621

J. Physiol (1978). 279, pp. 621-640 With 2 text-figures Printed in Great Britain

ALBUMIN PERMEABILITY OF THE PERITUBULAR CAPILLARIES IN RAT RENAL CORTEX

BY D. R. BELL*, G. G. PINTER AND P. D. WILSON From the Departments of Physiology and Social and Preventive Medicine, University of Maryland School of Medicine, Baltimore, Maryland 21201, U.S.A.

(Received 28 June 1977) SUMMARY

1. Two series of experiments were carried out to determine the permeability of the renal cortical peritubular capillaries to albumin under control conditions in the concentrating kidney and after an infusion of hypo-osmotic fluid amounting to 6% body weight. 2. In the first series of these experiments the turnover of the interstitial albumin pool of the renal cortex was studied. Specifically, the mean transit time of albumin molecules from arterial plasma to renal lymph was measured in nine rats of each group. Mean values of 39-0 + 2-8 and 30-6 + 2-2 (s.E. of mean) min were found for the control and infused groups, respectively. 3. In the second series of experiments the interstitial distribution volume of plasma albumin in renal cortex was determined in twenty-three control and twenty-two infused rats. Mean values of the extravascular distribution volumes were 1-66 + 0-21 and 1-37 + 0-18 (s.E. of mean) /d./100 mg tissue, respectively. 4. The unidirectional clearance of albumin from the capillary to the interstitium in the control and infused groups, respectively, was calculated to be 7-1 + 1-0 and 7-5 + 0-9 (s.E. of mean) ml. sec-1 10-4 in 100 g cortical tissue. 5. For the reabsorbing surface of the peritubular capillaries in the renal cortex, a lower bound was calculated for A-, the reflexion coefficient of albumin. The reflexion coefficient was found to be higher than 0-998 under both experimental conditions. INTRODUCTION

The balance of hydrostatic and colloid osmotic pressures, as conceived by Starling (1896), has remained over the years the most important consideration in quantitative descriptions of fluid movement across the capillary wall. This same balance is thought to govern the entry of tubular reabsorbate into the peritubular capillary lumen in the kidney. As albumin is the most abundant colloidal solute in blood plasma with a relatively small molecular weight, it should play a significant role in determining the colloid osmotic effect across the capillary wall. In this context it is of importance to consider the permeability of the capillary wall to albumin. * Present address: Department of Human Physiology, University of California, Davis, California 95616, U.S.A. Requests for reprints: Dr G. G. Pinter, Department of Physiology, SM, UMAB, 660 W. Redwood St, Baltimore, Md. 21201, U.S.A.

D. R. BELL AND OTHERS 622 In principle, the permability of capillary wall to albumin should exert an influence in two separate but related ways: First, the rate of entry of albumin into the interstitium from the capillaries, together with the rate of drainage of albumin from the interstitium, should determined the steady-state concentration in the interstitium. Secondly, the reflexion coefficient to albumin of the capillary wall should modulate the effective colloid osmotic pressure which is sustained by the capillary membrane. In several regions of the body the permeability of the capillary wall to macromolecules has been extensively studied (cf. chapter 8 in Crone & Lassen, 1970). A quantitative measurement was devised by Renkin (1964) who, for the general case, assumed that convective movement of macromolecules across the capillary membrane is insignificant. For measuring the permeability times surface area (PS) product, Renkin derived the following formula: PS = LR/(1 -R), (1) where L is volume flow rate of lymph from unit wt. of tissue, and R is the ratio of the concentration of the macromolecule in lymph to that in plasma. Thus, PS is equivalent to clearance and has the dimension of volume flow. The same formula was derived also by Johnson (1966), and it was used by Garlick & Renkin (1970) for measuring the permeability to albumin of the capillaries in the hind limb of dogs under varying conditions. In the renal cortical interstitium a relative large volume of tubular reabsorbate flows from tubules into capillaries, and this convective flow may affect the movement of macromolecules. For this reason, the effect of convective transport in the kidney has been taken into consideration by Dean, Ueki & Brenner (1976) in a recent study of capillary permeability to albumin and to dextran fractions of varying molecular wt. The result of their calculation of the reflexion coefficient was in agreement with that of Pinter, Atkins, Bell & Stork (1975). Both studies led to the conclusion that the reflexion coefficient to albumin is essentially unity. In developing the above formulations of both Renkin (1964) and Dean et al. (1976), it was assumed that the concentration of macromolecules in the interstitium is equal to that in the lymph. Although Dean et al. cited evidence which supports this assumption, in some other instances the assumption was not confirmed. Thus, Killskog & Wolgast (1973) observed that the albumin concentration of the subcapsular fluid and lymph in the rat kidneys were equal in the concentrating kidney, but differed after saline infusion. Casley-Smith & Sims (1976) reported that, in the gut and hind limb, protein concentrations were different in interstitial fluid and small lymphatic vessels. Therefore, it appeared desirable to investigate the permeability of the peritubular capillaries to albumin without any specific assumption regarding either convective transport or equality between interstitial and lymph concentrations of albumin. In this report we describe such a study. The experiments were carried out on two groups of rats: one under control conditions and another after an i.v. infusion of hypotonic fluid. The latter series of experiments were prompted by an earlier observation of faster than normal equilibration between albumin specific activities in plasma and renal lymph following a hypotonic fluid load in dogs (Pinter, O'Morchoe & Atkins, 1972).

ALBUMIN AND PERITUBULAR CAPILLARIES

623

METHODS

Principle In this study the well established central volume theorem (Stephenson, 1948; Meier & Zierler, 1954; Perl, Lassen & Effros, 1975) was used. With reference to flow through a system in steady state the theorem states that the product of the mean transit time and the flow rate is equal to the volume of the system. In applying this relationship to the interstitial albumin pool in the renal cortex, we write: (2) T.* O = et. Here, the average of all residence times in the interstitium is denoted by r (min); sb(mg/min) stands for the flow of albumin through the interstitial pool and g (mg/t00 mg tissue) is the amount of albumin in the interstitial pool in 100 mg tissue. No particular structure of the renal interstitium, either simple or complex, is implied by the use of eqn. (2). The entire albumin pool is assumed to be in steady state. It is assumed further that albumin enters the renal cortical interstitium exclusively from the capillary plasma. Entry of albumin by tubular reabsorption is neglected for two reasons. First, in glomerular filtrate the concentration of albumin has been found to be less than 1 mg/t00 ml. in normal young rats (Oken & Flamenbaum, 1971). Secondly, as reviewed recently by Maunsbach (1976), there is strong experimental evidence that peritubular release of albumin which has been taken up by tubular cells does not occur. The purpose of the study is to calculate qS/cp, the clearance of albumin through the capillary wall, where cp refers to the arterial plasma concentration of albumin. The quantity 0/cp is equivalent dimensionally to the PS product, as both are measured in units of volume flow. However, whereas Renkin's (1964) PS product (eqn. (1)) is defined as the net clearance of albumin from capillary to interstitium, 0/cp is a measure of the unidirectional clearance of albumin from the capillary to the interstitium. Henceforth, we refer to this unidirectional clearance as ?1r. From (2) we obtain 0 (2A) p cp T cp in formula (2A) are not directly measurable.

Some of the quantities However, we measure a distribution volume, Vi, which corresponds to 4u/cp, and a mean transit time, 4, which corresponds to r. The distribution volume of the interstitial albumin, Vi, is defined as the difference between the total distribution volume, V, and the intravascular distribution volume, V1, of tracer albumin in renal cortex: Vi = V-Vv (3) and

VI.cp = /t.

(4) Instead of r, the average residence time of albumin molecules in the interstitial pool, we measure 4, the mean transit time of albumin molecules from plasma to lymph. It is apparent that both V1 and I are defined operationally, whereas the corresponding quantities, lt/cp and T, are components of the model. To keep in view the

D. R. BELL AND OTHERS potential differences between these respective quantities, experimental measurement which we calculate as: 624

Vt

=

I

we use

#' to denote

/t.

our

(5)

In the discussion we clarify the conditions under which we consider Y' ib. The experimental study was divided in two parts, which were carried out a' separate series of experiments: A, measurements of the mean transit time of albumin =

from

arterial

plasma

to

renal

lymph;

and

B,

measurements

of the

interstitial

dis-

tribition volume of albumin. (A)

Measurement of the mean transit time of albumin from plasma to lymph

These experiments were carried out on eighteen male Sprague Dawley rats of 8-11 weeks of age, weighing 250-330 g. The animals were anaesthetized with sodium thiopentone 50 mg/kg

I.P. Body temperature of the rats was maintained at 38 0C

with

a

servo-controlled heating pad.

The trachea was intubated and two polyethylene catheters were inserted into the left femoral vein, one for infusion of fluids and the other for isotopic tracer injections. A heparinized cannula was inserted into the left femoral artery. The rat was laid on its right side and the left kidney

was exposed by an incision of the abdominal muscles parallel with the last rib. The kidney was gently freed from peritoneal fasciae and eased into a special holder frequently used in micropuncture studies, where it was covered and held in a fixed position with cotton cushions soaked in mineral oil. The hilum was observed under a stereoscopic operating microscope and lymphatic vessels were located near the renal artery. One of the lymphatics was tied off and a polyethylene cannula of approximately 80-100 usm inner diameter and 5 cm in length was inserted and tied in place with no. silk thread. Cannulae were prepared from no. 205 PE tubing by heating and pulling to the desired size. In constrast to a recent article by Hargens, Tucker & Blantz(1977), in our experience both the extrarenal contribution to renal lymph and the tying off of tributary lymphatic vessels could be avoided by cannulating a renal lymphatic vessel just near enough to the renal hilum. Unless clear lymph flowed immediately from the cannula, the experiment was not pursued further. The average rate of lymph flow was somewhat over ul. /min and no correction was made for time delay of lymph in the collecting cannula the volume of which was approximately #l. Lymph was collected in heparinized microhaematocrit tubes of uniform and known cross section. The volume of the collected lymph was determined by measuring the length of the fluid column in the tube. After completion of the lymph collection, both ends of the tubes were 8

1

0O2-0-3

flame sealed. Nine of the rats received no fluid infusion and served as controls. Nine rats were infused I.v. with a solution containing 2-5 % glucose and 0-25 % NaCl; the infusion volume was equivalent to 6% of body weight and was administered in 15 min. An additional sustaining infusion of the same solution was maintained at an average rate of twice the urine flow from the exposed left kidney. The experiment was started 45min or later after the initial infusion. Blood pressure was measured by means of a Grass strain gauge transducer and osmolality in plasma and urine with a Wescor osmometer. Microhaematocrit tubes were used in measuring the arterial haematocrit and plasma volume was calculated by using the 5min arterial plasma concentration of tracer albumin. Two human albumin tracer preparations, one tagged with 1211 and the other with 1811, were used in these experiments. Both tracer preparations were produced by the Mallincrodt Co., St Louis, Mo. In a separate study it was shown that the pair of albumin tracers obtained from this supplier gave nearly identical volumes of distribution in rat kidneys (Bell, Wilson, Rasmussen & Pinter, 1977); moreover, the volume of distribution so obtained was not different from that measured with homologous rat albumin, as shown by Rasmussen & Iversen (1976). Before use the tracer preparations were dialysed overnight against normal saline at 4 00. This reduced the inorganic radioactivity below 1 % in both preparations as estimated by precipitation with a 10% trichloroacetic acid solution. To verify the equivalence of the two preparations, a mixture of each pair of tracers was injected into a rat and the ratio of activity in plasma followed over a period of 2 hr. Within this time, approximately fifteen plasma samples were taken, a few m

ALBUMIN AND PERITUBULAR CAPILLARIES

625

microlitres each. The pair of tracers were used in further experiments only if the ratio of activities in the plasma remained within preset limits as verified by statistical analysis. The frequency function of transit times and the mean transit time of albumin molecules from plasma to renal lymph were derived from the specific activity versus time measurements of albumin in arterial plasma and renal lymph. Accurate resolution of the specific activity versus time function required frequent collection of samples of both plasma and lymph which, in turn, put a limitation on the volume of each sample. The determination of specific activity by measuring albumin concentrations in small samples in our hands was highly variable. For this reason, we adopted a procedure that involved the use of two equivalent tracers of albumin. A dose of approximately 50 #sCi 125I albumin was injected i.v. early during the surgical preparation. A waiting period followed which allowed a distribution of this tracer to reach a near steady state in plasma and renal lymph. The experimental measurements were carried out 2-5-3 h later by injecting 131I-tagged albumin. Blood samples were collected frequently at the beginning of the experiment and every 10 min past the 40 min mark, and lymph samples were taken every 5 min in the first hour and every 10 min thereafter. The experiment lasted 90 min, during which arterial blood pressure and urine and lymph flows were nearly steady. Instead of specific activity measured directly as '3'I activity per mass of albumin, the ratio of 131I to 1251 protein bound activities was determined. This substitution was based on the assumption that 125I albumin reached a steady level during the waiting period, and its specific activity was uniform and constant in both plasma and renal lymph during the experimental measurenments of the passage of 131I albumin from plasma to lymph. The relationship of the activity ratio to specific activity is expressed by the following formulae: in sample 125I albumin specific activity = k (constant) = cpm(125) albumin in sample'

131I albumin specific activity

f(t)

cpm(131) in sample albumin in sample As both activities are measured in the same sample, the denominators are equal. Therefore =

=

cpm(131) f(t) cpm(125) k Thus, the ratio 1311I to 125I activities equals the specific activity of 131I albumin divided by a scaling factor which is constant in each experiment. In the subsequent treatments of the data, in each experiment the constant appears only as a common scaling factor for plasma and lymph and is eliminated. We have also explored the case when the specific activity of 125I is not a constant, but decays exponentially with time. This case is discussed in Appendix I. Radioactivity was measured in a Packard well-type gamma scintillation counter equipped with a three-channel energy discriminator and an automatic sample changer. The punched paper tape output of the counter was fed into a Wang 2200 minicomputer by means of an electronic tape reader. Calculations included the averaging of two counts for each sample, correction for interference of 1311 emissions with measurement of 125I, and for decay of 131I during counting which lasted for about 24 h. More than 80,000 counts were accumulated for each isotope in each sample. A single exponential function of the form P(t) = Pl + P2e-at was fitted to the plasma specific activity versus time curve, and a two component exponential function of the form L(t) = L1 + L2-L1efi8t-L2e-fut to the lymph specific activity vs. time curve in each experiment. Non-linear curve fitting was carried out by the recursive algorithm described in Walker & Duncan (1967) as applied to single and multi-exponential regression functions. The number of exponential terms was chosen because an increase in the number of terms (when it was possible to achieve convergence) did not improve the fit in any experiment. In a few instances a single exponential function to the lymph specific activity v8. time curve represented the data equally well com-

pared to the double exponential fit. However, for the sake of uniformity, the double exponential format for the lymph was retained in all experiments. The Laplace transforms (McCallum & Brown, 1965) for both the P(t) and the L(t) exponential functions were obtained. The impulse response, denoted as h(t), which is the frequency function of transit times, was obtained by inverting the transfer function L(s)/P(s). The first moment of h(t) provided the estimate for the mean transit time.

626

D. R. BELL AND OTHERS

We did not explore the possible significance of the number of exponential components in the functions P(t) and L(t) in regard to the structural or functional pattern of the respective albumin pools of plasma, renal lymph and interstitium. These functions were used only to describe the experimental findings so that they may be extrapolated beyond the time of data collection, in order to allow computation of the integral

ft h(t)dt = 1. (B) Measurement of the extravawcular ditribution volume of albumin Two approaches have been generally employed in partitioning the total albumin pool of the kidney into intravascular and extravascular components. One of these is the use of an intravascular tracer together with albumin (Pinter, 1967; Rasmussen, 1975). The other is allowing only a brief mixing time (about 1 min) for the tracer albumin, in order to confine the distribution volume to intravascular plasma (Gairtner, Vogel & Ulbrich, 1968; Rasmussen, 1974, 1975). Both approaches have potential difficulties. On the one hand, large molecules and particles suitable as strictly intravascular markers may be phagocytized or otherwise incorporated into cells. On the other hand, a brief mixing period may not allow sufficient time for the equilibration of tracer concentrations between capillary plasma and plasma in large blood vessels. In the present study we used a modification of the brief mixing time method. Two equivalent tracers of plasma albumin were administered to rats. One of these, 126I-labelled albumin, was permitted to equilibrate over a 2-5-3 hr period, and its volume of distribution was taken to be indicative of the total albumin pool in the kidney. The other tracer, 13II-labelled albumin, was allowed to equilibrate for a period of 3-4 min, long enough to allow homogeneous mixing of the tracer with intravascular plasma. However, even though the mixing time of the second tracer was brief, a finite quantity of the second tracer had already crossed the capillary wall into the interstitium, as evidenced by the presence of 131I albumin in lymph. A correction was made for that fraction of the tracer which crossed into the interstitium. The formula for determining the magnitude of T' is a modification of eqn. (3)

1--(*I

(3a)

P(*)

Here, the symbol V(*) stands for the distribution space (i.e. radioactivity in unit wt of tissue divided by radioactivity in unit volume of plasma) with the 3-4 min brief mixing time; I(*) and P(*) are specific activities in the interstitium and plasma of that tracer. Derivation of formula (3a) is shown in Appendix II. On the right hand side of eqn. (3 a), I(*) is the only variable that cannot be measured directly. To use eqn. (3a) we assumed that the specific activity of the interstitial albumin is the same as that of albumin in lymph. Note that here no assumption is made regarding the relationship of concentrations of albumin in the interstitium and lymph. These experiments were carried out on forty-five Sprague-Dawley rats divided into two groups: twenty-two animals received the hypotonic infusion as already described. The rest of the rats served as controls. The age and weight of the rats, anaesthesia, and handling of the tracers were the same as described for the experiments in which the transit time of albumin was measured. Surgically, however, these animals were treated differently as the abdomen was not opened until a few minutes after the 131I albumin was injected. At the accurately timed moment of tying off the hila of both kidneys, a blood sample was also withdrawn from the aorta. The kidneys were immediately frozen in liquid nitrogen and kept frozen at -20 'C. While still frozen, duplicate sections weighing 150-300 mg were cut from each kidney, weighed and counted as already described. The time allowed for mixing of the 131I tracer for the control rats ranged from 2-2 to 4-3 min with a mean value of 3-4 min. For the experimental rats it ranged from 2-6 to 4-4 min with a mean of 3.3 min. Use of the tracers was not randomized; the 125I tracer was always administered first, as the inorganic activity of the 125I preparation was slightly but consistently lower than that of the 131I. In this manner the chance for accumulation of inorganic iodine in renal tissue was reduced. Counting of radioactivity was carried out as in the experiments of series A.

ALBUMIN AND PERITUBULAR CAPILLARIES

627

RESULTS

Table 1 shows the physiological variables measured and the data summary of these variables for the eighteen rats that were used for determining the mean transit time of albumin from plasma to lymph (series A) and for the forty-five rats in which distribution volumes were measured (series B). The rats noted as 'expanded' were given a hypotonic infusion, amounting to 6% body wt. The rest (control) received no infusion. While, in series A, there was no difference in mean arterial blood pressure between the expanded and control groups, the other measured variables showed the effects of the infusion. The average osmolality of urine in the infused group remained above the level of iso-osmolality with plasma. In a few of the infused rats the urine osmolality was less than 290 m-osmole/kg, but these rats did not appear to be set apart from the rest of the infused group in any other respect and all infused animals were handled statistically as a homogenous group. TABLE 1. Physiological variables measured in the control and fluid expanded rats in both series of experiments. Series A: nine rats in each group; in these animals the mean transit time, t, of albumin from plasma to renal lymph was measured. Series B: the number of measurements is indicated as n under each entry in the Table. In these rats the interstitial distribution volume of albumin, 17, was measured. The values shown are means + s.E. of mean. Comparison of group means was made by the t-test. The degree of statistical significance is indicated by the superscripts in this and subsequent Tables as follows: a: P < 0.05, b: P < 0.02, c: P < 0.01, d: P < 0*001 A B

Mean arterial B.P. (mmHg) Haematocrit (%) Plasma vol. (ml./100 g body wt.)"

Plasma osmolality (m-osmole/kg)d Urine osmolality (m-osmole/kg)d

Urine flow (ul./min)d

Control Expanded Control Expanded 112 + 2 113±+ 2 49-6 + 0'8 47.5±+ 0 -6 3-56 + 0-20 4.25 + 0.11 3-96+ 0 09 4 09+ 009 (n= 17) (n= 16) 306 ± 2 291 + 1 3-06+ 4 288+ 2 (n= 23) (n= 22) 1765+ 221 428 + 59 1293+ 126 362+ 52 (n= 23) (n= 22) 1 55+ 0-15 17.8±+ 3 -8

Table 2 gives t and the parameters in P(t) = P1 + P2e-""t, L(t) = L1(1 -e-flit) + L2(1efl2t) for each rat. The average mean transit time of each group is also shown in Summary Table 4. It is apparent that in the infused animals the mean transit time was shorter; by using the t test the difference was seen to be statistically significant at the P < 0.01 level. Table 3 shows the rates of lymph flow, albumin flow (expressed in terms of plasma clearance) and lymph to plasma albumin concentration ratio as measured in series A experiments. In comparing the control to the infused group, the statistical evaluation was done by using the Mann-Whitney U test, as the sample distributions did not appear to be normal. The infusion brought about a statistically significant

628 D. R. BELL AND OTHERS increase in lymph flow, but other variables did not show a significant change. One animal in the expanded group had an exceptionally high lymph flow rate. When this rat was excluded and the mean value for the remaining eight animals was calculated, the mean flow of lymph was 2-45 /sl./min. The average flow of albumin for these TABLE 2. Parameters of exponential functions fitted to plasma and lymph specific activities and mean transit time, !, of albumin between plasma and lymph. Dimensions of the P's and L's are specific activity. Those of a and the ft's are min-. The functions for the plasma were of the form: P(t) = P + P2e at, and for the lymph: L(t) = LI + L2-Lle-ii -Lse~st. The mean transit time, 1, was calculated by Laplace transformation as described in the text

Expt. no.

3/28 10/24 10/26 11/04

11/11

01/28 02/11 03/21 03/26

05/05

09/19

10/26 11/14

11/21 03/06

03/04 03/25 05/20

L1 P1 P2 -MI (X 102) (X 102) (X 102) (X 102) Control 31-21 2-284 6*059 1-436 72-28 24-35 14*40 17-36 45*94 5-589 4'446 42-27 60 39 5-801 2*459 14-16 95*53 15-87 2.621 32-79 53-95 4-835 4 130 18-80 61-57 9 380 4.734 22-31 123'04 19-47 1'754 72-20 119-04 16X98 2X107 10-93 Expanded 168-84 55 08 4-148 17-11 82-81 20 08 7*038 23 65 245'4 36-49 5-764 78-26 86*26 11'64 4.377 28*30 97*67 13*35 1-667 44-39 112-35 27-32 2-340 20-05 3 026 96-58 209-39 31-16 5-823 54 50 169X59 16-59 83-89 15*40 3-952 71*41

-f1 L2 -Alu (X 102) (X 102) (X 102)

29*28 75*02

t

1.975 49.69

34-76 6-599 2.001 40*72 3-584 3*274 2.270 34-34 44 09 24X78 2'875 31*88 55.94 9.794 3.221 30 08 31-09 15-32 1*950 36-59 36-58 9.193 2.654 30 74 33-13 2-764 1-719 52-12 10-46 19-19 2*387 45 20

154-79

6*466 3.778 2-289 14*70 5*280 12-64 3*266 11*24 1.712 14-54 3*900 12-11 2.091 18-74 2.216 4 400 1.829

37*39 14-05 127-68

39*08 50-29 22-74 101-86 108 54 3.952

32-24 32-97

16*91 24 05

39-91 32-37

33*48 33650 29 05

TABLE 3. Measurements on lymph collected from a renal hilar lymphatic vessel in nine control and nine expanded rats, in which the mean transit times were measured. The values shown are means + s.E. of mean. In parentheses the ranges are also indicated. Comparison of group means was done by using the Mann-Whitney U test as populations did not appear to be normally distributed Control Expanded flowb ± 1-47 0-20 Lymph 2-66 + 0 47 (0.64- 2 54) (1.49- 5 64) (1l./min) Albumin flow 0*404+ 0l038 0 692 ± 0*196 (0-202- 0.582) (0'296- 2 120) (/d./min) L/P ratio 0-325 + 0-047 0-251 ± 0-036

(0.181 -0 654)

(0 155-0*481)

was 0-389 + 0.098 (S.E. of mean) ,ll. plasma/min. The mean transit time and lymph to plasma albumin concentration ratio measured in the outlying animal were near to the respective means for the rest of the group. The statistical evaluation led to the same conclusion regardless of whether the outlying individual rat was included or not.

eight animals

629 ALBUMIN AND PERITUBULAR CAPILLARIES The distribution volumes of interstitial albumin in renal cortex are shown in the summary Table 4. The means of the quasi steady state total distribution volumes, V, were 12-6 + 0-3 S.E. of mean, and 12-9 + 0-8 S.E. of mean 4tl./100 mg tissue, respectively, in the control and volume expanded groups. These means were not different statistically. The denominator of eq. (3a), i.e. the correction factor, was 0-96 at 2 min and 0-90 at 4 min. The last line of Table 4 shows the values of ii' calculated as the ratio of V1/t. The standard errors of the respective means for V"' were calculated by the method given in Kendall & Stewart (1963). It is apparent that the unidirectional clearance of albumin in both conditions remained steady in these experiments. TABix 4. Summary table. The means and s.z. of mean are shown for the measurements of mean transit time of albumin from plasma to renal lymph, t, and extravascular distribution volume of albumin in the renal cortex, V. The unidirectional clearance of albumin from peritubular capillary to interstitium, O', was calculated as Vil/ and the variance of V' was derived by assuming that measurements of t and Y4 were independent. Control Expanded Z (min)a 39-04+2-77 30-61±2-21 (n= 9) (n= 9) V (mL./100 g) 1-37±0-18 1-66±0-21 (n = 22) (n = 23) Y' (ml./sec x 10-4 X 100 g) 7-5 + 0-9 7-1 ± 1-0 DISCUSSION

Relation of this method to those used in other studies In these studies, a quantitative estimate of the peritubular capillary permeability to albumin (V') was deduced from two separate measurements: the volume of distribution of extravascular albumin pool and the rate of turnover of that pool. This approach does not allow the determination of both Vi and t in an individual animal, but requires two separate sets of experiments on groups of animals kept under identical experimental conditions. This limitation of the technique is not unique since the approaches of Dean et al. (1976) and of Renkin (1964) also require an estimation of total lymph drainage from a unit mass of tissue, a point of information which was measured in a different group of animals. In the present experiments total renal lymph flow is not known, therefore Renkin's PS product cannot be calculated. However, from the data available in the literature (tlfendahl, Pinter, Atkins, Wolgast & Agerup, 1973; Dean et al. 1976), a highly approximate PS value of about 10 x 10-4 ml./(sec. 100 g) may be estimated for the control condition. Although we cannot assign confidence limits to this figure, it does not appear much different from 7-1 x 10-4 ml./(sec. 100 g) which was the control value of V" found in these experiments. The apparent similarity of these figures, however, does not constitute sufficient grounds to affirm the validity of the assumptions underlying the PS measurement. Since renal lymph originates mostly from the cortex (Kriz & Dieterich, 1970; Atkins, O'Morchoe & Pinter, 1972), all of these measurements should characterize the cortical peritubular capillaries. In earlier experiments we found that the specific activities of albumin in plasma and renal lymph nearly equilibrate within 2 hr. Presumably, this indicates that all

D. R. BELL AND OTHERS 630 pools of albumin in the kidney which communicate with lymph also approached the state of equilibration within the same period. Rasmussen & Iversen (1976) found the distribution volume of endogeneous rat albumin to be 13-4 + 0-9 (s.E. of mean, n = 17) F1l./100 mg renal cortex, and we obtained a figure of 12-60 + 0-34 (s.E. of mean, n = 23). In our studies, the inorganic activity in tissue never exceeded 5% of the total. This fact and the near equality of our result and that of Rasmussen & Iversen (1976), suggested that the 125I albumin tracer used in these experiments was distributed in the total renal albumin pool. M$

M Cli

.'~~~~~~~~~

~M'

fc

M3

0= 01902

-M1 +M2+M3=Mi Fig. 1. The hypothetical structure of the renal cortical interstitial albumin pool as assumed in these studies. Three components are visualized in the pool: M1 in rapid exchange with plasma and lymph, M, exchanges slowly with plasma and lymph, and M. is a plasma exchange pool which does not release albumin into the lymph either directly or indirectly. The total mass of albumin in the interstitial pool is assumed to be ju, measurable as Ml. Albumin enters the pool from the peritubular capillaries at a rate of OS1, into M1 and M2, and at a rate of 02 into the plasma exchange pool, Ma. Components do not represent compartments. See text.

As in the studies of Dean et al. in our experiments lymph was the carrier of the information from the interstitial albumin pool. However, whereas in the experiments of Dean et al. the point of information was albumin concentration, in the present studies we measured specific activity of albumin which is independent of movement of water in and out of the lymphatic vessels, and in steady state should remain invariant over interstitium and lymph under a broad set of conditions. In non-steady

ALBUMIN AND PERITUBULAR CAPILLARIES 631 states, the specific activity of albumin in lymph should follow, with a time delay and additional dispersion, that of the interstitial albumin. Hypothetical plasma exchange pool Fig. 1 is introduced at this point as a visual aid for reference in the following discussion. This Figure is not intended to suggest a preconceived compartmental model, and it is important to note that the data analysis did not proceed from compartmental model assumptions. Data analysis was not dependent on any model assumptions other than linearity and stationarity (discussed below). Fig. 1 depicts the interstitial albumin pool as containing several components: M1 denotes a part of the pool which exchanges rapidly with both plasma and lymph. It exchanges also with another component, marked M2, which is a more slowly exchanging part of the albumin pool. A third component, Ms, represents a potential plasma exchange pool. By definition, such a component as M8 does not signal its existence through the lymph. It may be detectable only through observation of a gradually enlarging plasma distribution volume soon after the injection of tracer. Gartner, Vogel & lJlbrich (1968) have measured the distribution volumes of 131I-tagged human albumin in the whole kidney of Wistar rats. These authors suggested that the distribution volume of the i.v. injected albumin tracer after 1 min mixing time was that of the intravascular plasma, and that this distribution space expanded exponentially up to 7 min. They suggested further that this expansion signified the passage of tracer into the interstitium, and that the estimated half-time of the expansion was 1-5 min. Such a rapid turnover of the interstitial albumin pool has not been detected in studies on renal lymph. Equilibration of albumin specific activity between plasma and lymph took nearly 2 hr in dogs (Pintar & O'Morchoe, 1970), sheep (McIntosh & Morris, 1971), and rats (Wolgast, Ulfendahl, Killskog, Rasmussen, Atkins & Pinter, 1974, and present study). A possible explanation for this lack of agreement is that, whereas tracer albumin might cross rapidly into the interstitium from the circulating plasma, the slow flow of lymph in the intrarenal lymphatic vessels might delay the appearance of the tracer at the point where lymph is collected. To examine this possibility we have determined the passage of labelled small molecules, inulin and creatinine, from plasma to lymph. These molecules enter the renal cortical interstitium exclusively from the peritubular capillaries, as they are not reabsorbed from the tubules. The simultaneous transit of inulin and creatinine was studied in four rats. The mean transit time for both substances was consistently less than 2 min. As fluid is transported by convective flow in the lymphatic channels, this finding shows that slow flow of lymph cannot be held responsible for the observed slow equilibration of albumin specific activities between plasma and lymph. It seems, therefore, possible that the rapid expansion of the plasma distribution volume, reported by Gartner et al. which is not noticeable in lymph, may be indicative of a plasma exchange pool of albumin. We have attempted to determine whether the plasma volume distribution measurements in our study would also show a tendency to expand with time. To this end we examined two correlations: (1) between the mixing time allowed for the 131I tracer (ranging from 2-2 to 4'4 min.) and the distribution volume of that tracer, V(*); and (2) between the same mixing time and the difference between the distribution volumes of the steady-state tracer and the tracer of short mixing time [V-V(*)]. We expected that an expanding plasma volume of distribution would be revealed by a significant correlation, and should suggest a process of filling of a plasma exchange pool. These statistical calculations were carried out for both control and expanded experiments separately and also as one pooled group. No significant correlation was found. Thus these calculations did not indicate that the albumin space was expanding within the time frame in which we were making observations. It is possible that, if such expansion had occurred, it was essentially complete by 2-2 min. Therefore, our measurement of the intravascular plasma volume, V(*), included any potential plasma exchange pool in both groups of animals. We concluded that in these experiments V, = V-V(*) was a measure of that pool of interstitial al. bumin which communicated with lymph and in which Z was also determined. Henceforth we will refer to the interstitial albumin pool as operationally defined in these experiments, namely such a pool which communicates with lymph.

632

D. R. BELL AND OTHERS

Validity of I as a measure of the residence time of albumin in the renal cortical interstitium The mean transit time from plasma to lymph, 4, was determined as the mean value of the impulse response of a linear and stationary system. Assumption of linearity was justified for a tracer system such as ours by Norwich & Het6nye (1971) and Jaquez (1972). Stationarity of the system was supported by monitoring and keeping the controllable physiological variables at a constant level. In earlier studies we verified the assumption of stationarity by observing that the mean transit time measurements were reproducible on the same animal when experimental conditions were kept constant. The mean transit time experiments (series A) were consistent with the volume of distribution experiments (series B) in respect to the intrarenal lymphatic channels: The albumin content of these vessels was included into the measurement of the extravascular albumin pool, and the time spent in them by tracer albumin molecules was also included into the measurement of t. Even though the plasma exchange pool of albumin is not considered in this context for operational reasons, the measured mean transit time, t, and the average residence time, I7, of albumin in the pool which communicates with lymph could still be different if there were multiple exits from the pool (such as re-entry into the capillaries) and the average transit time through these exits were different from t. Re-entry of albumin from the interstitium into the capillaries should not be disregarded, as vesicular transport of macromolecules is likely to proceed in both directions (Mayerson, Wolfram, Shirley & Wasserman, 1960; Johnson, 1966). Furthermore, Casley-Smith (1975) proposed recently a mechanism whereby large molecules may be swept back into the capillaries from the interstitium by convective flow of fluid which is generated by the colloid osmotic pressure difference across the capillary wall. Although in cases of multiple exits there are general conditions for the equivalence of t and r, the only condition open to us for experimental verification was the case of the single well mixed compartment. While the circumstances for rapid mixing in the interstitial space may be unfavourable in most organs, the case of the kidney cortex may be unique. A relatively large volume of tubular reabsorbate flowing through the interstitium may generate sufficient mixing for rapid disappearance of specific activity gradients. In these experiments we were led to conclude that there is a relatively rapid mixing in the renal cortical interstitial space for the following reason. In addition to the exponential curve fitting technique described in the Methods section (A), we used also numerical deconvolution to compute the frequency function of transit times across the delaying and dispersing labyrinth between plasma and lymph (Maseri, Caldini, Permutt & Zierler, 1971). To this end, the specific activity vs time functions were smoothed by hand and values were read from the smoothed curves at every 2 min. The deconvolution was carried out to 90 min when, in most experiments, data collection was terminated. The frequency function so obtained was plotted as cumulative frequency distribution, which is equivalent to recreating the specific activity versus time response in lymph to a step function input in plasma. The cumulative frequency functions of transit times, averaged over animals and shown separately for the control and expanded groups, are represented in Fig. 2A, B, together with a superimposed function of a rising single exponential function fitted to these points. Although the fits are not perfect and the deviations from the fitted curves are not random, it is apparent that even the largest deviations are quite small. A perfectly fitting single exponential response should emerge if the interstitium-lymph system were a single instantaneously mixed compartment. Because of the small deviation from such a response, we put forward the tentative conclusion that the renal cortical interstitium shows some of the characteristics of a rapidly mixing compartment. However, this conclusion should be qualified in a specific respect. Whereas, in the model of a well mixed compartment, all particles have equal probabilities to be at any site within the compartment, this specific point is not applicable to the renal cortical interstitium. Rather, it is suggested that the cortical interstitium consists of a set of a very large number of microscopically

ALBUMIN AND PERITUBULAR CAPILLARIES 09

633

A

0-8

0-7

0-6 `

05 0-4

Tot03 F

~~~~~~~~Control

0-2 0-1 0

I

I

I

I

10

20

30

40

I

I

50 60 Time (min)

I

I

I

70

80

90

i 100

B

Expanded

03

0*1 0

20

30

40

50 60 Time (min)

70

80

90

100

Fig. 2. A,B. The plotted values (small circles) were obtained by reconstructing the specific activity of albumin in lymph, as an output response, to a step function input of the specific activity in plasma. For further details see text. The vertical bars denote 95% confidence limits at arbitrarily chosen times based on nine observations at such times; these limits, therefore, do not represent confidence bounds on the entire function. The continuous line is a single rising exponential function fitted to the data shown by circles. The equations for the exponential functions are as follows. In Fig. 2A, H(t)A = 0*870 (l-e-05298t), and in Fig. 2B, H(t)B=0855 (l-e-0,0"4t).

634

D. R. BELL AND OTHERS

small subunits, all of which behave nearly identically over time. To each subunit belong capillaries, tubules and lymphatics; rapid mixing is manifested by the rapid disappearance of specific activity gradients within each subunit. Tracer particles that arrive to each subunit from a common source behave almost identically, and information pertaining to the entire cortical interstitium may be gained by sampling any one or a subset of the subunits or existing lymphatics. However, in this model, if tracer is deposited into one single subunit, it will not spread immediately and evenly among all subunits. Therefore, the renal cortical interstitial space is a 'compartment' only in the sense that the term has been used often for the red cell compartment, i.e. subunits that behave identically are combined into a single compartment (Sheppard, 1962).

Thus, in the sense clarified and qualified above, the average response of the interstitial albumin of the renal cortex is similar to that of a homogenous pool, and the use of t for characterizing the mean residence time in that pool appears to be justified. As described above, the volume of distribution of interstitial albumin, as measured in these experiments, designates that pool which is drained partially or totally by lymph. Therefore we can now specify the conditions under which the quantity Vr = (,u/cp). (1t/), which we set out to measure, and /' = Vi/t, which was actually measured, are equivalent: . 1. If there is no plasma exchange pool separated from lymph, then i'lr' 2. If a plasma exchange pool exists, V' refers to the unidirectional clearance of albumin which passes through the pool from which lymph albumin is derived, but provides no information concerning, and is unaffected by, the kinetics of the plasma exchange pool. In the latter case, with reference to Fig. 1, *f

=

01+02 cp

and

At(

cp

The reflexion coefficient of the peritubular capillary wall to albumin The results of these studies can be interpreted in relationship to the reflexion coefficient to albumin of the peritubular capillaries: In considering the reflexion coefficient, we have taken as the point of departure a recent model by Perl (1975) in which, in any organ, the area of capillary circulation was divided into two regions: one in which fluid is filtered from the capillaries into the interstitium, and the other in which fluid is reabsorbed into the capillaries from the interstitium. Since, throughout the entire peritubular capillary region, tubular reabsorbate is entering into the lumen of the vessels, we considered that these capillaries are represented by the reabsorbing region in Perl's model. We have assumed further that the passage of albumin from the capillaries into the interstitium occurs at discrete sites of the capillary wall, separate from the reabsorbing portions. Such a separation may be anatomical in that release of albumin may occur from the small venules rather than from the capillaries, or there may exist an inhomogeneity of the capillary wall that allows the escape of large molecules at distinct sites interspersed with reabsorbing surfaces. A morphological inhomogeneity of the peritubular capillary wall, consistent with the latter possibility, was observed by Pedersen & Maunsbach (1973). We state the following inequality: the magnitude of albumin flow carried by convection from the interstitium back into the capillaries,

635 ALBUMIN AND PERITUBULAR CAPILLARIES IJJ,. (1 -o-)c (Katchalsky & Curran, 1965), is smaller than the magnitude of the inflow of albumin into the interstitium, i'I .cp. That is

IJJvl(10-a)c < 1'11.cjp.

(6)

Here, IJhI is the magnitude of the flow of reabsorbate into the peritubular capillaries in 100 g renal cortex, o- is the reflexion coefficient, and c is the average concentration of albumin in the membrane. The justification of this statement is that some albumin that has entered the interstitium leaves by the lymph and only the remaining fraction is available to return into the capillaries by convective flow. By rearranging the inequality we obtain a lower bound for a: Ir>_11 1..

(7)

According to Katchalsky & Curran (1965) c may be approximated by the arithmetic mean of the concentrations on both sides of the membrane: in the present case (c' + ci)/2, where c' and cl are the concentrations of albumin at the luminal and the interstitial sides, respectively, of the capillary wall. There are several points to be noted about this approximation. The accurate concentration of albumin in the peritubular capillaries, cj is not known; it is higher than cp in the systemic circulation owing to the process of glomerular filtration. The concentration should be highest near the glomeruli and become gradually diluted by the reabsorbed tubular fluid. The shape of albumin concentration and length of peritubular capillary are also not known. They may also be irrelevant because the permeability of the peritubular capillary wall to albumin may not be uniform along the length of the capillary. Furthermore, the interstitial concentration of albumin in the fluid layer adjacent to the capillary wall is unknown. Thus, the lack of information about the concentration profile in and around the peritubular capillaries may seem overwhelming. However, to satisfy the inequality expressed in (7) it is sufficient to find a bound for c. By noting that c1 > 0, the interstitial concentration of albumin exceeds 0, a minimal bound is set for ci. Furthermore, by noting c' > c the lowest limit for cp is specified which may be approached but never reached in the peritubular capillary network. It should be noted also that substituting these minimal bounds (cp > cp; ci > 0) into c (cp+c1)/2, should provide compensation for the possibility that the arithmetic mean may over-estimate the value of c. A lower bound for oc is thus a,> 1-2.

(7a)

By substituting values into (7a) we obtain a- >

100g) = 0-9986. I1- 2. 7-1 x10-4ml./(sec. 1 ml./(sec. 100g)

On the right hand side of the inequality I VYJ was measured as 7-1 ml. x 10-4/sec in 100 g cortex; an approximate estimate of IJI, i.e. the rate of tubular reabsorption in 100 g rat renal cortex, is 1-0 ml./sec (Smith, 1951). If the solvent drag reflexion coefficient is equal to the osmotic reflexion coefficient, the osmotic effect of plasma albumin across the reabsorbing portions of peritubular capillary wall is not modulated

D. R. BELL AND OTHERS 636 by a reflexion coefficient much different from unity. By using the data obtained in earlier studies on the dog (Pinter, Atkins & Bell, 1974), we found the limit o > 0 99. It is apparent that only the third and fourth digits after the decimal point are subject to change with the various estimates of the quantities that enter the calculations of 0'.

Pertinence of these measurements to physiological processes It should be emphasized that the values of A1r' and o calculated in this manner are pertinent to the process of tubular reabsorption only if the tubular reabsorbate flows through that region of the renal cortical interstitium which is in communication with the lymph compartment. Should the bulk of the reabsorbed tubular fluid enter into the peritubular capillaries without crossing such interstitial spaces (e.g. through a region as M3 in Fig. 1 or at sites where the tubular and capillary basement membranes are closely apposed) neither this present study, nor any other based on renal lymph should be expected to provide information which is relevant to the process of tubular reabsorption. In addition, mucopolysaccharides may contribute, to a potentially important degree, to the oncotic pressure in the renal cortical interstitium and influence the process of fluid movement between interstitium and capillaries. Infusion of a hypotonic solution amounting to 6% body weight did not affect the permeability of peritubular capillaries to albumin in these rats. Our experiments indicated that the interstitial albumin pool may have decreased in size, and that a definite shortening of the mean residence time of albumin in the pool occurred. It seems probable that the primary effect of the hypotonic fluid infusion was an increase in fluid flow through the interstitium. The increased flow of fluid during the transient phase of the experiment, may have washed out some of the albumin from the interstitial space. A new steady state condition was then attained such that the quantity of interstitial albumin was reduced compared to that in the renal cortex of control animals. The shorter transit time of albumin appears to be related to the decreased pool size rather than to an increased flow of the interstitial albumin. APPENDIX I

Effect of non steady state in 125I on determination of mean transit time In the foregoing study the assumption was made in measuring the specific activity of 131I tagged albumin that the injection of 1311 occurs at or after the time at which the 126I plasma and lymph specific activity curves are identical and constant in time. If, following the 1311 injection, the 125I specific activity is falling monoexponentially rather than remaining constant, the effect on the impulse response h(t) may be seen as follows: Let Ke-at, a > 0, be the decay of the 125J specific activity, y(t) be the 131J specific activity in lymph, x(t) be the l3lI specific activity in plasma, h(t) be the true impulse response, and A(t) be the computed impulse response. The convolution integral relating input and output specific activity via the impulse response is y(t) = h(T)x(t - r) dr. 0

ALBUMIN AND PERITUBULAR CAPILLARIES 637 Using the ratio approach and the above assumptions, our computation of h(t) will be based on x(t -r) yMt f Ke-at j0 I(r) Ke-a(t-7) dr which may be rearranged as follows: y(t) =

A(r)ea'Tx(t - r) dr

f

0

A(t)e-at or (t) = h(t)eat.

which shows that h(t)

=

The effect on the computation of mean transit time t may be seen by approximating eat by 1 + at (the linear terms in the McLauren expansion): dt fth(t) 0

th(t) dt + f t2h(t) dt = ?1+ca

t2h(t) dt. Jo This expression shows that if the specific activity of the 125I tracer is decaying in the plasma at the time of the injection of the 131J tracer, the calculation of the mean transit time is positively biased. Our data suggest that the second moment of h(t) is in the order of 1000 and that the t1/2 of the decay of 125J specific activity at the relevant time is not less than 5 hr. Thus the bias in the mean transit time should be not in excess of about 8% 0

0

APPENDIX II

Derivation of eqn. (3a) Let Q and Q(*) denote the amount of 125I tracer present in 100 g renal cortical tissue at steady state, and 1311 tracer after a brief mixing time, respectively. Let P and P(*) denote the plasma specific activities in the same conditions of these tracers, and I(*) the average interstitial specific activity of the 131I tracer. Let M, and Mi be the masses of the vascular and extravascular pools, and let M be the mass of the total pool of albumin present in one hundred grams tissue. The following two equations state the relationships between tracer quantities, pools and specific activities. + Q/P = M -Mv A=

Q(*) = Mvp(*)+MI(*) By solving the second equation for Mv and substituting into the first we obtain M = Q( *)-M

+

By writing M(*) for Q(*)/P(*) and rearranging, we find the mass of the extravascular pool:

MXM(*)

P(*)

D. R. BELL AND OTHERS The working equation is obtained by dividing both sides with cp, the concentration of albumin in arterial plasma. Thus we measure pools as distribution volumes: 638

Vi

VV(*)

(3a)

P(*) where V and Vi are as defined for eqn. (3) (in main text) and V(*) = M(*)Icp. Eqn. (3a) states that the interstitial distribution volume of albumin, Vi, is measured as the difference between the volumes of distribution at steady state, V, and after a brief mixing time, V(*), divided by the correction factor (1- I(*)/P(*)). If the second tracer does not enter the interstitium, I(*) = 0 and the correction factor reduces to 1. Some of the data presented in this paper were used in a thesis by D. R. Bell in partial fulfilment of the requirements for the Ph.D. degree by the graduate School of the University of Maryland. Parts of this research were supported by grants nos. HL17781 and AM 17093 of the U.S. Public Health Service. REFERENCES

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