Joanna Stachowska-Pietka

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

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.

Computer simulations of osmotic ultrafiltration and small-solute transport in peritoneal dialysis: a spatially distributed approach

The aim of this study was to simulate clinically observed intraperitoneal kinetics of dialysis fluid volume and solute concentrations during peritoneal dialysis. We were also interested in analyzing relationships between processes in the peritoneal cavity and processes occurring in the peritoneal tissue and microcirculation. A spatially distributed model was formulated for the combined description of volume and solute mass balances in the peritoneal cavity and flows across the interstitium and the capillary wall. Tissue local parameters were assumed dependent on the interstitial hydration and vasodilatation induced by glucose. The model was fitted to the average volume and solute concentration profiles from dwell studies in 40 clinically stable patients on chronic ambulatory peritoneal dialysis using a 3.86% glucose dialysis solution. The model was able to describe the clinical data with high accuracy. An increase in the local interstitial pressure and tissue hydration within the distance of 2.5 mm from the peritoneal surface of the tissue was observed. The penetration of glucose into the tissue and removal of urea, creatinine, and sodium from the tissue were restricted to a layer located within 2 mm from the peritoneal surface. The initial decline of sodium concentration (sodium dip) was observed not only in intraperitoneal fluid but also in the tissue. The distributed model can provide a precise description of the relationship between changes in the peritoneal tissue and intraperitoneal dialysate volume and solute concentration kinetics. Computer simulations suggest that only a thin layer of the tissue within 2-3 mm from the peritoneal surface participates in the exchange of fluid and small solutes between the intraperitoneal dialysate and blood.

Kinetics of plasma refilling during hemodialysis sessions with different initial fluid status.

Removal of fluid excess from the plasma volume by ultrafiltration during hemodialysis (HD) is balanced by plasma refilling from the interstitium, driven mainly by the increase in plasma oncotic pressure. We calculated the plasma refilling coefficient (Kr, a parameter expressing the ratio of refilling rate to the increase in oncotic pressure) for nine patients, each undergoing two HD sessions differing by pretreatment fluid status and session time (shorter session, SH, 3.5 h, and longer session, LH, 4.5h). Relative blood volume change was measured online, and solute concentrations were measured regularly during the sessions. The volume of body compartments was measured by bioimpedance. The patients were more volume expanded before LH session (higher initial body mass and total body water). Oncotic pressure was similar for both sessions. The refilling rate, despite higher fluid overload in the LH sessions, was similar for both sessions. The final Kr values stabilized on similar levels (SH: 136.6 ± 55.6 ml/mm Hg/h and LH: 150.7 ± 73.6 ml/mm Hg/h) at similar times, notwithstanding the difference in initial fluid overload between the two groups, suggesting that Kr at dry weight is relatively insensitive to the initial fluid status of the patient.

Threefold Peritoneal Test of Osmotic Conductance, Ultrafiltration Efficiency, and Fluid Absorption

♦ Background: Fluid removal during peritoneal dialysis depends on modifiable factors such as tonicity of dialysis fluids and intrinsic characteristics of the peritoneal transport barrier and the osmotic agent—for example, osmotic conductance, ultrafiltration efficiency, and peritoneal fluid absorption. The latter parameters cannot be derived from tests of the small-solute transport rate. We here propose a simple test that may provide information about those parameters. ♦ Methods: Volumes and glucose concentrations of drained dialysate obtained with 3 different combinations of glucose-based dialysis fluid (3 exchanges of 1.36% glucose during the day and 1 overnight exchange of either 1.36%, 2.27%, or 3.86% glucose) were measured in 83 continuous ambulatory peritoneal dialysis (CAPD) patients. Linear regression analyses of daily net ultrafiltration in relation to the average dialysate-to-plasma concentration gradient of glucose allowed for an estimation of the osmotic conductance of glucose and the peritoneal fluid absorption rate, and net ultrafiltration in relation to glucose absorption allowed for an estimation of the ultrafiltration effectiveness of glucose. ♦ Results: The osmotic conductance of glucose was 0.067 ± 0.042 (milliliters per minute divided by millimoles per milliliter), the ultrafiltration effectiveness of glucose was 16.77 ± 7.97 mL/g of absorbed glucose, and the peritoneal fluid absorption rate was 0.94 ± 0.97 mL/min (if estimated concomitantly with osmotic conductance) or 0.93 ± 0.75 mL/min (if estimated concomitantly with ultrafiltration effectiveness). These fluid transport parameters were independent of small-solute transport characteristics, but proportional to total body water estimated by bioimpedance. ♦ Conclusions: By varying the glucose concentration in 1 of 4 daily exchanges, osmotic conductance, ultrafiltration efficiency, and peritoneal fluid absorption could be estimated in CAPD patients, yielding transport parameter values that were similar to those obtained by other, more sophisticated, methods.

Fluid Transport in Peritoneal Dialysis: A Mathematical Modeland Numerical Solutions

A mathematical model of water flow between dialysis fluid in the peritoneal cavity and blood through the capillary wall and homogeneous interstitium driven by high hydrostatic and osmotic pressure of dialysis fluid is formulated. The model is based on nonlinear equations of reaction-diffusion-convection type. Numerical simulations provide the distribution profiles for hydrostatic pressure, glucose concentration, and water flux in the tissue for different times from the infusion of dialysis fluid into the peritoneal cavity for different transport parameters that represent clinical treatments of peritoneal dialysis.

Concomitant bidirectional transport during peritoneal dialysis can be explained by a structured interstitium.

Clinical and animal studies suggest that peritoneal absorption of fluid and protein from dialysate to peritoneal tissue, and to blood and lymph circulation, occurs concomitantly with opposite flows of fluid and protein, i.e., from blood to dialysate. However, until now a theoretical explanation of this phenomenon has been lacking. A two-phase distributed model is proposed to explain the bidirectional, concomitant transport of fluid, albumin and glucose through the peritoneal transport system (PTS) during peritoneal dialysis. The interstitium of this tissue is described as an expandable two-phase structure with phase F (water-rich, colloid-poor region) and phase C (water-poor, colloid-rich region) with fluid and solute exchange between them. A low fraction of phase F is assumed in the intact tissue, which can be significantly increased under the influence of hydrostatic pressure and tissue hydration. The capillary wall is described using the three-pore model, and the conditions in the peritoneal cavity are assumed commencing 3 min after the infusion of glucose 3.86% dialysis fluid. Computer simulations demonstrate that peritoneal absorption of fluid into the tissue, which occurs via phase F at the rate of 1.8 ml/min, increases substantially the interstitial pressure and tissue hydration in both phases close to the peritoneal cavity, whereas the glucose-induced ultrafiltration from blood occurs via phase C at the rate of 15 ml/min. The proposed model delineating the phenomenon of concomitant bidirectional transport through PTS is based on a two-phase structure of the interstitium and provides results in agreement with clinical and experimental data.

Distributed Models of Peritoneal Transport

There are several methods to model the process of water and solute transport during peritoneal dialysis (PD). The characteristics of the phenomena and the purpose of modelling influence the choice of methodology. Among others, the phenomenological models are commonly used in clinical and laboratory research. In peritoneal dialysis, the compartmental approach is widely used (membrane model, three-pore model). These kinds of models are based on phenomenological parameters, sometimes called “lumped parameters”, because one parameter is used to describe the net result of several different processes that occur during dialysis. The main advantage of the compartmental approach is that it decreases substantially the number of parameters that have to be estimated, and therefore its application in clinical research is easier. However, in the compartmental approach, it is usually very difficult to connect the estimated parameters with the physiology and the local anatomy of the involved tissues. Therefore, these models have limited applications in the explanation of the changes that occur in the physiology of the peritoneal transport. For example, the membrane models describe exchange of fluid and solute between peritoneal cavity and plasma through the “peritoneal membrane”. However, this approach does not take into account the anatomy and physiology of the peritoneal transport system and cannot be used for the explanation of the processes that occur in the tissue during the treatment. Basic concepts and previous applications of distributed models are summarized in Section 2. A mathematical formulation of the distributed model for fluid and solute peritoneal transport is also presented in Section 2. The effective parameters, which characterize transport through the peritoneal transport system, PTS (i.e. the fluid and solute exchange between the peritoneal cavity and blood), can be estimated from the local physiological parameters of the distributed models. The comparisons between transport parameters applied in phenomenological description and those derived using a distributed approach, are presented in Sections 3 and 4 for fluid and solute transport, respectively. Typical distributed profiles of tissue hydration and solutes concentration in the tissue are presented in Section 5.