INTRODUCTION

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1996 MARKED THE 100TH ANNIVERSARY of Starling's (20) pioneering paper outlining his hypothesis for the filtration and reabsorption of water in capillaries and the formation of lymph. He hypothesized that the difference in concentration of plasma proteins between the plasma and tissue was responsible for an oncotic pressure, which opposed the hydrostatic filtration. Thus the driving force for fluid filtration rate across the vessel wall is determined by four pressures: the hydraulic and colloid osmotic pressures in the vessel and in the tissue space, respectively, i.e.,

(1)

Here J_v/A is the fluid filtration flux across the capillary wall per unit area; L_p is hydraulic permeability of the capillary wall;  is the oncotic reflection coefficient; and P_c, _c, P_i, and _i are global values for the hydrostatic and colloid osmotic pressures in the capillary and interstitial compartments, respectively. The term (_c  i), which opposes the fluid filtration across the endothelial wall, is called the Starling oncotic force.

Starling's equation has been applied across the entire transendothelial barrier, and the Starling forces have been evaluated by global measurements of P and  in the plasma and the tissue space. However, there is growing recognition that the application of the Starling equation is much subtler than has previously been realized. There exists a discrepancy between the measured Starling forces in the plasma and tissue and the forces that actually appear to determine filtration (11, 21). Furthermore, Levick and McDonald (13) have demonstrated that in the synovium, the effect of extravascular albumin on fluid exchange is much less than the effect of intravascular albumin.

In Michel (16) and Weinbaum (24), a new hypothesis is proposed for the effective oncotic barrier that acts across capillary endothelium. Hu and Weinbaum (8) present a detailed cellular-level microstructural model to quantitatively examine this hypothesis. In this spatially heterogeneous microstructural model, the endothelial surface glycocalyx, which covers the entire capillary endothelium, serves as the primary molecular filter for plasma proteins and thus the principal barrier that determines the effective oncotic force for water flow across the interendothelial cleft. Therefore, the effective oncotic force across the capillary is determined by the local difference in protein concentration across the surface-matrix layer rather than the global difference in concentration between the plasma and the interstitial fluid in the tissue. Consequently, the pressures P_i and _i that appear in Eq. 1 will be the local hydrostatic and oncotic pressures behind the surface glycocalyx, where the effective oncotic pressure is felt, and not P_i and _i in the tissue space at the cleft exit.

In the present studies, the relation between the filtration rates across the capillary wall and the hydrostatic and oncotic pressure difference has been investigated by use of a combined experimental and theoretical approach in single perfused microvessels of frog mesentery. The idea for these experiments arose from the quantitative predictions by Hu and Weinbaum (8) that the protein concentration in the tissue space may differ significantly from that just behind the glycocalyx if there are other parallel nonconvective transcellular pathways for protein flux in addition to the convective pathway through the interendothelial cleft of continuous capillaries. This model shows that the presence of a junction strand with small breaks and pores greatly inhibits back diffusion from the tissue into the shielded region on the lumen side of the junction strand. This leads to a significant reduction in the fluid flux filtered by the capillaries compared with the magnitude predicted by the classical Starling equation.

We also present new experimental results on individually perfused microvessels to demonstrate that the effective oncotic pressure across the capillary endothelium is not the global difference in oncotic pressure between blood and tissue. The novel aspect of the present experiments is that tissue albumin concentration was maintained at levels equal to that in the perfusate by the continued presence of albumin in the superfusate, ensuring the back diffusion of albumin from the superfusate into the tissue surrounding the microvessel. The effective filtration rates with albumin in the tissue were compared with the results on the same microvessel when albumin was present only in the perfusate. We show that loading the tissue with albumin from the tissue side produces only small changes in the effective oncotic pressure. These results have been interpreted by use of a detailed three-dimensional model of the surface glycocalyx, the endothelial cleft, and mixing in the tissue space surrounding the cleft exit. We also investigate the effect of the location of the junction strand and the spacing of junction breaks on the Starling forces.

	METHODS

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Experimental Methods

A key requirement of the experimental design when albumin is added to the superfusate experiments is to set the albumin concentration in the tissue equal to the albumin concentration in the perfusate. To establish the time required for albumin in the superfusate to diffuse into the tissue surrounding the test microvessel, a scanning confocal microscope (Bio-Rad MRC600) was used to record images such as those in Fig. 1. Figure 1 shows the distribution of tracer in the tissue space as a function of time after initiation of superfusion with albumin. The frog mesentery preparation was as above. Figure 1A is a fluorescent confocal microscope image taken transverse to the longitudinal axis of a venular capillary in frog mesentery. The superfusate contains FITC-albumin (2 mg/ml), and fluorescence intensity is directly proportional to the local concentration of FITC-albumin. The lumen of the venular capillary in this image is perfused with the frog's own plasma and is not fluorescent. To reduce the resistance of the mesothelium to albumin diffusion, the mesothelium ~100 µm from either side of the venular microvessel was gently stroked with a fine glass rod to irritate the mesothelial cells and facilitate solute diffusion between the tissue fluid space and superfusate. Figure 1B shows profiles of relative tissue concentration of albumin measured close to the centerline of the tissue over a period of 1-13 min. On this scale, the superfusate concentration was 160 units. Therefore, after 13 min, the albumin concentration had reached 75% of the superfusate concentration. We found that there was no difference between tissue and superfusate concentrations after 15-20 min. In our experiments, we allowed up to 45 min for albumin to diffuse into the tissue.

View larger version (46K): [in this window] [in a new window]   Fig. 1.   Concentration gradients of FITC-albumin in the tissue of the frog mesentery obtained by use of a fluorescence confocal microscope to form images (A) of the mesentery transverse to the longitudinal axis of a venular capillary. Before the experiment, the mesothelium (~100 µm on either side of the capillary) was gently stroked with a fine glass rod to disrupt the mesothelial barrier to facilitate albumin diffusion into the tissue (B). After 12 min, the albumin tracer concentration was close to 130 units, and after 20 min, it was equal to that in the superfusate (160 units).

Figure 1B shows that even though the tissue was stroked at a distance up to 100 µm from the vessel, there are no significant gradients in the tissue at distances >10 µm from the vessel wall. Furthermore, the shapes of the gradients close to the wall reflect the geometry of the vessel wall, which is not a perfect cylinder and is surrounded by pericytes. The nonuniformities in the concentration gradient in the tissue indicate sites where isolated cells or clusters of collagen fibrils that exclude albumin are located.

Two different types of experiments were designed. In the first set, paired measurements were made of the effective oncotic pressure of albumin in the perfusate, first when there was no albumin in the tissue (control) and then when albumin was added to the superfusate at the same concentration as the perfusate. These are called transient experiments because the effective oncotic pressures were measured by rapid reduction of pressures in the vessel, as explained below. In the second series of experiments, we measured the steady-state filtration rates at a series of pressures in each microvessel, with the same albumin in both perfusate and the superfusate, and compared these to the filtration rates expected at each pressure if no oncotic forces oppose filtration. To calculate the latter, we also measured the L_p for each vessel by use of the transient protocol. In each group of experiments, only one microvessel in each animal was studied. The albumin concentration in all experiments was 50 mg/ml.

During control measurements in the first series of experiments, the upper surface of the tissue was continuously bathed with protein-free Ringer superfusate. The fluid flux per unit area (J_v/A) was estimated from the motion of marker erythrocytes by use of the modified Landis technique. Before each measurement, the pressure in the vessel was held at 35 cmH₂O for 2 min by partial occlusion. This established a high-filtration steady state in which the BSA concentration on the downstream side of the selectivity barrier was washed down to a minimal level, thus maximizing the effective oncotic pressure difference. This is another way of saying that the downstream BSA concentration approaches the convective limit, (1-)C_c, where C_c is the concentration in the capillary lumen (15, 17). The steady filtration rate was measured by occluding the vessel briefly (5-7 s) and then releasing the occlusion. The measurements of J_v/A at a pressure of 10 cmH₂O were made after setting up steady filtration at 35 cmH₂O and then rapidly (0.5 s) switching the capillary pressure from 35 to 10 cmH₂O after occluding the microvessel. Reabsorption was marked by the movement of flow marker erythrocytes away from the site of cannulation as fluid moved into the capillary. Three to five measurements of transcapillary water flow per unit area of vessel wall (J_v/A) were made at each pressure. Thus the control relationship between J_v/A and pressure is determined by the oncotic effects of the BSA gradients established at high-filtration pressure and having no added protein in the superfusate. The slope of the relation measures L_p, and the effective oncotic pressure exerted across the filtration barrier in the microvessel wall was measured from the intercept on the pressure axis.

To investigate the effect of the addition of albumin to the tissue on the effective oncotic pressure exerted across the capillary wall in this first series of experiments, measurements were repeated on each of the vessels, with the same protocol as that described above (perfusate albumin concentration 50 mg/ml), except that the superfusate also contained albumin at a concentration of 50 mg/ml, applied for 45 min before the start of measurements of J_v/A (compare Fig. 1). Thus paired measurements of J_v/A at pressures of 35 and 10 cmH₂O with and without albumin in the superfusate were made on each microvessel. If a significant oncotic pressure was exerted across the glycocalyx, even when the albumin concentration was equal in the tissue and the perfusate, we expected to measure net reabsorption of water across the vessel wall at the low pressure.

The second series of experiments were designed to test whether oncotic gradients could be established across the surface matrix when albumin was added to the tissue at filtration rates that were lower than those set up at 35 cmH₂O. We thus measured filtration rates after steady-state filtration was set up not only at 35 cmH₂O but also at 10 and 20 cmH₂O on the same capillary. The same protocol used to set up steady-state filtration at 35 cmH₂O was also used at the lower pressures. The pressure in the microvessel was set by partially occluding the microvessel to increase resistance and raise the capillary pressure to that in the water manometer connected to the pipette. Two minutes were allowed for the new steady state to be achieved in the tissue at the cleft exit. This method to set up steady-state filtration at a series of pressures in the same microvessels is the same as that used by Michel and Phillips (18) and Huxley et al. (9).

Theoretical Methods

Model description. Figure 2 shows the idealized mathematical model that was used to interpret our experimental data. This model is similar to the one introduced in Hu and Weinbaum (8) except for the boundary conditions applied in the tissue space and the location of the junction strand. The essential physics of the model is contained in four regions. The first region is a surface glycocalyx of thickness L_f, which covers the entire endothelial surface including the entrance region to the interendothelial cleft. The second region is the cleft itself showing the idealized junction strand with periodically distributed orifice breaks, the gap height of which is the same as the wide part of the cleft. In Hu and Weinbaum (8), the junction strand was located at the midpoint, x = 200 nm, of the cleft depth for simplicity. However, experimental measurements (see Ref. 2) show that the junction strand is frequently close to the cleft entrance, with an effective average distance of the junction strand from the cleft entrance (L₁) of only 25 nm. In the present paper, we investigated the effect of the location of the junction strand on the Starling forces. We also explored two possible approaches in matching the measured value of L_p. In one we changed the spacing of the junction-strand breaks (2D), and in the other we changed the width of the junction orifice (2d). The other dimensions shown in Fig. 2 are based on the measurements by Adamson and Michel (2) of cleft ultrastructure in frog mesentery.

View larger version (31K): [in this window] [in a new window]   Fig. 2.   Schematic of idealized mathematical model showing surface-matrix layer, cleft region A with junction strand, and tissue regions B and C describing mixing at cleft exit. Dimensions shown are typical for frog mesentery capillary. A: top view through midplane of the cleft (z = 0), showing the junction strand with periodically distributed junction breaks in the intercellular cleft. Pc, hydrostatic pressure in capillary; LB, radius of region B; Ca, concentration at edge of region B. Lengths L, Lf, L1, and L2 are shown. B: side view of the clefts, showing idealized geometry for the mixing at the cleft exit and blowup of the single cleft with exit mixing in region B.

Mathematical formulation. The model consists of an ordered matrix at the endothelial surface, which forms the primary molecular filter to macromolecules, in series with pathways for water and solute through infrequent breaks in the junctional strand. The geometry of these breaks in frog mesenteric microvessels has been quantified by use of serial-section electron microscopy (2). Thus the model is an extension of the fiber-matrix model of Curry and Michel (5), which is modified to take into account the three-dimensional geometry of the cleft between adjacent endothelial cells and the breaks in strand and a more rigorous description of the hydraulic resistance due to the surface-matrix layer. The development and evaluation of the three-dimensional model with the use of permeability data from frog mesenteric microvessels (including permeability coefficients for small and intermediate-sized solutes) have been described in a series of papers over the past decade from our laboratories (6, 7) and have been reviewed in detail recently (17, 24).

(2)

(3)

Parameters. The geometry of the junction strand and surface matrix is shown in Fig. 2, A and B. We shall also present results for other junction-strand geometry to show the effect of orifice spacing, orifice width, and junction-strand location on the filtration flow and effective oncotic pressure. Small solutes have only a minor influence on the oncotic force across the surface matrix, because the fiber matrix offers only a minor resistance to the small solutes. In a previous study by our laboratory (7), we showed that the primary resistance for small solutes was determined by the two-dimensional diffusion through the breaks in the junction strand of the interendothelial cleft. The selection of the diffusion coefficient (D_f) for albumin in the surface glycocalyx is determined by the requirement that our current model provides an optimum fit to the measured steady-state filtration profile in the absence of tissue loading. The model predicts a dense matrix, the effective value of which for D_f for albumin is three orders of magnitude smaller than its value in solution. This is discussed at length in Hu and Weinbaum (8). _f for albumin in the surface matrix is determined by our experimental measurements of the effective oncotic pressure in the high-filtration limit (_f²_c) in Tables 1 and 2. The values of _f fall in the range of 0.8-0.94.

View this table: [in this window] [in a new window]   Table 2.   Summary of Lp and values

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Experimental Results

7

View larger version (16K): [in this window] [in a new window]   Fig. 3.   Experimental results from an experiment in which steady-state filtration was set up at 35 cmH2O, and fluid flux per unit area (Jv/A) was measured at capillary pressures of 35 and 10 cmH2O immediately after occlusion of the vessel (transient measurements). Three to four measurements of Jv/A were made at each pressure. Filtration was measured by transiently occluding the microvessel for 5-7 s, with up to 1-2 min between occlusions. Solid line, control measurements with albumin perfusate concentration set at 50 mg/ml and no albumin in the superfusate; dotted line, measurements with the high protein concentration (50 mg/ml, same as perfusate concentration) in the superfusate. The arrow points to the effective oncotic pressure, demonstrating that the effective oncotic pressure with tissue loading is nearly indistinguishable from the control. Hydraulic permeability (Lp) = 4.6 × 107 cm/(cmH2O · s).

To further test our hypothesis, we extended this approach to set up initial steady states not only at 35 cmH₂O but also at lower capillary pressures, as outlined in the methods for the second series of experiments (see METHODS). Figure 4 compares the transient reabsorption rates measured at 10 cmH₂O with additional filtration measurements made after setting up steady-state filtration at a pressure of 10 cmH₂O. Albumin was in the superfusate throughout the experiment. If albumin was able to diffuse into the water pathway at lower filtration rates, then we expected that the effective oncotic pressure difference would be close to zero and the filtration rate would be determined mainly by the difference in capillary pressure across the wall, in this case, 10 cmH₂O. The dotted line is the expected filtration rate if there were no effective oncotic difference. The line has the same slope as the initial transient experiments [dashed-dotted line, L_p = 2.44 × 10⁷ cm/(cmH₂O · s)]. The results of the experiment show that, after establishing steady-state filtration at 10 cmH₂O, the filtration rate was 0.0054 × 10⁴ cm/s, which is 20% of the filtration rate expected in this microvessel if no oncotic force were opposed to the applied pressure of 10 cmH₂O. This result indicates that there was a significant oncotic pressure due to an albumin concentration difference even under low-filtration-rate conditions. The results suggest that some mechanism protects a region on the downstream side of the filtration barrier from back diffusion. The same result was obtained in four microvessels. Three additional experiments were carried out in which steady-state filtration was set up at pressures of 10, 20, and 35 cmH₂O. The results of all four experiments are shown in Fig. 5, A-D, where each experiment has been specifically modeled by use of the approach explained below. The transient measurements for these four experiments are not plotted in Fig. 5, A-D, for simplification. The L_p values and the oncotic pressure intercepts () for these four experiments are shown in Table 2. The mechanisms leading to the maintenance of the concentration difference of albumin across the endothelial glycocalyx under our experimental conditions are illustrated by use of the following theoretical results, which model the experimental conditions described above.

View larger version (15K): [in this window] [in a new window]   Fig. 4.   The results of an experiment in which the transient filtration (at 35 cmH2O) and reabsorption (at 10 cmH2O) were first measured with albumin in the perfusate after steady-state filtration at 35 cmH2O (as in Fig. 3). Three to four measurements of Jv/A were made at each pressure. Lp was 2.44 × 107 cm/(cmH2O · s), and the effective oncotic pressure of albumin was close to 21 cmH2O (dashed-dotted line). After albumin was loaded into the tissue, there was no change in the measured filtration rate at 35 cmH2O (as in Fig. 3). Instead of rapidly dropping pressure to 10 cmH2O, as in Fig. 3, we set the capillary pressure at 10 cmH2O for 2 min and then measured the filtration rate resulting from this new low pressure steady state. The filtration rate was only 20% of that expected if the oncotic pressure difference due to albumin had been abolished under these low-filtration-rate conditions (dotted line). The results of this experiment, together with 3 additional experiments with steady-state filtration measured at 10, 20, and 35 cmH2O, are shown in Fig. 5, where they are compared with the model predictions.

View larger version (31K): [in this window] [in a new window]   Fig. 5.   Comparison of the Jv/A predicted by the present model for the steady state with the experimental value from 4 experiments (including Fig. 4). , measured experimental data; solid lines, steady-state curves in the presence of tissue loading [the albumin concentration at the edge of region C (Ci) has the same protein concentration as the superfusate (Cc); Ci = Cc]; dotted lines, steady state without tissue loading (Ci = Js/Jv, where Js is total protein flux entering the tissue space and Jv is total fluid flux into the tissue space) predicted by the present 3-dimensional heterogeneous model; dashed lines, based on the 1-dimensional (1-D) theory in work of Michel and Phillips (18) with an adjusted Lp. This range of reflection coefficient (f) values corresponds to a net effective oncotic force in the high-filtration limit of 17-23 cmH2O (calculated as f2c, where c is the colloid osmotic pressure in capillary) in Tables 1 and 2 in the absence of tissue albumin. Dashed-dotted lines, based on classical theory, where hydrostatic pressure in interstitial compartments (Pi) and colloid osmotic pressure in interstitial compartments (i) are evaluated in the tissue space. It indicates that the classical theory overestimates the fluid filtration, and the present model can predict the experimental fluid filtration results very well except in C. A: Lp = 0.67 × 107 cm/(cmH2O · s), and average spacing of the junction-strand breaks (2D) = 10,160 nm. B: Lp = 1.2 × 107 cm/(cmH2O · s), and 2D = 5,666 nm. C: Lp = 3.0 × 107 cm/(cmH2O · s), and 2D = 2,266 nm. D: (data from Fig. 4) Lp = 2.44 × 107 cm/(cmH2O · s), and 2D = 2,786 nm. A-D: average width of the junction-strand breaks (2d) = 150 nm, radius of region C (LC) = 95 µm, and average distance of the junction strand from the cleft entrance (L1) = 25 nm. Plasma albumin concentration (Cc) = 50 mg/ml, and the corresponding oncotic pressure (c) = 27.2 cmH2O.

Theoretical Results

Detailed concentration distribution. The key predictions of the theoretical model corresponding to the experimental results shown in Figs. 3-5 are presented in Figs. 6-8, where the concentration profiles for albumin from the lumen to the tissue are plotted at three positions within the cleft: along the centerline (y = 0) of the orifice break in the junctional strand; along the edge of the orifice (y = 75 nm); and at y = 2,160 nm, corresponding to y = D, the one-half spacing of the neighboring orifices. The junction strand lies at the midpoint of the cleft depth (x = 200 nm), and the other parameters are shown in Fig. 2, which are the typical values based on the microstructural measurements of frog mesentery capillaries (2). Thus the L_p of the wall is evaluated to be 2.43 × 10⁷ cm/(cmH₂O · s), which is similar to the mean value of L_p in Tables 1 and 2. The effect of junction-strand geometry and location will be examined later. The concentration profiles in the surface glycocalyx, the cleft, and tissue space when the albumin is in the perfusate alone are shown in Fig. 6 for the high-filtration flow, P_c = 35 cmH₂O. The protein concentration just behind the surface glycocalyx at y = 0 and within the break is 0.066 for _f = 0.94. The values approach the high-filtration limit, (1  _f)C_c, as expected when the concentration leaving the tissue is determined by the steady-state flux of albumin and water through the vessel wall. The tissue concentration is set at zero at a distance of 100 µm from the vessel wall, because the resistance of the mesothelium was deliberately reduced by placing a glass rod on the tissue to damage the mesothelial barrier. As a result, the albumin concentration falls toward zero in the tissue side of the cleft and in the tissue. It is important to note that, because of the wide spread of the water flow in the tissue space, the Peclet number Pe in the tissue, region C in the model, is 1, and this region is diffusion dominated. Thus the concentration decreases almost linearly with distance in the tissue, as shown in Fig. 6, inset.

View larger version (27K): [in this window] [in a new window]   Fig. 6.   Predictions of the theoretical model without tissue loading for dimensionless concentration profiles in the cleft and tissue space at different y locations for the high-filtration steady state (Pc = 35 cmH2O). Protein concentration at x = 0, just behind the surface glycocalyx, approaches the convection limit [(1-f)Cc]. Curves y = 0 and y = 75 nm nearly overlap. Inset, concentration in region C decreases nearly linearly with distance to x = 100 µm, where tissue concentration is assumed to be the same as in the superfusate. Plasma albumin concentration (Cc) = 50 mg/ml, and the corresponding oncotic pressure (c) = 27.2 cmH2O. The superfusate albumin concentration (Ci) = 0, f of the surface glycocalyx = 0.94, and the diffusion coefficient of the matrix (Df) = 0.001D.

View larger version (29K): [in this window] [in a new window]   Fig. 7.   Predictions of the theoretical model with tissue loading for dimensionless concentration profiles in the cleft and tissue space at different y locations for the high-filtration steady state (Pc = 35 cmH2O). Protein concentration at x = 0, just behind the surface glycocalyx, approaches the convection limit [(1-f)Cc]. Inset, concentration in region C increases linearly with distance to tissue loading site at x = 100 µm. Cc = 50 mg/ml, the same as the superfusate concentration, and c = 27.2 cmH2O. All other parameters are the same as in Fig. 6.

View larger version (27K): [in this window] [in a new window]   Fig. 8.   Predictions of the theoretical model with tissue loading for dimensionless concentration profiles in the cleft and tissue space at different y locations for the low-filtration steady state (Pc = 10 cmH2O). Protein concentration at x = 0, just behind the surface glycocalyx, is now raised because of diffusion through the surface matrix and back diffusion from the tissue, because the Peclet number at the junction-strand pore is less than unity. Inset, concentration in region C increases linearly with distance. Cc = 50 mg/ml, the same as superfusate concentration, and c = 27.2 cmH2O. All other parameters are same as in Fig. 6.

Filtration-pressure curves. The comparison of the experimental results with the predictions of the theoretical model are shown in Fig. 5, A-D, for four microvessels with hydraulic conductivity (L_p) ranging from 0.67 to 3.0 × 10⁷ cm/(cmH₂O · s). Also shown are the theoretical predictions of the classical Starling theory with tissue loading and the steady-state predictions of the present model and the earlier one-dimensional model of Michel and Phillips (18) without tissue loading. Because Adamson and Michel (2) found that the length of the breaks in the junction strand in frog vessel was relatively constant, L_p was varied by changing break frequency. The filled circles in Fig. 5 are our experimental measurements for tissue loading. The value of _f in our experiment ranged from 0.8 to 0.94. To show the effect of the variation of _f, we show results for the two extreme values, _f = 0.8 and _f = 0.94. The solid curves in Fig. 5 are the steady-state relations between the fluid filtration and capillary pressure when the tissue has been loaded to the same protein concentration as the plasma. The dotted and dashed curves show the steady-state relation without tissue loading, where the tissue concentration achieves the equilibrium value C_i = J_s/J_v. The dotted curves are the predictions of the present spatially heterogeneous model, and the dashed curves are the predictions of the homogeneous one-dimensional model (18) with an adjusted L_p. The dashed-dotted line is the result calculated by use of the classical Starling equation, where P and  are evaluated with the use of the global values for the concentration in the lumen and tissue. When the interstitial protein concentration is the same as the plasma (C_i = C_c), Eq. 1 reduces to J_v/A = L_p(P_c  P_i).

Effect of junction-strand structure and location. We also investigated the effect of changes in the length and frequency of the breaks in the junction strand by determining combinations of length and frequency that give the same L_p as measured. For example, for L_p = 4.6 × 10⁷ cm/(cmH₂O · s), we can either maintain a 2d of 150 nm but decrease the spacing of the junction-strand orifices to 2D = 1,478 nm or double the break length to 2d = 300 nm and have a 2D = 2,010 nm. Although break length has been doubled from 150 to 300 nm, the change in the fluid filtration curve is negligible, as shown in Fig. 9. Similar results are presented for L_p = 0.67 × 10⁷ cm/(cmH₂O · s), a low-filtration rate that approaches mammalian muscle capillaries, where results are shown for 2d = 40 and 150 nm and 2D = 6,696 and 10,160 nm, respectively. For both high and low L_p, one observes that the detailed structure of the strand has only a minimal effect on the curves for the steady-state water flux.

View larger version (24K): [in this window] [in a new window]   Fig. 9.   Effect of spacing of the junction strand and junction orifice on the Starling force. There is only a minor change in the fluid filtration for the different spacings of the junction strand and junction orifice if Lp is unchanged. LC = 95 µm, and Cc = Ci = 50 mg/ml. 2D and 2d are shown. All other parameters are the same as in Fig. 5.

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View larger version (18K): [in this window] [in a new window]   Fig. 10.   Effect of the junction-strand location on the Starling force. Solid line, a junction strand at L1 = 200 nm, midway across cleft; dotted line, a junction strand close to the cleft entrance (L1 = 25 nm). There was a small increase in back diffusion when the junction strand moved toward the cleft entrance.

Diffusion distance in tissue. The length of region C is determined by the location at which the mesothelium is opened to facilitate diffusion from the superfusate to the tissue. The exact location is difficult to control and thus we have explored different values of the radius of region C (L_C). For a short distance (L_C = 15 µm), the boundary condition C_i = C_c is applied much closer to the microvessel at a distance that is the sum of L_B and L_C (20 µm) by use of our present model. The results shown in Fig. 11 indicate that even if the albumin concentration near the cleft exit is increased by reduction of the diffusion distance in the tissue, the increased tendency for back diffusion remains small and would account for at most a 15 percent increase in filtration above that predicted for a diffusion distance of 100 µm.

View larger version (21K): [in this window] [in a new window]   Fig. 11.   Effect of the diffusion distance in the tissue on the fluid filtration. Solid line, LC = 15 µm, close to the cleft exit; dotted line, LC = 95 µm, far from the cleft exit. Other parameters are the same as in Fig. 5.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Both the current experiments with loading of albumin in the tissue and their theoretical interpretation conform to the hypothesis that for the continuous capillaries of frog mesentery, the oncotic and hydrostatic pressures that determine transcapillary fluid flux apply across the endothelial cell glycocalyx. Furthermore, the results demonstrate that the local protein concentration and pressure behind the surface-matrix layer can differ greatly from the tissue concentration and pressure, with the result that the Starling forces across the surface-matrix layer will depart significantly from the global Starling forces across the entire endothelial layer, as shown in Figs. 3, 4, 7, and 8. The novel aspect of our experimental design and calculations is the focus on the gradients in the cleft and tissue and the precise link between gradients of albumin in the tissue and the albumin concentrations and hydrostatic pressures in the cleft. In the following discussion, we first review the ultrastructural basis for the model in frog mesenteric capillaries and evaluate new aspects of our experimental design and then consider the application of this conclusion to mammalian microvessels. We note in particular that Levick (12) demonstrated that high-velocity water flows downstream from localized fenestrae resulted in a larger oncotic pressure difference across the fenestral diaphragm than expected from the blood-to-tissue concentration difference after loading of the tissue with elevated albumin concentrations.

Mechanism of the Junction-Strand Shielding

The concentration behind the surface glycocalyx is raised because of the back diffusion when Pe at the junction orifice is <1, but is still washed down to a value lower than the tissue space, as shown in Fig. 8. In fact, the value of the albumin concentration at the back of the glycocalyx (0.75 C_c) predicts that the oncotic pressure difference across the glycocalyx is 8.6 cmH₂O. This value is comparable with the predicted value of 9.9 cmH₂O from the steady-state formula of Michel and Phillips (18), which does not take into account back diffusion. Note that under the same conditions, the concentration of albumin at the cleft exit approaches 90% of the concentration in the tissue, and the maximum oncotic pressure across the entire capillary wall is <3 cmH₂O. These results clearly demonstrate that oncotic gradients across the entire capillary wall are not the determinants of the fluid balance. Rather, the fluid balance is determined by the albumin concentration differences across the surface glycocalyx, maintained by a protected region between the downstream side of the surface glycocalyx and the break in the junctional strand. The principal mechanism acting to prevent albumin accumulation on the tissue side of the glycocalyx is the throat effect of the break in the strand, which increases the local fluid velocity sufficiently to reduce the tendency of albumin to back diffuse from the tissue and thereby abolish the concentration difference across the glycocalyx.

Pathways for Water and Solutes

At present, the evidence for the structure of glycocalyx is only indirect, because the matrix under most conditions is difficult to stain and preserve intact for electron microscopy. The most convincing evidence that the sieving structure is confined to a surface layer is the detailed calculations for L_p for frog mesentery in Fu et al. (7), the measurements of the surface-matrix layer thickness for frog mesenteric microvessels in Adamson and Clough (1), and the recent theory and experiments for the labeling of the cleft with the use of high-molecular-weight tracers (6). Furthermore, serial-section electron micrographs (2) clearly reveal that the gap height of the breaks in the junction strand (20 nm) is essentially the same as the wide part of the cleft. Thus the junction strand itself is unlikely to provide the molecular sieve for plasma proteins. This combined evidence has led Michel (16), Weinbaum (24), and Hu and Weinbaum (8) to hypothesize that the surface glycocalyx is the molecular filter, at least for frog mesentery capillaries.

Detailed evaluations of the model parameters and the methods to solve the coupled nonlinear equations to describe the flows of water and albumin through the matrix, cleft, and tissue spaces have been described (8). The new variations of the model described in the present work include a modification of size and frequency of the breaks in the junctional strand to describe the actual range of experimental L_p values measured in our test vessels (Fig. 5, A-D) and to demonstrate that such variation in the junction geometry does not significantly modify the predictions of the model (Fig. 9). There is a tendency for the experimental data to fall slightly higher than the predicted values. One source of this discrepancy may be experimental, reflecting the difficulty of maintaining a uniform pressure in the vessel during partial occlusion while steady-state filtration was set up at a pressure of 10 cmH₂O. For example, if the capillary pressure were close to 7 cmH₂O during partial occlusion instead of 10 cmH₂O, the increase in pressure after occluding the vessel to measure filtration, combined with a smaller transcapillary albumin concentration difference, would impose a small transient filtration on the steady-state flux. This small transient would cause an overestimate of steady-state water flux, but the extent of the error is ~20%.

The other model parameter that we evaluated, both experimentally and theoretically, was the diffusion distance from the vessel wall to the region where the mesothelium was disrupted. In control experiments, we found that placing a glass rod at four to five positions along the length of a vessel at a distance of ~100 µm from the vessel disrupted the mesothelium sufficiently to allow albumin to diffuse into the tissue but did not damage the microvessel wall as demonstrated by a constant microvessel L_p before and after the procedure. The glass rod had a diameter of at least 15 µm and disrupted mesothelial cells with a mean diameter of at least 30 µm. Thus albumin was likely to cross the barrier at distances closer than 100 µm from the vessel. Our calculation shows that there is no significant change in the fluid filtration for a low L_p, and degree of increase in fluid filtration depends on the frequency of the junction orifice.

Mammalian Microvessels

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There is still some controversy as to whether the surface glycocalyx or small pores in the junction strand provide the molecular filter for proteins. Bundgaard (3) also observed narrow gaps with a width of 4-6 nm and a height of 10-20 nm between adjacent membranes using ultrathin 10- to 15-nm electron microscopy sections and suggested that these gaps might serve as a molecular sieve. Although such small pores could serve as a molecular filter for albumin, they do not account for the fact that most of the water and solute would pass through the nonselective large breaks (40-50 nm) in the junction strand, the height of which is the same as the wide part of the cleft. Vink and Duling (23) have used fluorescent tracers to measure the thickness of a glycocalyx layer in hamster cremaster muscle capillary in vivo. They found that the thickness of the layer that excludes FITC-dextran is 0.4-0.5 µm. It is not known whether all or a fraction of this layer would serve as a molecular sieve for plasma proteins or what the displacement of the cationized ferritin layer would be if an experiment equivalent to Adamson and Clough (1) could be performed on hamster cremaster microvessels. Experiments are needed to investigate the surface glycocalyx and the size and frequency of junction-strand breaks in mammalian microvessels.

The role of highly localized water flows on the downstream side of fenestrae has been examined both experimentally and theoretically by Levick and co-workers (12, 13) with reference to fluid exchange in the synovium. In experiments in which the tissue concentration of albumin was increased, these investigators also showed that the effects of extravascular albumin on fluid exchange were much less than that of intravascular albumin. The explanation in the fenestrated vessel is that the high water velocity exiting the fenestra decreases the albumin concentration downstream of the fenestra in a region that extends a few micrometers into the tissue. Our calculations show that such tissue gradients also form at the cleft exit in continuous capillaries, although the water velocities are much lower than in fenestrated microvessels. However, for continuous capillaries, the primary interaction of high water velocities and tissue protein occurs within the cleft at the highly localized breaks in the junctional strand. Nevertheless, the elegant studies of Levick and his colleagues (12, 13) in synovium also conform to the hypothesis tested in the present experiments that the Starling forces that determined transcapillary fluid exchange are not the global difference in hydrostatic and oncotic pressure between blood and tissue but the hydrostatic and oncotic pressure across a selective matrix across the glycocalyx or fenestral diaphragm.

Finally, we emphasize that for either frog or mammalian microvessels, it is very difficult, if not impossible, to measure the concentration distribution of the oncotic protein within the cleft itself under experimental conditions. A detailed theoretical model is thus essential to fill in the gaps and provide essential insights as to what is occurring at the cellular microstructural level. The power of the theoretical model is that it has the flexibility to explore in detail the effect of detailed junctional ultrastructure on measured macroscopic behavior.