NDT Advance Access originally published online on February 13, 2008
Nephrology Dialysis Transplantation 2008 23(7):2286-2298; doi:10.1093/ndt/gfm938
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Dosing intermittent haemodialysis in the intensive care unit patient with acute renal failure—estimation of urea removal and evidence for the regional blood flow model
1 Section of Dialysis and Extracorporeal Therapy, Department of Hypertension/Nephrology, OH, USA 2 Department of Renal Medicine, Newcastle-upon-Tyne Hospitals NHS Foundation Trust, UK 3 Department of Biostatistics and Epidemiology, Cleveland Clinic Foundation, OH 4 Department of Medicine, University of Illinois College of Medicine at Chicago, IL 5 Division of Nephrology, University of California Davis Medical Center, Sacramento, CA, USA
Correspondence and offprint requests to: Nigel S. Kanagasundaram, Department of Renal Medicine, Freeman Hospital, High Heaton, Newcastle-upon-Tyne NE7 7DN, UK. Tel: +44-0191-233-6161 ext 37149; Fax: +44-0191-2231233; E-mail: suren.kanagasundaram{at}nuth.nhs.uk
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Abstract |
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Background. Blood-side dosing methods may overestimate urea removal in comparison to dialysate-side measurements during intermittent HD (IHD) for acute renal failure (ARF). The present study sought to quantify this mass balance error (MBE) and explore potential explanatory factors.
Methods. Prospective, formal, blood-side urea kinetic modelling was performed in serial sessions (n = 42) in 18 intensive care unit ARF patients. Three blood-side estimates of urea removal were calculated and these were compared to urea removal derived from fractional dialysate sampling and use of an on-line urea monitor. We also examined urea rebound in these patients, as expressed by the intercompartmental urea clearance (Kc), and in a subset of patients examined the relation of Kc to cardiac output and systemic vascular resistance (SVR).
Results. The mean % MBE (MBE = blood – dialysate-estimated urea removal) was about 9% using conventional two-pool modelling based on a 60-min post-dialysis blood urea nitrogen (BUN) with or without the use of one or more intra-dialytic BUN values. The extent of MBE could not be explained by the clinical or dialytic variables that were measured. Part of the MBE error was due to overestimation of the intradialytic BUN profile, because model-independent profiling of intra-dialytic BUN values to compute urea removal reduced the MBE to 
6%. The log Kc was correlated with cardiac output and showed trends towards an inverse correlation with SVR.
Conclusions. Classical, two-pool, blood-side UKM produces a modest overestimate of urea removal in IHD for critically ill ARF patients. The source of this small, residual MBE is unknown. The amount of urea rebound, as reflected by Kc, varied among patients and associated with cardiac output and SVR, as predicted by the regional blood flow model.
Keywords: mass balance error; multi-compartment modelling; renal replacement therapy; urea kinetic modelling; vasopressors
Abbreviations: BUN, blood urea nitrogen • BUNeq, equilibrated BUN calculated using Runga–Kutta algorithm • DDQ, direct dialysis quantification • E, dialyzer extraction ratio • eKt/V, equilibrated Kt/V • eKt/ Vrate, equilibrated Kt/V calculated from rate equation • eKt/Vref, equilibrated Kt/V calculated using Runga–Kutta algorithm • fVDDQ, dialysate-side estimate of V using fractional DDQ • G, urea generation rate • IHD, intermittent haemodialysis • Kc, inter-compartmental mass transfer coefficient • Kd, dialyzer clearance • Kdcross, cross-dialyzer clearance • Kdcross 1–3, cross-dialyzer clearance at start, mid-point, end of session, respectively • KoA, mass transfer area coefficient for urea • Kr UN, residual renal clearance of urea nitrogen • MBE, mass balance error • Qb, extracoporeaal blood flow rate • Qd, dialysate flow rate • Quf, ultrafiltration rate • REMbl-dp, blood-side UN removal using two-pool curve fit to peri-dialysis BUNs • REMbl-intra, blood-side UN removal using two-pool curve fit to intradialysis BUNs • REMbl-emp, blood-side UN removal using empirical curve fit to intradialysis BUNs • REMdi, actual UN removed measured from fractional dialysate collection • REMdi-bio, actual UN removed measured by Biostat 1000 • SIRS, systemic inflammatory response syndrome • spKt/V, single-pool Kt/V • Td, treatment time • UKM, urea kinetic modelling • UN, urea nitrogen • V, urea distribution volume • Vdp, double-pool V • Vdprate, double-pool V based on rate equation • Vdpref, double-pool V calculated using Runga–Kutta algorithm • Vdp(wtadj), weight-adjusted value of estimated Vdprate (see text) • Vsp, single-pool V • Watson V, Watson anthropometric estimate of total body water
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Introduction |
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Despite increasing attention being paid to the issue of dosing in acute renal replacement therapy, it still remains unclear whether the kinetic relationships that exist in end-stage renal disease (ESRD) still hold true in the critically ill patient with acute renal failure (ARF). These concerns are not just theoretical, they may have a significant bearing on actual delivered dose and, ultimately, upon outcome.
Single-pool assumptions about urea distribution volume (V) fail to account for the urea disequilibrium that develops over the course of a haemodialysis session resulting in an overestimation of urea removal in comparison to the ‘gold standard’ of dialysate-side quantification [1]. Double-pool models provide more accurate estimates of urea removal, at least in ESRD [1].
Only a limited number of studies have actually examined intermittent haemodialysis (IHD) dosing in ARF [2–6]. Under-prescription and prescription-delivery shortfalls have been described [4], but interpretation of results is hampered by the use of various simplified kinetic formulae. None prospectively examined dose using formal single- or double-pool urea kinetic modelling (UKM) techniques and only one group [5,6] employed direct dialysis quantification (DDQ). The suggestion from previous work was that blood-side, double-pool dosing, as determined by the solute removal index, overestimated urea removal by a very considerable amount, in the range of 35% [5]. Although robust kinetic analyses were not performed, if true, such an error would invalidate the application of conventional, two-pool UKM in an acute care setting.
In a previous paper, in which we applied formal, two-pool, blood-side UKM in a prospective study of serial haemodialysis sessions performed in intensive care unit ARF patients [7], we confirmed the high urea generation rates typically found in these patients. There was considerable inter-session variability in a wide variety of clinical and dialytic parameters. The kinetically determined urea distribution volume, V, systematically exceeded anthropometric estimates of V, as distinct from the situation in chronic dialysis patients. The main objective of the present study was to compare urea removal by blood- versus dialysate-side kinetics in an ICU population, to determine whether a substantial mass balance error (MBE) does exist, and to examine factors that might theoretically be associated with such an MBE, including intra-dialytic fluid administration (which lowers intra-dialytic BUN by dilution), access recirculation (which lowers effective clearance) and severe compartment disequilibrium (which might lead to overestimation of the true intra-dialytic BUN).
A secondary objective was to examine the extent of urea rebound in these patients, and in a subgroup, to determine if urea rebound, as expressed by the inter-compartmental urea mass transfer clearance (Kc) was related to haemodynamic variables, as flow-mediated disequilibrium [8] would be expected to be highly prevalent in the ICU population.
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Serial dialysis sessions (maximum of 7 per patient) were studied, from dialysis initiation, in intensive care patients with ARF. Inclusion criteria and ARF definition were as previously described [7].
Twenty-two patients (14 male) were studied. Their mean age was 64.1 ± 9.6 years (46–78), with the following racial mix: white (n = 18), African American (1) and Middle-Eastern (3). The primary diagnoses were cardiothoracic surgical (n = 11), other surgical (2), cardiac medical (5) and other medical (4). Renal diagnoses were acute tubular necrosis (14), acute on chronic renal failure (5) and ARF, unspecified (3).
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Methods |
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Intermittent haemodialysis prescription
Details of the dialysis prescription are noted in Appendix 1. Two dedicated dialysis machines were used during the study. Each was calibrated once monthly to ensure that the volume of effluent collected over 1 h of ongoing dialysis was within 2% of that predicted from the prescribed dialysate flow, Qd, and ultrafiltration rate, Quf [42 measurements; mean% error = 0.08 (–1.08–1.21)].
Data collection
The following were recorded at each session: pre- and post-dialysis weights, details of the dialysis prescription along with any subsequent changes during treatment, interruptions (which were timed) and complications, and fluid losses (excluding ultrafiltration) and infusions (if >500 mls). Blood urea nitrogen (BUN) was measured pre- and post-dialysis and at post +60 min. Immediate post-dialysis blood sampling used a modification of the stop pump method [9] to negate access recirculation, as previously described [7].
Weights were recorded with a sling scale or, if the patient was too unstable, via the bed scale, but only after careful calibration prior to the first studied session, to allow reproducibility. Height was taken from the patient's records or, if unavailable, by bedside measurement.
Total urea nitrogen removal was calculated using the fractional dialysate collection technique of Ing et al. [10] (see Appendices 2 and 3) and, in a subset of sessions, using the Biostat 1000 on-line urea monitor (Baxter Healthcare Corporation, McGaw Park, IL, USA) [11,12] (see Appendix 3). The percentage access recirculation was reported as the mean of two readings measured 30 min after starting HD by the Transonic method [13] (Transonic HD-01 monitor, Transonic Systems, Ithaca, NY, USA), with these readings repeated if the blood lines were later reversed. The in vivo mass transfer area coefficient for urea (in vivo KoA) and cross-dialyzer clearance (in vivo Kdcross) were calculated in 49 sessions utilizing the dialyzer extraction ratio (Appendix 4). The percentage change in blood volume over the session was measured by the Critline IIR or III optical haematocrit monitor (In-Line Diagnostics, Farmington, UT, USA) [14–16]. In those patients with a pulmonary artery catheter in situ averaged session values for the systemic vascular resistance (SVR) and cardiac output were calculated from readings taken at 15 min, mid-way through the session and at the end of the session. Averaged session values for the systolic BP, diastolic BP, mean arterial pressure and heart rate used measurements taken at 15 min, 60 min and then every hour up to the end of the session. The presence or absence of SIRS (the systemic inflammatory response syndrome) was determined, at each session, according to standard criteria [17].
Residual renal urea clearance (Kr UN) was estimated between sessions with timed urine collections, provided daily urine output was 
200 mL (Appendix 5). Inter-dialysis blood samples for BUN were recorded and accurately timed to allow for better monitoring of changes in the urea generation rate, G.
The Watson anthropometric estimate of total body water (Watson V) was calculated [18] using the post-dialysis weight.
Sessions were excluded from further kinetic analysis for one or more of the following reasons: line reversal after 20 min, no fractional dialysate collection UN or missing BUNs (the pre-HD, post-HD or delayed post-HD BUN), periods of isolated ultrafiltration, session length <2 h or other missing data preventing calculation of the equilibrated post-dialysis BUN. Of the 79 sessions followed, in total, 52 remained after applying these exclusions. All 22 patients were still included and were studied for a mean of 2.4 ± 1.6 sessions per patient (range 1–5 sessions). This broader data set of 52 sessions was used to define the relationship of invasive haemodynamic parameters (cardiac output and SVR) to blood-side measures of disequilibrium (the inter-compartmental mass-transfer coefficient, Kc). The MBE was studied in the 43 sessions in which an intra-dialytic BUN profile could be plotted from the dialyzer inlet BUN measurements used for estimation of cross-dialyzer clearance. One session with an unfeasible MBE (>20 g UN) was discarded leaving 42 sessions (in 18 patients) for subsequent analysis of potential explanatory factors.
Urea kinetic modelling
For each modelled session, an estimate of the single-pool urea distribution volume, Vsp, was calculated using the single-pool, variable-volume model (Appendix 6). The rate correction of Daugirdas and Schneditz [19] was applied to this estimate of Vsp to obtain an estimated double-pool V (Vdprate, Appendix 7). A weight-adjusted value of the estimated Vdprate [Vdp(wtadj), Appendix 8] was then calculated to minimize the impact of erroneous weight measurements, of variations in total body water and of errors in the kinetically determined V, all of which may be more frequent in the acute renal failure setting.
This sequence of calculations was repeated twice, now using Vdp(wtadj) rather than the Watson V to estimate G at each iteration. After the final iteration, the following kinetic parameters were computed:
- G = mean of the final pre- and post-HD estimates of G
- Vsp = result of applying the single-pool, variable-volume model to G, Kd, Kr UN, Td and the pre- and post-dialysis weights
- spKt/V = single-pool Kt/V = Kd x Td/Vsp
- eKt/Vrate = equilibrated Kt/Vrate = spKt/V – 0.47 K/V + 0.02
- Vdprate = adjustment of Vsp (see above and Appendix 7)
- Vsp = result of applying the single-pool, variable-volume model to G, Kd, Kr UN, Td and the pre- and post-dialysis weights
The expression for eKt/Vrate is the Daugirdas–Schneditz rate equation for eKt/V when venous accesses are used [20]. In this expression, K/V is calculated as (spKt/V)/Td expressed in hour–1.
A curve-fit solution to the double-pool, variable-volume model [21] was generated by applying the Runge–Kutta algorithm [22], in order to estimate the equilibrated BUN (BUNeq) (Appendix 9) as well as the true two-pool V (Vdpref), the inter-compartmental mass-transfer coefficient (Kc) and the equilibrated Kt/V (eKt/Vref).
We also calculated a dialysate-side estimate of V using fractional DDQ to yield fVDDQ (Appendix 10).
Five estimates of total urea nitrogen removal were obtained for each session—two dialysate-side (REMdi and REMdi-bio) and three blood-side (REMbl-dp, REMbl-intra and REMbl-emp).
The dialysate-side estimates represented actual UN removal measured from the fractional dialysate collection (REMdi) or the Biostat 1000 (REMdi-bio). REMdi-bio was utilized as a quality assurance for the fractional dialysate technique and was not subsequently used to define any MBE.
The first blood-side estimate of UN removal, REMbl-dp, was the integral of total dialyzer clearance, Kd (Appendix 6), to the two-pool, variable-volume curve fit to the pre-, post- and delayed-post-dialysis BUNs. This estimate of urea removal reflected the theoretical intra-dialytic BUN profile predicted by the two-pool model and would be equivalent to the change in total body urea over HD, utilizing the Vdpref and BUNeq (as shown in Appendix 3).The second blood-side estimate of UN removal, REMbl-intra, was calculated by integrating Kd to a two-pool curve fit to the intra-dialytic BUNs, alone (i.e. excluding the post- and delayed post-dialysis BUNs). By using the actual intra-dialytic BUN profile, we hoped to show that any MBE evident from assuming a theoretical intra-dialytic curve fit in calculating REMbl-dp would correct.
We observed faster declines in BUN at the first intra-dialytic measurement (observed a median of 10 min after the start of dialysis) than could be accommodated by the full intra-dialytic two-pool curve fit. Thus, our third blood-side estimate of urea removal, REMbl-emp, was calculated by integrating Kd with an adjustment to the two-pool intra-dialytic curve fit. This was obtained by using a quadratic extrapolation to fit the BUNs prior to the first intra- dialytic BUN, and then fitting the remainder of the intra-dialytic BUN profile by applying the two-pool intra-dialytic curve fit to the remainder of the dialysis session, starting at the first intra-dialytic BUN.
The MBE for urea removal by each of the three blood-side estimates was calculated as REMbl-dp/intra/emp—REMdi. Each of the three estimates of the MBE was examined in terms of haemodynamics, extracorporeal circuit saline flush frequency, intra-dialytic extracorporeal and systemic fluid infusion volume (recorded if >500 mL), mean G, Kc and log Kc, % 
blood volume, mean Kdcross, vasopressor use, the presence or absence of SIRS, ultrafiltration volumes and % access recirculation.
In vivo Kdcross was compared at the different, measured time points (start versus middle, start versus end and middle versus end).
Statistical analysis
Descriptive comparisons of the various estimates of urea removal were performed using the concordance correlation coefficient, Rc, with bias indicated by the median of the differences (Med ), and scatter by the median of the absolute values of differences (Med II). Formal tests of deviations of the mean MBEs from zero were performed using a mixed effects model with a compound symmetry assumption for the residuals to account for the multiple assessments in the same patients.
The various potential explanatory factors for the MBE, detailed above, were compared with each other, on an individual session basis, using the Pearson correlation.
Where available in the broader data set of 52 sessions, cardiac output and SVR were compared to log Kc using the Pearson correlation.
The impact of the potential explanatory factors on the different estimates of the MBE was explored using a general regression analysis for multiple independent variables with a mixed effects model. For these regression analyses the MBE estimates were expressed as the difference between the respective log-transformed blood-side estimates of urea removed and the dialysate-side estimates. Under the log transform the effects of the predictor variables on the MBE were expressed as a percentage of the magnitude of the urea removed, thus avoiding confounding by proportionate errors at higher levels of urea removal. A compound symmetry assumption for the residuals was again applied to account for multiple sessions in the same patients.
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In the 42 sessions utilized in analysis of the MBE, the extracorporeal circuit was maintained with saline flushes in 28 sessions and systemic anticoagulation and/or pre-filter, unfractionated heparin in 14 sessions (2 sessions with a combined flush and anticoagulation strategy). Of the 28 sessions in which a saline flush strategy was used, 12 involved 2–6 flushes and 12, 7 or more flushes. One saline flush was used in the remaining 4 sessions.
Seven sessions had mean intra-dialytic fluid losses (other than through ultrafiltration) of 339 ± 401 mL (65–1154). Thirty-one sessions had intra-dialytic fluid infusions (including extracorporeal saline flushes) of over 500 mL. In these sessions, the mean fluid infusion volume was 1578 ± 598 mL (600–2628).
The in vivo urea KoA for the F50 dialyzer, used in the urea kinetic model above, was taken to be the median (457 mL/min; 25th percentile 431, 75th percentile 495, SE 11), over the 49 sessions, of the average of the three in vivo KoAs measured at the three time points during these sessions (in comparison, the in vitro KoA of the F50 is reported to be 577 mL/min [manufacturer's data]).
Summary of UKM parameters
In the 42 sessions utilized in analysis of the MBE, basic treatment parameters are summarized in Tables 1a and 1b (solute levels are shown with plasma water correction [21]), and derived UKM parameters in Tables 2a and 2b. In keeping with our previous work [7], the subset of sessions used in the present study showed low delivered dialysis doses. The median Kr UN was 0.9 mL/min (10th percentile 0, 90th percentile 13.1) although 6 of the 18 patients studied had a daily urine output of <200 mL over the period of study.
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The mean delivered treatment time, Td and Transonic Qb were 219 min and 351 mL/min, respectively, taken on an individual sessional basis. The mean urea generation rate, G, on a per patient basis was 10.6 ± 5.7 mg/min. The mean patient double-pool V from the curve-fit solution to the two-pool model, Vdpref, was 46.9 ± 11.9 L in comparison to a mean single-pool V of 45.9 ± 11.1 L and Watson V of 41.1 ± 7.8 L.
The median inter-compartmental mass transfer coefficient of urea, Kc, over all 52 modelled dialysis sessions was 916 mL/min with 25th and 75th percentiles of 579 and 1721 mL/min, respectively.
Measurement of cross-dialyzer clearances
There was a clear decline in cross-dialyzer clearance over the course of these sessions. The median difference between the first and third estimates was 13 mL/min or around 6% of the initial estimate. This seemed to arise, predominantly, from a reduction in convective clearance (the median decline in Quf was 16%) rather than in diffusive clearance (median decline in the dialyzer extraction ratio, E (see Appendix 4), was 5%, and in Transonic Qb, under 3%).
Estimates of urea removal and the mass balance error
Estimates of urea removal are shown in Tables 3a and 3b. Although the fractional dialysate collection technique is well validated, it was reassuring to note a close agreement between the fractional dialysate collection estimate of urea removal (REMdi) and the real-time estimate from the Biostat 1000 equipment (REMdi-bio), as shown in Figure 1. Regular calibration of the two dedicated study haemodialysis machines assured a total dialysate effluent volume estimate within 1.3% of the actual volume.
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As shown in Figure 2 and Tables 3a and 3b, REMbl-dp (the blood-side estimate of urea removal derived from the conventional curve fit to the pre-, post- and post+60’ BUNs) overestimated urea removal in comparison to the dialysate-side measurement, REMdi. The mean MBE was 2.4 ± 3.3 g or 8.6 ± 11.9% (median 7.9% with 10th and 90th percentiles of –2.9 and 23.7%, respectively). Estimation of urea removal using the two-pool curve fit to the intra-dialysis BUNs (REMbl-intra) did not appreciably improve the MBE (Figure 3) although the empirical curve-fit estimate (REMbl-emp) did have some impact (Figure 4). Even use of this empirical estimate, though, failed to correct the MBE, with a median residual MBE of 5.9% (Tables 3a and 3b).
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Vasopressor agents were used in 14 of the 42 sessions. Patients were defined as having SIRS in 29 of the 42 studied sessions. Predictably, systolic BP and mean arterial pressure were inversely associated with vasopressor use (mean ± SD systolic BP 126.7 ± 25.4 mmHg without vasopressor use versus 104.5 ± 13.2 with vasopressor use; MAP 80.1 ± 13.6 mmHg without vasopressor use versus 71.4 ± 6.7 with vasopressor use). Descriptive statistics for other potential explanatory factors for the MBE are shown in Table 4a (if not described elsewhere). A correlation between log Kc and cardiac output provided evidence for the regional blood flow model (Figure 5a) although numbers were small. Figure 5b shows the relationship between log Kc and SVR. Although this was compatible with regional blood flow disequilibrium, numbers were small and the correlation did not quite reach significance.
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None of the potential predictor variables showed a significant association with the MBE. Table 4b illustrates this for the MBE defined as REMbl-dp – REMdi, but the lack of any association held true for the other estimates of MBE, too. Effects were estimated in terms of %MBE to prevent confounding by proportionate errors at higher levels of urea removal. P-values are those derived from the mixed effects model.
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Discussion |
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Previous studies have suggested that a MBE of very considerable magnitude may exist in ARF patients undergoing intermittent HD (IHD), and that this may have been due to alterations in the distribution of urea in body water [5,6]. The suggestion from this work was that blood-side, double-pool dosing, as determined by the solute removal index, overestimated urea removal by, on average, 35% [5]. However, this conclusion was not derived using formal urea kinetic methodology; simplified assumptions about total body water volume and an erroneous dismissal of the impact of G hampered interpretation.
Our study is the first to apply formal blood- and dialysate-side UKM in this setting and is the first to actually do so in serial sessions.
We used these techniques to estimate urea removal using both blood- and dialysate-side methods, and we did find a more modest difference, or MBE of 9% on average higher using blood-side kinetics compared to dialysate recovery. In blood-side kinetics, the amount of urea removed is computed as the product of the time-averaged intra-dialytic serum urea level and the dialyzer clearance. If either of these two quantities is overestimated, an MBE can result. Alternatively, an MBE can also result if the amount of urea recovered from the dialysate is underestimated, either due to an error in measuring or estimating the volume of dialysate collected, or to an error in properly measuring the urea nitrogen concentration in the spent dialysate. Our study was uniquely equipped to explore the potential causes of this MBE.
The first cause of a blood-positive MBE that we examined was an overestimation of the time-averaged intradialytic urea concentration. We did so by examining a theoretical intra-dialytic profile from a two-pool curve fit to the peri-dialysis BUNs, a curve fit to the actual intra-dialytic profile using two-pool assumptions, and finally a curve fit to the actual intra-dialytic profile using a best-fit algorithm not dependent on any two-pool assumptions in the initial phase of BUN reduction.
A dialyzer can remove only that amount of urea that is present in the inflow blood line during treatment. The time-averaged intra-dialytic UN concentration is somewhere between the pre- and post-dialysis values. In single-pool kinetics, the intra-dialytic time-averaged concentration of urea nitrogen (TAC-UN) is estimated as a mono-exponential decay between the starting and ending values. In double-pool kinetics, an exaggerated early fall in BUN occurs due to early removal of urea from a more proximal compartment. This will lower the intra-dialytic TAC-UN. In the classical two-pool model, the extent of this early fall in UN during dialysis depends on the amount of resistance between the two compartments from which urea is removed; these represent a distal, intra-cellular space and a proximal, extra-cellular space, with relative volumes of 2:1. This resistance is expressed as a clearance (Kc, in mL/min), which occurs between the two compartments during dialysis. When the resistance to urea ‘flow’ between the compartments is high, Kc will be low; this will result in a more pronounced early fall in BUN, and for the same level of pre- and post-dialysis BUN, a lower intra-dialytic TAC-UN. When performing blood-sided modelling, multiple intra-dialytic BUN measurements are not routinely made, only pre- and post-BUN values are measured. The intra-dialytic BUN is inferred based on the mathematical shape of the curve connecting these two points. When Kc is very high, one has a single-pool model, and this curve is mono-exponential. The lower the Kc, the more inflected this curve is, and the lower the intradialytic TAC-UN. So a correct measure of the amount of urea removed based on blood-sided modelling depends on knowing the correct value for Kc. Because compartmental disequilibrium is also responsible for post-dialysis urea rebound, the value for Kc can be estimated from a 60-min post-dialysis BUN. By this time, re-equilibration is thought to be nearly complete, and the extent of the post-dialysis rise versus the immediate post-dialysis BUN can be used to compute the Kc, and then this value for Kc is used to find the shape of the intra-dialytic UN curve, which is used to compute intra-dialytic TAC-UN.
Among the ways that ICU patients receiving dialysis are unique is that they are quite often receiving intradialytic infusions of electrolyte-containing solutions, and/or saline flushes in the course of heparin-free dialysis. Either of these will tend to dilute the urea present in the blood, and might cause a lowering of the intradialytic-TAC-UN and a blood-positive MBE. To rule this out, we looked for associations between the frequency of saline flushes or volume of infusions received during dialysis with MBE, and found none.
The second potential cause of a blood-side positive MBE is underestimation of dialysate-side urea removal. Direct measurement of urea removal has been proposed as an alternative to blood-side, clearance-based methods [10,23–31] and is regarded by some as the ‘gold standard’ for measuring dialysis dose. Others, however, have raised concerns about the technique because of the potential for contamination with urease-producing bacteria [11,29] and because relatively small errors in kinetic inputs amplify to much more significant errors in output; a 7% dialysate collection error could cause a 20% error in eKt/V, for instance [32]. In the present study, however, repeated machine calibration, prompt sample analysis and rigorous application of the fractional collection technique, itself, helped assure its reliability, and was confirmed by comparable estimates of urea removal by the fractional dialysate and Biostat 1000 methods.
The final potential cause of a blood-side positive MBE is overestimation of dialyzer clearance. Access recirculation can reduce effective dialyzer clearance by virtue of dilution of the urea in the blood entering the dialyzer. We measured the amount of access or catheter recirculation using ultrasound dilution (Transonics) and corrected clearance for recirculation when it was present. Dialyzer clearance is often overestimated from in vitro numbers; in vivo measurements are better, but even these are sometimes overestimated due to inaccurate values for the blood flow rate. Our study aimed to overcome these drawbacks by measuring cross-dialyzer clearances in a majority of dialysis sessions, and by measuring blood flow rate using the Transonics flow meter.
Despite our efforts at ensuring accurate dialysate-side estimates of urea removal and use of the actual, intra-dialytic UN profile, a modest, residual MBE still persisted even when an empirical, intra-dialytic curve fit was used. Leaving overestimation of dialyzer clearance as the potential explanation, inaccuracies in Transonic Qb would have been the most likely component of this (see Appendix 4). Calibration of the Transonic equipment to the diameter of the blood tubing is an important factor in optimizing the accuracy of subsequent measurements. Although this may be enough to satisfy the usual practical applications of the technology, we speculate that residual inaccuracies may have explained the persistent MBE. Certainly, no other component of dialyzer clearance (Appendix 4) could easily be identified as the cause of such a systematic error.
Thus, although we have shown that the classical two-pool model results in an MBE, our use of formal kinetics has shown that this is much lower in magnitude than cruder methodology has previously suggested [5].
For practical purposes, if two-pool dosing is used, IHD should be prescribed to ARF patients at a level that will accommodate a reduction in delivery of up to 10% that will result from the associated MBE. Our study raises more fundamental questions about the utility of the classical two-pool model in this setting, though.
In comparison to the stable ESRD setting, ICU patients are unique in that they may have poor perfusion, during dialysis, of organs such as muscles that are rich in urea but to which the blood flow rate may be reduced either because of physiological or pharmacological vasoconstriction. The regional blood flow model [33–35] is an alternative multi-pool model of urea compartmentalization which is able to completely explain the amount of urea rebound usually seen after dialysis on the basis of division of the body into a poorly perfused, high-volume urea space (thought to be muscle), and a well-perfused, low-volume urea space (thought to be brain and viscera) [33,34]. Although the compartment volumes are somewhat different than in the classical model, in the RBF model, one predicts that patients who are vasodilated, with high cardiac output, will have less urea compartmentalization, and less post-dialysis rebound, which in fact has been found to occur [36]. On the other hand, patients who are vasoconstricted, with low cardiac output, should have more urea compartmentalization (e.g., in muscle to which flow during dialysis has been effectively shut down) [8,33,34,37], and a higher degree of post-dialysis rebound. Many of our ICU patients, in whom both cardiac output and SVR were measured, did fall into this latter category. In fact, although numbers were small, we did find a substantial correlation between log Kc and cardiac output, and, at least a trend towards an inverse correlation between log Kc and SVR; this is what one would expect if flow-mediated events were responsible for urea sequestration. Nevertheless, enhanced urea compartmentalization per se should not result in a blood-positive MBE, as long as the intra-dialytic TAC-UN could be accurately calculated based on the Kc values that we inferred from the 60-min post-dialysis BUN. In fact, low cardiac output or elevated SVR was not associated with the extent of blood-positive MBE in our patients.
Further, inferential evidence for the regional blood flow model was provided by the superiority of the empirical curve fit to the intra-dialytic UNs over either two-pool intra-dialytic profile. We speculate that dynamic changes in the volumes of high and low flow pools caused by changing patterns of perfusion during the dialysis process itself may have given rise to an intra-dialytic profile that could not simply be described by the predictable relationship between an intra-cellular and extra-cellular compartment.
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We have shown that formal, two-pool, blood-side modelling of IHD in critically ill patients with ARF commonly overestimates urea removal, but the resultant MBE is modest. Urea kinetic relationships might be best described by the regional blood flow model for which we provide evidence.
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Appendix |
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Appendix 1. Intermittent haemodialysis (IHD) prescription
IHD utilized F50 dialyzers (Fresenius, Lexington, MA, USA), single-pass, proportioning dialysis machines (Althin 1000; Althin CD Medical Inc., Miami, FL, USA), bicarbonate dialysate and temporary or tunnelled veno-venous access, according to standard unit protocol. The dialysis prescription was that of the particular attending nephrologist, who included one of the study group (E. P. Paganini). In a majority of sessions, a heparin-free dialysis method was used, with 200 mL saline flushes infused through the extracorporeal blood circuit every 30 min. Additional flushes were administered to prevent circuit clotting during both heparin-anticoagulated and heparin-free sessions at the discretion of the dialysis nurse. Dialysate temperature was maintained at 37°C.
Appendix 2. Fractional dialysate collection
The technique used in the present study was that of Ing et al. [10]. The sample was collected, at room temperature, in a plastic container that was sealed during the period of collection. The collection was commenced at the start of the session (when dialysate flow was brought out of bypass after Qb and Quf had been established), continued for 2 min after the end of the session (when dialysate flow had been put back into bypass) and discontinued during interruptions to treatment. At the end of dialysis, the fractional collection was mixed, vigorously. A 50 mL sample was taken within 1 h of the end of dialysis for prompt analysis for dialysate (UN) on a model 747 or 917 Hitachi analyser using the urease reaction. The plastic fractional collection container and extension tubing were bleach sterilized and dried between each dialysis session. The technique was revalidated against the total dialysate collection method in six sessions in the present study.
The median fractional collection volume was 1397 mls (25th percentile 1053, 75th percentile 4563).
Appendix 3. Calculation of total UN removal
REMdi = dialysate effluent volume * fractional dialysate collection [UN]/100 (dialysate effluent volume = (Qd * actual fractional dialysate collection time) + total ultrafiltration volume).
REMdi-bio was calculated directly from the Biostat 1000 software.
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Wt = pre-HD – post-HD weights, BUNeq = equilibrated BUN calculated from the Runga–Kutta algorithm, G = mean of the final pre and post-HD estimates of G, Td = treatment time and Kr_rem_z is an estimate of intra-dialytic UN removal, calculated by integrating Kr with the intra-dialytic, extra-cellular BUN profile from the two-pool, curve-fit solution.
Appendix 4. Calculation of in vivo KoA and in vivo cross-dialyzer clearance, Kdcross
In 49 sessions, simultaneous measurements of the Transonic extracorporeal blood flow (Transonic Qb) and in vivo dialyzer extraction ratios (calculated from a dialyzer inlet and outlet BUN) were obtained after the start, at the mid-point, and before the end of the session, to calculate the in vivo mass transfer area coefficient for urea (in vivo KoA). The in vivo cross-dialyzer clearance (in vivo Kdcross) was calculated at each of these time points (Kdcross 1–3).
Formulae used were as follows:
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In vivo KoA was then calculated through a rearrangement of Michael's equations [38]:
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In vivo Kdcross was calculated according to Depner [21] as
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Appendix 5. Calculation of residual renal clearance of urea, Kr UN
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Appendix 6. Calculation of Vsp
For each modelled dialysis, an initial estimate of the pre-HD G was calculated from Kr UN, the Watson V [18] plus net ultrafiltration, and the BUN over an immediate pre-HD period of at least 4 h. Post-HD G was similarly calculated using Kr UN, Watson V and the BUN over a post-HD period of at least 4 h starting from post +60 min. The pre- and post-dialysis estimates of G were averaged to obtain a mean G for the session, as described previously [7]. Calculation of G from the observed changes in BUN before and after dialysis avoids the need to assume a constant G over time, an assumption that is likely to be frequently violated in the intensive care. This value of G, the dialyzer clearance, Kd (computed from the median in vivo KoA, the Transonic Qb recorded at the time of the in vivo measurements, Qd and Quf), Kr UN, the treatment time (Td), the pre- and post-dialysis BUNs and the pre- and post-dialysis weights were used to compute the single-pool urea volume (Vsp), based on the single-pool, variable-volume model.
Formulae used were as follows.
Total dialyzer clearance, Kd0 (including both diffusive and convective components), was computed according to Michael's equations [38]:
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The total dialyzer clearance, inputted into the spvv model, was corrected for access recirculation through the following equation:
where Kd0 = total dialyzer clearance calculated according to Michael's equations (as above), AR = mean of access recirculation measurements taken during session/100.
The corrected Kd was then inputted into the single-pool, variable-volume model defined by the following equation from Depner [21]:
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Appendix 7. Calculation of Vdprate
Let pre BUN and post BUN denote the pre- and post-dialysis BUN, respectively, let BUNeqrate denote the equilibrated post-BUN based on the rate equation and let Vsp denote the single-pool V. Then define
- Fdp = post BUN/BUNeqrate
- Vratio = log(Fdp x (pre BUN/post BUN))/(Fdp x log(pre BUN/post BUN))
- Vdprate = Vsp/Vratio.
- Vratio = log(Fdp x (pre BUN/post BUN))/(Fdp x log(pre BUN/post BUN))
Appendix 8. Calculation of Vdp (wtadj)
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The purpose of this preliminary weight-adjustment was to minimize the impact of major errors in weight measurement in an individual session. The median Vdp(wtadj-prelim) across all modelled sessions provided an updated estimate of patient V, which was used to produce a final, weight-adjusted Vdprate, Vdp(wtadj), for each session, as follows:
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Appendix 9. Calculation of the equilibrated BUN (BUNeq) using differential equations for the two-pool, variable-volume model
In order to estimate the equilibrated BUN (BUNeq) based on the observed post-dialysis rebound at 60 min, the Runge–Kutta algorithm [22] was used to obtain curve-fit solutions to the double-pool, variable-volume model [21] (see differential equations below). Input parameters comprised the pre-HD, post-HD and post +60 min HD BUNs. Kr UN, Kd and the final value of G (calculated, as described above); output parameters included the two-pool V (Vdpref), the inter-compartmental mass-transfer coefficient (Kc), BUNeq and equilibrated Kt/V (eKt/Vref):
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Appendix 10. Calculation of fVDDQ, the dialysate-side estimate of V using fractional DDQ
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Wt = pre-HD – post-HD weights, pre BUN = pre-dialysis BUN and BUNeq = equilibrated post-dialysis BUN from the two-pool, curve-fit solution.
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Acknowledgments |
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N.S.K. was funded by the Satoru Nakamoto, Endowed Clinical Dialysis Fellowship and from NIH grant RO1 DK 53411-01AL. T.G., A.B.L. and T.A.D. were part-funded by NIH grant RO1 DK 53411-01AL. We are extremely grateful for the assistance of Dale Bednarz, Pat Davis and the nursing staff of M82, and to the renal technical staff, Eugene Wright, Keith Kickel, Rocky Mercer, Jerry Ohman and Orlandus Robinson. We are extremely grateful for the assistance of Dr Nicholas Hoenich (University of Newcastle-on-Tyne, UK) in reviewing the revised manuscript.
Conflict of interest statement. None declared.
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Accepted in revised form: 18.12.07
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