Search

BackgroundIcodextrin induces ultrafiltration (UF) during long-dwell exchanges by creating a difference in oncotic pressure between the peritoneal cavity and plasma; however, the mechanisms governing intra-patient and inter-patient variability in UF when icodextrin is used remain largely unexplained. In the present study, we show theoretically that differences in peritoneal residual volume ( VR) have a more profound effect on UF with icodextrin use than with glucose use. This phenomenon is attributed to a differential effect of VRon oncotic, rather than osmotic, pressure between the peritoneal cavity and plasma.MethodsThe three-pore model was used to calculate the effect on UF of VRbetween 150 mL and 1200 mL when 7.5% icodextrin (ICO) or 3.86% glucose solution is used at the end of a 12-hour dwell in the four patient transport groups (that is, fast to slow). Oncotic (with ICO) and osmotic (with glucose) pressure differences averaged over the entire dwell were also calculated.ResultsAs expected, at a nominal VRof 300 mL, UF with glucose differed substantially between the four patient transport groups (2 – 804 mL), whereas UF with ICO did not (556 – 573 mL). When VRwas increased to 1200 mL from 150 mL, the concentrations of the oncotic and osmotic agents at the start of the dwell with an infusion volume of 2 L decreased to 4.9% from 7.0% with ICO and to 2.5% from 3.6% with glucose. The decrease in UF on average was greater with ICO [to 252 mL from 624 mL: that is, a reduction of 372 mL (60%)] than with glucose [to 292 mL from 398 mL: that is, a reduction of 106 mL (27%)]. Those trends agreed with the calculated reductions in the oncotic pressure difference with ICO [reduction of 12 mmHg (49%)] and the osmotic pressure difference with glucose [reduction of 19 mmHg (33%)].ConclusionsWhen ICO is used, VRmodifies the oncotic pressure difference between the peritoneal cavity and plasma to substantially alter UF. This modification suggests that potential causes of increased VRshould be considered when UF with ICO is considerably less than expected. Prospective clinical studies evaluating the relationship between VRand UF with ICO are warranted to validate the theoretical predictions in this report.

Background Remaining edema-free is a challenge for many automated peritoneal dialysis (APD) patients, especially those with fast (“high”) transport characteristics. Although increased use of peritoneal dialysis (PD) solutions with high glucose concentrations may improve volume control, frequent use of such solutions is undesirable. Methods We used the 3-pore kinetic model to evaluate 4 alternative therapy prescriptions for the APD day exchange in anuric patients with high, high-average, and low-average transport characteristics. Four prescriptions were modeled: Therapy 1: Optimal, individualized dwell times with a dry period Therapy 2: Use of a midday exchange Therapy 3: Use of an icodextrin-containing dialysate during a 14-hour dwell Therapy 4: Use of optimal, individualized dwell times, followed by an icodextrin dwell to complete the daytime period The alternative therapies were compared with a reference standard therapy using glucose solution during a 14-hour dwell. The nighttime prescription was identical in all cases (10 L over 10 hours), and all glucose solutions contained 2.27% glucose. Net ultrafiltration (UF), sodium removal (NaR), total carbohydrate (CHO) absorption, and weekly urea Kt/V for a 24-hour period were computed and compared. Results The UF and NaR were substantially higher with therapy 1 than with standard therapy (1034 mL vs 621 mL and 96 mmol vs 51 mmol respectively), without significant changes in CHO absorption or urea Kt/V. However, therapy 1 resulted in reduced β2-microglobulin clearance (0.74 mL/min vs 0.89 mL/min with standard therapy). Compared with therapy 1, therapy 2 improved UF and NaR (1062 mL vs 1034 mL and 99 mmol vs 96 mmol); however, that improvement is likely not clinically significant. Therapy 2 also resulted in a higher Kt/V (2.07 vs 1.72), but at the expense of higher glucose absorption (difference: 42 g). The UF and NaR were highest with a long icodextrin-containing daytime dwell either preceded by a short optimized dwell (1426 mL and 155 mmol) or without such a dwell (1327 mL and 148 mmol). Conclusions The 3-pore model predictions revealed that patient-specific optimal dwell times and regimens with a longer day dwell might provide improved UF and NaR options in APD patients with a variety of peritoneal membrane transport characteristics. In patients without access to icodextrin, therapy 1 might enhance UF and NaR and provide a short-term option to increase fluid removal. Although that approach may offer clinicians a therapeutic option for the overhydrated patient who requires increased UF in the short term, APD prescriptions including icodextrin provide a means to augment sodium and fluid removal. Data from clinical trials are needed to confirm the predictions from this study.

Our recent work proposed a pseudo one-compartment model for describing intradialysis and postdialysis rebound kinetics of phosphorus. In this model, phosphorus is removed directly from a central distribution volume with the rate of phosphorus mobilization from a second, very large compartment proportional to the phosphorus mobilization clearance. Here, we evaluated factors of phosphorus mobilization clearance and postdialysis central distribution volume from 774 patients in the HEMO Study. Phosphorus mobilization clearance and postdialysis central distribution volume were 87 (65, 116) ml/min, median (interquartile range), and 9.4 (7.2, 12.0) liter, respectively. The phosphorus mobilization clearance was significantly higher for male patients than for female patients. Both the phosphorus mobilization clearance and the postdialysis central distribution volume were significantly associated with postdialysis body weight but negatively with the predialysis serum phosphorus concentration. The postdialysis central distribution volume was also significantly associated with age. Overall, the postdialysis central distribution volume was 13.6% of the postdialysis body weight. Thus, the phosphorus mobilization clearance during hemodialysis is higher when predialysis serum phosphorus concentration is low and higher in male patients than in female patients. The central distribution volume of phosphorus is a space approximating the extracellular fluid volume.

The kinetics of plasma phosphorus concentrations during hemodialysis (HD) are complex and cannot be described by conventional one- or two-compartment kinetic models. It has recently been shown by others that the physiologic (or apparent distribution) volume for phosphorus (Vr-P) increases with increasing treatment time and shows a large variation among patients treated by thrice weekly and daily HD. Here, we describe the dependence of Vr-P on treatment time and predialysis plasma phosphorus concentration as predicted by a novel pseudo one-compartment model. The kinetics of plasma phosphorus during conventional and six times per week daily HD were simulated as a function of treatment time per session for various dialyzer phosphate clearances and patient-specific phosphorus mobilization clearances (K(M)). Vr-P normalized to extracellular volume from these simulations were reported and compared with previously published empirical findings. Simulated results were relatively independent of dialyzer phosphate clearance and treatment frequency. In contrast, Vr-P was strongly dependent on treatment time per session; the increase in Vr-P with treatment time was larger for higher values of K(M). Vr-P was inversely dependent on predialysis plasma phosphorus concentration. There was significant variation among predicted Vr-P values, depending largely on the value of K(M). We conclude that a pseudo one-compartment model can describe the empirical dependence of the physiologic volume of phosphorus on treatment time and predialysis plasma phosphorus concentration. Further, the variation in physiologic volume of phosphorus among HD patients is largely due to differences in patient-specific phosphorus mobilization clearance.

The kinetics of plasma phosphorus during different hemodialysis (HD) modalities are incompletely understood. We recently demonstrated that a pseudo one-compartment kinetic model including phosphorus mobilization from various body compartments into extracellular fluids can describe intradialytic and postdialytic rebound kinetics of plasma phosphorus during conventional and short 2-hour HD treatments. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter, the phosphorus mobilization clearance (K(M)). In this report we determined K(M) in patients treated by in-center nocturnal HD (ICNHD) and short daily HD (SDHD) with low dialyzer phosphate clearance. In the ICNHD study, eight patients underwent 8-hour HD treatments where intradialytic and postdialytic plasma samples were collected; K(M) values were determined by nonlinear regression of plasma concentration as a function of time. In the SDHD study, five patients were studied during 28 treatments for approximately 3 hours. Here, K(M) was calculated using only predialytic and postdialytic plasma phosphorus concentrations. Dialyzer phosphate clearances were 134 ± 20 (mean ± SD) and 95 ± 16 mL/min during ICNHD and SDHD, respectively. K(M) values for the respective therapies were 124 ± 83 and 103 ± 33 mL/min, comparable to those determined previously during conventional and short HD treatments of 98 ± 44 mL/min. When results from ICNHD, SDHD, and previous HD modalities were combined, K(M) was directly correlated with postdialytic body weight (r = 0.38, P = 0.025) and inversely correlated with predialytic phosphorus concentration (r = -0.47, P = 0.005). These findings suggest that phosphorus kinetics during various HD modalities can be described by a pseudo one-compartment model.

♦Background Intermittent peritoneal dialysis (IPD) is an old strategy that has generally been eclipsed, in the home setting, by daily peritoneal therapies. However, for a select group of patients with exhausted vascular access or inability to receive PD at home, in-center IPD may remain an option or may serve as an incremental strategy before initiation of full-dose PD. We investigated the residual kidney clearance requirements necessary to allow thrice-weekly IPD regimens to meet current adequacy targets. ♦Methods The 3-pore model of peritoneal transport was used to examine 2 thrice-weekly IPD dialysis modalities: 5 – 6 dwells with 10 – 12 L total volume (low-dose IPD), and 50% tidal with 20 – 24 L total volume (high-dose IPD). We assumed an 8-hour dialysis duration and 1.5% dextrose solution, with a 2-L fill volume, except in tidal mode. The PD Adequest application (version 2.0: Baxter Healthcare Corporation, Deerfield, IL, USA) and typical patient kinetic parameters derived from a large dataset [data on file from Treatment Adequacy Review for Gaining Enhanced Therapy (Baxter Healthcare Corporation)] were used to model urea clearances. The minimum glomerular filtration rate (GFR) required to achieve a total weekly urea Kt/V of 1.7 was calculated. ♦Results In the absence of any dialysis, the minimum residual GFR necessary to achieve a weekly urea Kt/V of 1.7 was 9.7 mL/min/1.73 m2. Depending on membrane transport type, the low-dose IPD modality met urea clearance targets for patients with a GFR between 6.0 mL/min/1.73 m2 and 7.6 mL/min/1.73 m2. Similarly, the high-dose IPD modality met the urea clearance target for patients with a GFR between 4.7 mL/min/1.73 m2 and 6.5 mL/min/1.73 m2. ♦Conclusions In patients with residual GFR of at least 7.6 mL/min/1.73 m2, thrice-weekly low-dose IPD (10 L) achieved a Kt/V urea of 1.7 across all transport types. Increasing the IPD volume resulted in a decreased residual GFR requirement of 4.7 mL/min/1.73 m2 (24 L, 50% tidal). In patients with residual kidney function and dietary compliance, IPD may be a viable strategy in certain clinical situations.

PURPOSE Mathematical models of phosphorus kinetics and mass balance during hemodialysis are in early development. We describe a theoretical phosphorus steady state mass balance model during hemodialysis based on a novel pseudo one-compartment kinetic model. METHODS The steady state mass balance model accounted for net intestinal absorption of phosphorus and phosphorus removal by both dialysis and residual kidney function. Analytical mathematical solutions were derived to describe time-dependent intradialytic and interdialytic serum phosphorus concentrations assuming hemodialysis treatments were performed symmetrically throughout a week. RESULTS Results from the steady state phosphorus mass balance model are described for thrice weekly hemodialysis treatment prescriptions only. The analysis predicts 1) a minimal impact of dialyzer phosphorus clearance on predialysis serum phosphorus concentration using modern, conventional hemodialysis technology, 2) variability in the postdialysis-to-predialysis phosphorus concentration ratio due to differences in patient-specific phosphorus mobilization, and 3) the importance of treatment time in determining the predialysis serum phosphorus concentration. CONCLUSIONS We conclude that a steady state phosphorus mass balance model can be developed based on a pseudo one-compartment kinetic model and that predictions from this model are consistent with previous clinical observations. The predictions from this mass balance model are theoretical and hypothesis-generating only; additional prospective clinical studies will be required for model confirmation.

We have recently developed a pseudo one-compartment model to describe intradialytic and postdialytic rebound kinetics of plasma phosphorus. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter; the phosphorus mobilization clearance (K(M) ). In this work, we propose a simple method to estimate K(M) from predialytic and postdialytic plasma phosphorus concentrations. Clinical data were collected from 22 chronic hemodialysis patients that underwent a 4-hour treatment session. A simple algebraic equation was derived from the pseudo one-compartment model to determine K(M) from predialytic and postdialytic plasma phosphorus concentrations. K(M) values computed using this equation were compared with values obtained from nonlinear regression of the full kinetic model to frequent intradialytic and postdialytic measurements of plasma phosphorus concentrations. There was good agreement between K(M) values (concordance correlation coefficient of 0.94) obtained from the simple method (105 ± 52 mL/min, mean ± SD) and from the full model (99 ± 47 mL/min). The 95% confidence interval for the difference between estimated K(M) values was -26 to 36 mL/min. The proposed simple method requires the use of only predialytic and postdialytic blood samples to estimate patient specific K(M) ; this approach may allow easy clinical evaluation of phosphorus kinetics in hemodialysis patients.

BackgroundContrary to ultrafiltration, the three-pore model predictions of icodextrin absorption from the peritoneal cavity have not yet been reported likely, in part, due to difficulties in estimating the degradation of glucose-polymer chains by α–amylase activity in dialysate. We incorporated this degradation process in a modified three-pore model of peritoneal transport to predict ultrafiltration and icodextrin absorption simultaneously in rats and humans.MethodsSeparate three-pore models were constructed for humans and rats. The model for humans was adapted from PD Adequest 2.0 including a clearance term out of the peritoneal cavity to account for the absorption of large molecules to the peritoneal tissues, and considering patients who routinely used icodextrin by establishing steady-state plasma concentrations. The model for rats employed a standard three-pore model in which human kinetic parameters were scaled for a rat based on differences in body weight. Both models described the icodextrin molecular weight (MW) distribution as five distinct MW fractions. First order kinetics was applied using degradation rate constants obtained from previous in-vitro measurements using gel permeation chromatography. Ultrafiltration and absorption were predicted during a 4-hour exchange in rats, and 9 and 14-hour exchanges in humans with slow to fast transport characteristics with and without the effect of amylase activity.ResultsIn rats, the icodextrin MW profile shifted towards the low MW fractions due to complete disappearance of the MW fractions greater than 27.5 kDa. Including the effect of amylase activity (60 U/L) resulted in 21.1% increase in ultrafiltration (UF) (7.6 mL vs 6.0 mL) and 7.1% increase in icodextrin absorption (CHO) (62.5% with vs 58.1%). In humans, the shift in MW profile was less pronounced. The fast transport (H) patient absorbed more icodextrin than the slow transport (L) patient during both 14-hour (H: 47.9% vs L: 40.2%) and 9-hour (H: 37.4% vs L: 31.7%) exchanges. While the UF was higher during the longer exchange, it varied modestly among the patient types (14-hour range: 460 – 509 mL vs 9-hour range: 382 – 389 mL). When averaged over all patients, the increases in UF and CHO during the 14-hour exchange due to amylase activity (7 U/L) were 15% and 1.5%, respectively.ConclusionThe icodextrin absorption values predicted by the model agreed with those measured in rats and humans to accurately show the increased absorption in rats. Also, the model confirmed the previous suggestions by predicting an increase in UF specific to amylase activity in dialysate, likely due to the added osmolality by the small molecules generated as a result of the degradation process. As expected, this increase was more pronounced in rats than in humans because of higher dialysate concentrations of amylase in rats.

The stability of wavy supercritical cylindrical Couette flow has been studied extensively, but few measurements of the velocity field in flow have been made. Particle image velocimetry was used to measure the azimuthal and radial velocities in latitudinal planes perpendicular to the axis of rotation for wavy cylindrical Couette flow in the annulus between a rotating inner cylinder and a fixed outer cylinder. These measurements were matched to previous measurements of the axial and radial velocity measured in several meridional planes resulting in an experimentally measured, time-resolved, three-dimensional, three-component velocity field for wavy cylindrical Couette flow. Using this complete velocity field it is possible to evaluate details of the flow field. The vortical motion transports azimuthal momentum radially while the axial exchange of fluid between vortices in wavy flow transports azimuthal momentum axially. As the Reynolds number increases, these effects strengthen. Streams of net axial flow stretch axially along the length of the annulus and wind around the vortices from the inner cylinder to the outer cylinder and back while also winding azimuthally in the annulus. The azimuthal velocity measured at the center of a vortex is similar to the azimuthal wave speed. Measurements of the azimuthal velocity in cylindrical surfaces concentric with the axis of rotation suggest that the origin of the waviness is related to a jet-like azimuthal velocity profile rather than the radial outflow jet. Near both cylinder walls, the shear stress is quite large, decreasing to near zero at the middle of the annular gap.

The flow of dilute suspensions in a rotating filter separator consisting of a rigid, porous, polyethylene cylindrical filter rotating within an outer cylindrical shell was studied using laser-based velocity measurement techniques. The centrifugal instability of the Taylor–Couette flow results in toroidal vortices stacked in the annulus. The velocity field of the particles is very similar to that of the fluid indicating that the vortical structure readily entrains particles. Profiles of the concentration of particles in the device show that the particles tend toward a concentration polarization layer near the porous inner cylinder due to the radial flow, but the concentration in the layer is reduced as the velocity gradient near the wall is increased. This steep velocity gradient is a consequence of the vortices in the flow redistributing the azimuthal momentum. The vortices also distribute the particles uniformly across the annulus between the porous inner cylinder and the outer shell. Particles typically form a thin cake on the inner cylinder due to the radial flow. However, there is a critical Taylor number, which is related to the rotational speed of the inner cylinder, above which the particles are swept off of the inner cylinder and resuspended in the vortical flow.

Chaotic transport and mixing in wavy cylindrical Couette flow has been studied in some detail, but previous studies have been limited to the velocity field at transition from Taylor–Couette flow to wavy flow or have used phenomenological, computational, or theoretical models of the flow. Recent particle image velocimetry measurements of wavy vortex flow provide the experimental three-dimensional, three-component velocity field at conditions well above the transition to wavy flow. Using this experimental velocity field, fluid tracer particles were tracked computationally to determine the nature of the mixing. The results show how mixing is enhanced with increasing rotating Reynolds number as a consequence of increased stretching and folding that occurs in meridional, latitudinal, and circumferential surfaces. The axial particle transport increases with the rotating Reynolds number as a consequence of stretching and folding within the vortices and the axial transport between vortices, both related to the waviness of the flow, as well as increased vortex strength. The calculated effective dispersion coefficient is very similar to that found experimentally and computationally confirming that chaotic advection is the mechanism responsible for enhanced mixing in wavy vortex flow.

♦ BackgroundIn recent years, results from clinical studies have changed the focus of peritoneal dialysis (PD) adequacy from small solute clearance to volume control, resulting in continued efforts to improve fluid and sodium removal in PD patients. We used a modified 3-pore model to theoretically predict fluid and solute removal using glucose-based and icodextrin solutions for a wide range of transport characteristics with automated PD (APD) and continuous ambulatory PD (CAPD) therapies.♦ MethodsSimulations were performed for the day (APD: 15-hr, 2.27% glucose and 7.5% icodextrin; CAPD: 3x5-hr, 1.36% and 2.27% glucose) and night (APD: 9-hr, 1.36% glucose; CAPD: 9-hr, 2.27% glucose and 7.5% icodextrin) dialysis periods separately. During APD, the number of night exchanges (N) was varied from 3 to 7. Ultrafiltration (UF), sodium removal (NaR), total carbohydrate absorption (CHO), UF efficiency (UFE), and sodium removal efficiency (NaRE) were calculated. Typical patients in fast (i.e. high, H), average (high-average, HA; low-average, LA), and slow (low, L) transport groups with no residual kidney function were considered.♦ResultsThe effective dwell times varied between 1.0 and 14.7 hours depending on the number of exchanges. With glucose-based solutions, differences in UF and NaR between H and L transport patients ranged from 140 mL and 2 mmol (APD night, n = 7) to 778 mL and 56.4 mmol (CAPD day, 2.27%). With icodextrin, differences in UF and NaR ranged from 1 mL and 1.1 mmol (CAPD night) to 59 mL and 6.1 mmol (APD day). The use of icodextrin resulted in greater CHO than 2.27% glucose (APD: 27.1 – 35.6 g more; CAPD: 17.1 – 17.5 g more). The UFE and NaRE were greater for all patients with icodextrin than with glucose-based solution in both therapy modalities, except for slow transport patients in CAPD.♦ ConclusionThis modeling study shows that the dependence of UF and NaR on patient transport type observed with glucose-based solutions can be minimized using icodextrin during the long dwells of APD and CAPD. While this approach simplifies the PD prescription by minimizing the dependencies of ultrafiltration and sodium removal on patient transport type when using icodextrin, it improves fluid and sodium removal efficiencies in fast and average transport patients without any added glucose exposure.

The key aspects of a new method, bubble-image barometry (BIB), which can measure both pressure and velocity, are described. BIB extends correlation-based particle-image velocimetry techniques to provide simultaneous pressure and velocity measurements over a global domain. The particles used in BIB (gas bubbles) serve two purposes: (i) they are small enough to track the flow and serve as tracers for the velocity field; and (ii) they behave as local pressure sensors by changing their size in response to the instantaneous pressure field. The present work explores the theoretical and practical issues involved in BIB by first introducing the relation between the bubble-image size and its spatial correlation function. Next, computer-generated bubble images are used to investigate the feasibility of the technique. Finally, a pressure-chamber experiment, wherein microscopic air bubbles are generated and used as tracer particles to measure pressure, is presented. Results obtained from the experiment show that BIB is a viable technique for a certain range of bubble sizes.

♦BackgroundPeritoneal dialysis (PD) solutions containing icodextrin as the osmotic agent have advantages during long dwells. The glucose polymers that constitute icodextrin are a heterogeneous mix of molecules with a polydispersity [ratio of weight-average to number-average molecular weight (Mw/Mn)] of approximately 2.6. The present study evaluates whether modifications in the polydispersity and concentration of glucose polymers can improve ultrafiltration (UF) without an associated increase in carbohydrate absorption (CA).♦MethodsComputer simulations using a three-pore model of peritoneal transport during a long dwell in PD patients predict that, in general, compared with 7.5% icodextrin, glucose polymers with a Mw greater than or equal to 7.5 kDa, a polydispersity less than 2.6, and concentrations greater than 7% could achieve higher UF without higher CA. Based on the simulations, we hypothesized that, compared with 7.5% icodextrin, glucose polymers with a Mw of 18 – 19 kDa and a polydispersity of 2.0 at 11% concentration could achieve higher UF without a higher CA. We tested this hypothesis in experimental studies using 8-hour dwells in New Zealand White rabbits. In those studies, UF was measured by complete fluid collection, and CA was measured by subtracting the total carbohydrate in the collected fluid from the carbohydrate initially infused.♦ResultsThe UF was higher with 11% 19 kDa glucose polymer than with 7.5% icodextrin (mean ± standard deviation: 89 ± 31 mL vs 49 ± 15 mL; p = 0.004) without higher CA (5.2 ± 0.9 g vs 5.0 ± 0.9 g, p = 0.7). Similar results were seen with the 11% 18 kDa glucose polymer, which, compared with 7.5% icodextrin, resulted in higher UF (mean ± standard deviation: 96 ± 18 mL vs 66 ± 17 mL; p < 0.001) without higher CA (4.8 ± 0.7 g vs 5.2 ± 0.6 g, p = 0.2).♦ConclusionsThe findings demonstrate that, compared with 7.5% icodextrin solution, long-dwell PD solutions containing 11% glucose polymers with a Mw of 18–19 kDa and a polydispersity of 2.0 can provide higher UF without higher CA.

Background/Aims: On-line hemodiafiltration (HDF) has been previously shown to result in modest reductions in predialysis serum phosphorus concentration compared with conventional hemodialysis (HD); however, understanding of phosphorus kinetics during these therapies remains limited. Methods: Previously published phosphorus kinetic data during HDF and HD were analyzed using a pseudo-one-compartment kinetic model. Phosphorus mobilization clearance (KM) and dialyzer phosphorus clearance (Kd) were simultaneously estimated from measured predialysis and postdialysis serum phosphorus concentrations and total removed phosphorus during each treatment. Results: KM varied among patients between 53 and 173 ml/min. Values of KM during HDF (105 ± 34, mean ± standard deviation, ml/min) and HD (112 ± 44 ml/min) were not different (p = 0.5); however, Kd during HDF (175 ± 23 ml/min) was higher (p = 0.01) than during HD (160 ± 14 ml/min). Conclusion: A pseudo-one-compartment kinetic model is useful for the analysis of phosphorus kinetic data during HDF. Lower predialysis serum phosphorus concentrations during HDF are likely due to increased extracorporeal phosphorus clearance.

The kinetics of plasma phosphorus concentrations during hemodialysis (HD) are complex and cannot be described by conventional one- or two-compartment kinetic models. It has recently been shown by others that the physiologic (or apparent distribution) volume for phosphorus (Vr-P) increases with increasing treatment time and shows a large variation among patients treated by thrice weekly and daily HD. Here, we describe the dependence of Vr-P on treatment time and predialysis plasma phosphorus concentration as predicted by a novel pseudo one-compartment model. The kinetics of plasma phosphorus during conventional and six times per week daily HD were simulated as a function of treatment time per session for various dialyzer phosphate clearances and patient-specific phosphorus mobilization clearances (K(M)). Vr-P normalized to extracellular volume from these simulations were reported and compared with previously published empirical findings. Simulated results were relatively independent of dialyzer phosphate clearance and treatment frequency. In contrast, Vr-P was strongly dependent on treatment time per session; the increase in Vr-P with treatment time was larger for higher values of K(M). Vr-P was inversely dependent on predialysis plasma phosphorus concentration. There was significant variation among predicted Vr-P values, depending largely on the value of K(M). We conclude that a pseudo one-compartment model can describe the empirical dependence of the physiologic volume of phosphorus on treatment time and predialysis plasma phosphorus concentration. Further, the variation in physiologic volume of phosphorus among HD patients is largely due to differences in patient-specific phosphorus mobilization clearance.

The kinetics of plasma phosphorus during different hemodialysis (HD) modalities are incompletely understood. We recently demonstrated that a pseudo one-compartment kinetic model including phosphorus mobilization from various body compartments into extracellular fluids can describe intradialytic and postdialytic rebound kinetics of plasma phosphorus during conventional and short 2-hour HD treatments. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter, the phosphorus mobilization clearance (K(M)). In this report we determined K(M) in patients treated by in-center nocturnal HD (ICNHD) and short daily HD (SDHD) with low dialyzer phosphate clearance. In the ICNHD study, eight patients underwent 8-hour HD treatments where intradialytic and postdialytic plasma samples were collected; K(M) values were determined by nonlinear regression of plasma concentration as a function of time. In the SDHD study, five patients were studied during 28 treatments for approximately 3 hours. Here, K(M) was calculated using only predialytic and postdialytic plasma phosphorus concentrations. Dialyzer phosphate clearances were 134 ± 20 (mean ± SD) and 95 ± 16 mL/min during ICNHD and SDHD, respectively. K(M) values for the respective therapies were 124 ± 83 and 103 ± 33 mL/min, comparable to those determined previously during conventional and short HD treatments of 98 ± 44 mL/min. When results from ICNHD, SDHD, and previous HD modalities were combined, K(M) was directly correlated with postdialytic body weight (r = 0.38, P = 0.025) and inversely correlated with predialytic phosphorus concentration (r = -0.47, P = 0.005). These findings suggest that phosphorus kinetics during various HD modalities can be described by a pseudo one-compartment model.

RATIONALE To measure adequacy in patients dialyzed other than three times per week, guidelines recommend the use of 'standard' Kt/V, which commonly is estimated from treatment Kt/V, time and frequency; however, the accuracy of equations that predict treatment Kt/V in patients being dialyzed other than three times per week has not been evaluated. METHODS In patients enrolled in the Frequent Hemodialysis Network (FHN) Daily and Nocturnal Trials who were being dialyzed three, four or six times per week, we tested the accuracy of the following Kt/V prediction equation: Kt/V = -ln(R - GFAC × T_hours) + (4-3.5 × R) × 0.55 × weight loss/V, where R = post-dialysis/pre-dialysis blood urea nitrogen and GFAC, originally set to 0.008 for a 3/week schedule (Daugirdas, J Am Soc Nephrol 1993), is a factor that adjusts for urea generation. RESULTS With the above equation, there was

Summary Background and objectives The kinetics of plasma phosphorus (inorganic phosphorus or phosphate) during hemodialysis treatments cannot be explained by conventional one- or two-compartment models; previous approaches have been limited by assuming that the distribution of phosphorus is confined to classical intracellular and extracellular fluid compartments. In this study a novel pseudo one-compartment model, including phosphorus mobilization from a large second compartment, was proposed and evaluated. Design, setting, participants, & measurements Clinical data were obtained during a crossover study where 22 chronic hemodialysis patients underwent both short (2-hour) and conventional (4-hour) hemodialysis sessions. The model estimated two patient-specific parameters, phosphorus mobilization clearance and phosphorus central distribution volume, by fitting frequent intradialytic and postdialytic plasma phosphorus concentrations using nonlinear regression. Results Phosphorus mobilization clearances varied among patients (45 to 208 ml/min), but estimates during short (98 ± 44 ml/min, mean ± SD) and conventional (99 ± 47 ml/min) sessions were not different ( P = 0.74) and correlated with each other (concordance correlation coefficient ρ c of 0.85). Phosphorus central distribution volumes for each patient (short: 11.0 ± 4.2 L and conventional: 11.9 ± 3.8 L) were also correlated (ρ c of 0.45). Conclusions The reproducibility of patient-specific parameters during short and conventional hemodialysis treatments suggests that a pseudo one-compartment model is robust and can describe plasma phosphorus kinetics under conditions of clinical interest.

We have recently developed a pseudo one-compartment model to describe intradialytic and postdialytic rebound kinetics of plasma phosphorus. In this model, individual patient differences in phosphorus kinetics were characterized by a single parameter; the phosphorus mobilization clearance (K(M) ). In this work, we propose a simple method to estimate K(M) from predialytic and postdialytic plasma phosphorus concentrations. Clinical data were collected from 22 chronic hemodialysis patients that underwent a 4-hour treatment session. A simple algebraic equation was derived from the pseudo one-compartment model to determine K(M) from predialytic and postdialytic plasma phosphorus concentrations. K(M) values computed using this equation were compared with values obtained from nonlinear regression of the full kinetic model to frequent intradialytic and postdialytic measurements of plasma phosphorus concentrations. There was good agreement between K(M) values (concordance correlation coefficient of 0.94) obtained from the simple method (105 ± 52 mL/min, mean ± SD) and from the full model (99 ± 47 mL/min). The 95% confidence interval for the difference between estimated K(M) values was -26 to 36 mL/min. The proposed simple method requires the use of only predialytic and postdialytic blood samples to estimate patient specific K(M) ; this approach may allow easy clinical evaluation of phosphorus kinetics in hemodialysis patients.

Background Recently, bimodal peritoneal dialysis (PD) solutions containing low concentrations of Na have been shown to increase 24-hour ultrafiltration (UF) or UF efficiency (UF volume per gram of carbohydrate or CHO absorbed) and Na removal in high (“fast”) transport patients during automated PD therapy. We used computer simulations to compare UF efficiency and Na removal at equivalent 24-hour UF volumes using either a generic bimodal solution (2.27% glucose + 7.5% icodextrin) during the long dwell or an increase in the glucose concentration during the short dwells, with all solutions containing Na at the conventional concentration (132 mEq/L). Methods The 3-pore model has been shown to accurately predict peritoneal transport for PD solutions containing glucose or icodextrin, or both. Here, we used that model to calculate 24-hour UF volume, CHO absorption, and Na removal for high (H), high-average (HA), and low-average (LA) transport patients on automated PD. Nighttime therapy consisted of 1.36% or 2.27% glucose solution (or both), and daytime therapy consisted of either Extraneal (Baxter Healthcare Corporation, Deerfield, IL, USA) or a bimodal solution. Results As expected, addition of glucose to either the long dwell or the short dwells resulted in increased UF volume and glucose absorption. The increase in UF was a function of patient transport type (bimodal range: 288 – 490 mL; short-dwell range: 323 – 350 mL), and the increase in CHO absorption was smaller with glucose added to short dwells than with bimodal solution (range: 18 – 30 g vs. 34 – 39 g). The 24-hour UF efficiency was higher when high glucose concentrations were used during short-dwell exchanges than when a bimodal PD solution was used for the long dwell (0.6 to 1.2 mL/g vs. –0.1 to 0.5 mL/g). By contrast, Na removal was lower with the short-dwell exchanges (28.3 – 30.7 mmol vs. 36.2 – 53.3 mmol), likely because of more pronounced Na sieving. Conclusions Our modeling studies predict that generic bimodal PD solutions will provide higher Na removal but not higher 24-hour UF efficiency compared with current automated PD prescriptions using Extraneal for the long dwell and glucose-containing solutions for the short dwells. The modeling predictions from this study require clinical validation.

Use of patient-specific drain-phase parameters has previously been suggested to improve peritoneal dialysis (PD) adequacy. Improving management of the drain period may also help to minimize intraperitoneal volume (IPV). A typical gravity-based drain profile consists of a relatively constant initial fast-flow period, followed by a transition period and a decaying slow-flow period. That profile was modeled using the equation VD(t) = (V(D0) - Q(MAX) x t) xphi + (V(D0) x e(-alphat)) x (1 - phi), where V(D)(t) is the time-dependent dialysate volume; V(D0), the dialysate volume at the start of the drain; Q(MAX), the maximum drain flow rate; alpha, the exponential drain constant; and phi, the unit step function with respect to the flow transition. We simulated the effects of the assumed patient-specific maximum drain flow (Q(MAX)) and transition volume (psi), and the peritoneal volume percentage when transition occurs,for fixed device-specific drain parameters. Average patient transport parameters were assumed during 5-exchange therapy with 10 L of PD solution. Changes in therapy performance strongly depended on the drain parameters. Comparing 400 mL/85% with 200 mL/65% (Q(MAX/psi), drain time (7.5 min vs. 13.5 min) and IPV (2769 mL vs. 2355 mL) increased when the initial drain flow was low and the transition quick. Ultrafiltration and solute clearances remained relatively similar. Such differences were augmented up to a drain time of 22 minutes and an IPV of more than 3 L when Q(MAX) was 100 mL/min. The ability to model individual drain conditions together with water and solute transport may help to prevent patient discomfort with gravity-based PD. However, it is essential to note that practical difficulties such as displaced catheters and obstructed flow paths cause variability in drain characteristics even for the same patient, limiting the clinical applicability of this model.

The ultrafiltration (UF) efficiency of peritoneal dialysis (PD) solutions, defined as the net UF divided by the amount of carbohydrate absorbed per dwell, has been shown to be higher during long dwells with 7.5% icodextrin solution (Extraneal: Baxter Healthcare Corporation, Deerfield, IL, U.S.A.) than during those with glucose-based solution (2.5% and 4.25% Dianeal: Baxter Healthcare Corporation), prompting a better understanding of UF efficiency. We used the three-pore kinetic model of PD transport to investigate UF efficiency for single long dwells and various combinations of multiple short glucose-based dwells during automated PD (APD). To demonstrate a practical consequence of the effect of dwell time, we simulated two hypothetical APD prescriptions (A and B) in which fluid with a high glucose concentration was used during either the long day dwell (A: 4.25%; B: 2.5%) or the short night dwells (A: 3 x 1.5% + 1 x 2.5%; B: 4 x 2.5%). Computer simulations showed that higher glucose concentrations and shorter dwell times increase the UF efficiency of a single dwell, and UF efficiency depends on patient transport status. When 24-hour APD therapy was simulated for a low-average transporter, the net UF did not differ considerably (A: 1132 mL; B: 1154 mL), but total carbohydrate absorption was higher when solution with a high glucose concentration was used during the single long dwell (A: 146 g; B: 137 g), resulting in lower UF efficiency (A: 7.8 mL/g; B: 8.4 mL/g). We conclude that the UF efficiency of the entire regimen should be considered in prescribing PD therapy. When available, Extraneal provides the best UF efficiency during long dwells. Our simulations suggest that raising the glucose concentration in the short dwells and lowering it in the long dwell is the optimal strategy to maximize UF efficiency during APD when Extraneal is not available.