JULY VOL. XXXIII
Circulation Research
An Official Journal of the American Heart Association
1973 NO. 1
Brief Reviews
Transcapillary Fluid Exchange in the Renal Cortex
By William M. Deen, Channing R. Robertson, and Barry M . Brenner • In the microcirculation of the renal cortex, fluid
exchange proceeds at very high rates in two anatomically and functionally distinct capillary systems, the glomerular and the peritubular capil-laries. Net ultrafiltration is confined to the glomeru-lus, which consists of a tuft of capillaries surround-ed by the ultrafiltrate enclossurround-ed within Bowman's capsule at the proximal end of the nephron. Normally, this ultrafiltrate is almost entirely reab-sorbed during passage along the renal tubule and returned to the circulation via uptake into the surrounding network of peritubular capillaries. Thus, the processes of ultrafiltration and absorption, which in the peripheral microcirculation typically occur across the arterial and venous ends of the capillaries, respectively, proceed in the kidney across two distinct sets of capillaries connected in series by the efferent arteriole.
The rate of fluid exchange through capillary walls is governed by the difference between the opposing hydrostatic and colloid osmotic pressures, as origi-nally conceived by Ludwig (1) and refined by Starling (2). At any point along a capillary this relationship may be expressed as
= fc[(Pc-P/)-(irc-ir,)], (1) where /„ is the net transcapillary fluid flux averaged over several cardiac cycles (positive for ultrafiltra-tion and negative for absorpultrafiltra-tion), AP and An- are the transcapillary hydrostatic and colloid osmotic pressure differences, respectively, Pc and irG are the hydrostatic and colloid osmotic pressures in the capillary, P/ and 717 are the corresponding pres-From the Department of Medicine, Veterans Administra-tion Hospital, San Francisco, California, the Department of Medicine, University of California, San Francisco, Califor-nia, and the Department of Chemical Engineering, Stanford University, Stanford, California.
Dr. Brenner is a Medical Investigator of the Veterans Administration.
Please address reprint requests to Dr. Brenner, Veterans Administration Hospital, 4150 Clement Street, San Francis-co, California 94121.
sures in the surrounding interstitial fluid, and k is the effective hydraulic permeability of the capillary wall measured in the presence of an osmotically active solute; k generally differs from the hydraulic permeability measured using pure water (Lp). To define k, the radially averaged protein concentra-tion is used to compute osmotic pressure, but the concentration at the capillary wall and thus the true osmotic pressure are likely to be somewhat different. Under these conditions, a radial concen-tration gradient will be manifested as a resistance to transcapillary fluid movement (R) in series with the resistance presented by the capillary wall.
l = TT
p + R-
(2)Evidence consistent with the Ludwig-Starling hypothesis has been inferred largely from studies of single capillaries in omentum, mesentery, and skeletal muscle of amphibia and mammals (3—5) and from studies using more indirect, isogravimetric or isovolumetric methods for estimating transcapillary fluid exchange in whole organs (6, 7). In general, this evidence shows that AP is slightly greater than A77 at the arterial end of a capillary (thereby favoring net ultrafiltration) and is slightly less than ATT at the venous end (favoring net absorption). The progressive decline in the local transcapillary driving pressure, AP — ATT, has been attributed primarily to the drop in capillary hydrostatic pressure (Pc) from the arterial to the venous end of a capillary (8-11). Typical colloid osmotic and hydrostatic pressures for an idealized peripheral capillary (12, 13) are summarized in Table 1. Since there is at present great uncertainty as to whether P/ is positive or negative (13-16), we have chosen a value of zero for illustration, TT, has yet to be measured in fluid obtained directly from the interstitial space because of present limitations in sampling interstitial fluid. The value for 777 in Table 1 is similar to that used by others (12, 13); values for 7T; are generally based on measurements of total protein concentration in tissue lymph. Accordingly,
Circulation Research, Vol. XXXIII, July 1973 1
for the idealized peripheral capillary in Table 1, AP - A17 declines from about 12 mm Hg at the arterial end to —5 mm Hg at the venous end. This decline in AP — ATT from positive to negative is consistent with the requirement that net fluid exchange across the entire capillary be close to zero (i.e., absorptions ultrafiltration). However, given the present difficulties in determining P/ and TTJ, the precise values of AP and ATT along a peripheral capillary remain uncertain.
For the glomerular capillary, evidence in accord with the Ludwig-Starling hypothesis was obtained in amphibia some 40 years ago (17-19), but until recently the absence of glomeruli on the surface of the renal cortex has prevented investigators from making similar direct pressure measurements in glomerular capillaries of mammals. However, the discovery1 of a mutant strain of Wistar rats possessing surface glomeruli and the development of servonulling pressure transducers (20) and ultramicroanalytical protein assay methods (21) have recently made possible direct measurements of the ultrafiltration driving forces in this mammalian species (22-26). Glomerular hydrostatic and oncotic pressures representative of those found in normally hydrated rats (22-24) are summarized in Table 1. Glomerular capillary hydrostatic pressure was found to be about 45 mm Hg or 40% of mean arterial blood pressure, a value considerably lower than estimates generally obtained using more indirect, stop-flow techniques (27-30). The drop in
'In the laboratory of Dr. Klaus Thurau of the Physiological Institute, Munich, Germany.
Po along a glomerular capillary, estimated to be no
more than 2-3 mm Hg (23), has been assumed to be 1 mm Hg (Table 1). The values of irc shown for the glomerulus are those at the afferent (TTA) &nd
efferent (TTE) arteriolar ends of the capillary; IT A is assumed to equal tr measured in femoral arterial plasma. Since the ultrafiltrate in Bowman's space is directly accessible to micropuncture, P7 and ITJ can be determined with a degree of precision not possible for the interstitial fluid surrounding capil-laries elsewhere; therefore, the glomerulus is an ideal system in which to study the dynamics of capillary ultrafiltration. AP — Aw in the normal hydropenic rat declines from 16 mm Hg at the afferent end of the glomerular capillary to essential-ly zero at the efferent end (Table 1). The close equality of AP and A7r normally achieved prior to the efferent end of the glomerulus (22-24, 31) is termed "filtration pressure equilibrium." The de-cline in AP —ATT along the glomerular capillary results primarily from the progressive increase in 7rc, which is due to the formation of a relatively large volume of essentially protein-free ultrafiltrate. Indeed, for the glomerular capillary, some 33% of the initial plasma volume becomes ultrafiltrate (filtration fraction = 0.33) (22-24, 32). Since for peripheral capillaries the filtration fractions are only about 0.001 (33), TT0 would be expected to change by a negligible amount along a capillary.
Peritubular capillary hydrostatic pressures are considerably lower than those in the glomerulus; they are generally below 10 mm Hg in hydropenia (23, 24, 32, 34, 35). For an axial pressure drop of 3 mm Hg and a P, of 3 mm Hg (36, 37), AP declines
TABLE 1
Comparison of Peripheral, Glomerular, and Perilubular Capillary Hydrostatic and Osmotic Pressures
Peripheral capillary (12, 13) Arterial end Venous end Glomerular capillary (22-24) Afferent end Efferent end Peritubular capillary (23, 24, 32, Arteriolar end Midcapillary pc 32 15 45 44 34-38) 8 5 r, ~ 0 ~ 0 10 10 ~ 3 ~ 3 25* 25* 19* 34 34 26{ ", ~ 5 ~ 5 0 0 ~6f ~6t AP 32 15 35 34 5 2 Ax 20 20 19 34 28 20 AP -AT 12 - 5 16 0 - 2 3 - 1 3
*I.n a given animal, values of KC in a peripheral capillarj' and at the afferent end of a glomerular capillary should be identical. The discrepancy here results from the use of different sources of data for the two types of capillaries.
fB. M. Brenner and J. L. Troy, unpublished observations.
fSince only part of the peritubular capillary network is considered here (see text), nc does not return to
the corresponding systemic value of 19 mm Hg.
Circulation Research, Vol. XXXIII, July 1973
from about 5 mm Hg to 2 mm Hg. Considering only the part of the peritubular capillary network which exchanges fluid with proximal tubule seg-ments on the surface of the renal cortex, TTC declines with uptake of reabsorbate from 34 mm Hg (corresponding to the measured efferent arteriolar plasma protein concentration of about 8.5 g/100 ml) to about 26 mm Hg (32, 36, 38). The proximal tubule segements on the surface of the renal cortex are accessible to micropuncture; they constitute about 60% of the total length of the proximal tubule and reabsorb some 50% of the total volume of ultra-filtrate produced by their glomeruli (21, 38). By con-sidering only the corresponding part of the peri-tubular capillary network, it is possible to relate peritubular capillary fluid exchange to tubule re-absorption up to the usual site of micropuncture in the last accessible proximal convolution. The value of TTJ for the peritubular capillary was estimated from the protein concentration in subcapsular fluid, which is similar to that found in renal lymph (39, 40). As shown in Table 1, ATT greatly exceeds AP throughout the peritubular capillary as a result of the high colloid osmotic pressure of postglomerular plasma and the low capillary hydrostatic pressure. Some of the reservations concerning the val-ues of Pi and 77/ discussed earlier for the periph-eral capillary apply for the peritubular capillary. However, since published values of Pj are almost uniformly positive (37, 41, 42), it is highly unlikely that the value of AP is much greater (although it may be lower) than that shown for the peritubular capillary in Table 1. Moreover, since subcapsular fluid is in close contact with the peritubular capillaries in the renal cortex, it is also unlikely that the true value of IT, differs greatly from IT measured in subcapsular fluid. Accordingly, the conclusion that Air normally far exceeds AP throughout the peritubular capillary appears war-ranted.
A yJ^ =DIP E N D E N C E Of GLOMERULAR ULTRAFILTRATION AND PERITUBULAR CAPILLARY ABSORPTION
Although the rate of plasma flow through a capillary does not appear explicitly in Eq. 1, it must modify the effective driving force for transcapillary fluid movement. For the glomerular capillary, high initial plasma flow rates ensure smaller increases in 77-c for a given volume of protein-free ultrafiltrate than do lower flows. Higher flows, therefore, favor higher values of AP - ATT. Similarly, for the peri-tubular capillary, high flow rates cause a given volume of reabsorbate to dilute the plasma proteins (thus lowering TTC) by a lesser amount than that
Circulation Research, Vol. XXXIII, July 1973
which occurs at lower flows, resulting in higher values of ATT - AP. Thus rates of ultrafiltration and absorption are greater at high plasma flow rates than they are at low plasma flow rates if all other determinants of transcapillary fluid exchange re-main constant. The extent to which transcapillary fluid exchange is plasma flow dependent does depend, however, on these other determinants.
To study the plasma flow dependence of glomerular ultrafiltration in the rat, Brenner et al. (23) purposely elevated glomerular plasma flow
(QA) by acute volume expansion either with
homologous rat plasma or Ringer's solution. Figure 1 (top) illustrates that both forms of volume expansion caused essentially proportional increases in single nephron glomerular filtration rate
(SNGFR) and QA. Thus, the single nephron
filtration fraction (SNFF = SNGFR/QA) remained essentially unchanged despite roughly twofold increases in QA. Figure 1 (bottom) illustrates that colloid-free (Ringer) loading diluted plasma pro-teins and lowered TTA. However, TTA was unchanged by isoncotic plasma loading. In both cases the mean
40 35 •SNGFH 3 0 (NL/MIN) 25 20 \-PRESSURE (MM HG) 40 30 -20 10
KYOROPENIA PLASMA HYDR0PEN1A RINGER LOADING LOADING
(K>%Dw)
FIGURE 1
Summary of effects of plasma loading (2.5% body weight) and Ringer loading (10% body weight) on some measured determinants of glomerular ultrafiltration. SNGFR — single nephron glomerular filtration rate, SNFF = single nephron filtration fraction, QA — initial glomerular capillary plasma
flow rate, *K = colloid osmotic pressure at the afferent end
of glomerular capillary, ^E = colloid osmotic pressure at the
efferent end of glomerular capillary, and AP = mean glo-merular transcapillary hydrostatic pressure difference.
transmembrane hydrostatic pressure difference (AP) closely equaled irE, demonstrating that fil-tration pressure equilibrium was maintained even at glomerular plasma flow rates roughly twice normal. Robertson et al. (24) found that reductions in QA were accompanied by parallel changes in
SNGFR. When renal perfusion was reduced in
plasma-loaded rats by graded levels of aortic constriction, SNGFR fell in proportion to QA, and AP remained essentially constant (24). This same maneuver in hydropenic rats caused SNGFR to fall more than in proportion to QA due to a concurrent fall in AP (24). Filtration pressure equilibrium was observed in both groups of rats (24).
The mechanism(s) responsible for the plasma flow dependence of glomerular ultrafiltration may be examined if we express SNGFR as
SNGFR = Kf(\P-An) = JtS(AP-ATT), (3)
where Kf, the ultrafiltration coefficient, is the product of the effective capillary hydraulic perme-ability (k, Eq. 1) and the surface area (S), and AP and Air are the transcapillary hydrostatic and colloid osmotic pressure differences, respectively, averaged over the length of a glomerular capillary for several cardiac cycles. According to Eq. 3, flow-induced changes in SNGFR may be mediated by changes in Kf (k, S, or both) or AP — Av. If the
mean ultrafiltration pressure, AP — Air, could be evaluated from the measurements of TTA, TTE, and
AP in the studies by Brenner et al. (23) and Robertson et al. (24), Eq. 3 (along with the measured values of SNGFR) could be used to determine whether Kf changed with QA. However, the existence of filtration pressure equilibrium makes it impossible to estimate AP — ATT and K, from these data alone, because attainment of equilibrium requires that the profile of ATT along a glomerular capillary be highly nonlinear and allows for any number of nonlinear ATT profiles to correspond to given measurements of TTA and TTE
(43). Curves 1 and 2 in Figure 2 show two possible
profiles. The nonlinearity in the AIT profile arises because the local rate of ultrafiltration is propor-tional to the local value of AP—ATT (Eq. 1), causing glomerular capillary protein concentration and ATT to increase most rapidly at the afferent end
of the capillary. For a given QA, curve 1
corresponds to a larger value of Kr than does curve 2. Generally, an increase in K; above the minimum value required to reach equilibrium results in a
PRESSURE, ARBITRARY UNITS 1 _ / / / / //ATT // // AP 1 / f 2 / / I / / 0 I NORMALIZED DISTANCE ALONG GLOMERULAR CAPILLARY
FIGURE 2
Profiles of transmembrane hydrostatic (AP) and colloid os-motic (An) pressure differences along an idealized glomerular capillary. Details of curves 1 and 2 are given in the text. (Reproduced with permission [25]).
more rapid approach to equilibrium (curve 1) but essentially the same final value of Air, measured as
TTE- Since AP — ATT is equal to the area between the
AP and A77 curves (Fig. 2), AP —ATT and Kt
cannot be uniquely determined from the available measurements at equilibrium.
However, when equilibrium is not reached, it can be shown theoretically (43) that only one ATT profile corresponds to given measurements of irA and TTE, thus making it possible to compute a unique value of Kf. To create this situation experimentally, Deen et al. (25) have recently studied glomerular ultrafiltration in the rat under conditions deliberately designed to achieve disequi-librium and to thereby allow the calculation of a unique Air profile and a unique value of Kf. Intravenous infusion of isoncotic rat plasma (5% of body weight) increased QA to a level approximately three times normal, which was sufficiently high to yield disequilibrium. After acquiring the measure-ments necessary to calculate Kf under this condi-tion, QA was either further increased by carotid occlusion or decreased by aortic constriction, always within a range of QA that continued to yield disequilibrium, to determine whether Kf varied with QA. Using a recently developed mathematical
model of glomerular ultrafiltration (43) to account for the expected nonlinearity of the A7r profile, K, was calculated by an ordinary, nonlinear differen-tial equation that gives the rate of change of protein concentration with distance along an idealized Circulation Research, Vol. KXXlll, July 1973
glomerular capillary. The derivation of this equa-tion has been previously described (43), and it treats the glomerular capillary bed as a rigid cylindrical tube of an equivalent total surface area. The rube is impermeable to plasma proteins and has a plasma flow rate and a protein concentration dependent only on distance along the capillary and a net transcapillary driving force determined by Eq. 1. The value of K, calculated by Deen et al. (25), 0.078 nliters/sec mm Hg"1, was remarkably insen-sitive to wide variations in QA within the range of very high plasma flows obtained in their study. Also, Deen et al. (25) found that their calculated value of Kf was consistent with data from previous studies from the same laboratory (22-24). These findings lead to the conclusion that the plasma flow dependence of SNGFR results primarily from flow-induced changes in mean ultraflltration pressure (AP — An) rather than from large changes in Kt.
When filtration pressure equilibrium was ob-served (23, 24), SNGFR was highly plasma flow dependent. Although SNGFR remained flow de-pendent during disequilibrium (25), the degree of flow dependence decreased progressively with increasing QA and, thus, with increasing departure from equilibrium. Viewed in terms of the filtration fraction, for given values of TTA and AP, progres-sively larger departures from equilibrium achieved by increasing QA resulted in progressive declines in the filtration fraction (25), a finding in accord with theoretical considerations (43). Therefore, absorp-tion by the peritubular capillaries would not normally be expected to be strongly plasma flow dependent, since ATT does not closely approach AP (Table 1). Brenner et al. (44) have recently provided data which allow assessment of the flow dependence of peritubular absorption. These work-ers found that partial aortic constriction in plasma-loaded rats selectively reduced efferent arteriolar plasma flow (QE) without significantly altering
mean peritubular capillary hydrostatic pressure
(Pc) or rrE (44). In this study (44), QB decreased
on the average from 154 to 114 nliters/min, but the absolute rate of fluid reabsorption by the proximal tubule (APR) fell only from 21.4 to 19.2 nliters/min. In the steady state, since lymph production per nephron is a negligible fraction of
APR, APR will essentially equal the peritubular
capillary absorption rate. Thus, the data of Brenner et al. (44) support the notion that peritubular capillary fluid exchange normally is relatively insensitive to changes in
QE-Circulation Research, Vol. XXXIII, July 197}
Deen et al. (36) have recently reported a theoretical analysis of peritubular transcapillary fluid exchange. A partial summary of this analysis is given in Figure 3; curves 1-4 in each section of the figure correspond to arbitrarily chosen values of P, and 777 that yield AP and Air curves relatively close to equilibrium (curve 4), very far from equilibrium (curve 1), or intermediate between these extremes (curves 2 and 3). Relatively small perturbations in efferent arteriolar protein concentration (CE) are
predicted to influence APR more than even large changes in QB. Changes either in CE or QE have their most pronounced effects when AP and ATT are closest to equilibrium (curve 4). From the available data (32, 36, 38, 44, 45) that argue in favor of little plasma flow dependence of APR, the values of P, and 7J7 that prevailed under the conditions of these experiments appeared to be intermediate between the values used in computing curves 2 and 3 (36). From previous studies (32, 38, 44) in which direct measurements were made of the changes in Pc, CK, and QE corresponding to the observed changes in APR, it has been calculated (36) that 777 would have to exceed P, by approximately 5 mm Hg. This value of TTJ — Pj for the peritubular capillary is remarkably similar to that (3 mm Hg) derived from the indirect measurements of TT/ and P/ (37) summarized in Table 1. The close quantitative agreement between theoretical calculations (36) and recent micropuncture studies in rat (32, 38, 44)
ABSOLUTE PROXIMAL REA&5ORPTION AS A FUNCTION OF 3Q EFFERENT ARTERIOLAR PLASMA R O W ,
A3S- PROX. JEAM.
ABSOLUTE PROXIMAL BEABSORPTION AS A FUNCTION O f EFFERENT AOTEflolAR PROTEIN CONCENTRATION
»—ioo—\so—20O~ao—360 EPfWff^T AETEflOLAR PIASMA H.OW, n l / i m
6 0 7 0 60 9 0 W o EFFKENT ABTFRCHAR PROTEIN
CONCENTRATION, , ™ / I O M
FIGURE 3
Absolute proximal reabsorption as a function of efferent ar-teriolar plasma flow and protein concentration. Details of curves 1-4 are given in the text- {Reproduced with permis-sion [36}).
and dog (42) strongly supports the concept that peritubular capillary uptake of fluid, not transport across the tubule epithelium, controls the net rate of isotonic fluid transport across the mammalian renal proximal tubule. Additional evidence in support of this concept has been reviewed elsewhere
(38,44).
Interestingly, in all of the published studies in which strong plasma flow dependence of APR has been observed (46-48), the experimental conditions favored equilibrium. Lewy and Windhager (46) found strong flow dependence of reabsorption during partial renal venous occlusion; Po was measured to be at least twice normal and therefore approached ir0 more closely than normal. Although not measured, Pc would likewise have been expected to be elevated in the studies by Daugharty et al. (47) and Schrier and Humphreys (48). The recent findings by Ott et al. (41) suggest that Ph estimated using implanted capsules, increases to a lesser extent than does Pc for a variety of conditions similar to those in the studies just cited (46-48). Therefore, in the studies exhibiting strong flow dependence of APR (46-48) it seems likely that elevations in Pc would have favored a closer approach to equilibrium than normal. Thus, by experimental design, these studies were such as to favor strong plasma flow dependence of APR as in curve 4 of Figure 3. Unfortunately, it is impossible to offer estimates of the interstitial pressures in these studies (46-48), because a number of the quantities needed as inputs for the peritubular absorption model (36) were not measured.
GLOMERULAR AND PERITUBULAR CAPILLARY EFFECTIVE HYDRAULIC PERMEABILITIES
Since Kf=kS (Eq. 3), the effective hydraulic permeability of the glomerular capillary (k) can be calculated from K, and the surface area available for ultrafiltration (S). Using S = 0.0019 cm2 for the rat glomerulus (49), k has been estimated to be 41 nliters/sec mm Hg-1 cm-2 (25), a value that exceeds those previously calculated from in-direct measurements (50, 51). By comparison, the peritubular absorption coefficient, K, (analogous to
Kf), has been found to be approximately 0.020
nliters/sec mm Hg-1 for the rat (36). Using the criteria supplied by Renkin and Gilmore (50), we estimated peritubular capillary surface area per nephron to be about 0.04-0.05 cm2 in the rat. Since, in arriving at a value of K (36), only that portion of the peritubular capillary network surrounding of the proximal convoluted tubule was
consid-ered, S was estimated to be, approximately 0.02 cm2. Estimated in this way, k for the rat peritubular capillary was about 1.0 nliter/sec mm Hg-1 cm-2, some forty times less than the value for the rat glomerular capillary. Despite this lower value of k, peritubular capillaries normally transport nearly the same volume of fluid as do the glomerular capillaries, probably because of the higher peri-tubular capillary surface area and the higher mean driving pressure favoring absorption. These esti-mates of k assume that the glomerular and the peri-tubular capillaries are completely impermeable to plasma proteins and that the estimates of S are valid. The former assumption can be justified for the glomerulus on the basis of the extremely small quantities of protein found in glomerular ultrafil-trate (52), but its validity for the peritubular cap-illaries remains uncertain. Although the estimates of S used here are only approximations, they are probably of the correct orders of magnitude.
The estimates of glomerular and peritubular capillary hydraulic permeabilities are compared in Table 2 with values of k measured for capillaries in several other tissues. As shown, k for the peritubu-lar capilperitubu-lary is very simiperitubu-lar to the value recently obtained for capillaries in skeletal (cremaster) muscle in the rat (5), and the glomerular permeability is one to two orders of magnitude larger than all other values shown.
In summary, evidence has been presented to indicate that the forces governing fluid movement across renal glomerular and peritubular capillaries are qualitatively, but not quantitatively, similar to the forces governing transcapillary fluid exchange in extrarenal tissues. In glomerular capillaries, the rate of ultrafiltration is highly plasma flow dependent, but absorption of fluid into peritubular capillaries is much less sensitive to changes in plasma flow. This difference is best explained by the extent to which transcapillary hydrostatic and colloid osmotic pres-sure differences approach one another by the ends
TABLE 2
Effective Hydraulic Permeability (fc) for Various Capillaries
Capillary source Mesentery (frog) (3, 53, .54) Cremaster muscle (rat) (5) Peritubular (rat) (36, text) Omentum (rabbit) (4, 55) Glomerular (rat) (25) k (nliters/sec mm Hg"' cm"!) 0.65-1.0 0.88 1.0 0.3-9 41
Circulation Research, Vol. XXXIII, July 1973
of the capillaries. For the glomerulus, these oppos-ing pressures normally equalize, but they fail to converge closely in the peritubular microcirculation. The hydraulic permeability of the glomerular capillary is one to two orders of magnitude greater than that of peritubular and extrarenal capillaries. This uniquely high glomerular permeability, combined with the accessibility to micropuncture of both the glomerular capillary tuft and the ultrafiltrate in which it is suspended, offer exciting opportunities for further study of the dynamics of transcapillary fluid movement.
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Orcuiation Research, Vol. XXXIll, July 1973
