A corrected equation for the calculation of reflection coefficients

New Insights into the Physiology of Peritoneal Fluid Transport

A review is given on the mechanisms of free water transport, the various methodologies for its measurement, its dependency on the osmotic gradient, and the assessment of osmotic conductance in individual patients. The importance of impaired free water transport in long-term ultra-filtration failure is discussed, relative to peritoneal solute transport status. Furthermore, the relationship of free water transport with locally released potassium is considered, together with a potential role of impaired K+ channel function with peritoneal alterations. Finally, the role of impaired osmotic conductance to glucose and its effects on free water transport in long-term patients with ultrafiltration failure is reviewed.

A gel-membrane model of glomerular charge and size selectivity in series

We have analyzed glomerular sieving data from humans, rats in vivo, and from isolated perfused rat kidneys (IPK) and present a unifying hypothesis that seems to resolve most of the conflicting results that exist in the literature. Particularly important are the data obtained in the cooled IPK, because they allow a variety of experimental conditions for careful analysis of the glomerular barrier; conditions that never can be obtained in vivo. The data strongly support the classic concept of a negative charge barrier, but separate components seem to be responsible for charge and size selectivity. The new model is composed of a dynamic gel and a more static membrane layer. First, the charged gel structure close to the blood compartment has a charge density of 35-45 meq/l, reducing the concentration of albumin to 5-10% of that in plasma, due to ion-ion interactions. Second, the size-selective structure has numerous functional small pores (radius 45-50 A) and far less frequent large pores (radius 75-115 A), the latter accounting for 1% of the total hydraulic conductance. Both structures are required for the maintenance of an intact glomerular barrier.

Pulmonary microvascular permeability. Responses to high vascular pressure after induction of pacing-induced heart failure in dogs

The pressure threshold for injury of pulmonary capillaries is approximately 50 to 55 cm H2O in the canine lung, as measured by changes in the filtration coefficient (Kf,c). Since the pulmonary endothelial basement membrane has been observed to thicken in patients with heart failure and pulmonary venous hypertension, we hypothesized that both baseline permeability and the threshold for high-vascular-pressure injury would be altered as a result. Dogs (n = 12) were chronically paced at 245 beats per minute for approximately 4 weeks, then were paced at 225 beats per minute for an additional 3 weeks. Lung lobes from anesthetized paced dogs and additional control dogs (n = 14) were then isolated, ventilated, and perfused with blood. Although vascular resistance was increased nearly threefold and vascular compliance reduced by 50% in the paced group, Kf,c referenced to 1 g blood-free dry weight was no different from control. Despite this lack of difference at normal pulmonary vascular pressures, several significant results were obtained. First, in the paced group there was a significant increase in the threshold for high-vascular-pressure injury: Kf,c measured at pulmonary vascular pressures commonly seen in heart failure (20 to 50 cm H2O) were significantly less in this group compared with control. Model predictions showed that in vivo, this difference in Kf,c would result in a 50% reduction in the amount of water and protein cleared across the pulmonary capillary endothelial barrier in the paced group.(ABSTRACT TRUNCATED AT 250 WORDS)

Fluid and solute transport in CAPD patients using ultralow sodium dialysate

Transcapillary ultrafiltration during CAPD is determined by the ultrafiltration coefficient of the peritoneal membrane and by Starling forces, the latter being mainly determined by the osmolality of the dialysate. Dialysate sodium concentration decreases during a dwell, implying that: (1) sodium passes the peritoneal membrane to a lesser extent than H2O, and (2) more H2O than sodium is removed in overhydrated patients. We therefore compared two dialysate solutions with similar osmolality, but different sodium concentration (Na+ 129 mmol/liter and 102 mmol/liter). Two peritoneal permeability tests (2 x 6 hrs, dextran 70 as volume marker) with an interval of two days were performed in 10 CAPD patients. Transcapillary ultrafiltration rate was higher with ultralow sodium dialysate (USD) than normal sodium dialysate (NSD): 1.80 +/- 0.16 ml/min versus 1.58 +/- 0.18 (P < 0.01). It was especially higher during the last two hours of the dwell: 0.49 +/- 0.12 ml/min (USD) versus 0.27 +/- 0.13 (NSD). The effective lymphatic absorption rate was not different: 1.01 +/- 0.12 ml/min (USD) versus 1.05 +/- 0.09 (NSD). Using two different kinetic models, the reflection coefficients for glucose, sodium and chloride were 0.032, 0.029 and 0.027 (for the convection model) and 0.033, 0.030 and 0.027 (for the diffusion model). As a consequence the decline in osmotic pressure was more gradual during the exchange with USD. The peritoneal membrane characteristics, that is the effective peritoneal surface area and the peritoneal restriction coefficient, were not altered by the composition of the dialysate.(ABSTRACT TRUNCATED AT 250 WORDS)

Computer simulations of peritoneal fluid transport in CAPD

To model the changes in intraperitoneal dialysate volume (IPV) occurring over dwell time under various conditions in continuous ambulatory peritoneal dialysis (CAPD), we have, using a personal computer (PC), numerically integrated the phenomenological equations that describe the net ultrafiltration (UF) flow existing across the peritoneal membrane in every moment of a dwell. Computer modelling was performed according to a three-pore model of membrane selectivity as based on current concepts in capillary physiology. This model comprises small "paracellular" pores (radius approximately 47 A) and "large" pores (radius approximately 250 A), together accounting for approximately 98% of the total UF-coefficient (LpS), and also "transcellular" pores (pore radius approximately 4 to 5 A) accounting for 1.5% of LpS. Simulated curves made a good fit to IPV versus time data obtained experimentally in adult patients, using either 1.36 or 3.86% glucose dialysis solutions, under control conditions; when the peritoneal UF-coefficient was set to 0.082 ml/min/mm Hg, the glucose reflection coefficient was 0.043 and the peritoneal lymph flow was set to 0.3 ml/min. Also, theoretical predictions regarding the IPV versus time curves agreed well with the computer simulated results for perturbed values of effective peritoneal surface area, LpS, glucose permeability-surface area product (PS or "MTAC"), intraperitoneal dialysate volume and dialysate glucose concentration. Thus, increasing the peritoneal surface area caused the IPV versus time curves to peak earlier than during control, while the maximal volume ultrafiltered was not markedly affected. However, increasing the glucose PS caused both a reduction in the IPV versus time curve "peak time" and in the "peak height" of the curves. The latter pattern was also seen when the dialysate volume was reduced. It is suggested that computer modelling based on a three-pore model of membrane selectivity may be a useful tool for describing the IPV versus time relationships under various conditions in CAPD.

Convection of macromolecules is the dominant mode of transport across horizontal 0.4- and 3-microns filters in diffusion chambers: significance for biologic monolayer permeability assessment

The purpose of the present study was to evaluate the permeability characteristics of fluorescein-labeled hydroxyethyl starch (FITC-HES, 20 less than molecular radius, aE less than 111 A) across large pore (0.4- and 3-microns polycarbonate) filters used in endothelial cell monolayer diffusion studies. Although the apparent permeability (P) of the FITC-HES macromolecules across these filters declined as the molecular radius increased, this decline was less than that associated with each solute's free diffusion (D0). Thus, the P/D0 anomalously increased as aE increased, a pattern not seen for free diffusion (flat P/D0 with increased aE) or restricted diffusion (decline in P/D0 with increased aE). Substantial natural convection across the porous filters produced the anomalous P/D0 curve for the following reasons: (1) this effect was elevated with positive pressure and ameliorated by zero driving pressure, and (2) the effect was much greater across filters with large (3 microns) vs small (0.4 microns) pore sizes. In addition, we estimated that less than half of macromolecular transport above 50 A probe radius at zero transmural pressure arrives by diffusion. The findings suggest that the property of restricted diffusion of biologic layers on these filters will be artifactually exaggerated when the measured resistance of the filter is subtracted from that of the filter plus biologic monolayer. Remedies for this problem may include using smaller pore filters, filters layered with extracellular material, or structural methods to determine true filter permeability.

Vascular clearance by the reticuloendothelial system--measurements using two different-sized albumin colloids

Normal and reticuloendothelial system (RES) stimulated rats were examined with dynamic liver RES scintigraphy using a computerized gamma camera. 99Tcm-labelled albumin colloid, albures (radius 250 nm) or nanocoll (radius 25 nm), or both were used as test substances to study the kinetics of vascular clearance after RES stimulation. Registrations were made of 30 s per frame for 5 min and 300 s per frame for 15 min or 25 min and a region of interest (ROI) was indicated over the liver. Whole body and liver RES clearance rate constants (k) were calculated from the liver uptake vs time curve. Liver parenchyma blood flow was estimated with 133Xe washout technique. The blood clearance rate constant of albures in non-activated rats was twice that for nanocoll (1.08 +/- 0.05 vs 0.49 +/- 0.02 10(-2)s-1). There was no mutual interaction between the two colloids, implying that they may be eliminated from the blood-stream by slightly different processes. In zymosan-stimulated animals, nanocoll given in a single injection showed a significantly increased k-value. Neither the albures clearance rate constant nor the nanocoll/albures k-value ratio revealed RES macrophage activation. By contrast the nanocoll/albures ratio, calculated for the liver, rose significantly. The final colloid uptake in the liver revealed RES macrophage activation. No changes in liver parenchyma blood flow per g tissue could be registered after administration of zymosan. The nanocoll and albures colloid particles did not impair the normal liver parenchyma blood flow.(ABSTRACT TRUNCATED AT 250 WORDS)

A phenomenological interpretation of the variation in dialysate volume with dwell time in CAPD

Intraperitoneal fluid volume (IPV) changes versus time were followed in patients undergoing continuous ambulatory peritoneal dialysis (CAPD) using a simple volume recovery method. In each patient dialysates containing 1.36 and 3.86 percent glucose as an osmotic agent were investigated. The patients' IPV versus time data were fitted to a function determined by four "arbitrary" coefficients, from which both the initial ultrafiltration (UF) rate immediately following intraperitoneal (i.p.) fluid instillation and the "final" peritoneal-to-blood fluid absorption rate could be assessed. The peritoneal osmotic conductance to glucose, that is, the peritoneal ultrafiltration coefficient (Kf), times the peritoneal osmotic reflection coefficient to glucose (sigma g), Kf sigma g, was determined using two related approaches. Kf sigma g is a major determinant of the transperitoneal volume exchange, and it was calculated to be 3.54 +/- 0.85 (+/- SE) and 3.81 +/- 0.52 microliters/min/mm Hg, respectively, depending on the assumption employed. Kf sigma g was further analysed according to a three-pore model of membrane permeability to determine the possible range of Kf and sigma g compatible with a peritoneal small solute sieving coefficient (phi) ranging from 0.3 to 0.61. According to these calculations both Kf and sigma g ranged from 0.043 to 0.081 (ml/min/mm Hg and dimensionless, respectively). The maximal peritoneal lymph flow (L) realistic according to this analysis, and compatible with a measured total peritoneal-to-blood fluid absorption rate of 1.25 +/- 0.14 ml/min, was 0.75 ml/min, the most plausible values, however, falling between 0.3 to 0.5 ml/min.

Simulations of peritoneal solute transport during CAPD. Application of two-pore formalism

Blood peritoneal clearances of various endogenous solutes in patients undergoing continuous ambulatory peritoneal dialysis (CAPD) were evaluated according to recent developments of the two-pore theory of membrane permeability, using a non-linear transport formalism for the analysis. Based on results obtained from these calculations and taking lymphatic drainage into account, transport from peritoneal cavity to the blood was also simulated. With respect to solute transport the data were compatible with a functional blood-peritoneal barrier consisting of a two-pore membrane containing a large number of paracellular "small pores" of radius 40 to 55 A and a small number of "large pores" of radius 200 to 300 A. Solutes smaller than 25 A in radius were found to be permeating across the peritoneal membrane mainly by means of diffusion across the small pores, whereas solutes larger than 40 A were calculated to reach the peritoneal cavity exclusively by unidirectional convection across the large pores. In addition, water was simulated to be transported through transcellular "ultrapores" (radius less than 8 A) not accessible to hydrophilic solute permeation. Small solute absorption from the peritoneal cavity was found to occur by diffusion across small pores. Molecules larger than 25 to 30 A in radius (molecular weight above 25,000) were simulated to be absorbed from the peritoneal cavity exclusively via non-size-selective lymphatic drainage.

Transcapillary albumin extravasation in rat skin and skeletal muscle: effect of increased venous pressure

Plasma-to-tissue transport of radioactively labelled albumin has been used to study the effect of increased venous pressure on transcapillary albumin transport. Venous pressure was increased by inflating a balloon catheter in the inferior caval vein. Plasma-to-tissue transport of albumin was taken as the extravascular distribution space (EValb) for 125I-labelled human serum albumin (I-HSA) after 1 h. Venous pressure was increased from 2 to 20 mmHg in the experimental group. Interstitial fluid volume (IFV) was measured as the extravascular distribution space for 51Cr-EDTA. In control EValb was 9.24 X 10(-3) ml g-1 d. wt (SD = 1.28, n = 8) and 3.67 X 10(-3) ml g-1 d.wt (SD = 0.94, n = 8) in skin and skeletal muscle, respectively. Increasing venous pressure raised EValb and IFV in skin and skeletal muscle, but the increase in EValb was about 3 and 5% of the rise in IFV, resulting in capillary reflection coefficients for albumin of 0.94 in skin and 0.98 in skeletal muscle. The low transcapillary albumin transport relative to water transport is compatible with a two-pore model of transcapillary exchange where large pores (250 A) accounts for less than 5.5 and 2.5% of the total capillary filtrate of fluid in skin and skeletal muscle, respectively.

Fluid and protein fluxes across small and large pores in the microvasculature. Application of two-pore equations

Treating the blood-tissue barrier as a two-pore membrane the separate fluid and solute fluxes occurring across 'small pores' and 'large pores' were modelled in continuous capillaries employing two-pore equations for the calculations together with the non-linear flux equation and theories for restricted diffusion and for the reflection coefficient (sigma). The two-pore equations derived proved useful for analyses of transvascular protein flux data obtained at low as well as at high filtration rates. These equations were applied to lymphatic protein flux data from dog paw (Renkin et al. 1977a, b) and to tracer albumin uptake data from rat skeletal muscle (Rippe et al. 1979). For both sets of data the small- and large-pore radii became closely similar, 44 vs. 45 A and 240 vs. 225 A, which also holds for the large-pore fractions of hydraulic conductivity (0.097 vs. 0.056). The main result of this analysis is that the passage of macromolecules normally occurring across the microvascular walls is almost entirely convective, and hence, dependent on the transmural hydrostatic and oncotic pressure gradients and on the hydraulic conductivity. For example, 75-90% of the transvascular passage of albumin was found to be due to convection through large pores at normal lymph flows, the remaining portion being mainly due to diffusion across small pores. Solutes larger than albumin were almost exclusively transported by convection across large pores. Two-pore heterogeneity was found to explain the previously observed variations of the apparent overall large solute diffusion capacity (PSapp) and the overall reflection coefficient (sigma f) with filtration rate and also previous overestimations of PS. Furthermore, the present results were not compatible with protein transport across any 'non-hydraulically conductive capillary pathways' as previously postulated from the lymphatic protein flux data analysed here (Renkin 1985).

Analysis of altered capillary pressure and permeability after thermal injury

In order to investigate the effects of thermal injury on microvascular hemodynamics and permeability, hindpaw arterial (PA), venous (PV), and capillary (PC) pressures, blood (QB) and lymph (QL) flows, and lymph (CL) and plasma (CP) total protein concentrations were measured before and for 3 hr after a 10-sec 100 degrees C scald burn in 11 dogs. Prior to injury in eight experiments (Group I--permeability analysis) venous pressure was elevated by outflow restriction until the minimal CL/CP was obtained. In three experiments (Group II--hemodynamic analysis) outflow was not restricted. Lymph and plasma protein fractions ranging in size from 37 to 120 A were measured using gradient gel electrophoresis and capillary equivalent pore sizes were calculated. In the early postburn period, PC increased from 24 +/- 2 (mean +/- SE) to 47 +/- 5 mm Hg (P less than 0.05) and precapillary resistance (RA) decreased from 6.6 +/- 0.2 to 2.5 +/- 0.2 mm Hg/ml/min/100 g (P less than 0.05) while postcapillary resistance (RV) remained unchanged. Pre- to postcapillary resistance (RA/RV) fell by 74%. The reflection coefficient for total proteins (calculated as sigma = 1 - CL/CP) decreased from 0.87 +/- 0.01 to 0.45 +/- 0.02 (P less than 0.01). Permeability of the postburn capillary endothelium was described by using two populations of equivalent pores. Preburn pore radii were 50 and 300 A with 13% of the capillary filtrate passing through the large pores. Pore radii increased after injury to 70 and 400 A with 49% of the filtrate passing through the large pores. The postburn total tissue filtration coefficient (Kf) increased to 2.4 times the control. Over the first 3 hr postburn, 53% of the increase in capillary filtration was attributable to increased capillary pressure and 47% to increased permeability. We conclude that the early rapid edema formation following thermal injury is the result of marked increases in both capillary filtration pressure and filtration through large nonsieving pores.

Influence of perfusate oncotic pressure on the transcapillary clearance of albumin in maximally vasodilated rat skeletal muscle

An external detection technique was developed for repetitive and reliable measurements of clearance (Cl) of 99mTc-albumin during alterations of serum colloid osmotic pressure (pi p). Isolated, maximally vasodilated rat hindquarters were perfused with serum of two pi ps (20 mmHg and 45 mmHg) at four or five different filtration rates (Fv) for each pi p in each animal. The recorded accumulation rates of 99mTc-albumin (AR) were converted into dimensions of albumin clearance, setting the isogravimetric Cl at normal vascular pressures (pi p = 20 mmHg) at 0.0246 +/- 0.0012 ml min-1 per 100 g, which was obtained in defined muscle samples in 11 separate experiments. Serum perfusion with higher colloid osmotic pressure (45 mmHg) shifted the albumin clearance values upwards, without affecting the slope of the Cl vs. Fv relationship. Thus, the reflection coefficient (sigma) for albumin did not seem to be affected by the changes in pi p, while the isogravimetric albumin clearance was increased to roughly 0.058 ml min-1 per 100 g. Explicit two-pore equations were found to describe the experimental data fairly well, yielding an average sigma for albumin of 0.92 and a minor contribution of diffusion to overall transport even at low Fvs. Moreover, a coupling of macromolecular clearance to pi p may serve to minimize alterations in plasma protein concentration.

Capillary permeability in rat hindquarters as determined by estimations of capillary reflection coefficients

Osmotic reflection coefficients (sigma) for a variety of solutes ranging from NaCl to albumin were determined in perfused maximally vasodilated rat hindquarters employing the osmotic transient method (Vargas & Johnson 1964). Measurements were performed at high flows and using short tubings with small volumes. Intracapillary solute concentrations of the osmotic transients were measured or estimated for solutes of the size of inulin or smaller. The PS for Cr-EDTA and cyanocobalamine were determined repeatedly in half of the experiments using an on-line modification of the single injection (indicator diffusion) method (Rippe & Stage 1978) and capillary filtration coefficients (CFC or LpS) were followed in all experiments. The capillary osmotic reflection coefficient was determined to 0.05 for NaCl, to 0.08 for sucrose, to 0.39 for inulin, to 0.57 for myoglobin and to 0.87 for albumin. These reflection coefficients were compatible with a 'small pore radius' of approximately 40 A (slit width (w) of approximately 50 A) according to modern hydrodynamic theories for the reflection coefficient and the parallel transcapillary pathway hypothesis. The best fit of the osmotic transient data to current theories for the reflection coefficient occurred if the major portion (86-87%) of the hydraulic conductivity (Lp) was accounted for by this paracellular 'small pore' (slit) pathway and if 3.0-4.1% of Lp could be ascribed to a transcellular pathway (sigma approximately I) while the remaining fraction (10%) of Lp was accounted for by a non-selective paracellular pathway (sigma approximately o); that is, by 'large pores'.

Fluid filtration and protein clearances through large and small pore populations in dog lung capillaries

Solvent drag reflection coefficients (sigma f) for six protein fractions with hydrodynamic radii ranging from 37 to 120 A were determined using dog lung lymph CL/CP data over a range of lung lymph flows (QL). Two equivalent pore populations with effective radii of 75-85 A and 200-325 A were determined for the pulmonary capillaries over a range of mean lymph flows for 1.8 to 6.3 times control. Fractional fluid clearance through the large pore population was observed to decrease from 0.28 to 0.16 as QL increased. These data indicate that lymph flow (filtration) increased primarily by an increased filtration through small pores with relatively little increase in filtration through the large pore population. The shift to small pore filtration at high filtration rates accounts for the dependence of the homoporous estimate of total protein sigma f on lymph flow previously observed using lung lymph (Parker et al., 1981). If capillary membrane heteroporosity is present then there should be a net convective clearance of protein across the capillary caused by a volume circulation between large and small pore populations. Minimal estimates of 6-10% of protein clearance are attributed to this mechanism even in the absence of net fluid movement across the capillary. The optimal solute radius for clearance due to volume circulation is about 60 A, based on the membrane pore sizes determined for lung capillaries. Although convective transport of macromolecules is generally acknowledged to account for most transcapillary protein clearance at high filtration rates, the inclusion of a volume circulation component suggests that convection may also be the dominant mode of macromolecular transport at low filtration rates.

Importance of molecular charge for the passage of endogenous macromolecules across continuous capillary walls, studied by serum clearance of lactate dehydrogenase (LDH) isoenzymes

Electrostatic capillary barrier characteristics was studied in the isolated maximally vasodilated rat hindquarter by use of a modified "tissue uptake" technique (Rippe et al. 1979). The hindquarters were artificially perfused with oxygenated horse serum at isogravimetry. As tracers two isoenzymes of lactate dehydrogenase (LDH) were used, having identical size (41 A, Mw approximately 140 000) but with differing molecular charge and labelled with two separable isotopes. LDH-H4 (125I) is negatively charged and LDH-M4 (131I) slightly positive, at physiological pH. The negatively charged protein LDH-H4 was more retarded in its transcapillary passage than LDH-M4. Net clearance of H4 was 0.0242 +/- 0.0045 ml/min X 100 g and that of M4 was 0.0748 +/- 0.0092 ml/min X 100 g (n = 11, p less than 0.001). This difference is suggested to be due to an interaction of the polyanionic tracer with a barrier of negative molecular charge, most effective at the small pore equivalent. Clearance data for H4 and for albumin (Rippe et al. 1979) are compatible with an equivalent large pore radius of 520 A. Neither vesicular transport (Palade 1953) nor the impact of fibre pore matrix (Michel 1980) is considered to be involved in the transcapillary passage of proteins. Negatively charged proteins probably pass through the large pore equivalent exclusively, while neutral macromolecules also utilize part of the small pore equivalent, for their transcapillary passage.

Vascular permeability and transvascular fluid and protein transport in the dog lung

We used steady state lymph-to-plasma concentration ratios of six endogenous protein fractions (effective hydrodynamic radii of 37, 40, 44, 53, 100, and 120 A) to estimate pulmonary capillary permeability characteristics. Pulmonary lymph was collected from an afferent lymphatic to the left tracheobronchial lymph node, and left atrial pressure was elevated in steps until the lymphatic protein concentration obtained a constant value. Lymph flow and transvascular protein flux increased with each increase in left atrial pressure. Convective flux was the predominant mode of transport for the smaller fractions, and solvent-drag reflection coefficients increased as lymph flow increased. This dependency on lymph flow (capillary filtration) indicates a heteroporous membrane system. For lymph flows greater than five times control, the solvent-drag reflection coefficients were: 0.59 +/- 0.11, 0.52 +/- 0.06, 0.66 +/- 0.05, 0.70 +/- 0.05, 1.01 +/- 0.04, and 1.05 +/- 0.03 for the six fractions. Osmotic reflection coefficients estimated from the minimal lymph-to-plasma concentration ratios were: 0.50 +/- 0.03, 0.59 +/- 0.02, 0.67 +/- 0.04, 0.72 +/- 0.03, 0.94 +/- 0.01, and 0.96 +/- 0.01 for the six protein fractions. The osmotic reflection coefficients are consistent with a two- "pore" exchange model possessing equivalent pore radii of 80 and 200 A. Theoretical considerations indicate that only the two largest protein fractions (100 A and 120 A radii) achieved filtration-independent concentrations in pulmonary lymph, even at the highest filtration rates. This suggests that the reported osmotic reflection coefficients of the four small protein fractions underestimate their true values.