80 research outputs found
A Mathematical Model for Two Solutes Transport in a Poroelastic Material and Its Applications
Using well-known mathematical foundations of the elasticity theory, a
mathematical model for two solutes transport in a poroelastic material (soft
tissue is a typical example) is suggested. It is assumed that molecules of
essentially different sizes dissolved in fluid and are transported through
pores of different sizes. The stress tensor, the main force leading to the
material deformation, is taken not only in the standard linear form but also
with an additional nonlinear part. The model is constructed in 1D space and
consists of six nonlinear equations. It is shown that the governing equations
are integrable in stationary case, therefore all steady-state solutions are
constructed. The obtained solutions are used in an example for healthy and
tumour tissue, in particular, tissue displacements are calculated and compared
for parameters taken from experimental data in cases of the linear and
nonlinear stress tensors. Since the governing equations are non-integrable in
non-stationary case, the Lie symmetry analysis is used in order to construct
time-dependent exact solutions. Depending on parameters arising in the
governing equations, several special cases with non-trivial Lie symmetries are
identified. As a result, multi-parameter families of exact solutions are
constructed including those in terms of special functions(hypergeometric and
Bessel functions). A possible application of the solutions obtained is
demonstrated.Comment: 6 figure
Hyaluronan prevents the decreased net ultrafiltration caused by increased peritoneal dialysate fill volume
Hyaluronan prevents the decreased net ultrafiltration caused by increased peritoneal dialysate fill volume. In the present study, we investigated (1) the effect of an increase in dialysate fill volume on peritoneal fluid and solute transport using a 1.36% glucose solution, and (2) the effect of intraperitoneal administration of hyaluronan on peritoneal transport characteristics when different fill volumes were used. A four-hour dwell study with frequent dialysate and blood sampling was performed in 26 male Sprague-Dawley rats with 131I albumin as the intraperitoneal volume marker. Each rat was injected intraperitoneally with 25ml (group Con25, N = 6) or 40ml (group Con40, N = 7) of 1.36% glucose dialysis solution alone or 25ml (group HA25, N = 6) or 40ml (Group HA40, N = 7) of 1.36% glucose dialysis solution with 0.01% hyaluronan. The peritoneal transport of fluid, glucose, urea, and total protein as well as the intraperitoneal hydrostatic pressure (IPP) with different fill volumes were evaluated. We found that IPP and peritoneal fluid absorption rate significantly increased with the increase in fill volume (P < 0.01), and therefore the net ultrafiltration volume was significantly lower in the Con40 group compared to the Con25 group despite a higher transcapillary ultrafiltration rate in the Con40 group. The addition of hyaluronan to dialysate significantly (P < 0.01) decreased the peritoneal fluid absorption rate (by 22% in HA25 vs. Con25 and by 29% in HA40 vs. Con40) and thus significantly increased the net peritoneal fluid removal. The diffusive mass transport coefficients for glucose, urea and total protein did not differ between the Con25 and Con40 groups or between the two hyaluronan groups as compared to their respective control groups. The peritoneal clearance of urea increased significantly in the high fill volume group (by 58% in Con40 vs. Con25) and in the two hyaluronan groups (by 21% in HA25 vs. Con25 and by 16% in HA40 vs. Con40). We conclude that: (1) An increase in dialysate fill volume using 1.36% glucose dialysis solution results in higher intraperitoneal hydrostatic pressure and higher peritoneal fluid absorption rate, and therefore lower net ultrafiltration. (2) Intraperitoneal addition of hyaluronan significantly decreases the peritoneal fluid absorption rate, and the decreasing effect is even more marked when a high fill volume is used. (3) Small solute clearances increase markedly with increases in fill volume, and then further increase by adding hyaluronan to the dialysate due to the increase in drainage volume. Thus, intraperitoneal administration of hyaluronan during a single peritoneal dialysis exchange may significantly increase the peritoneal fluid and solute removal by decreasing peritoneal fluid absorption, and may thereby prevent the decreased net ultrafiltration caused by an increase in dialysate fill volume
Peritoneal Fluid Transport rather than Peritoneal Solute Transport Associates with Dialysis Vintage and Age of Peritoneal Dialysis Patients
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, αu was 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
Mean Transit Time and Mean Residence Time for Linear Diffusion–Convection–Reaction Transport System
Characteristic times for transport processes in biological systems may be evaluated as mean transit times (MTTs) (for transit states) or mean residence times (MRT) (for steady states). It is shown in a general framework of a (linear) reaction–diffusion–convection equation that these two times are related. Analytical formulas are also derived to calculate moments of exit time distribution using solutions for a stationary state of the system
Mathematical modeling of fluid and solute transport in peritoneal dialysis
Optimization of peritoneal dialysis schedule and dialysis fluid
composition needs, among others, methods for quantitative assessment of
fluid and solute transport. Furthermore, an integrative quantitative
description of physiological processes within the tissue, which
contribute to the net transfer of fluid and solutes, is necessary for
interpretation of the data and for predictions of the outcome of possible
intervention into the peritoneal transport system. The current project
includes the investigations of 1) the effectiveness of crystalloid
osmotic agents in evoking ultrafiltration from blood, 2) the impact of
ultrafiltration on protein transport, 3) the evaluation of the role of
perfusion in the peritoneal transport, and 4) the integration of the
physiological data about transport characteristics of the capillary wall,
the tissue, and lymphatic absorption for the description of the net
peritoneal transport, using the methods of mathematical modeling.
Three different methods were tested for the estimation of fluid transport
parameters. All three provided good description of the data, however some
differences were found, especially in time dependence of the parameters
during a single dwell study. The effectiveness of glucose as an osmotic
agent, evaluated as osmotic conductance, were much lower in the patients
with permanent ultrafiltration capacity (UFC) loss related to the
increased transport of small solutes than in stable patients on
continuous ambulatory peritoneal dialysis (CAPD). In contrast, patients
with permanent UFC loss related to the increased absorption of fluid from
the peritoneal cavity bad similar osmotic conductance as stable patients.
A discriminative impact of ultrafiltration on peritoneal transport of
albumin, [beta]2-microglobulin, and total protein, was found in stable
patients on CAPD: in some patients sieving coefficients for the proteins
were high and the initial increase of the protein concentration in
dialysate was fast; in another group, with low sieving coefficients for
the proteins, and the increase of the protein concentration in dialysate
was slow. No difference in the diffusive mass transport coefficients for
the proteins and small solutes, neither for fluid transport, between
these two groups of patients was found.
The perfusion rate of the tissue with blood was included into the
distributed model of peritoneal transport. It was shown that changes of
perfusion rate during a single dwell study, which might be induced by
vasodilatory effect of dialysate, could explain the time - dependence of
the diffusive mass transport coefficients (described previously). The
model could also explain why the estimations of the effective peritoneal
blood flow yielded much different values for gases and than for small
solutes.
Transport characteristics for the capillary wall, the tissue, and the
rate of lymphatic absorption from the tissue, were incorporated into the
distributed model, to provide an integrated mathematical description of
diffusive and convective transport of solutes of any size. The
phenomenological transport parameters, diffusive mass transport parameter
and sieving coefficient, the solute penetration depth, and effective
peritoneal blood flow, were described as functions of the local,
physiological parameters of the peritoneal transport system
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