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.

Can the three pore model correctly describe peritoneal transport of protein?

The three pore model (3PM) includes large pores for the description of protein leak to the peritoneal cavity during peritoneal dialysis. However, the reliability of this description has been not fully tested against clinical data yet. Peritoneal transport parameters were estimated using 3PM, extended 3p model (with estimation of fraction of large pores, ext3PM), ext3PM with modified size of pores and proteins (mext3PM), and simplified two pore (2PM, small and ultrasmall pores) models for 32 patients on peritoneal dialysis investigated using the sequential peritoneal equilibration test (consecutive peritoneal equilibration test [PET]: glucose 2.27%, 4 h, and miniPET: glucose 3.86%, 1 h). Urea, creatinine, glucose, sodium, phosphate, albumin, and IgM concentrations were measured in dialysis fluid and plasma. Ext3PM and mext3PM, with large pore fraction of about 0.14, provided a good description of fluid and small solute kinetics, but their predictions for albumin transport were less accurate. Two pore model precisely described the data on fluid and small solute transport. The 3p models could not describe the diffusive-convective transport of albumin as precisely as the transport of fluid, small solutes, and IgM. The 2p model (not applicable for proteins) was an efficient tool for modeling fluid and small solute transport.

A regional blood flow model for glucose and insulin kinetics during hemodialysis.

The distribution and elimination of a bolus of glucose injected during hemodialysis (HD) was examined using a distributed double-pool regional blood flow model. Intracorporeal glucose disposal was assumed as insulin-independent (λ) in the central high-flow compartment comprising blood, brain, and internal organs, including pancreatic insulin secretion (a, C1) and hepatic insulin clearance (α). Insulin-dependent (γ) glucose utilization was allocated to the low-flow system comprising muscle, skin, and bone. This model was compared with a compact single-pool model using the same model parameters except for the distribution volume (V). Six parameters (C1, a, α, λ, γ, and V) were identified from data obtained in seven nondiabetic patients (59-115 kg). The fraction Fd of glucose removed by HD significantly (p < 0.05) correlated with baseline glucose concentration Cg,0 (5.561 ± 0.646 mmol/L; r = 0.535), extracorporeal clearance Kg (0.137 ± 0.024 L/min; r = 0.537), a (0.278 ± 0.095 L/mmol, r = -0.586), and λ (0.099 ± 0.078 L/min, r = -0.587). V was much larger in the double-compartment (17.8 ± 5.1 L) than in the single-compartment model (10.0 ± 3.0 L). The modeled glucose compartment volumes could be of interest for fluid management in HD patients. The use of extracorporeal glucose disposal to detect impaired glucose utilization (a, λ) remains to be validated in diabetic HD patients.

Sequential peritoneal equilibration test: a new method for assessment and modelling of peritoneal transport.

BACKGROUND: In spite of many peritoneal tests proposed, there is still a need for a simple and reliable new approach for deriving detailed information about peritoneal membrane characteristics, especially those related to fluid transport. METHODS: The sequential peritoneal equilibration test (sPET) that includes PET (glucose 2.27%, 4 h) followed by miniPET (glucose 3.86%, 1 h) was performed in 27 stable continuous ambulatory peritoneal dialysis patients. Ultrafiltration volumes, glucose absorption, ratio of concentration in dialysis fluid to concentration in plasma (D/P), sodium dip (Dip D/P Sodium), free water fraction (FWF60) and the ultrafiltration passing through small pores at 60 min (UFSP60), were calculated using clinical data. Peritoneal transport parameters were estimated using the three-pore model (3p model) and clinical data. Osmotic conductance for glucose was calculated from the parameters of the model. RESULTS: D/P creatinine correlated with diffusive mass transport parameters for all considered solutes, but not with fluid transport characteristics. Hydraulic permeability (L(p)S) correlated with net ultrafiltration from miniPET, UFSP60, FWF60 and sodium dip. The fraction of ultrasmall pores correlated with FWF60 and sodium dip. CONCLUSIONS: The sequential PET described and interpreted mechanisms of ultrafiltration and solute transport. Fluid transport parameters from the 3p model were independent of the PET D/P creatinine, but correlated with fluid transport characteristics from PET and miniPET.

Membrane transport of several ions during peritoneal dialysis: mathematical modeling.

Peritoneal dialysis utilizes a complex mass exchange device created by natural permselective membranes of the visceral and abdominal muscle tissues. In mathematical modeling of solute transport during peritoneal dialysis, each solute is typically considered as a neutral, independent particle. However, such mathematical models cannot predict transport parameters for small ions. Therefore, the impact of the electrostatic interactions between ions on the estimated transport parameters needs to be investigated. In this study, transport of sodium, chloride, and a third ion through a permselective membrane with characteristics of the peritoneal transport barrier was described using two models: a model with the Nernst-Planck (NP) equations for a set of interacting ions and a model with combined diffusive and convective transport of each ion separately (DC). Transport parameters for the NP model were calculated using the pore theory, while the parameters for the DC model were estimated by fitting the model to the predictions from the NP model. Solute concentration profiles in the membrane obtained by computer simulations based on these two models were similar, whereas the transport parameters (diffusive mass transport parameters and sieving coefficients) were generally different. The presence of the third ion could substantially modify the values of diffusive mass parameter for sodium and chloride ions estimated using the DC model compared with those predicted by NP. The extent of this modification depended on the molecular mass and concentration of the third ion, and the rate of volumetric flow. Closed formulas for the transport parameters of the DC model in terms of the NP model parameters, ion concentration profiles in the membrane, and volumetric flow across the membrane were derived. Their reliable approximations, which include only boundary ion concentrations instead of spatial intramembrane concentration profiles, were formulated. The precision of this approximation was demonstrated by numerical simulations of the investigated three-ion system. Our modeling demonstrated that the fitted transport parameters depend not only on ion molecular weight but also on the characteristics and concentration of all other ions in the fluid as well as on the fluid flow rate through the membrane. Therefore, theoretical predictions of ion transport parameters need to take into account multi-ionic character of dialysis and body fluids. The transport parameters estimated using the DC model for one ion may vary with the ionic composition, ion concentrations in the fluids, and volumetric flow and may not reflect the theoretical description of diffusive and convective characteristics of single ion.

Mathematical modeling of the glucose-insulin system during peritoneal dialysis with glucose-based fluids.

The purpose of this study was to analyze the effect of peritoneal dialysis with glucose-based solution on plasma glucose and insulin responses in patients on continuous ambulatory peritoneal dialysis (CAPD), describe the glucose-insulin system using a mathematical model, and identify abnormalities in this system. Six-hour dwell studies--using glucose 3.86% solution with a volume marker--were performed in 13 stable, fasting, nondiabetic CAPD patients. We used a mathematical model based on the previous works of Stolwijk and Hardy (1974) and Tolic et al (2000) to estimate the parameters of glucose-insulin system, insulin sensitivity index (Sl), and glucose effectiveness at basal (SG) and zero (GEZI) insulin. The individual peaks in plasma glucose and insulin concentrations occurred after 30-60 minutes of the dwell, with the average increase of 52% and 168% over the initial values, respectively. Increased insulin resistance was found in most of these patients. Both clinical and simulation results demonstrated a high interpatient variability in glucose and insulin kinetics and glucose-insulin system parameters in the patients. We demonstrated a successful control of increasing plasma glucose by insulin, despite an increased insulin resistance, during CAPD.

Kinetic analysis of peritoneal fluid and solute transport with combination of glucose and icodextrin as osmotic agents.

BACKGROUND: Controlling extracellular volume and plasma sodium concentration are two crucial objectives of dialysis therapy, as inadequate sodium and fluid removal by dialysis may result in extracellular volume overload, hypertension, and increased cardiovascular morbidity and mortality in end-stage renal disease patients. A new concept to enhance sodium and fluid removal during peritoneal dialysis (PD) is the use of dialysis solutions with two different osmotic agents. AIM: To investigate and compare, with the help of mathematical modeling and computer simulations, fluid and solute transport during PD with conventional dialysis fluids (3.86% glucose and 7.5% icodextrin; both with standard sodium concentration) and a new combination fluid with both icodextrin and glucose (CIG; 2.6% glucose/6.8% icodextrin; low sodium concentration). In particular, this paper is devoted to improving mathematical modeling based on critical appraisal of the ability of the original three-pore model to reproduce clinical data and check its validity across different types of osmotic agents. METHODS: Theoretical investigations of possible causes of the improved fluid and sodium removal during PD with the combination solution (CIG) were carried out using the three-pore model. The results of computer simulations were compared with clinical data from dwell studies in 7 PD patients. To fit the model to the low net ultrafiltration (366+/-234 mL) obtained after a 4-hour dwell with 3.86% glucose, some of the original parameters proposed in the three-pore model (Rippe & Levin. Kidney Int 2000; 57:2546-56) had to be modified. In particular, the aquaporin-mediated fractional contribution to hydraulic permeability was decreased by 25% and small pore radius increased by 18%. RESULTS: The simulations described well clinical data that showed a dramatic increase in ultrafiltration and sodium removal with the CIG fluid in comparison with the two other dialysis fluids. However, to adapt the three-pore model to the selected group of PD patients (fast transporters with small ultrafiltration capacity on average), the peritoneal pore structure had to be modified. As the mathematical model was capable of reproducing the clinical data, this shows that the enhanced ultrafiltration with the combination fluid is caused by the additive effect of the two different osmotic agents and not by a specific impact of the new dialysis fluid on the transport characteristics of the peritoneum.

Combination of crystalloid (glucose) and colloid (icodextrin) osmotic agents markedly enhances peritoneal fluid and solute transport during the long PD dwell.

BACKGROUND: Fluid and sodium removal is often inadequate in peritoneal dialysis patients with high peritoneal solute transport rate, especially when residual renal function is declining. METHOD: We studied the effects of using simultaneous crystalloid (glucose) and colloid (icodextrin) osmotic agents on the peritoneal transport of fluid, sodium, and other solutes during 15-hour single-dwell exchanges using 3.86% glucose, 7.5% icodextrin, and a combination fluid with 2.61% glucose and 6.8% icodextrin in 7 prevalent peritoneal dialysis patients with fast peritoneal solute transport rate. RESULTS: The combination fluid enhanced net ultrafiltration (mean 990 mL) and sodium removal (mean 158 mmol) compared with 7.5% icodextrin (mean net ultrafiltration 462 mL, mean net sodium removal 49 mmol). In contrast, the 3.86% glucose-based solution yielded negligible ultrafiltration (mean -85 mL) and sodium removal (mean 16 mmol). The combination solution resulted in significantly improved urea (+41%) and creatinine (+26%) clearances compared with 7.5% icodextrin. CONCLUSION: A solution containing both crystalloid (glucose 2.61%) and colloid (icodextrin 6.8%) osmotic agents enhanced fluid removal by twofold and sodium removal by threefold compared with 7.5% icodextrin solution during a dwell of 15 hours, indicating that such a combination solution could represent a new treatment option for anuric peritoneal dialysis patients with high peritoneal solute transport rate.

Impact of convective transport on dialyzer clearance.

The results of predictions of three mathematical models used to describe the impact of convective flow on dialyzer clearance are presented. These models are based on the ordinary differential equations, which describe changes of solute concentration and solute and fluid flows along the module length. One of the models takes into consideration the existence of the boundary layers on both sides of the membrane wall, by including in the equations two parameters kB and kD, which describe mass transport coefficients in blood and dialysate, respectively. In the second model, the boundary layers are included in one lumped membrane permeability parameter. The diffusive membrane permeability was calculated from pure diffusive clearance, which was taken from experimental results. In the third model, a linear dependence of transmittance coefficient and ultrafiltration flow was proposed. The theoretical results were compared with data obtained in experiments carried out in vitro with four types of high-flux hollow-fiber dialyzers. The comparisons demonstrate that the first two models are of similar accuracy and the third model is not suitable for small solutes.