit invalidates the significance of the rate conslant X and the use of Gertz’s equations 3-6. In this work, the goodness of each exponential fit was tested by means of a x2 test (Table 5). It was found that 94 70 of split drop A and 73 % of split drop B shrunk as a single exponential when calculated with the meniscus correction. This percentage dropped to 19 and 27 Y’o, respectively, in the absence of meniscus correction. At the present time, the meniscus correction has been utilized in only a few laboratories for net flux calculations in the rat. Higher reabsorptive rates have been found (15, 20) than those in this study. This difference will be discussed below. Recently, it was also suggested that a smaller meniscus correction should be used, since the effective tubular diameter of the saline droplet might be less than its estimate at the oil drop le mvel (22). Such discrepancy might be due to fl attening of the brush border by the oil and /or to the difference in surface tension of the oil and saline droplets. The discrepancy would be more pronounced when intraluminal pressure is low. A new meniscus correction was proposed (22) (Fig. 5). Using it, and taking into account the estimates of the P effect on r at the saline droplet level (22), slightly higher flow rates were found in split drop A and B than with the classical meniscus correction (Table 5). HOWever, the x2 tes ts of the goodness of the exponential fits were not i mproved. On the contrary, the minimum sums (Table 5) of x2 were found when the conventional meniscus correction (15, 18) was used. It indicates that the effective saline droplet volume might have been underestimated when the new meniscus correction (22) was used. DISCUSSION
The role of intraluminal hydrostatic pressure on proximal tubular fluid reabsorption was studied by two modifications of the Gertz’s split-drop method in techniques A and B. Significant pressure differences were found. In split drop A, with a downstream stationary block, intraluminal pressure is high and similar to the stop-flow pressure. In split drop B, with an upstream stationarv block, it is lower and of the
,_
Gertz
)FIG.
Gertz
of saline droplet according (1% 18) , and to Sat0 (22).
2 The pressure asymmetry, which fluid reabsorption might produce both sides of the mobile upstream oil drop, seems to be rapidly compensated by an axial displacement of the mobile oil drop. This is indicated by the similarity between tubular stop flow pressure and the pressure in split drop A, as confirmed in Necturus (12). Any artificial induced change of pressure, above a split drop A, is immediately and completely transmitted to the saline droplet (Table 4, in ref. 12). This is probably due to the small size and the low adhesiveness of the small mobile oil drop. 3 None of the conventional methods of determination of fluid absorption gives values for the flux across the true surface area of the tubular wall. The extent of the membrane, as increased by the macroscopic and microscopic infoldings, is unknown. Js is then an overestimate of the flux across the true epithelial surface, since it is defined on the basis of right circular cylinder.
on
Sato 5. Diagram of estimate of length (9), to Nakajima et al. and Gyiiry
same range as in the surrounding free-flow proximal tubules. These results are similar to those reported for the amphibian kidney (12) but in a larger pressure range, since aortic pressure is one order of magnitude higher in the rat than in Nectwus. In both techniques intraluminal pressure remains stable in time, in spite of progressive reabsorption of the saline droplet. The following mechanisms may account for the different pressure level observed with each technique. With technique A a fluid cylinder is formed, which is limited by the beginning of the proximal tubule and by the upper meniscus of the stationary oil block. At one of its extremities the cylinder is subject to the stop-flow glomerular pressure head, and at the other one to the counterpressure applied to the oil block. Due to the incompressibility of the tubular fluid, all the fluid phases of the cylinder are exposed to the the glomerular stopsame hydrostatic pressure. 2 Therefore, flow pressure is homogenously distributed to the upper segments of the tubule, to the mobile oil drop, and to the saline droplet. With technique B, intraluminal pressure is lower. It might reflect the overall intrarenal pressure, which is of a similar magnitude when measured by inserting a small needle into the kidney (10). In renal proximal tubule, net fluid reabsorption is commonly expressed as a function of tubular length (JL) from free-flow micropuncture or continuous microperfusion data, or as rate constant (h) of the exponential shrinkage of a split drop. J s is then calculated3 from either X or JL and from simultaneous radius measurements using equation 1 or 6. Thus, the validity of the estimates of Js critically depends on (I) the constancy of the radius during the determination, and (2) the accuracy of the radius measurement. Techniques A and B satisfy both of these conditions. The radius values remain unchanged during the whole period of drop shrinkage due to the constancy of pressure and due to the fact that saline was injected more than 1 min after tubular blockage by oil. The I-min delay is important, since the suddenly occluded tubule progressively dilates for about 1 min until a steady size is reached (Fig. 4). The radius determinations are also accurate, since the scatter of the estimate is minimized using the least-squares method (Fig. 2). Because of the tubule radius differs by 3.3 pm the pressure difference, between split drop ,4 and B. This radius change agrees with the 3.6 pm predicted from the compliance characteristics of the proximal tubular wall (Ar/AP = 0.225 pm/mmHg (8)). In both techniques A and B, the radius values are larger than those usually reported in the literature. Smaller values of the luminal membrane radius were found (16-18 r,cm) by
to
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
818
GRANDCHAMP,
TABLE
-
5. Reabsorption
Technique Technique Technique Technique Gertz (9) Technique Technique
A B A B A B
The mean values the x2 test confirmed t Calculated values
characteristics with and without meniscus correction
Meniscus Correction
x, 10-2 s-1
a a None None None b b
2.48 2.98 6.46 6.33 7.07-/3.73 4.27
are given. a = According the significance of the using equation I or 4.
T;,
s
Js,
1~~
cm3 cm-2 s-l
30.6 26.7 12.2 12.8 9.8 20.3 18.8
2.72 2.78 7.07 5.94 5.5 3.31 3.03
to refs. 15 and monoexponential
18. fit
SCHERRER,
--______ MonoExponential Fit*
r, 10-a cm
3.77 3.27 9.76 7.04 5.36t 3.74 2.72
21.9 18.6 21.9 18.6 15.5 17.7 14.1
b = According at the 0.95 level.
to ref. A high
h
FIG. 6.
Predicted effect paths in proximal
of a change tubule.
in tubular
radius
on density
Sum of ~2 in Split Drops
A
-
B 97 123
1,410 1,113
88% 73%
183 177
22. * Percentage percentage validates
TV2
BORNAND
________
_____-
w% 730/, 19% 27%
Theoretical ~- -~ Theoretical ~ Theoretical
1o-2 set-’
AND
~__
JL , lo-’ cm3 cm-1 s-1
v
transport
SCHOLER,
function function function
of split drops in which the use of equations 3-6.
if JL if JS if h
= constant = constant = constant
JS
set
JL
10-5cm3cm-2
set -I 10-7cm3cm-1sec-’
of
several authors working in conditions most probably closer to technique A than to technique B (15, 20). Splitting the oil during the 1st min of tubular dilatation and/or at unsteady and lower P values might account for smaller radius reported. In split drop B the radius is larger than in free flow; this is probably due to the flattening of the brush border by the oil drop. It was a surprise to find low values of X (and long T1, n> in split drops of technique A, since this technique at a first view seerns relatively close to the methodology used in other laboratories. As shown above (Table 5), this difference is explained in part by previous failure to utilize the meniscus correction. However, the values of X with technique A are still at variance with the higher reabsorptive rates reported by two authors who used the meniscus correction (15, 20). It could be related to the larger radii found in the present work. Due to the large ratio of the fluid volume to tubular wall surface, a split drop from technique A might have a smaller reabsorptive rate constant than split drops having a smaller radius. On the other hand, the tubule radii might also have been underestimated in previous work; in particular, if they were measured at the beginning of the tubular dilatation. As demonstrated mathematically, underestimation of the radius value used in the meniscus correction leads to an overestimation 01 X I\?$. An effect of intraluminal hydrostatic pressure on fluid reabsorption micght be expected because of: I) a direct influence on active sodium transport (19); 2) an alteration of the ion permeability of the epithelium (11); or 3) a change in the fraction of the reabsorbate, which is ultrafiltered through the permeable tubular wall (14, 2 1, 26). These effects may be directly due to the change in pressure
proximal
tubule
radius
low4 cm
7. Relationship between radius and reabsorption of split drop A and R. Heavy lines are theoretical functions derived from equations 1 and 4-6, assuming JL as a constant. Thin and dotted lines represent theoretical functions, when Js and X, respectively, are taken as constant. Mean values (zt SE) of split drops A and B are reported. Split drops A (with larger radii than split drops B) are located on right of each plot. FIG.
or indirectly due to the tubular dilatation caused by the pressure increase. However, the difference in pressure in technique A and B did not affect net fluid reabsorption per unit area (Js). The lack of effect of pressure on Js might either be the consequence of opposite effects of the three predictable factors mentioned above, or it might be that the resultant effect of these factors is small enough so that it cannot be detected by the shrinking-drop method. One additional effect of pressure on Js can be predicted, since increased intraluminal pressure in split drops A resulted in a significantly greater tubular radius and apparent surface of tubular wall. The change in radius might per se affect net fluid reabsorption ( Js). As shown in Fig. 6, an increase in tubular radius decreases the density of the epithelial transport paths per apparent surface of tubular wall. In contrast, it should not affect the number of transport paths per unit length of tubule. Therefore, JL should remain constant, and Js should be affected by the change in radius. This efTect on Js can be predicted ma thema tically from the relationship existing between Js and JL (equation I) :
Js Tubular
dilatation
= (1 /&rr) J LcOnstant
should
also influence
(7) X and
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
T1,2, when
INTRALUMINAL JL remains
PRESSURE
constant
(equations X =
T1/2
( I/&)
IN SPLIT
DROPS
819
4 and 5) : J Lconstant
= 0.693m2/
J Lconstant
(8)
(9)
The dark lines in Fig. 7, corresponding to equations 7-9, demonstrate the influence of changes in radius on X, Tl,2 , and Js when Jr, is constant. 4 Accordingly, the significant change in radius between split drop A and B should decrease X by 0.8* 1O-2 s-l and Js by 0.4. 10e5 cm3 crnm2 s-l and increase Tl,z by 5 s. As can be seen from Fig. 7, X, Ja, and J L of technique A were higher than predicted from the curves for constant JL. The deviations, although not statistically significant, are in a direction to suggest an increase in fluid reabsorption. From the deviation in Js, a coefficient of apparent hydraulic conductivity (LsPP) of 1.6 & 1.2 10-T cm3cm--2s-1 (cmHzO)-’ (mean =t SE) may be calculated, a value of the same order of magnitude as that found by other methods (14, 26). different from zero, it Although this Lapp is not significantly
may be used to estimate an upper limit for LBPP of 4.0. lo-7 cm3 cmw2 s-l (cmHzO)-l. We did not attempt to improve the significance of this value by inducing larger changes in intraluminal pressure. The pressure and radius changes would be far from physiological variations, and the L,,, would not be representative of the permeability of the tubular wall. In conclusion, the absence of a net effect of luminal hydrostatic pressure on J s may reflect the interaction of several opposing factors on the determinants of transepithelial fluid reabsorption. Among these, a pressure-induced change in the density of the epithelial transport paths may produce a possible effect. We during for his This National Fonds Received
are indebted the course of critical reading investigation Suisse de Edmee Maus
to Dr. E. L. Boulpaep for his sustained interest this study. We are also grateful to Dr. K. R. Spring of the manuscript. was supported by Grant 3.775.72 from the Fonds la Recherche Scientifique and grants from the and from the Montus Foundation.
for publication
5 August
1974.
REFERENCES 1. BENTZEL, C. J. Proximal tubule structure-function relationships during volume expansion in Necturus. Kidney Intern. 2 : 324-335, 1972. 2. BRENNER, B. M., J. L. TROY, AND T. M. DAUGHARTY. On the mechanism of inhibition in fluid reabsorption by the renal proximal tubule of the volume-expanded rat. J. Clin. Invest. 50: 15961602, 1971. 3. BRENNER, B. M., AND J. L. TROY. Postglomerular vascular protein concentration: evidence for a causal role in governing fluid reabsorption and glomerulotubular balance by the renal proximal tubule. J. Ciin. Invest. 50: 336-349. 1971. 4. BRUNNER, F. P., F. C. RECTOR, JR., AND D. W. SELDIN. Mechanism of glomerulotubular balance. II. Regulation of proximal tubular reabsorption by tubular volume, as studied by stopped-flow microperfusion. J. Ciin. Invest. 45: 603-6 11, 1966. 5. BIJLGER, R. E., W. B. LORENTZ, JR., R. E. COLINDRES, AND C. W. GOTTSCHALK. Morphologic changes in rat renal proximal tubules and their tight junctions with increased intraluminal pressure. Lab. Invest. 30 : 136-144, 1974. 6. BURG, M. B., AND J. ORLOFF. Control of fluid absorption in the renal proximal tubule. J. Clin. Znuest. 47 : 2016-2024, 1968. 7. CORTELL, S., hl. DAVIDMAN, F. J. GENNARI, AND W. B. SCHWARTZ. Catheter size as a determinant of outflow resistance and intrarenal pressure. Am. J. Physiol. 223 : 910-915, 1972. 8. CORTELL, S., F. J. GENNARI, hi. DAVIDMAN, W. H. BOSSERT, AND W. B. SCHWARTZ. A definition of proximal and distal tubular compliance. Practical and theoretical implications. J. Clin. Invest. 52 : 2330-2339, 1973. 9. GERTZ, K. H. Transtubulaere Natriumchloridfluesse und Permeabilitaet fuer Nichtelectrolyte im proximalen und distalen Konvolut der Rattenniere. P_puegers Arch. 276 : 226-256, 1963. 10. GOTTSCHALK, C. W. A comparative study of renal interstitial pressure. Am. J. Physiol. 169 : 180-l 87, 1952. 11. GRANDCHAMP, A., AND E. L. BOULPAEP. Pressure control of sodium reabsorption and intercellular backflux across proximal kidney tubule. J. C/in. lnvcst. 54 : 69-82, 1974. 12. GRANDCHAMP, A., AND E. L. BOULPAEP. Effect of intraluminal pressure on proximal tubular sodium reabsorption. A shrinking drop micropuncture study. Yale J. Biol. A4ed. 45: 275-288, 1972. 13. GRANTHAM, J. J., P. B. QUALIZZA, AND L. W. WELLJNG. Influence 4 In Fig. 7 the thin and dotted lines represent the theoretical functions given by equations I and 4-6, when either X or Js is considered as constant. These functions are mentioned in reference to the work of Brunner et al. (4), who studied the relationship between JL and r. Note that the constancy of X found in ref. 4 (glomerulotubular balance and increased ureteral pressure experiments) most probably was due to the interactions between several transport mechanisms (11, 17), rather than to the unioue effect of a change in tubular geometry.
of serum proteins on net fluid reabsorption of isolated proximal tubules. Kidney Intern. 2 : 66-75, 1972. 14. GREEN, R., E. E. WINDHAGER, AND G. GIEBISCH. Protein oncotic pressure effects on proximal tubular fluid movement in the rat. Am. J. Physiol.
226 : 265-276,
1974.
15. GY~RY, A. 2. Reexamination of the split oil droplet method as applied to kidney tubules. Pf’uegers Arch. 324: 328-343, 197 1. 16. HAYSLETT, J. P. Effect of changes in hydrostatic pressure in peritubular capillaries on the permeability of the proximal tubule. J. Clin. Invest. 52 : 1314-13 19, 1973. 17. LEWY, J. E., AND E. E. WINDHAGER. Peritubular control of proximal tubular fluid reabsorption in the rat kidney. Am. J. Physiol. 214: 943-954, 1968. 18. NAKAJIMA, K., J. R. CLAPP, AND R. R. ROBINSON. Limitations of the shrinking-drop micropuncture technique. Am. J. Physiol. 210: 345-357; 1970. 19. NUTBOURNE, D. M. The effect of small hydrostatic pressure gradients on the rate of active sodium transport across isolated living frog skin membranes.
Role
of luminal
tubular
fluid
hydrostatic reabsorption
pressure
in proximal
in the rat
ALAIN GRANDCHAMP, JEAN RAOUL SCHERRER, DIETER SCHOLER, AND JACQUELINE BORNAND Labora toire de NJphrologie Exphimen tale, Division de N@hrologie, D@artement de A&de&e, et Division d’hformatique Mdicale, Universiti de GenZve, Hb’pital Cantonal, CH 1211 Gentve 4, SzvitJs, andJL-
K/2
SCHOLER,
mm&
27.5 40.0 36.5 33.0 28.0 24.0 32.5 29.5 34.0 30.0 32.0
24.0 15.0 18.0 23.0 21 .o 11 .o 7.5 15.0 8.5 8.5
significant.
average of 2.2 pm within 1 min and did not change afterward. Saline reabsorption characteristics. The data calculated from the shrinkage observation of split drop A and B are shown in Table 4 and Fig. 7. In spite of the significant difference in tubular dilatation, net fluid reabsorption per unit of the tubular wall area (Js> was similar in split drop A and B: 2.72 =t 0.20 and 2.78 =t 0.33 10-S cm3 crnv2 s-l, respectively. The 2 70 difference between these values was below the level of significance. J L, X, and Tl,z varied to a larger extent, but below the 0.05 levei of significance. The changes in A, T1/2 , and JL in split drop A amounted, respectively, to - 17 %, +- ‘15 70, and +- ‘I 5 70 uf the corresponding va’lue:s in @zt & Dp B. In comparison with the data of the literature, reduced reabsorptive rates were found in the present study. The observed half-times of 26.7 and 30.6 s in both techniques are markedly different from the value of 10 s considered to be normal since the original publication of Gertz (9). This discrepancy is almost entirely explained by the previous investigators’ use of equation 2 without meniscus correction,’ as suggested by the recent publications of Nakajima et al. (18) and Gyory (15) (Fig. 5). In the absence of a meniscus
(minutes)
suddenly
occluded
by Fig.
l v/v, 5.
=
L/L,,
in place
of: V/V,
=
(L
+
2r)/(L,
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
+
2r).
See
INTRALUMINAL
PRESSURE
IN
SPLIT
817
DROPS
correction, the rate constant A is overestimated (15, 18). The influence of an absence of meniscus correction in split drop A and B is shown in Table 5. The uncorrected flow parameters of split drop A and B approach the original Gertz’s values. It was also demonstrated that in the absence of meniscus correction, the volume decrease of the saline droplet is not a single exponential function (15, 18), as it should be in theory (9). Lack of an exponential fit invalidates the significance of the rate conslant X and the use of Gertz’s equations 3-6. In this work, the goodness of each exponential fit was tested by means of a x2 test (Table 5). It was found that 94 70 of split drop A and 73 % of split drop B shrunk as a single exponential when calculated with the meniscus correction. This percentage dropped to 19 and 27 Y’o, respectively, in the absence of meniscus correction. At the present time, the meniscus correction has been utilized in only a few laboratories for net flux calculations in the rat. Higher reabsorptive rates have been found (15, 20) than those in this study. This difference will be discussed below. Recently, it was also suggested that a smaller meniscus correction should be used, since the effective tubular diameter of the saline droplet might be less than its estimate at the oil drop le mvel (22). Such discrepancy might be due to fl attening of the brush border by the oil and /or to the difference in surface tension of the oil and saline droplets. The discrepancy would be more pronounced when intraluminal pressure is low. A new meniscus correction was proposed (22) (Fig. 5). Using it, and taking into account the estimates of the P effect on r at the saline droplet level (22), slightly higher flow rates were found in split drop A and B than with the classical meniscus correction (Table 5). HOWever, the x2 tes ts of the goodness of the exponential fits were not i mproved. On the contrary, the minimum sums (Table 5) of x2 were found when the conventional meniscus correction (15, 18) was used. It indicates that the effective saline droplet volume might have been underestimated when the new meniscus correction (22) was used. DISCUSSION
The role of intraluminal hydrostatic pressure on proximal tubular fluid reabsorption was studied by two modifications of the Gertz’s split-drop method in techniques A and B. Significant pressure differences were found. In split drop A, with a downstream stationary block, intraluminal pressure is high and similar to the stop-flow pressure. In split drop B, with an upstream stationarv block, it is lower and of the
,_
Gertz
)FIG.
Gertz
of saline droplet according (1% 18) , and to Sat0 (22).
2 The pressure asymmetry, which fluid reabsorption might produce both sides of the mobile upstream oil drop, seems to be rapidly compensated by an axial displacement of the mobile oil drop. This is indicated by the similarity between tubular stop flow pressure and the pressure in split drop A, as confirmed in Necturus (12). Any artificial induced change of pressure, above a split drop A, is immediately and completely transmitted to the saline droplet (Table 4, in ref. 12). This is probably due to the small size and the low adhesiveness of the small mobile oil drop. 3 None of the conventional methods of determination of fluid absorption gives values for the flux across the true surface area of the tubular wall. The extent of the membrane, as increased by the macroscopic and microscopic infoldings, is unknown. Js is then an overestimate of the flux across the true epithelial surface, since it is defined on the basis of right circular cylinder.
on
Sato 5. Diagram of estimate of length (9), to Nakajima et al. and Gyiiry
same range as in the surrounding free-flow proximal tubules. These results are similar to those reported for the amphibian kidney (12) but in a larger pressure range, since aortic pressure is one order of magnitude higher in the rat than in Nectwus. In both techniques intraluminal pressure remains stable in time, in spite of progressive reabsorption of the saline droplet. The following mechanisms may account for the different pressure level observed with each technique. With technique A a fluid cylinder is formed, which is limited by the beginning of the proximal tubule and by the upper meniscus of the stationary oil block. At one of its extremities the cylinder is subject to the stop-flow glomerular pressure head, and at the other one to the counterpressure applied to the oil block. Due to the incompressibility of the tubular fluid, all the fluid phases of the cylinder are exposed to the the glomerular stopsame hydrostatic pressure. 2 Therefore, flow pressure is homogenously distributed to the upper segments of the tubule, to the mobile oil drop, and to the saline droplet. With technique B, intraluminal pressure is lower. It might reflect the overall intrarenal pressure, which is of a similar magnitude when measured by inserting a small needle into the kidney (10). In renal proximal tubule, net fluid reabsorption is commonly expressed as a function of tubular length (JL) from free-flow micropuncture or continuous microperfusion data, or as rate constant (h) of the exponential shrinkage of a split drop. J s is then calculated3 from either X or JL and from simultaneous radius measurements using equation 1 or 6. Thus, the validity of the estimates of Js critically depends on (I) the constancy of the radius during the determination, and (2) the accuracy of the radius measurement. Techniques A and B satisfy both of these conditions. The radius values remain unchanged during the whole period of drop shrinkage due to the constancy of pressure and due to the fact that saline was injected more than 1 min after tubular blockage by oil. The I-min delay is important, since the suddenly occluded tubule progressively dilates for about 1 min until a steady size is reached (Fig. 4). The radius determinations are also accurate, since the scatter of the estimate is minimized using the least-squares method (Fig. 2). Because of the tubule radius differs by 3.3 pm the pressure difference, between split drop ,4 and B. This radius change agrees with the 3.6 pm predicted from the compliance characteristics of the proximal tubular wall (Ar/AP = 0.225 pm/mmHg (8)). In both techniques A and B, the radius values are larger than those usually reported in the literature. Smaller values of the luminal membrane radius were found (16-18 r,cm) by
to
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
818
GRANDCHAMP,
TABLE
-
5. Reabsorption
Technique Technique Technique Technique Gertz (9) Technique Technique
A B A B A B
The mean values the x2 test confirmed t Calculated values
characteristics with and without meniscus correction
Meniscus Correction
x, 10-2 s-1
a a None None None b b
2.48 2.98 6.46 6.33 7.07-/3.73 4.27
are given. a = According the significance of the using equation I or 4.
T;,
s
Js,
1~~
cm3 cm-2 s-l
30.6 26.7 12.2 12.8 9.8 20.3 18.8
2.72 2.78 7.07 5.94 5.5 3.31 3.03
to refs. 15 and monoexponential
18. fit
SCHERRER,
--______ MonoExponential Fit*
r, 10-a cm
3.77 3.27 9.76 7.04 5.36t 3.74 2.72
21.9 18.6 21.9 18.6 15.5 17.7 14.1
b = According at the 0.95 level.
to ref. A high
h
FIG. 6.
Predicted effect paths in proximal
of a change tubule.
in tubular
radius
on density
Sum of ~2 in Split Drops
A
-
B 97 123
1,410 1,113
88% 73%
183 177
22. * Percentage percentage validates
TV2
BORNAND
________
_____-
w% 730/, 19% 27%
Theoretical ~- -~ Theoretical ~ Theoretical
1o-2 set-’
AND
~__
JL , lo-’ cm3 cm-1 s-1
v
transport
SCHOLER,
function function function
of split drops in which the use of equations 3-6.
if JL if JS if h
= constant = constant = constant
JS
set
JL
10-5cm3cm-2
set -I 10-7cm3cm-1sec-’
of
several authors working in conditions most probably closer to technique A than to technique B (15, 20). Splitting the oil during the 1st min of tubular dilatation and/or at unsteady and lower P values might account for smaller radius reported. In split drop B the radius is larger than in free flow; this is probably due to the flattening of the brush border by the oil drop. It was a surprise to find low values of X (and long T1, n> in split drops of technique A, since this technique at a first view seerns relatively close to the methodology used in other laboratories. As shown above (Table 5), this difference is explained in part by previous failure to utilize the meniscus correction. However, the values of X with technique A are still at variance with the higher reabsorptive rates reported by two authors who used the meniscus correction (15, 20). It could be related to the larger radii found in the present work. Due to the large ratio of the fluid volume to tubular wall surface, a split drop from technique A might have a smaller reabsorptive rate constant than split drops having a smaller radius. On the other hand, the tubule radii might also have been underestimated in previous work; in particular, if they were measured at the beginning of the tubular dilatation. As demonstrated mathematically, underestimation of the radius value used in the meniscus correction leads to an overestimation 01 X I\?$. An effect of intraluminal hydrostatic pressure on fluid reabsorption micght be expected because of: I) a direct influence on active sodium transport (19); 2) an alteration of the ion permeability of the epithelium (11); or 3) a change in the fraction of the reabsorbate, which is ultrafiltered through the permeable tubular wall (14, 2 1, 26). These effects may be directly due to the change in pressure
proximal
tubule
radius
low4 cm
7. Relationship between radius and reabsorption of split drop A and R. Heavy lines are theoretical functions derived from equations 1 and 4-6, assuming JL as a constant. Thin and dotted lines represent theoretical functions, when Js and X, respectively, are taken as constant. Mean values (zt SE) of split drops A and B are reported. Split drops A (with larger radii than split drops B) are located on right of each plot. FIG.
or indirectly due to the tubular dilatation caused by the pressure increase. However, the difference in pressure in technique A and B did not affect net fluid reabsorption per unit area (Js). The lack of effect of pressure on Js might either be the consequence of opposite effects of the three predictable factors mentioned above, or it might be that the resultant effect of these factors is small enough so that it cannot be detected by the shrinking-drop method. One additional effect of pressure on Js can be predicted, since increased intraluminal pressure in split drops A resulted in a significantly greater tubular radius and apparent surface of tubular wall. The change in radius might per se affect net fluid reabsorption ( Js). As shown in Fig. 6, an increase in tubular radius decreases the density of the epithelial transport paths per apparent surface of tubular wall. In contrast, it should not affect the number of transport paths per unit length of tubule. Therefore, JL should remain constant, and Js should be affected by the change in radius. This efTect on Js can be predicted ma thema tically from the relationship existing between Js and JL (equation I) :
Js Tubular
dilatation
= (1 /&rr) J LcOnstant
should
also influence
(7) X and
Downloaded from www.physiology.org/journal/ajplegacy at Washington Univ (128.252.067.066) on February 14, 2019.
T1,2, when
INTRALUMINAL JL remains
PRESSURE
constant
(equations X =
T1/2
( I/&)
IN SPLIT
DROPS
819
4 and 5) : J Lconstant
= 0.693m2/
J Lconstant
(8)
(9)
The dark lines in Fig. 7, corresponding to equations 7-9, demonstrate the influence of changes in radius on X, Tl,2 , and Js when Jr, is constant. 4 Accordingly, the significant change in radius between split drop A and B should decrease X by 0.8* 1O-2 s-l and Js by 0.4. 10e5 cm3 crnm2 s-l and increase Tl,z by 5 s. As can be seen from Fig. 7, X, Ja, and J L of technique A were higher than predicted from the curves for constant JL. The deviations, although not statistically significant, are in a direction to suggest an increase in fluid reabsorption. From the deviation in Js, a coefficient of apparent hydraulic conductivity (LsPP) of 1.6 & 1.2 10-T cm3cm--2s-1 (cmHzO)-’ (mean =t SE) may be calculated, a value of the same order of magnitude as that found by other methods (14, 26). different from zero, it Although this Lapp is not significantly
may be used to estimate an upper limit for LBPP of 4.0. lo-7 cm3 cmw2 s-l (cmHzO)-l. We did not attempt to improve the significance of this value by inducing larger changes in intraluminal pressure. The pressure and radius changes would be far from physiological variations, and the L,,, would not be representative of the permeability of the tubular wall. In conclusion, the absence of a net effect of luminal hydrostatic pressure on J s may reflect the interaction of several opposing factors on the determinants of transepithelial fluid reabsorption. Among these, a pressure-induced change in the density of the epithelial transport paths may produce a possible effect. We during for his This National Fonds Received
are indebted the course of critical reading investigation Suisse de Edmee Maus
to Dr. E. L. Boulpaep for his sustained interest this study. We are also grateful to Dr. K. R. Spring of the manuscript. was supported by Grant 3.775.72 from the Fonds la Recherche Scientifique and grants from the and from the Montus Foundation.
for publication
5 August
1974.
REFERENCES 1. BENTZEL, C. J. Proximal tubule structure-function relationships during volume expansion in Necturus. Kidney Intern. 2 : 324-335, 1972. 2. BRENNER, B. M., J. L. TROY, AND T. M. DAUGHARTY. On the mechanism of inhibition in fluid reabsorption by the renal proximal tubule of the volume-expanded rat. J. Clin. Invest. 50: 15961602, 1971. 3. BRENNER, B. M., AND J. L. TROY. Postglomerular vascular protein concentration: evidence for a causal role in governing fluid reabsorption and glomerulotubular balance by the renal proximal tubule. J. Ciin. Invest. 50: 336-349. 1971. 4. BRUNNER, F. P., F. C. RECTOR, JR., AND D. W. SELDIN. Mechanism of glomerulotubular balance. II. Regulation of proximal tubular reabsorption by tubular volume, as studied by stopped-flow microperfusion. J. Ciin. Invest. 45: 603-6 11, 1966. 5. BIJLGER, R. E., W. B. LORENTZ, JR., R. E. COLINDRES, AND C. W. GOTTSCHALK. Morphologic changes in rat renal proximal tubules and their tight junctions with increased intraluminal pressure. Lab. Invest. 30 : 136-144, 1974. 6. BURG, M. B., AND J. ORLOFF. Control of fluid absorption in the renal proximal tubule. J. Clin. Znuest. 47 : 2016-2024, 1968. 7. CORTELL, S., hl. DAVIDMAN, F. J. GENNARI, AND W. B. SCHWARTZ. Catheter size as a determinant of outflow resistance and intrarenal pressure. Am. J. Physiol. 223 : 910-915, 1972. 8. CORTELL, S., F. J. GENNARI, hi. DAVIDMAN, W. H. BOSSERT, AND W. B. SCHWARTZ. A definition of proximal and distal tubular compliance. Practical and theoretical implications. J. Clin. Invest. 52 : 2330-2339, 1973. 9. GERTZ, K. H. Transtubulaere Natriumchloridfluesse und Permeabilitaet fuer Nichtelectrolyte im proximalen und distalen Konvolut der Rattenniere. P_puegers Arch. 276 : 226-256, 1963. 10. GOTTSCHALK, C. W. A comparative study of renal interstitial pressure. Am. J. Physiol. 169 : 180-l 87, 1952. 11. GRANDCHAMP, A., AND E. L. BOULPAEP. Pressure control of sodium reabsorption and intercellular backflux across proximal kidney tubule. J. C/in. lnvcst. 54 : 69-82, 1974. 12. GRANDCHAMP, A., AND E. L. BOULPAEP. Effect of intraluminal pressure on proximal tubular sodium reabsorption. A shrinking drop micropuncture study. Yale J. Biol. A4ed. 45: 275-288, 1972. 13. GRANTHAM, J. J., P. B. QUALIZZA, AND L. W. WELLJNG. Influence 4 In Fig. 7 the thin and dotted lines represent the theoretical functions given by equations I and 4-6, when either X or Js is considered as constant. These functions are mentioned in reference to the work of Brunner et al. (4), who studied the relationship between JL and r. Note that the constancy of X found in ref. 4 (glomerulotubular balance and increased ureteral pressure experiments) most probably was due to the interactions between several transport mechanisms (11, 17), rather than to the unioue effect of a change in tubular geometry.
of serum proteins on net fluid reabsorption of isolated proximal tubules. Kidney Intern. 2 : 66-75, 1972. 14. GREEN, R., E. E. WINDHAGER, AND G. GIEBISCH. Protein oncotic pressure effects on proximal tubular fluid movement in the rat. Am. J. Physiol.
226 : 265-276,
1974.
15. GY~RY, A. 2. Reexamination of the split oil droplet method as applied to kidney tubules. Pf’uegers Arch. 324: 328-343, 197 1. 16. HAYSLETT, J. P. Effect of changes in hydrostatic pressure in peritubular capillaries on the permeability of the proximal tubule. J. Clin. Invest. 52 : 1314-13 19, 1973. 17. LEWY, J. E., AND E. E. WINDHAGER. Peritubular control of proximal tubular fluid reabsorption in the rat kidney. Am. J. Physiol. 214: 943-954, 1968. 18. NAKAJIMA, K., J. R. CLAPP, AND R. R. ROBINSON. Limitations of the shrinking-drop micropuncture technique. Am. J. Physiol. 210: 345-357; 1970. 19. NUTBOURNE, D. M. The effect of small hydrostatic pressure gradients on the rate of active sodium transport across isolated living frog skin membranes.
