Simulations of osmotic ultrafiltration failure in CAPD using a serial three-pore - 《American Journal of Physiology》美国生理学杂志干细胞之家



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发表于 2009-4-22 09:43 |只看该作者 |倒序浏览 |打印

作者：Bengt Rippe and Daniele Venturoli作者单位：Department of Nephrology, University Hospital of Lund, Lund, Sweden
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      【摘要】
   Ultrafiltration failure (UFF) is a common complication of long-term peritoneal dialysis (PD). Functionally UFF is in most cases characterized by an enhanced peritoneal mass transfer area coefficient for glucose (PS g ) combined with a largely unchanged peritoneal glucose osmotic conductance (L p S g ). Morphologically, marked UFF occurs with fibrosis of the submesothelial zone in the peritoneum, combined with vasculopathy and vascular proliferation in deeper tissues. To computer simulate UFF, changes both in the vasculature and in the interstitium have to be taken into account. For that purpose, we used a three-pore membrane/fiber matrix serial barrier model, applying the three-pore model to the capillaries and the fiber-matrix model to the interstitium. The parameters of the three-pore model have been published previously. The interstitial fiber density was set at 0.5% (vol/vol) and the fiber radius ( r f ) at 6 Å during control. If the interstitial fiber density was increased from 0.5 to 3%, and r f to 7.5 Å (cf. collagen) while the capillary surface area was increased by 40% from control, then PS g increased from 9.3 to 11.5 ml/min, while the UF coefficient (L p S) was largely unchanged. Further increases in vascular surface area combined with further increases in fiber density caused further increments in PS g, whereas L p S remained unchanged. It is concluded that a matrix of fibers coupled in series with a three-pore membrane may be used for simulating the pathophysiological alterations occurring in the peritoneum in UFF, explaining the commonly observed "uncoupling" of small solute transport (PS) from the peritoneal UF coefficient (L p S) in this condition. + X- e# X% R; X* Q2 C& D
      【关键词】 capillary permeability fibrosis interstitium osmotic reflection coefficient hydraulic conductance glucose+ a7 P, f# h4 m9 x$ g& H) H. }2 `
   ULTRAFILTRATION FAILURE (UFF) occurs in at least 30% of CAPD patients after 5 yr of treatment ( 9 ). Marked UFF is associated with fibrosis of the submesothelial zone of the peritoneum, which becomes avascular, usually combined with vasculopathy and vascular proliferation in deeper tissues ( 13, 37 ). Pathophysiologically, UFF is in a majority of cases characterized by an increase in small-solute transport [or dialysate-to-plasma concentration ratio (D/P) of creatinine] in the absence of large increments in the UF coefficient (L p S), or more precisely, in the peritoneal osmotic conductance to glucose (L p S g ) ( 4, 10 ). The enhanced glucose reabsorption in patients who show an increased transperitoneal small-solute transport, results in rapid dissipation of the glucose osmotic gradient during the dwell, causing a lower maximum UF volume and an earlier peak of the UF vs. time curve ( 10 ). Such alterations are incompatible with an increased vascular surface area alone, which would increase both the L p S g and the transport of small solutes (PS for glucose) across the peritoneum. Mechanistically, these two changes tend to cancel, so that the height of the UF curve (maximum UF) would remain almost unchanged, but with an earlier "peak" of the curve ( Fig. 1 ), when both PS and L p S increase to the same extent ( 10, 22 ). Only if there is an "uncoupling" between PS and L p S UFF will result. There are several potential mechanisms by which such an uncoupling can occur. Since small-solute transport is blood flow limited ( 29 ), while L p S g is not ( 1, 18 ), an uncoupling between PS g and L p S g may occur (to some extent) just because of increases in local peritoneal blood flow. Another possibility, directly correlating the morphological changes in the peritoneal membrane in long-term PD to the altered function, is the appearance of peritoneal neovascularization ( 13 ), and/or recruitment of microvessels in the peritoneum, together with fibrotic alterations in the tissue outside the capillaries ( 37 ).' i2 ^) l3 \( g9 Z6 w

Fig. 1. Drained volume vs. time curves during control conditions using the basic ("lumped") parameters of Table 4 (solid line), but where PS for glucose (PS g ) has been "inflated" (to 15.3 ml/min) according to ( 22, 25 ). Dotted line depicts the situation in which the vascular surface area is doubled, and hatched line depicts the situation in which "lumped" A 0 / X (PS for glucose) is doubled while keeping L p S unperturbed. Note that an increased vascular surface area alone will only marginally impact on the drained volume at 4 h, whereas an "uncoupling" of increases in PS g from L p S will cause marked reductions in drained volume at 4 h (ultrafiltration failure; UFF).) H0 ?  D# K5 h) C2 O' s$ R9 [
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In the present study, we investigate the functional impact of a combination of an increased small-solute mass transfer at the capillary level with ultrastructural (fibrotic) alterations of the interstitial tissue. Hence, we model the blood-peritoneal barrier as composed of two transport resistances coupled in series ( 33 ). The capillary wall is modeled using the planar three-pore model, whereas the interstitium is modeled as a second barrier outside the capillaries, normally having a low density of randomly oriented (glycosaminoglycan or proteoglycan) fibers of radius ( r f ) 6 Å ( Fig. 2 A ). We then investigate the impact of increasing the effective vascular surface area (S) concomitantly with altering the fiber composition and by adding (collagen) fibers ( r = 7.5 AÅ) to the interstitium. Interestingly, the deposition of fibers in the interstitium appears to be very efficient in reducing the UF capacity of the total capillary-interstitial barrier, while only little affecting small-solute transport (PS to glucose) and g. Interstitial fibrosis may thus explain the uncoupling of PS g from L p S g frequently observed in UFF.

Fig. 2. A : schematic illustration of a porous membrane (a three-pore membrane) series coupled with a "normal" interstitium containing a loose matrix of fibers. The capillary surface area is "normal" (A 0 / X = 23,660 cm; S = 1). Overall transport parameters are in line with those used previously for simulations of an average patient ( 22 ) using the planar (noncomposite) three-pore model ( Table 4 ). B : schematic illustration of a situation of simulated UFF. A dense fiber matrix has replaced the interstitium outside the capillaries. In this example, the capillary surface area is enlarged by 80%. Now, the mass transfer area coefficient for glucose (PS g ) is increased 45%, while L p S is completely unchanged and g moderately reduced ( Table 5 ). The presence of a dense fiber matrix uncouples increases in small solute transport (PS g ) from L p S.
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METHODS: S5 T! Z' P: r) m, X3 J& g& P9 h

Pore theory of peritoneal exchange. The three-pore model of peritoneal transport has been presented in detail previously ( 21, 22, 25, 34 ). According to this model, the equivalent peritoneal membrane is characterized as a membrane crossed by small pores, large pores and transcellular pores. The small pores, of radius ( r ) 43-45 Å, approximately account for 90% of the hydraulic conductance (L p S) and represent the main route of passage for small solutes (accounting for more than 99% of the total pore area for solute exchange), whereas 7-8% of the hydraulic conductance is accounted for by large pores ( r 250 Å), allowing the passage of macromolecules. Transcellular pores, representing a water-only conductive pathway [corresponding to aquaporin (AQP)-1], account for the remaining 2% of the hydraulic conductance. The three-pore model has been successfully applied to large sets of experimental data in studies of fluid and solute exchanges in PD ( 22, 24, 26, 31, 32 ). The three-pore model is basically a nonasymmetric model, and therefore problems arise when it is applied to the disappearance of macromolecules from the peritoneal cavity to the peritoneal tissues (and to plasma). To account for the asymmetry of macromolecular transport, a modification of the three-pore model, i.e., a serial heteroporous peritoneal membrane model, has been developed ( 33 ). In this double-layered peritoneal equivalent membrane, the blood-facing side of the membrane had a small pore radius of 43 Å accounting for 90% of the UF coefficient, a large pore radius of 250 Å accounting for 8% of L p S, while aquaporins accounted for 2% of the total L p S. The best fitting serial heteroporous membrane (representing the interstitium) had a small pore radius of 67 Å accounting for 4% of the L p S, while the large pore radius was 2,300 Å accounting for 95% of the L p S. In addition, 2% of total L p S was also represented by transcellular pores ( 33 ).! C" W: C: U/ E" d# x4 A
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Serial pore membrane/fiber matrix model. The present strategy is similar to that taken in our previous publication ( 33 ) on serial peritoneal transport barriers, except that the membrane facing the dialysate side, i.e., the interstitium, is now modeled as a gel containing fibers similar in radius to proteoglycans ( 6 Å). The reason we abandoned the pore model for describing the serial interstitial diffusion/filtration resistance is that a fiber matrix concept represents a more realistic model in describing the transport properties of the interstitium, especially when affected by fibrosis. Furthermore, an altered fiber matrix proved to be very efficient in increasing the interstitial filtration resistance compared with the corresponding small-solute diffusive resistance. Intuitively, according to the pore concept, convective transport would indeed be reduced more efficiently than small solute diffusive transport when the average (interstitial) large pore radius ( r ) is reduced (cf. fibrosis). Diffusion is namely dependent on the total pore (cross-sectional) area (proportional to r 2 ), while filtration events are dependent on the fourth power of the radius ( r 4 ) according to Pouiseuille's law. Thus a 10-fold reduction in interstitial pore radius, while maintaining A 0 / X constant (by increasing the numbers of pores by a factor 100), will result in a hundredfold increase in filtration resistance. Simultaneously, small solute diffusion will be only moderately affected, since A 0 / X is unaltered and the degree of diffusion restriction to small solutes is only moderately reduced, by such a pore narrowing., }3 E( J; u4 e
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In the "classical" fiber matrix theory of capillary permeability, a matrix of fibers is postulated to account for the entire selectivity of the capillary wall by partly (or completely) filling out the spaces in between individual endothelial cells (the so-called interendothelial "clefts") ( 14 ). A fiber matrix showing restrictive properties similar to that of most peripheral continuous capillaries (e.g., present in muscle, adipose tissue, connective tissue, and in the peritoneum), is typically one with a fiber density of 5-6% [void vol. ( ) 94-95%] and a fiber radius of 5-6 Å ( 14 ). We selected a much lower density of the assumed fiber matrix in the interstitium, namely 0.5% (void vol. 99.5%) and a fiber radius of 6 Å ( 28 ) under control conditions consistent with the known presence of proteoglycan molecules as the dominant interstitial fiber type. The latter fiber composition yields transport (sieving) characteristics essentially similar to those characterizing "large pores" (radius 250-300 Å) of the simple three-pore model of peritoneal transport ( Fig. 2 A ). Using current theories for two barriers coupled in series, capillary barrier characteristics were adjusted to match this "interstitium" provided with an A 0 / X being about threefold higher than that of the capillary wall alone, so as to obtain values for "overall" (total) L p S, total PS for glucose, and total g compatible with measured data predicted by the simple planar three-pore model. Adjusting the interstitial matrix composition under normal conditions so that overall (total) A 0 / X, L p S and PS g became within the range characteristic of peritoneal transport, as modeled by the simple three-pore theory, made it necessary to adjust g of the capillary wall alone to 0.06. This value is markedly higher than that of the composite barrier, indicating that the aquaporin density of the capillary wall proper may be much higher than that reflected by the c of the three-pore model. However, 0.06 is more or less exactly consistent with measured values of for glucose for continuous capillary walls proper ( 3, 19 ). By contrast, the overall (capillary-interstitial) UF coefficient was more or less identical to that characteristic of the capillary wall, i.e., of the three-pore model. The basic equations determining the permeability coefficients according to the pore theory, and according to the fiber matrix theory are shown in Tables 1 and 2, respectively. The series array permeability coefficients are evident from Table 3. A value of 5 is chosen for the so-called Kozeny coefficient ( 14 ). Mainly for the sake of simplicity the effects of "unstirred layers" were not included in our modeling. Furthermore, it is likely that the impact of the capillary wall and the interstitial transport barriers per se would (markedly) exceed that of nonmixed conditions in, e.g., the interstitium ( 6 ).& M: ~9 e$ h+ f! ^0 i# I+ b

Table 1. Basic permeability coefficients according to the pore theory$ s1 P/ {/ `! ~6 b4 e3 X

Table 2. Permeability coefficients according to the fiber matrix theory; P: j4 U( @0 J
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Table 3. Basic permeability coefficients for a serial barrier model( ]0 O8 @$ n- ?  E4 u2 \
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One inherent inconsistency in modeling capillary permeability using pore models is the commonly observed "mismatch" between L p S and PS. In whole organ settings PS, and hence, A 0 / X, with the remarkable exception of the glomerular capillaries ( 12, 17 ), is markedly underestimated compared with L p S ( 23 ). The reason is that PS is extremely blood flow limited and sensitive to both the heterogeneity in pore configuration and the distribution of the capillaries in the interstitium. This reduces PS much below the "true" value ( 29 ). However, L p S is more or less unaffected by all the mentioned factors ( 1, 18 ). When L p S is calculated from a markedly underestimated A 0 / X, this estimate will naturally become much lower than the value experimentally assessed. It should be noted that the discrepancy between measured and calculated A 0 / X is inherent in the planar three-pore model ( 21, 22 ), in which the L p S value, when calculated from an A 0 / X of 25,000 cm would be only 0.0072 ml·min -1 ·mmHg -1 ( 24 ). This is one order of magnitude less than the L p S value measured and employed in the three-pore model for calculating fluid transport. Actually, the introduction of a serial interstitial barrier into the three-pore model only partly corrects for the problem. To overcome this problem of discrepancy between A 0 / X-calculated L p S vs. "true" L p S we have introduced an "inflation parameter" (Z cap ) for the calculated capillary barrier L p S, which was here set at 9 (see Tables 1 and 2 ).
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Capillary and interstitial changes in UFF. To model the capillary and interstitial changes in UFF, we assumed that there is either an increased number of capillaries, or an increased blood flow, leading to an increased A 0 / X, and hence, PS for small solutes (= PS for glucose) at the capillary level. These changes are then combined with an increment in fiber density up to 5% ( Fig. 2 B ). Further increments in fiber density would make the interstitium become nearly as impermeable as normal continuous capillary walls, which would be a rather unlikely scenario. Furthermore, in "fibrosis" the average fiber radius was increased from 6 Å to 7.5 Å ( 28 ) to mark a change in fiber composition, with mainly proteoglycan fibers under normal conditions, and collagen fibers, with larger radius, under conditions of interstitial scarring.3 u8 f7 B5 r. P

The blood-to-tissue transport of large solutes, which is mainly convection driven, can be adequately handled by the planar three-pore model ( 20, 23 ). However, the complexity of modeling macromolecular transport increases markedly in a serial barrier model. Among other things, transport now becomes asymmetric, and furthermore, concentration polarization phenomena may potentially occur due to upconcentration of solute in between the (serial) barriers. Due to the complexity of macromolecular transport, we chose in the present study to focus only on the transport of fluid and of small solutes in UFF, leaving the treatment of large solute transport to a forthcoming publication.: k5 p  D1 l( E. `' D  Z

A number of different scenarios are possible with respect to increases in capillary surface area and in fiber density, but generally speaking, the presence of an increasing density of fibers in the interstitium will tend to markedly reduce L p S (and macromolecular transport) while "sparing" PS g (and g ) from being affected (reduced) when microvascular surface area is simultaneously increased.2 j4 ?& m6 t& n
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RESULTS

Basic parameters. The basic parameters selected are shown in Table 4 and Fig. 2 A. In the serial barrier model 80% of the total small solute diffusion resistance of the composite barrier (reciprocal of PS for glucose) is offered by the capillary wall while 20% is offered by the interstitium. For the hydraulic conductance (L p S) corresponding figures are 99.1 and 0.9%, respectively. It should be noted that total (capillary matrix) g is (markedly) reduced compared with that of the capillary wall alone due to the presence of the interstitium (0.047 for the two-layered barrier vs. 0.058 for the capillary barrier). Therefore, the fractional capillary L p S accounted for by the transcellular pathway ( c ) was adjusted from 0.02 to 0.03 in this model to match an overall g of 0.047, characteristic of the simple planar three-pore model. The fractional L p S accounted for by small pores ( s ) was, however, the same as in previous three-pore modeling using single membrane formalism.3 i9 O; p  r) e/ E0 ]( f1 O. f

Table 4. Basic parameters-serial three-pore/fiber matrix model8 K. W; }) |1 Q6 E1 o

Simulations of changes in capillary surface area (S) combined with increases in interstitial fiber thickness (r f ) and density (1- ). The situation described by Table 5 corresponds to a 40% increase in the capillary A 0 / X, from 31,000 cm to 43,400 cm, while the interstitial A 0 / X is kept constant. Furthermore, the fiber density (1- ) is increased from 0.5% to 3%, and r f from 6 to 7.5 Å, respectively, to account for a change in matrix composition from mostly proteoglycans to a more compact mesh of collagen fibers. Whereas an increased fiber density will increase restriction to transport, an increased fiber radius has the opposite effect. The net result is still, in this case, an increased hindrance of the transport of water (and solutes) across the interstitium. Raising capillary barrier A 0 / X by 40%, the total (two-layered) A 0 / X was increased by 28% and total PS for glucose by 25%, i.e., from 9.20 to 11.54 ml/min. At the same time, the composite L p S was almost unchanged, i.e., it increased by only 5%. This is because the interstitial resistance to fluid filtration increased 25 times by increasing the fiber density of the interstitium. Already at these rather moderate changes in capillary surface area and fiber density there was thus a large uncoupling between changes in PS g and L p S while g fell only slightly ( 10%). Furthermore, the L p S g was slightly reduced from 3.66 to 3.45 µl·min -1 ·mmHg -1.
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Table 5. Permeability coefficients for a serial barrier model" ]1 B/ w9 ^3 r8 z

Further increasing the capillary A 0 / X to 1.8 times the control value (55,800 cm) and increasing the fiber density to 4%, led to a PS g value 46% higher than control, while L p S remained almost unchanged. L p S g slightly dropped further to 3.02 µl·min -1 ·mmHg -1 ( Table 5 ) This particular scenario is schematically depicted in Fig. 2 B. In this example, an even greater discrepancy than in the former scenario between the changes in PS g and L p S can be observed.

In a third scenario ( Table 5 ), the fiber density of the interstitium was further increased to 5%, while the capillary surface area was increased to 150% above control (2.5 x control). With these dramatic changes in both capillary surface area and in fiber density, the PS g increased by 75% from control while L p S actually decreased somewhat from control (by 10%), as did the reflection coefficient to glucose (from 0.047 to 0.031). In this situation the osmotic conductance to glucose was dramatically reduced to 2.39 µl·min -1 ·mmHg -1.; R" J0 K" Q6 [5 m* {

Ultrafiltration and sodium sieving in UFF. Figure 3 demonstrates the simulated drained volume curves obtained for the four scenarios shown in Tables 4 and 5. Clinically, manifest UFF (drained UF-volume - n9 m0 A3 o6 N. v3 M9 _

Fig. 3. Computer-simulated drained volume curves obtained for the 4 scenarios shown in Table 4 (solid line) and in Table 5 (squares), (triangles), and (circles), respectively. Manifest UFF at 4 h is evident in the last 2 scenarios. Note that in the scenario tabulated in Table 5, the initial UF rate is nearly unchanged compared with the basic ("normal") situation. In the scenarios described by Table 5 ( bottom 2 curves), L p S g is reduced, causing a reduction in the initial UF rate./ H1 ?- I: b; X2 t# V

Fig. 4. Sodium sieving curves corresponding to the scenarios depicted in Fig 3. Note that the sodium sieving is progressively reduced when the vascular surface area and the interstitial fibrosis both progress in parallel, despite that fact that the capillary C (reflecting the relative capillary density of aquaporins) is kept unchanged.

Fig. 5. A : simulated rates of UF across the three separate pathways of the three-pore model plotted as a function of dwell time under "normal" conditions ( Table 4 and Fig. 2 A ). Solid line represents the total rate of UF, circles represent aquaporin-mediated water flow, crosses small pore-mediated water flow, and stars large pore UF. Total UF is about equally partitioned among small pores and aquaporins, respectively, under "normal" conditions. The rate of lymphatic absorption is set at -0.3 ml/min (not shown). B : simulated rates of UF across the 3 separate pathways of the three-pore model as function of dwell time during conditions of UFF, as depicted in Fig. 2 B (and Table 5 ). In UFF both the aquaporin-mediated water flow and the small pore UF are about equally reduced, although there is a tendency for a more pronounced relative reduction in small pore UF, especially for longer dwell times. Symbols are as in A.2 R" \0 `& \4 l. e1 _; ~7 e

DISCUSSION

The essential result of the present simulations is that a serial three-pore membrane/fiber matrix model can be used for simulating peritoneal transport parameters under normal conditions and in situations similar to those of UFF. The latter condition is usually associated with an enhanced peritoneal mass transfer of small solutes in the absence of large increases in peritoneal UF coefficient ( 10 ). In most cases, UFF is morphologically associated with an increased number of microvessels ( 13 ) accompanying marked interstitial fibrosis, the latter preferentially affecting the submesothelial zone ( 37 ). The present simulations clearly demonstrate that interstitial fibrosis can very markedly reduce the overall UF coefficient of the membrane and also reduce the osmotic reflection coefficient to glucose when the "effective" vascular surface area is concomitantly increased. At the same time, however, small solute transport is barely affected. This can explain why an increased "effective" vascular surface area combined with interstitial fibrosis may lead to increases in overall transperitoneal small solute transport, while the peritoneal ultrafiltration capacity is usually little affected.
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Detailed analyses of the longitudinal PD cohort data of Davies ( 4 ), indicate that increases in PS for small solutes can be rather large over time in long-term PD and that PS is particularly increased in UFF. In the present study adjustments between increases in vascular surface area (S) and in matrix density (1- ) were done to largely maintain L p S constant when both S and (1- ) were increased. However, if changes in effective vascular surface area are effectively larger than those simulated here, then there would be less of uncoupling between PS g and L p S g. By contrast, if changes in interstitial fiber matrix (collagen) deposition are more predominant, then there would be an exaggerated reduction of L p S g, and hence, a larger uncoupling between PS g and L p S g than obtained in the present simulations. Furthermore, we avoided the complication of mixing fibers of varying dimensions in our modeling both during control and UFF conditions. Had the fiber radius been fixed at 6 Å also for the UFF situation, the matrix effect on the uncoupling of PS from L p S g had been even more pronounced, i.e., it had occurred at a lower fiber density, than in the present simulations.

Data concerning exact correlations of morphological to functional peritoneal changes in UFF are essentially lacking. It is, for example, not known how increases in interstitial fiber density are actually matching the concomitant increases in vascular surface area. Particularly, the relationships between increases in small solute mass transfer area coefficients (PS) and in changes of the UF coefficient are not known in detail. In a recent study assessing solute transport in small chambers affixed to the parietal rat peritoneum, fluid and solute transport between the chamber fluid and the underlying peritoneal tissue was determined after 2 mo of subjecting rats (200-300 g) to daily intraperitoneal injections of either 4% glucose or 4% N -acetylglucosamine (NAG) ( 7 ). In both glucose- and NAG-treated animals, vessel density increased markedly in the parietal peritoneum concomitant with increases in both collagen and hyaluronan concentrations in the tissue. Especially in the NAG group, these changes were linked to reductions in protein transport and hydraulic permeability of the tissue accompanied by tendency for a decreased osmotic filtration. However, the increases in the mass transfer area coefficient to mannitol were insignificant. It should, however, be noted that small solute transport was studied in the peritoneal-to-tissue direction. In this direction there could be considerable (lateral) diffusion of small solutes out of the cup region into the peritoneal tissue, curtailing the "true" peritoneal-to-plasma diffusion rates. Large solute transport across the peritoneum is asymmetric ( 22, 24, 33 ). Hence, large solute transport into and through the tissues is at least an order of magnitude higher than that from plasma to peritoneum across the composite capillary/interstitial barrier. Indeed, in the present model the interstitial component of macromolecular transport could be calculated to be markedly affected by fibrosis, because increasing the fiber density from 0.5% ( r f = 6 Å) under normal conditions to 5% ( r f = 7.5 Å) during UFF caused an increase in for albumin across the fiber matrix from 0.0436 to 0.635 according to theory (cf. Tables 2 and 3 ).
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Flessner ( 5 ) recently discussed how an increase in thickness and "density" of the submesothelial, avascular compact zone, combined with an increased vascularity in deeper layers, would markedly increase the diffusive gradient across the peritoneal avascular tissue, thereby reducing the glucose concentration, and hence, the osmosis at the capillary walls. It was pointed out that diffusive transport could still be rapid across the avascular interstitial fibrotic layer, while UF may be more markedly affected (reduced) by the fibrosis. Although this reasoning is in principal agreement with ours, the statements were not founded on mathematical derivations provided in the article. Thus it should be pointed out that reductions in interstitial A 0 / X, due to just increases in transport path length ( X) would about equally increase the interstitial resistance to small solute diffusion and to convection (UF) in the present simulations (cf. Tables 1 and 2 ). The present article emphasizes the importance of the presence of structural changes in the interstitial avascular layer, i.e., an increase in density of the interstitial fibers, to create the observed dissociation between diffusive and convective transport changes occurring in UFF.( F& ~6 P1 Y  p; q4 y# w7 |  r. K) l; ~

The results of the present study indicate that reductions in total (capillary matrix) g can occur due to moderate interstitial fibrosis, whereas more pronounced fibrosis can actually produce increases in g (data not shown). Reductions in L p S g in the presence of an increased vascular surface area and fibrosis can thus be easily explained without invoking a reduced contribution of aquaporin-mediated water transport ( c ). Already in the unperturbed ("normal") situation the presence of a loose fiber matrix in the interstitium had a marked effect on the apparent fraction of L p S accounted for by aquaporins, so that the "apparent" (capillary matrix) c ( Table 4 ) was actually considerably lower than the actual value of the capillary wall ( 11 ). Furthermore, in the presence of advanced interstitial fibrosis (marked) further reductions of L p S g occurred when modeled using the present principles.4 X+ u* i) E! d2 Q
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The osmotic conductance for glucose has only been seldomly assessed in clinical studies. A simple technique for the clinical evaluation of L p S g was introduced by Stelin and Rippe ( 31 ), who measured a L p S g of 3.54 µl·min -1 ·mmHg -1 in 12 patients without UFF. Using a similar approach, Vonesh and Rippe ( 34 ) assessed a closely similar value (3.60 µl·min -1 ·mmHg -1 ) in five non-UFF patients. Applying a slightly different, more mathematical approach, Waniewski et al. ( 35 ) measured a 30% reduction in osmotic conductance in eight CAPD patients with permanent UFF and "high" small solute transfer, whereas three patients with UFF and a high fluid absorption rate displayed a rather unaltered osmotic conductance to glucose. According to the three-pore model, a high fluid absorption rate would be mainly dependent on an increased UF coefficient (L p S) of the peritoneal membrane ( 27, 31 ). Thus there may be a subgroup of patients with UFF in which the UF coefficient is (moderately) increased, while exhibiting an unchanged or moderately reduced L p S g (cf. the scenario in Table 5 ). In these patients there may be a reduction in g in excess of that predicted to occur following interstitial fibrosis. It has been suggested, supported by clinical data, that a reduction in the fractional L p S accounted for by aquaporins ( c ) may be partly responsible for the UFF under such conditions ( 30, 36 ). Furthermore, it cannot be ruled out that an increased lymphatic absorption may contribute to UFF in some cases ( 36 ). However, a majority of patients with UFF seem to exhibit increases in small solute transport (PS), largely uncoupled from changes in L p S g ( 4, 10, 36 ).
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In the literature there is a large experimental body of data validating pore-containing membrane transport models. Furthermore, the models used for restricted transport through pores have been amply validated in vitro using, for example, track-etched membranes ( 2, 16 ). Still, the fiber matrix model has become increasingly popular over the last two decades, not the least in the description of transglomerular transport ( 8 ) and in microvascular transport physiology in general ( 15 ). The rationale for using the fiber matrix theory in the context of glomerular and microvascular transport is that it is assumed to be more "realistic" than pore models, especially in describing transglomerular transport ( 8 ). For example, the fiber matrix theory can reconcile the high selectivity of fenestrated vs. non-fenestrated (continuous) capillaries, despite widely different configurations of the permeable pathways, i.e., fenestrae vs. paracellular slits ( 14 ). In the context of transcapillary permeability, a fiber matrix is usually inserted in series with the interendothelial slits (or pores) as a "prefilter." In the simplest variant of this model, the paracellular slits in-between endothelial cells in continuous microvessels (or the transcellular pores in fenestrated endothelium) are assumed to be almost completely nonrestrictive, with the main size-selectivity attributed to the matrix itself. The major limitation of the fiber matrix model, however, compared with pore models, is that it does not offer any advantages with respect to the degree of freedom (the number of adjustable parameters) or its general behavior with respect to the nature of size-restriction or filtration resistance offered. Thus there is presently no way by which one can experimentally distinguish the fiber matrix model from the pore model. We have preferred to use fiber matrix modeling for the interstitial barrier, mainly due to the histological appearance of the interstitium, and for similar reasons, we continue to apply the three-pore model for describing the capillary barrier properties. It should be pointed out, however, that the interstitium can be equally well described by a set of parallel large pores, positioned in series with the capillary walls, as done in a previous study ( 33 ). Furthermore, interstitial fibrosis can be simulated by markedly reducing the interstitial large pore radius (down to 60-70 Å), while maintaining the cross-sectional interstitial pore area (A 0 / X) unaltered or just moderately reduced.( ~' T& g9 {3 M: E( ^7 A4 J" h
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The presence of a fiber matrix outside the capillary wall may help to explain, not only the pathophysiological alterations occurring in UFF, but also how vectorial osmotic water flow can occur through the normal peritoneum. In the distributed model of peritoneal exchange ( 6 ) there is in PD a tissue glucose concentration gradient directed from the peritoneal cavity (the mesothelial surface) into 200-400 µm of the peritoneal tissue. Superficial capillaries are thus exposed to a relatively high glucose concentration, producing a steep concentration gradient across the capillary walls. For progressively deeper capillaries, however, the transcapillary concentration gradients are correspondingly lower. Whatever magnitude of the transvascular osmotic concentration gradient, there is osmotic fluid flow across the capillary wall. This osmotic flow is directed toward the peritoneal cavity, guided by the tissue concentration gradient of glucose. How can this occur when the net hydraulic pressure gradient actually acts in the opposite direction ( 38 )? An answer to this enigma may be that, in the presence of a fiber matrix in any infinitesimal volume of the interstitium, there is a partitioning of solute from water by the matrix, which actually produces osmosis in a direction opposite to the tissue glucose concentration gradient and opposite to the prevailing net hydraulic pressure gradient. In the present model the interstitial portion of the glucose osmotic conductance was well preserved during UFF due to the canceling effects of the progressive fall of interstitial L p S and the concomitant increase in interstitial g with increases in interstitial fiber density (1- ).
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In conclusion, the present computer simulations indicate that a matrix of fibers positioned in series with a three-pore membrane may be used for simulating normal peritoneal transport characteristics and also the pathophysiological alterations occurring in the peritoneum in a majority of cases of UFF. An increased vascular surface area combined with an increased fiber density of the interstitium yields comparably large increases in small solute transport, while the changes in UF coefficient or the reflection coefficient to glucose are rather moderate. Thus a serial membrane-fiber matrix model may explain the hitherto puzzling "uncoupling" occurring between the increased small solute transport and the rather unchanging peritoneal UF coefficient commonly observed in UFF., [% s4 j, E* F8 p6 K- v6 j

GRANTS

This study was supported by grants from the Swedish Research Council (Grant 14X-08285), the Lundberg Medical Foundation, and European Union Contract FMRX-C98-2019.( y, u* H* i. }

ACKNOWLEDGMENTS* U4 k0 Z- I9 E6 q: j

The expert secretarial assistance by K. Wihlborg is gratefully acknowledged.
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