Mathematical Models for Peritoneal Transport Characteristics

1999 ◽  
Vol 19 (2_suppl) ◽  
pp. 193-201 ◽  
Author(s):  
Jacek Waniewski
Keyword(s):  
Mathematical Models ◽  
Peritoneal Cavity ◽  
Fluid Transport ◽  
Driving Forces ◽  
Experimental Studies ◽  
Theoretical Description ◽  
Distributed Model ◽  
Transport Parameters ◽  
Pore Model ◽  
Peritoneal Transport

Four mathematical models and for the description of peritoneal transport of fluid solutes are reviewed. The membrane model is usually applied for (1) separation of transport components, (2) formulation of the relationship between flow components and their driving forces, and (3) estimation of transport parameters. The three-pore model provides correct relationships between various transport parameters and demonstrates that the peritoneal membrane should be considered heteroporous. The extended threepore model discriminates between heteroporous capillary wall and tissue layer, which are assumed to be arranged in series; the model improves and modifies the results of the three-pore model. The distributed model includes all parameters involved in peritoneal transport and takes into account the real structure of the tissue with capillaries distributed at various distances from the surface of the tissue. How the distributed model may be applied for the evaluation of the possible impact of perfusion rate on peritoneal transport, as recently discussed for clinical and experimental studies, is demonstrated. The distributed model should provide theoretical bases for the application of other models as approximate and simplified descriptions of peritoneal transport. However, an unsolved problem is the theoretical description of bi-directional fluid transport, which includes ultrafiltration to the peritoneal cavity owing to the osmotic pressure of dialysis fluid and absorption out of the peritoneal cavity owing to hydrostatic pressure.

Changes of Peritoneal Transport Parameters with Time on Dialysis: Assessment with Sequential Peritoneal Equilibration Test

2017 ◽  
Vol 40 (11) ◽  
pp. 595-601 ◽  
Author(s):  
Jacek Waniewski ◽  
Stefan Antosiewicz ◽  
Daniel Baczynski ◽  
Jan Poleszczuk ◽  
Mauro Pietribiasi ◽  
...  
Keyword(s):  
Solute Transport ◽  
Fluid Transport ◽  
Transport Processes ◽  
Model Parameters ◽  
Hydraulic Permeability ◽  
Transport Parameters ◽  
Peritoneal Equilibration Test ◽  
Transport Barrier ◽  
Pore Model ◽  
Peritoneal Transport

Background Sequential peritoneal equilibration test (sPET) is based on the consecutive performance of the peritoneal equilibration test (PET, 4-hour, glucose 2.27%) and the mini-PET (1-hour, glucose 3.86%), and the estimation of peritoneal transport parameters with the 2-pore model. It enables the assessment of the functional transport barrier for fluid and small solutes. The objective of this study was to check whether the estimated model parameters can serve as better and earlier indicators of the changes in the peritoneal transport characteristics than directly measured transport indices that depend on several transport processes. Methods 17 patients were examined using sPET twice with the interval of about 8 months (230 ± 60 days). Results There was no difference between the observational parameters measured in the 2 examinations. The indices for solute transport, but not net UF, were well correlated between the examinations. Among the estimated parameters, a significant decrease between the 2 examinations was found only for hydraulic permeability LpS, and osmotic conductance for glucose, whereas the other parameters remained unchanged. These fluid transport parameters did not correlate with D/P for creatinine, although the decrease in LpS values between the examinations was observed mostly for patients with low D/P for creatinine. Conclusions We conclude that changes in fluid transport parameters, hydraulic permeability and osmotic conductance for glucose, as assessed by the pore model, may precede the changes in small solute transport. The systematic assessment of fluid transport status needs specific clinical and mathematical tools beside the standard PET tests.

scholarly journals Peritoneal Fluid Transport rather than Peritoneal Solute Transport Associates with Dialysis Vintage and Age of Peritoneal Dialysis Patients

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jacek Waniewski ◽  
Stefan Antosiewicz ◽  
Daniel Baczynski ◽  
Jan Poleszczuk ◽  
Mauro Pietribiasi ◽  
...  
Keyword(s):  
Peritoneal Dialysis ◽  
Solute Transport ◽  
Fluid Transport ◽  
Peritoneal Membrane ◽  
Transport Parameters ◽  
Patient Age ◽  
Pore Model ◽  
Peritoneal Transport ◽  
Patient Âgé ◽  
Dialysis Vintage

During peritoneal dialysis (PD), the peritoneal membrane undergoes ageing processes that affect its function. Here we analyzed associations of patient age and dialysis vintage with parameters of peritoneal transport of fluid and solutes, directly measured and estimated based on the pore model, for individual patients. Thirty-three patients (15 females; age 60 (21–87) years; median time on PD 19 (3–100) months) underwent sequential peritoneal equilibration test. Dialysis vintage and patient age did not correlate. Estimation of parameters of the two-pore model of peritoneal transport was performed. The estimated fluid transport parameters, including hydraulic permeability (LpS), fraction of ultrasmall pores (αu), osmotic conductance for glucose (OCG), and peritoneal absorption, were generally independent of solute transport parameters (diffusive mass transport parameters). Fluid transport parameters correlated whereas transport parameters for small solutes and proteins did not correlate with dialysis vintage and patient age. Although LpS and OCG were lower for older patients and those with long dialysis vintage,αuwas higher. Thus, fluid transport parameters—rather than solute transport parameters—are linked to dialysis vintage and patient age and should therefore be included when monitoring processes linked to ageing of the peritoneal membrane.

A Three-Pore Model of Peritoneal Transport

1993 ◽  
Vol 13 (2_suppl) ◽  
pp. 35-38 ◽  
Author(s):  
Bengt Rippe
Keyword(s):  
Peritoneal Cavity ◽  
Protein Transport ◽  
Water Soluble ◽  
Fluid Loss ◽  
Peritoneal Membrane ◽  
Reasonable Accuracy ◽  
Lymphatic Absorption ◽  
Pore Model ◽  
Peritoneal Transport ◽  
Order Of Magnitude

The three-pore model of peritoneal transport treats the capillary membrane as a primary barrier determining the amount of solute that transports to the interstitium and the peritoneal cavity. According to the three-pore model, the principal peritoneal exchange route for water and water-soluble substances is a protein-restrictive pore pathway of radius 40–55 A, accounting for approximately 99% of the total exchange (pore) area and approximately 90% of the total peritoneal ultrafiltration (UF) coefficient (LpS). For their passage through the peritoneal membrane proteins are confined to so-called “large pores” of radius approximately 250 Å, which are extremely few in number (0.01% of the total pore population) and more or less nonrestrictive with respect to protein transport. The third pathway of the three-pore model accounts for only about 2% of the total LpS and is permeable to water but impermeable to solutes, a so-called “water-only” (transcellular?) pathway. In contrast to the classical Pyle-Popovich (P&P) model, the three-pore model can predict with reasonable accuracy not only the transport of water and “small solutes” (molecular radius 2.3–15 Å) and “intermediatesize” solutes (radius 15–36 Å), but also the transport of albumin (radius 36 Å) and larger molecules across the peritoneal membrane. The model operates with reflection coefficientsa (a's) for small solutes <0.1. These are approximately one order of magnitude lower than the & sigma's In the P&P model. Furthermore, the peritoneal LPS is one order of magnitude higher than In the P&P model. As a consequence, the major portion of the “fluid loss” from the peritoneal cavity In continuous ambulatory peritoneal dialysis (CAPD) can be explained by the operation of the so-called Starling forces (the transcapillary hydrostatic pressure gradient opposed by the plasma colloid osmotic pressure as multiplled by the LpS), and to a much lesser extent by lymphatic absorption (L). Furthermore, In contrast to the P&P model, the three-pore model can with reasonable accuracy predict the UF profiles produced when glucose Is substituted by high molecular weight solutes as osmotic agents In CAPO.

On the change of transport parameters with dwell time during peritoneal dialysis

2020 ◽  
pp. 089686082097151
Author(s):  
Jacek Waniewski ◽  
Joanna Stachowska-Pietka ◽  
Bengt Lindholm
Keyword(s):  
Peritoneal Dialysis ◽  
Clinical Data ◽  
Dwell Time ◽  
Dialysis Fluid ◽  
Transport Parameters ◽  
Satisfactory Description ◽  
Pore Model ◽  
Vasodilatory Effect ◽  
Peritoneal Transport ◽  
Molecular Radius

The transitory change of fluid and solute transport parameters occurring during the initial phase of a peritoneal dialysis dwell is a well-documented phenomenon; however, its physiological interpretation is rather hypothetical and has been disputed. Two different explanations were proposed: (1) the prevailing view—supported by several experimental and clinical studies—is that a vasodilatory effect of dialysis fluid affects the capillary surface area available for dialysis, and (2) a recently presented alternative explanation is that the molecular radius of glucose increases due to the high glucose concentration in fresh dialysis fluid and that this change affects peritoneal transport parameters. The experimental bases for both phenomena are discussed as well as the problem of the accuracy necessary for a satisfactory description of clinical data when the three-pore model of peritoneal transport is applied. We show that the correction for the change of transport parameters with dwell time provides a better fit with clinical data when applying the three-pore model. Our conclusion is in favor of the traditional interpretation namely that the transitory change of transport parameters with dwell time during peritoneal dialysis is primarily due to the vasodilatory effect of dialysis fluids.

How Accurate is the Description of Transport Kinetics in Peritoneal Dialysis According to Different Versions of the Three-Pore Model?

2008 ◽  
Vol 28 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Jacek Waniewski ◽  
Malgorzata Debowska ◽  
Bengt Lindholm
Keyword(s):  
Peritoneal Dialysis ◽  
Solute Transport ◽  
Peritoneal Fluid ◽  
Dwell Time ◽  
Transport Kinetics ◽  
Transport Parameters ◽  
Pore Model ◽  
Peritoneal Transport ◽  
Endogenous Protein ◽  
Dialysate Volume

Objective The three-pore model of peritoneal transport is used extensively for modeling peritoneal fluid and solute transport, but the currently used versions include certain modifications of the transport parameters that have not been validated quantitatively versus detailed data on fluid and solute kinetics. The aim of this study was to evaluate different versions of the three-pore model. Method Detailed clinical peritoneal fluid and solute transport data were obtained from 40 peritoneal dwell studies in clinically stable continuous ambulatory peritoneal dialysis patients in whom the dialysate volume was measured using a macromolecular volume marker (RISA). Results Using a new version of the three-pore model with several adjusted transport parameters, good agreement between the measured and the simulated values of dialysate volume and concentrations of small solutes and RISA (but not of endogenous protein) versus dwell time was obtained; however, the predicted peritoneal absorption for longer than the investigated dwell time would be too high. Conclusion The three-pore model, with some adjustments proposed in this study, may be used for detailed description of peritoneal transport kinetics, but it should be pointed out that, even after these adjustments, it still does not provide the correct description of peritoneal fluid absorption and transport of macromolecules.

Distributed modeling of osmotically driven fluid transport in peritoneal dialysis: theoretical and computational investigations

2009 ◽  
Vol 296 (6) ◽  
pp. H1960-H1968 ◽  
Author(s):  
Jacek Waniewski ◽  
Joanna Stachowska-Pietka ◽  
Michael F. Flessner
Keyword(s):  
Peritoneal Dialysis ◽  
Fluid Transport ◽  
Present Report ◽  
Capillary Wall ◽  
Distributed Model ◽  
Hydraulic Permeability ◽  
Transport Parameters ◽  
Distributed Modeling ◽  
Dialysis Solution ◽  
Osmotic Agent

Based on a distributed model of peritoneal transport, in the present report, a mathematical theory is presented to explain how the osmotic agent in the peritoneal dialysis solution that penetrates tissue induces osmotically driven flux out of the tissue. The relationships between phenomenological transport parameters (hydraulic permeability and reflection coefficient) and the respective specific transport parameters for the tissue and the capillary wall are separately described. Closed formulas for steady-state flux across the peritoneal surface and for hydrostatic pressure at the opposite surface are obtained using an approximate description of the concentration profile of the osmotic agent within the tissue by exponential function. A case of experimental study with mannitol as the osmotic agent in the rat abdominal wall is shown to be well described by our theory and computer simulations and to validate the applied approximations. Furthermore, clinical dialysis with glucose as the osmotic agent is analyzed, and the effective transport rates and parameters are derived from the description of the tissue and capillary wall.

Impact of the Liver on Peritoneal Transport

1996 ◽  
Vol 16 (1_suppl) ◽  
pp. 205-207 ◽  
Author(s):  
Michael F. Flessner
Keyword(s):  
Peritoneal Cavity ◽  
Transport Coefficients ◽  
Diffusion Chamber ◽  
Solute Diffusion ◽  
Distributed Model ◽  
Peritoneal Membrane ◽  
Peritoneal Transport ◽  
Dialysis Solution ◽  
Mass Transport Coefficient ◽  
Small Solute

Previously, we developed a distributed model of plasma-peritoneal small solute diffusion for specific tissues surrounding the peritoneal cavity and related the transport coefficients to the mass transport coefficient (MTC) of the “peritoneal membrane” model. Based on this theoretical analysis, we calculated tissue-specific MTCs for sucrose from microvascular data in the literature and found that the MTC for the liver was five times the magnitude of other tissues. We hypothesized that the liver was potentially the most significant single transport organ during peritoneal dialysis. To test this hypothesis, we measured the mass transfer from the plasma to fluid contained in diffusion chambers, which were glued to one of four tissues surrounding the peritoneal cavity. We determined that the rate of small solute transport from the plasma to each diffusion chamber was similar for all four tissues. We calculated the MTC of the liver to be no greater than other visceral or parietal surfaces. We therefore disproved our hypothesis concerning the liver. We conclude that the importance of a particular tissue to plasma-peritoneal transport is primarily dependent on the surface area exposed to the dialysis solution.

Formation of coagulated colloidal silica in high-temperature mineralizing fluids

2002 ◽  
Vol 66 (4) ◽  
pp. 547-553 ◽  
Author(s):  
B. J. Williamson ◽  
J. J. Wilkinson ◽  
P. F. Luckham ◽  
C. J. Stanley
Keyword(s):  
High Temperature ◽  
Hydrothermal Fluid ◽  
Colloidal Silica ◽  
Fluid Transport ◽  
Experimental Studies ◽  
Hydrothermal Fluids ◽  
Ore Formation ◽  
Colloidal Gel ◽  
Material Forming ◽  
Mineralizing Fluids

AbstractRecent experimental studies have suggested that colloidal silica can form in high-T (300 to >700°C) hydrothermal fluids (Wilkinson et al., 1996). Natural evidence in support of this was found by Williamson et al. (1997) who proposed a colloidal (gel) silica origin for <50 μm irregularly-shaped inclusions of quartz contained in greisen topaz from southwest England. Confocal and microprobe studies, presented here, strengthen this argument although rather than forming a gel in the hydrothermal fluid, it is suggested that the colloidal silica aggregated as a viscous coagulated colloid, with much of its volume (<10 to 30 vol.%) consisting of metal (mainly Fe) -rich particles. This is evident from the largely solid nature of metal-rich shrinkage bubbles contained at the margins of the inclusions of quartz which shows that the material forming the inclusions contained much less liquid than would be expected in a silica gel. These findings may have important implications for models of ore formation since the precipitation of a coagulated colloid could inhibit hydrothermal fluid transport and cause co-deposition of silica and entrained ore-forming elements. The mode of formation of the colloidal silica and further implications of the study are discussed.

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