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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.

Effective conductivity clearance (K(ecn)) has been reported to be a surrogate for effective urea clearance (K(eu)), where both are usually defined respectively as the dialyzer conductivity and urea clearances (K(cn), K(u)) corrected for access recirculation (R(ac)). However, many investigators have reported K(ecn)/K(eu) to be1 and postulated anatomic distribution of Na in plasma water, cardiopulmonary recirculation (R(cp)), and high rates of urea clearance (K(u)) as causes. The aims of these studies were to devise analytic models of these mechanisms and to clinically evaluate the modeled relationships.We modeled and measured: (1) Na osmotic distribution volume flow rate (Q(osmNa)) in dialyzer blood flow; (2) the separate and combined effects of R(ac) and R(cp) on K(u) and K(cn); and (3) a novel mechanism reducing the conductivity diffusion gradient during measurement of K(cn) by recirculation through the dialyzer (R(s)) of a change in systemic blood conductivity (Delta Cn(s)) induced by the abrupt changes in dialysate inlet Na (Delta C(diNa)) required for the measurement of K(cn).The ratio Q(osmNa)/Q(bi)= 1.00 +.03, N= 19 (Q(bi)= total blood water flow rate). Modeling showed that the effects of R(ac), R(cp), and R(s) on K(cn) can be quantified as K(ecn)= K(cn)(1 -Delta Cn(bi)/Delta Cn(di)), where Delta C(nbi) is any change in conductivity in the dialyzer blood inlet stream during a measurement, and the effect of a combination of these mechanisms is the product of the effects of individual mechanisms. A single-step dialysate profile (with R(ac)= 0) resulted in measured Delta C(biNa)/Delta C(diNa)= 2.5/15, K(ecn)/K(eu)= 0.83, N= 21 because of R(s) and R(cp), but with a two-step, high/low profile (P(h/L)) we found these respective values to be -0.6/20 and 0.97, N= 19. The ratio K(ecn)/K(eu3)= 1.06 +.02, M + SE, N= 35 (K(eu3)= Ku corrected to reflect both access and cardiopulmonary recirculation). The ratio K(ecn)/K(eu1) (K(eu1) is K(u) corrected to reflect access recirculation only) = 1.01 +.07, N= 297, with no bias on Bland Altman analysis.We conclude that (1) the osmotic Na distribution volume in blood is total blood water; (2) K(ecn) measured with a short, high/low, and asymmetric dialysate profile shows R(ac) effect but neither R(cp) nor R(s) effects on K(ecn) and K(ecn)/K(eu)= 1.0; (3) the K(ecn)/K(eu) ratio is strongly dependent on the type of dialysate profile used, which must be optimized to minimize net Na transfer to and from blood during measurement of conductivity clearance to avoid erroneous underestimation of K(ecn) and K(ecn)/K(eu) ratios1.

Urea as a marker of adequacy in hemodialysis: Lesson from in vivo urea dynamics monitoring. Background "Dialysis dose," a concept developed by Sargent and Gotch based on urea kinetic modeling, is a useful and recognized tool that is used to quantitate and optimize a dialysis-efficacy program. However, it has been shown that oversimplification of the "dialysis adequacy" concept to the Kt/V index might lead to dramatic underdialysis and subsequent deleterious consequences on morbidity and mortality of dialysis patients. With this perspective, the determination of Kt/V must be very cautious and rely on accurate measurement of postdialysis urea concentration and its use integrated as a tool in a quality-assurance process. Methods In this study, we analyzed urea dynamics by means of a blood side (ultrafiltrate) continuous online urea monitoring system interfaced with a two-pool model hosted in amicrocom puter. The study was designed to provide instantaneous dialysis performances (body and dialyzer clearances, dialyzer mass transfer coefficient) and to determine the in vivo functional permeability characteristics of the patient [intercompartment urea mass transfer coefficient (K c )]. Thirteen end-stage renal disease patients (age 54 ± 16 years; 12 male and 1 female) were studied during nine consecutive dialysis sessions (3 weeks). Results Urea kinetics obtained from the urea monitoring system fitted closely the urea kinetic modeling prediction, confirming the validity of the double-pool model structure. Effective in vivo urea mass transfer coefficient averaged 912 ± 235 mL/min/1.73 m 2 , a value close to those reported with more invasive methods. Large variations ranging from 363 to 1249 mL/min were observed among patients, confirming very large interindividual patient permeability differences. Interestingly, the urea mass transfer coefficient was inversely correlated with the postdialysis rebound values. Intraindividual variations were also noted as a function of time denoting functional changes in urea mass transfer coefficient values. The urea distribution volume was 38.1 ± 7, 8 L (53 ± 8% body weight). V1 referring to the extracellular volume and V2 to the intracellular volume were 9 ± 2L (13 ± 2% body weight) and 29.2 ± 6.6 L (41 ± 1.3% body wt), respectively. The extracellular/intracellular volume ratio was 0.31 (approximately one third) and was not as usually defined by the paradigm 1/2 ratio. Conclusion Online double-pool urea kinetic modeling gavea new insight in urea kinetic modeling approach. Urea dynamics fit perfectly a double-compartment model structure. Accessible extracellular volume to hemodialysis is smaller than expected. The in vivo urea mass transfer coefficient must be considered as an individual and variable characteristic of ESRD patients that should be taken into consideration when prescribing the hemodialysis schedule.

Accuracy of hemodialysis modeling. Background One- and two-compartmental models of hemodialysis (HD) are well known. These models make it possible to analyze the course of treatment and to predict the effect of dialysis procedures. Mathematical modeling helps physicians to match dialysis therapy to the individual needs of the patient; however, the efficiency of the models depends on the accuracy of the coefficients. How to select coefficients in the case of one-compartmental models is known for urea and creatinine. Less information is available for two-compartmental models. Results on modeling of uric acid concentrations have not been published. Methods The identification of the mathematical model coefficients was based on the concentration measurements of three markers of uremic toxicity (urea, creatinine, and uric acid) in both patients' blood and dialysate. Blood samples were taken from the arterial line several times throughout the dialysis period. Simultaneously, dialysate samples were taken from a test port in the dialyzer outflow line. The mathematical model parameters were determined so as to minimize the deviations between the measured points and the calculated curves. In this way, distribution volumes, cellular clearances, and dialyzer mass transfer coefficients were estimated. Results For a one-compartmental model, the median value of distribution volume V = 0.56 DW was obtained, where DW is the patient's dry weight. For a two-compartmental model, intercompartment volume Vi = 0.36 DW and extracompartment volume Ve = 0.21 DW. The following median values for cellular clearances were established: urea 415 (mL/min), creatinine 207 (mL/min), and uric acid 257 (mL/min). Conclusions One- and two-compartmental models describe the concentration of the urea, creatinine, and uric acid very effectively, in contrast with phosphorus, in which modeling results are not satisfactory. Although two-compartmental models are more effective, they are much more complicated than one-compartmental models, which justifies using the one-compartmental model for hemodialysis modeling. A two-compartmental model must be used in the case of rebound phenomenon modeling. The total body water values we have obtained are similar to the anthropometrically based values for urea and creatinine and to a lesser degree for uric acid. Distribution volumes for one- and two-compartmental models obtained from patient weight are the simplest coefficients for mathematical models and have sufficient precision as well. The global value of both compartments is slightly greater than the corresponding value for a one-compartmental model. The effectiveness of dialyzers is in practice lower than might be expected on the basis of the data provided by their manufacturers. Urea cellular clearance is two times greater than creatinine and uric acid cellular clearances. The clearance differences are more prominent for the cellular membrane than for artificial semipermeable membranes.

Quasi-steadiness approximation for the two-compartment solute kinetic model. We analytically solved the equation of the variable volume, two-compartment solute kinetic model (TCSKM). From the solution, we constructed an expression of weekly concentration profiles developing in the patient's body by routine hemodialyses. Obtained formulas can be used to calculate Kt/V, solute reduction index (SRI), the solute generation rate (G) per unit distribution volume (V), and a mass transfer coefficient (MTC) between the two compartments. To estimate these parameters, the formulas only need three-point data during a dialysis, that is, pre-, one-hour, and post-dialysis solute concentrations instead of four that would otherwise be needed. A 48 hour data point is not required. The weekly concentration profiles can be easily calculated by the formulas. As examples of clinical applications, we calculated Kt/V, G/V, and SRI of urea, Cr, and uric acid using plasma data of 121 hemodialyzed patients. Then the results were compared with the single-compartment solute kinetic model (SCSKM). The obtained mean MTC/V values, that is, 1.08 (1/hr) for urea, 0.53 (1/hr) for Cr, and 1.11 (1/hr) for uric acid, were consistent with the previous works. SCSKM overestimated the mean G/V by 7.1%, 15.9%, and 10.0%, and the mean SRI by 6.7%, 18.6%, and 10.0%, for urea, Cr, and uric acid, respectively. The solute distribution volume ratio of TCSKM to SCSKM, (V)TCSKM/(V)SCSKM, depended on the value of MTC/V and the hemodialysis duration. Using pedometers, we measured the total number of steps the patients took during a week. We found that the total number of steps in a week was significantly correlated with the Cr generation rate (r = 0.285, P < 0.03), but that it was not significantly correlated with the other generation rates (r = 0.204, P > 0.09 for urea, and r = 0.209, P > 0.08 for uric acid). These data suggest that the Cr generation rate is related to the patient's physical activity. We conclude that the formulas can estimate an adequate dialysis prescription for the hemodialyzed patient.

Determination of urea distribution volume for Kt/V assessed by conductivity monitoring. Background Kt/V can be calculated continuously during dialysis without blood samples using the ionic dialysance method. Unlike the usual method using blood samples, a precise value for the patients' urea distribution volume is required. This study compared different methods for the determination of urea distribution volume (V) to evaluate their use in Kt/V measurement, based on conductivity monitoring. Methods Ten patients were studied during 40 dialysis sessions. Total body water and V were determined using bioimpedance spectroscopy (BIS), anthropometric data, and blood-based kinetic data. Ionic dialysance was measured by conductivity monitoring. Results Total body water measured by bioimpedance was determined as V BIS = 37.0 ± 7.1L or 49.6 ± 4.4% of body weight. V determined using ionic dialysance as input to urea kinetic modeling (UKM) was found to correlate well with total body water (V Kecn = 36.4 ± 5.2 L). All anthropometric equations overestimated measured V: V Watson = 40.7 ± 3.9L, V Hume = 41.8 ± 2.5L, V Chertow = 44.6 ± 3.3L, and V Chumlea = 43.1 ± 2.9L. Single-pool Kt/V obtained by kinetic modeling was used as reference (Kt/V) SPVV = 1.49 ± 0.15. Using different Vs as the V component in the ionic dialysance Kt/V, we obtained: K ecn *t/V Watson = 1.34 ± 0.12, K ecn *t/V BIS = 1.51 ± 0.21 and K ecn *t/V Kecn = 1.52 ± 0.18. Conclusion The single-pool Kt/V calculated using the ionic dialysance method agreed with the conventional blood sample method provided that V was calculated using BIS or urea kinetics. V by either method was reproducible and varied little in an individual patient. Monthly determination of V allows determination of Kt/V for each dialysis session by ionic dialysance.

Blood-based urea kinetic modeling (UKM) permits estimation of the urea distribution volume V that may be compared with the anthropometrically-predicted volume to determine if the kinetic modeling results are plausible. Various confounding factors may cause differences between the true distribution volume and that measured by UKM. During hemodialysis, three principal mechanisms are likely to contribute to an effective multicompartmental distribution of urea: access recirculation, cardiopulmonary recirculation and distribution of urea between intraand extracellular, and/or low and high blood flow, compartments [1]. The effect of each of these mechanisms is to reduce the efficiency of dialysis by lowering the intradialytic serum blood urea nitrogen (BUN) profile. After dialysis, the serum BUN level will rebound with different time scales for access recirculation (over a period of approximately 10 seconds [1]), cardiopulmonary recirculation (typically over a period of 2 mm [2]), and the compartmental effects (over a period of 30 to 60 mm [3, 4]). Ideally blood drawn for urea kinetic modeling should be drawn after all three rebounds have occurred, 30 to 60 minutes postdialysis. If this is done, single-pool modelling based on the expected dialyzer urea clearance estimate will give an inflated estimate of the urea distribution volume. Single pool modeling assumes that the dialyzer clearance results in a monoexponentially decreasing plasma urea profile from the preto the post-dialysis BUN samples. Because of the recirculation/compartmental effects noted above effective dialyzer clearance will be less than that expected (K), and this is mathematically equivalent to an increased urea distribution volume V for a given exponent K/V. When blood is sampled before rebound has occurred, the situation is more complex; single-pool IJKIvI can underestimate, correctly estimate, or overestimate the true urea distribution volume, depending on the level of urea reduction that has occurred [1, 5]. This is because two counteracting effects are in play [6]. On the one hand, the fraction of urea distribution volume cleared (Kt/V) is overestimated, and this causes an underestimation of the urea distribution volume for the expected V value. On the other hand, the intradialytic urea profile is still lower than that estimated by a monoexponential curve from the predialysis BUN

Beta 2 -microglobulin kinetics in end-stage renal failure. The kinetics of β-microglobulin (β 2 m) were studied in five anephric or anuric hemodialysis patients. Human β 2 m was isolated from peritoneal dialysate using ion-exchange and gel chromatography and radiolabeled with 125 I. Patients were injected with 10 µCi labeled β 2 m. In one study (N = 4), plasma activity was measured over 72 hours. In a second study (N = 4), patients received low-flux dialysis 24 hours after injection and high-clearance dialysis (Belico BL655) at 48 hours. Plasma activities were fitted to a three-compartment, variable volume model. Endogenous β 2 m levels (radioimmunoassay) were 56 ± 6 mg/liter. The β 2 m distribution volume was 12.7 ± 2.0 liter (0.20 ± 0.03 liter/kg) and the non-renal clearance was 3.0 ± 0.4ml/min. The generation rate, 9.9 ± 1.7 mg/hr (0.16 ± 0.04 mg/kg/hr), was similar to that measured in subjects with normal renal function. The three compartment model derived from the turnover data gave an adequate fit of the arterial concentrations of endogenous and exogenous β 2 m during low-flux (nil β 2 m clearance) and high-clearance (β 2 m clearance of 19 ml/min) dialysis. Simulations based on this model indicate that extracorporeal treatment can at best remove about 50% of weekly production. These results suggest that β 2 m production is not increased in dialysis patients, that there is substantial non-renal β 2 m clearance, and that the amount of β 2 m that can be removed by extracorporeal therapy is therefore limited.

To the Editor: In the February 2006 issue of Kidney International, Di Filippo et al.1 claimed that urea distribution volume (V) decreases over time in stable hemodialysis patients. We challenge these conclusions for the following reasons

Relationship between apparent (single-pool) and true (double-pool) urea distribution volume Background The volume of urea distribution (V) is usually derived from single-pool variable volume urea kinetics. A theoretical analysis has shown that modeled single-pool V (Vsp) is overestimated when the urea reduction ratio (URR) is greater than 65 to 70% and is underestimated when the URR is less than 65%. The "true" volume derived from double-pool kinetics (Vdp) does not exhibit this effect. An equation has been derived to adjust Vsp to the expected Vdp. Methods To validate these theoretical predictions, we examined data from the Hemodialysis (HEMO) Study to assess the performance of Vdp as estimated from Vsp using the previously published prediction equation. For increased precision, both Vsp and Vdp were factored by anthropometric volume (Va). Patients were first dialyzed with a target equilibrated dialysis dose (eKt/V) of 1.45 during a baseline period and were then randomly assigned to eKt/V targets of either 1.05 (a URR of approximately 67%) or 1.45 (a URR of approximately 75%). A blood sample was obtained one hour after starting dialysis during one dialysis in each patient. Results Vsp/Va was (mean ± SD) 1.014 ± 0.127 in 795 patients during the baseline period when the URR was approximately 1.45. During the first modeled dialysis after randomization, the Vsp/Va fell to 0.961 ± 0.138 in the group with an eKt/V target of 1.05, but did not change significantly under the high eKt/V goal. The correction of Vsp to Vdp using the prediction equation resulted in a Vdp/Va ratio of 0.96 to 0.98 in all three circumstances without significant differences. When a blood sample was drawn one hour after starting dialysis, the apparent Vsp/Va ratio at one hour was much lower at 0.708 ± 0.139. However, the mean Vdp/Va ratio, computed using the correction equation, was 0.968 ± 0.322, which was similar to the Vdp/Va ratio calculated from the postdialysis blood urea nitrogen. Conclusions These data suggest that the previously derived formula for adjusted Vsp is valid experimentally. The Vsp/Vdp correction should be useful for prescribing hemodialysis with either a very low Kt/V (for example, daily and early incremental dialysis) or a very high Kt/V.

Causes, kinetics and clinical implications of post-hemodialysis urea rebound. The rapid increase in end-dialysis urea concentration (Co) immediately after the end of dialysis (HD), which greatly exceeds that expected as an effect of urea generation and defined as “net rebound,” was assessed in 21 chronic HD patients. The curve of serial values of net rebound correlated (r = 0.70) with the theoretical curve predicted by the two pool urea kinetics model (UKM). A mean equilibrium concentration (Ce) was achieved in 48 minutes, with a 7.58% increase in Co. Stabilized rebound (Re) was compared after four different HD procedures, and significant correlations were found between the magnitude of Re and the indexes of HD efficiency, dialyzer clearance (r = 0.75) and Kt/V (r = 0.68). The highest values of Re (8.6% and 8.8%) were observed after the procedures with largest urea removal, irrespective of the biocompatibility conditions (new or reused dialyzers). The single pool UKM applied with the stabilized end-HD urea concentration Ce instead of Co resulted in more physiological values of urea distribution volume (56.1% vs. 50.5% of body wt) and in lower values of Kt/V (0.64 vs. 0.73, P < 0.001) and protein catabolic rate (1.07 vs. 1.17 g/kg/day, P < 0.001). A reequilibration process, rather than protein hypercatabolism, seems to be responsible for most rebound, the magnitude of which correlated with the efficiency of the procedure. Only by considering Ce as the true end-HD urea concentration is it possible to minimize the errors arising from the application of a single pool analysis to a two pool system.

Kinetic behavior of urea is different from that of other water-soluble compounds: The case of the guanidino compounds.BackgroundAlthough patients with renal failure retain a large variety of solutes, urea is virtually the only currently applied marker for adequacy of dialysis. Only a limited number of other compounds have up until now been investigated regarding their intradialytic kinetics. Scant data suggest that large solutes show a kinetic behavior that is different from urea. The question investigated in this study was whether other small water-soluble solutes, such as some guanidino compounds, show a kinetic behavior comparable or dissimilar to that of urea.MethodsThis study included 7 stable conventional hemodialysis patients without native kidney function undergoing low flux polysulphone dialysis (F8 and F10HPS). Blood samples were collected from the inlet and outlet bloodlines immediately before the dialysis session, after 5, 15, 30, 120 minutes, and immediately after discontinuation of the session. Plasma concentrations of urea, creatinine (CTN), creatine (CT), guanidinosuccinic acid (GSA), guanidinoacetic acid (GAA), guanidine (G), and methylguanidine (MG) were used to calculate corresponding dialyzer clearances. A two-pool kinetic model was fitted to the measured plasma concentration profiles, resulting in the calculation of the perfused volume (V1), the total distribution volume (Vtot), and the intercompartmental clearance (K12); solute generation and overall ultrafiltration were determined independently.ResultsNo significant differences were observed between V1 and K12 for urea (6.4 ± 3.3L and 822 ± 345mL/min, respectively) and for the guanidino compounds. However, with respect to Vtot, GSA was distributed in a smaller volume (30.6 ± 4.2 L) compared to urea (42.7 ± 6.0L) (P < 0.001), while CTN, CT, GAA, G, and MG showed significantly higher volumes (54.0 ± 5.9 L, 98.0 ± 52.3 L, 123.8 ± 66.9 L, 89.7 ± 21.4 L, 102.6 ± 33.9 L, respectively; P = 0.004, = 0.033, = 0.003, < 0.001, = 0.001, respectively). These differences resulted in divergent effective solute removal: 67% (urea), 58% (CTN), 42% (CT), 76% (GSA), 37% (GAA), 43% (G), and 42% (MG).ConclusionThe kinetics of the guanidino compounds under study are different from that of urea; hence, urea kinetics are not representative for the removal of other uremic solutes, even if they are small and water-soluble like urea.

Ionic dialysance allows an adequate estimate of urea distribution volume in hemodialysis patients. Background An adequate estimation of urea distribution volume (V) in hemodialysis patients is useful to monitor protein nutrition. Direct dialysis quantification (DDQ) is the gold standard for determining V, but it is impractical for routine use because it requires equilibrated postdialysis plasma water urea concentration. The single pool variable volume urea kinetic model (SPVV-UKM), recommended as a standard by Kidney Disease Outcomes Quality Initiative (K/DOQI), does not need a delayed postdialysis blood sample but it requires a correct estimate of dialyser urea clearance. Methods Ionic dialysance (ID) may accurately estimate dialyzer urea clearance corrected for total recirculation. Using ID as input to SPVV-UKM, correct V values are expected when end-dialysis plasma water urea concentrations are determined in the end-of-session blood sample taken with the blood pump speed reduced to 50 mL/min for two minutes (U pwt2′ ). The aim of this study was to determine whether the V values determined by means of SPVV-UKM, ID, and U pwt2′ (V ID ) are similar to those determined by the "gold standard" DDQ method (V DDQ ). Eighty-two anuric hemodialysis patients were studied. Results V DDQ was 26.3 ± 5.2 L; V ID was 26.5 ± 4.8 L. The (V ID –V DDQ ) difference was 0.2 ± 1.6 L, which is not statistically significant ( P = 0.242). Anthropometric volume (V A ) calculated using Watson equations was 33.6 ± 6.0 L. The (V A –V DDQ ) difference was 7.3 ± 3.3 L, which is statistically significant ( P Conclusion Anthropometric-based V values overestimate urea distribution volume calculated by DDQ and SPVV-UKM. ID allows adequate V values to be determined, and circumvents the problem of delayed postdialysis blood samples.

We would like to thank Dr Basile1 for giving us this opportunity to underline two important aspects of our paper:2 (1) the difference between the variability of urea distribution volume (V) in individual patients and its variability in the total study population; and (2) the relevance of the statistical phenomenon of regression to the mean.