The post-hemodialysis rebound: Predicting and quantifying its effect on Kt/V

Transcription

1 Kidney Interntionl, Vol. 5 (1996), pp The post-hemodilysis rebound: Predicting nd quntifying its effect on Kt/V JMS. TTTRSLL, DOMINI DTKTS, PL HMNY, ROGR N. GRNWOOD, nd KN FRRINGTON Lister Hospitl, Stevenge, Herts, nglnd, nited Kingdom The post-hemodilysis rebound: Predicting nd quntifiing its effect on Kt/V. Immeditely fter hemodilysis, the ure concentrtion rebounds upwrds s ure continues to be trnsferred into the rteril circultion from peripherl body comprtments. This rebound tkes t lest 3 minutes to complete. Hemodilysis is quntified s the Kt/V, clculted prom pre- nd post-dilysis ure smples. nless the post-dilysis smple is tken t lest 3 minutes fter dilysis, the Kt/V will be overestimted. This overestimtion will be reltively greter in short high-efficiency dilyses, which hve greter post-dilysis rebounds. We propose method of correction tht uses only the conventionl pre- nd immedite postdilysis smples nd is bsed on the physiologiclly-pproprite ptient clernce time (tp). This is the time needed to cler ll body comprtments when the dilyzer clernce is infinite. The tp cn be clculted from the pre-, immedite post- nd 3-minute post-dilysis ure concentrtions nd ws 35 minutes (SD 16) in 29 ptients undergoing short (149 mm) hemodifiltrtion nd stndrd (243 mm) hemodilysis the following week. There ws no significnt difference between tp vlues clculted during the two tretments. Stndrd Kt/V cn be corrected by multiplying by t/(t + tp) nd dilysis time should be incresed by tp X Kt/V minutes to compenste for the rebound. Despite individul vritions in tp, vlue of tp = 35 ws sufficient to correct Kt/V in ll ptients. Kt/V corrected in this wy greed with Kt/V clculted using 6-minute post-dilysis smple (r =.856, P <.1). The method predicted the 6-minute post-rebound concentrtion (S.5 mi, r =.983, P <.1) nd the ddition of 35 minutes to the tretment time corrected for the rebound in both conventionl nd short tretments. Similr simple equtions corrected the error in V cused by rebound effects. The Kt/V is now the preferred method of quntifying dilysis [1], where K is the dilyzer clernce rte, V is the ure distribution volume (the body wter volume) nd t is the durtion of the dilysis session. Kt/V is in effect the clered volume/ptient volume rtio. Kt/V cn be controlled by vrying dilysis time nd clernce rte. Nutritionl sttus, uremic symptoms nd clinicl outcome hve been shown to relte to the Kt/V delivered to the ptient. The Kt/V concept llows prospective predictions nd plnning of the dilysis. n estimte of probble Kt/V my be obtined by using vlue of V clculted from the Wtson eqution [2] (or from body wt X.57), K red from the dilyzer dt-sheet, nd t, the proposed dilysis time. The dilysis time Received for publiction pril 23, 1993 nd in revised form June 3, 1996 ccepted for publiction July 8, by the Interntionl Society of Nephrology needed to chieve desired Kt/V (dkt/v) my be clculted from the eqution V = dkiiv>< Single-pool Kt/V (Kt/V,7,) Since V nd K cnnot esily be mesured ccurtely, Kt/V is normlly mesured directly from pre- nd immedite post-dilysis blood ure concentrtions using the eqution: fpre Kt/V= ln( v,ost Kt/V cn be clculted precisely in this wy since vlues for K nd V re not required. librtion errors in ure mesurement re lso irrelevnt s only the rtio of pre/post-concentrtions ffect the result. More complex versions of this eqution correct for the effects of residul renl function, ure genertion nd ultrfiltrtion during dilysis. These require n pproximte vlue for K (usully clculted from the dilyzer dt, blood nd dilyste flow rtes). Since the reltive contribution of these fctors to Kt/V is smll, errors in K do not hve gret influence on clculted Kt/V. Post-dilysis rebound The rte t which ure is removed from the ptient depends not only on the dilyzer clernce, K, but lso on the rte t which ure is trnsferred from peripherl comprtments of the ptient's body into the fistul [3]. While it is possible to increse K (using higher blood flow rte or lrger dilyzer), the rte of internl trnsfer of ure is property of the ptient nd cnnot be mnipulted so esily. The effect of this internl trnsfer is to reduce the effective clernce nd to cuse rpid upwrd rebound of blood ure concentrtion s ure continues to be trnsferred into the centrl circultion fter the end of dilysis. These effects re reltively greter in short, rpid dilyses. The mjor component of the post-dilysis rebound is due to solute trnsfer between comprtments [4], such s cells, gut, regions of the body where there is reltively low blood flow, the min blood circultion nd the fistul. The mechnism of solute trnsfer between comprtments my be diffusion, for exmple 294

2 Tttersll et l. Quntifying the post-dilysis rebound 295 cross cell membrnes, or it my be flow, for exmple from poorly perfused res into the min circultion. smller component of the post-dilysis rebound is cused by crdiopulmonry recircultion. Solute concentrtions mesured in the fistul normlly represent only those in the rteril tree nd re significntly lower thn the those in the ven cv. This is becuse some dilyzed blood entering the fistul recircultes to the fistul through hert nd lungs by-pssing the systemic circultion. oncentrtions in the fistul rebound upwrds fter dilysis s the recirculted blood clers the pulmonry circultion. This component of the post-dilysis rebound tkes bout one minute [51. ) ', ci ', ) ) -J quilibrted KtIJ/ (Kt/V.q) Idelly, n equilibrted Kt/V (Kt/Veq) should be clculted using post-dilysis smple tken fter the rebound is complete (t lest 3 mm post-dilysis). This Kt/Veq will reflect the reltive mss of ure removed from the ptient, llowing for the effects of recircultion nd inter-comprtment trnsfer. The conventionl Kt/V using n immedite post-dilysis smple overestimtes Kt/Vcq by up to 25% nd is n indequte mesure of dilysis, especilly high-efficiency tretments [6, 7]. To chieve trget Kt/V4, it is necessry to prescribe higher Kt/V [8], gin especilly in high-efficiency tretments. J",, nd Vq lthough precise vlues for K nd t re not needed to clculte Kt/V, errors in these inputs will result in n inversely proportionl error in V. The vlues Vsp nd Veq re virtul volumes nd re only equivlent to the "rel" ure distribution volume (V) if precise vlues for K nd t re known nd if single-pool kinetics pply. Since rebound effects lwys cuse Kt/Vei to be lower thn Kt/V, it follows tht V4 is lwys higher thn V. The vlue V is greter thn the "rel" ure distribution volume, lthough the term Kt/Veq will correctly reflect the dose of dilysis delivered. The vlue is less thn V if Kt/Vcq < 1 nd greter thn V if Kt/Veq > 1 [7]. Historiclly, dilyses hve generlly delivered Kt/Vcq round 1, t which point nd V re similr nd hve been used interchngebly. The differences between the virtul volumes nd Vcq nd the "rel" V increse with incresing efficiency of dilysis. s prt of the qulity ssurnce of the dilysis process, V is commonly clculted from the mesured Kt/VSP, t nd n ssumed vlue for K. If rebound effects re ignored nd the expected K hs been delivered throughout the tretment, should be close to the V clculted independently (such s the Wtson eqution [2]). If Kt is underdelivered for ny reson, should be higher thn expected, lerting the physicin. If this pproch is tken, should he corrected for rebound effects using n pproprite lgorithm [7]. The Smye method Smye et l [9] observed tht the mthemtics of the two-pooi ure kinetic model predict tht, fter pproximtely 8 minutes of dilysis, the log ure concentrtions in both the rteril blood nd the totl body wter (equilibrted) fll linerly t n lmost identicl slope (Fig. 1). The difference between the two intercepts is equl to the upwrd rebound fter dilysis. sed on this, Smye proposed n eqution to predict the equilibrted (post-rebound) ure concentrtion (eq) using pre- nd post-dilysis rteril Time, minutes Fig. 1. The fll in log ure concentrtion during short hemodifiltrtion. The lines represent concentrtions in rteril blood clculted by double-pool (thin solid line) nd single-pool (dotted) models fitted to the ptients dt. The slope of the single-pool log concentrtion (5) is equl to KJV.. The dshed line represents the equilibrted concentrtion. fter the first 4 minutes of dilysis, both rteril nd equilibrted log concentrtions fll linerly t the sme slope equl to K/Vcq. The vlue tp is the time dimension seprting the two regressions (horizontl double-heded rrow). The rebound (R, verticl double heded rrow) is equl to Kt/V Kt/V1 nd log() log(1). smples (, 1) nd n dditionl smple (111) tken t known time fter the strt of dilysis t bout 9 minutes (eqution 1 in the ppendix). The Dugirds method Dugirds nd Schneditz [1] observed tht the difference between the single-pool Kt/V (Kt/V) nd Kt/Vcq is proportionl to K/V nd tht Kt/Veq could be predicted with cliniclly useful precision from Kt/V nd K/V (eqution 2). This reltionship is predicted by the regionl blood flow model nd the 2-pool diffusion model provided tht the blood flows nd inter-comprtment diffusion coefficients re proportionl to V. Ptient clernce time We observed tht the time seprting Smye's two log-liner prllel slopes is constnt whtever the rte of dilysis. This is consistent with Dugirds's findings. This time represents both inter-comprtment trnsfer nd crdio-pulmonry recircultion. We hve clled this the ptient clernce time (tp) [11]. It cn be considered s the time needed to cler ll prts of the body (so tht Kt/Veq = 1) when dilyzer clernce is infinite. If two-pool model is ssumed, the vlue of tp is equl to Vi/Ki X Vi/V where Vi is the volume of the peripherl comprtment nd Ki is the inter-comprtment mss trnsfer rte (flow rte or diffusion coefficient). The component due to crdio-pulmonry recircultion cn similrly be clculted from V/crdic output. sing Ki, Vi nd Vi/V vlues suggested in the literture, tp should hve vlue round 3 minutes. The mthemtics of these derivtions become more complex when more relistic multi-comprtment models re used. The vlue of tp is specific for individul ptients nd solutes nd independent of the rte nd durtion of dilysis. The vlue tp is sufficient to quntify inter-comprtment disequilibrium nd rebound effects whtever their mechnism. y re-rrngement of Smye's eqution nd ccording to the

3 296 Tttersll et l: Quntifying the post-dilysis rebound log-liner pproximtion model, tp my be clculted from eqution 3, where cq is the mesured post-rebound concentrtion with n llownce for solute genertion. Further re-rrngements yield equtions 4 to 8 which cn be used to correct for multicomprtment effects. qution 4 predicts the post-rebound concentrtion from pre- nd immedite post-dilysis concentrtions. This predicted concentrtion my be used to clculte Kt/Veq nd NPR without the need for third smple. qutions 5 nd 6 correct Kt/V nd V, clculted conventionlly, using pre- nd immedite post-dilysis concentrtions in the single-pool equtions. qution 7 corrects the error in V which results from using the post rebound concentrtion in the single-pool eqution. In the prescription of dilysis, corrected time tking rebound into ccount my be clculted using eqution 8. If, s shown by Dugirds, the rte of inter-comprtment trnsfer is reltively constnt function of V, then the vlue of tp will not significntly differ between ptients. In this cse, tp need not be mesured but men vlue used in the equtions. Since the tp concept is bsed on Smye's nlysis, it lso is subject to the limittions of tht pproch. Smye's pproximtion produces results which re lmost identicl to precise multicomprtment nlysis if dilysis times re significntly greter thn the tp vlue (such s 2 X tp). The tp method breks down when t < tp. The purpose of this pper is to compre methods of rebound correction nd to test the ptient clernce time method. Method Ptients Twenty-nine stble chronic hemodilysis ptients gve informed consent to be studied. Their medin ge ws 54 yers (rnge 19 to 81). ll ptients were shown to hve no ccess recircultion by sline-dilution method [12 with sensitivity of 5%. Hemodilysis ll dilyses were performed using Fresenius 28D hemodilysis mchines, bicrbonte dilysis fluid, polysulfone dilyzers (Fresenius F6 nd HF8O). lood flow rtes were 253 to 545 mi/mm nd dilyste flow rtes were 5 to 8 ml/min. Hemodifi It rtion Hemodifiltrtion (HDF) ws performed using the sme equipment s for HD but 1 to 12 ml/min filtrtion ws performed simultneously. Replcement fluid ws generted by filtrtion of the dilyste using the Fresenius on-line HDF system. Protocol Ptients were studied during short HDF (medin 148 mm) nd conventionl HD (medin 248 mm) on consecutive weeks nd the sme dy of the week. The prescribed times (t) were clculted for both conventionl HD nd short HDF using eqution 8 with desired Kt/V = 1, tp = 3, V clculted using 2-pool model in previous dilyses nd K from previous in vivo mesurements under the sme conditions. Smples were tken from the rteril needle before the strt of HD/HDF () nd from the rteril line t six eqully spced time intervls during the HD/HDF nd t the end of the tretment (1) without slowing the blood pump. Further smples were tken t 2, 15, 3 nd 6 minutes post-dilysis from the fistul needle. The wshbck ws performed fter the two minutes smple. lernce ws clculted from simultneous smples tken from rteril nd venous lines pproximtely 2 minutes fter the strt of HD/HDF. Smple ssy oncentrtions of ure nd cretinine in lithium-heprin nticogulted plsm were mesured using Hitchi-717 utonlyzer. The coefficient of vrition (V) for the method ws 1.76% nd 1.14%, respectively. Hemtocrit ws mesured in the predilysis smple by the microcentrifuge method. lernce rtes The ultrfiltrtion nd interdilytic fluid gin rtes (Qf nd OW) were clculted from pre- nd post-dilysis weight. The blood flow rte (Qb) ws mesured fter the dilysis by timed volumetric mesurement under the sme conditions s obtined during dilysis. Dilyzer clernce ws clculted from dilyzer inlet nd outlet concentrtion mesurements, tking Qb, Of nd hemtocrit into ccount. Residul renl ure clernce (Kr) ws clculted from the volume nd ure concentrtion in n interdilytic timed urine collection nd the ure concentrtion in timed blood smples t the beginning nd end of the interdilytic period. quilibrted post-dilysis ure concentrtion (c.q) The mesured 6-minute post-dilysis ure concentrtion ws djusted to tke ccount of ure genertion by subtrcting G/V X 6. eq ws lso predicted by the Smye eqution (eqution 1) nd the tp method (eqution 4 using tp = 35 for ure nd tp = 66 for cretinine). Single-pool Kt/V, V nd NPR Kt/V, nd NPRSP were clculted from the mesured K, Kr, Of, OW, dilysis time (t), pre- nd immedite post-dilysis ure concentrtions ( nd ) using the single-pool method. Kt/Veq, Veq nd NPReq were clculted in the sme wy but using eq insted of in the equtions. V,1 V, were clculted using the six intrdilytic smples insted of 1 in the single-pool eqution. lcultion of tp Vlues for tp were clculted from t,, 1 nd eq using eqution 3. Vlues were clculted independently for ech ptient during conventionl HD nd short HDF. Men vlues of tp = 35 for ure, tp = 66 for cretinine were used in equtions 5 to 7 to correct Veg nd Kt/V. Dt nlysis Pired dt were nlyzed by prmetric nd non-prmetric nlysis s pproprite. greement between mesured nd clculted concentrtions ws quntified by liner regression, stndrd error (S; the verge bsolute difference between pirs) nd lnd-ltmn nlysis [13]. Results The medin residul renl ure clernce ws 1.95 mi/mm (rnge to 4.53). The men mesured vlues for ure nd cretinine K were 285 (± SD 24) nd mi/mm for the short HDF nd nd ml/min for the conventionl HD.

4 Tttersll et!: Quntifying the post-dilysis rebound 297 Q ) ) -J ) ) ) -J Time, minutes Time, minutes Fig. 2. The symbols represent the men of 29 ure concentrtion () nd cretinine concentrtion mesurements () mde in different ptients undergoing short HDF (tringles) nd conventionl HD (squres) on consecutive weeks'. The lines re s in Figure 1. lthough KlVcq is greter in short HDF compred to conventionl HD, tp is the sme. R is equl to K/Vcq >< tp. In both tretments, 3 minutes were dded to the dilysis time clculted by single-pool model. lthough, is lower nd Kt/V higher in the short tretment, cq nd Kt/Vcq re similr, indicting tht the ddition of 3 minutes hs effectively compensted for the rebound in both conventionl nd short tretments. Post-dilysis rebound The ure nd cretinine rebound (log eq log,) ws reltively greter fter the short HDF thn the conventionl HD (Fig. 2 nd Tble 1). The concentrtions 6 minutes fter the short HDF were similr to those fter the conventionl I-ID (Tble 1). ffect of rebound on Kt/V re nd cretinine Kt/Vs clculted from pre- nd immedite post-dilysis concentrtions using the single-pool model (Kt/V) were 19% nd 35% higher thn those clculted using the 6-minute post-dilysis concentrtion (Kt/Veq) (Tble 1). This overestimtion of Kt/V ws significntly greter during the short HDF thn the conventionl dilysis (23%vs. 14%, P <.1, N = 29). The overestimtion of ure Kt/V by the single pool model ws Tble 1. omprison between conventionl HD nd short HDF in the sme ptients ) I ). onventionl HD Short HDF Men SD men SD S P re mm cq mm , mm <.5 Kt/V Kt/V tp mm <.5 retinine ILM nq.os <.5, p.m <.1 Kt/V <.5 Kt/Vrp <.5 tp mm t mm II....., tp long HDF, minutes Fig. 3. The vlue of ure tp clculted from, nd,q fter both conventionl HD nd short HDF tretments. Regression plot with line of identity. No common dt were used to clculte ny two tp vlues. The ptient's tp vlues tend to be reproducible despite different dilysis conditions. linerly proportionl to K/V (Kt/V Kt/Veq = K/V X 35, r =.51, P <.5). Individul tp vlues The tp mesured during the HDF ws 33 (± SD 15) minutes for ure nd minutes for cretinine (Tble 1). These tp vlues were similr when clculted during the conventionl dilysis (37 16 for ure, for cretinine). The stndrd error between the tp mesured during short HDF nd conventionl HD ws 11 minutes for ure nd 1 for cretinine. There ws significnt correltion between tp vlues clculted during the short HDF nd conventionl HD (ure r =.656, cretinine r =.679, P <.1; Fig. 3). The ure Kt/Veq for the short HDF correlted negtively with tp mesured during the conventionl HD (r =.526, P <.5; Fig. 4). rteril cretinine concentrtion mesured before the conventionl HD correlted significntly with tp mesured during the short HDF (r =.489, P <.1). Similrly, rteril ure concentrtions mesured before the short HDF correlted with tp mesured during the conventionl HD (r =.46, P <.1; Fig. 4)..

5 298 Tttersll et l: Quntifying the post-dilysis rebound I 1 - o ; tp long HDF, minutes ) (ci ) 9 ) -, : eq ure mesured 6 minutes post-dilysis, m I ) ) I Rebound compenstion The ddition of 3 minutes to dilyses prescribed Kt/V I effectively compensted for the ure rebound in both conventionl nd short dilyses (Fig. 2 nd Tble 1). lthough the immedite post-dilysis ure concentrtions were lower fter short HDF thn conventionl HD, the 6-minute post-dilysis concentrtions were similr fter llowing for ure genertion. oth short HDF nd conventionl HD hd Kt/Vcq close to 1. The 3 minute ddition ws lso lmost sufficient to compenste for the cretinine rebound. ) ) (ci ) ) ) ) ! -. m _ z = lcultion of V V clculted by the single-pool method vried ccording to whether ure or cretinine ws used s the mrker solute nd whether or eq ws used s the post-dilysis concentrtion (Tble 5). When V1, ws clculted using cretinine, it vried significntly between conventionl HD nd short HDF. orrection using the tp equtions eliminted these differences (Tble 5) eq ure mesured 6 minutes post-dilysis, m Fig. 5. Predicting the equilibrted ure concentrtions by the tp method () nd Smye method (). lnd ltmn [131 plots representing the difference between clculted nd mesured q ure concentrtions in 29 ptients fter short HDF (tringles) nd conventionl HD (squres). The solid lines represent men 2 SD. tp long HDF, minutes Fig. 4. Reltionship between tp clculted during the conventionl HD nd dequcy prmeters clculted during short HDF in the sme ptient the following week Regression lines re shown. Ptients with the gretest tp tend to hve the lowest Kt/Vcq () nd the highest pre-dilysis blood ure concentrtion (). Rebound prediction oth the Smye eqution nd the tp method (using men tp vlues) ccurtely predicted the ure nd cretinine rebound (Fig. 5 nd Tble 2). The Kt/Veq nd NPR clculted using Smye nd tp methods greed with those clculted from the 6-minute post-dilysis smple (Fig. 6 nd Tbles 3 nd 4). Tble 2. Predicting the ure (in mm) nd cretinine (in /LM) rebound by different methods in ll 58 tretments re q mesured msi, eq predicted by Smye eq predicted by tp-35 retinine eq..si, predicted by Smye cq predicted by tp-66 Men S P r P ref ref <.1 <.1 < <.1 <.1 <.1 <.1 <.1 <.1

6 Tttersll et l: Quntifying the post-dilysis rebound ±' Predicting Kt/Vcq using different methods in ll 58 tretments men S P r P &J--- -m--- iii"tble..iii re Kt/Vcq 1.62 Smye 1.37 tp = <.1 Dugirds <.1 Kt/V < <.1 retinine ref <.1 Kt/Vcq.815 ref. Smye <.1 tp = <.1 Kt/V, <.1.62 < X 1.,) q + ( x '!' iii- iii iii iii - '.. KtNeq KtNeq Kt/Veq Fig. 6. Regression plots showing identity lines nd symbols s in Figure 5. onventionl single-pool Kt/V significntly overestimtes Kt/Vcq (). Predicting ure Kt/V,,q by tp method () or Dugirds method () eliminte the systemtic error. Tble 4. NPR (in g/kg/dy) clculted by different methods in ll 58 tretments The vrious corrected V vlues were, on verge, 1.2 liters lower thn V returned by the Wtson equtions (P <.1). When V ws clculted using the six intr-dilytic smples s the post-dilysis concentrtion (V11 V16), it ws lower thn when clculted conventionlly: the erlier the smple, the greter the difference. V clculted using eq ('eq) ws significntly higher thn when clculted conventionlly (Fig. 7 nd Tble 6). If the tp equtions were used to correct V, these differences disppered except for V11, using the first intrdilytic smple (tken pproxmen S P r P NPRq.97 ref. Smye <.1 tp = <.1 NPR < <.1 Tble 5. Reproducibility of V (in liters) clculted in conventionl HD nd short HDF in the sme ptients by different methods. nd Vcq were clculted using the conventionl immedite post-dilysis smple (i) nd the post-rebound smple (q) s the post-dilysis smple in the single-pool equtions ncorrected ure V ure cretinine V cretinine orrected V, corr ure Veq corr ure V, corr cret. Vq corr cret. V Wtson onventionl HD men SD Short HDF men SD S P <.1 <.5 <.1 V., corr nd Veq corr were corrected using equtions 6 nd 7. The men bsolute difference between vlues clculted during conventionl HD nd short HDF for ech ptient re shown (S). N = 29. imtely 2 mm fter the strt of dilysis). The tp eqution significntly overcompensted for the error in V11 (Fig. 7). Discussion Despite prescribing Kt/Veq = 1 in these experimentl dilyses, the delivered Kt/Veq rnged from.65 to 1.21 (Fig. 6). This emphsizes the difficulty in delivering trget KtIV nd the importnce of mesuring the dose of dilysis ctully delivered. The overestimtion of Kt/V cused by the rebound (Kt/V Kt/Veq) ws similr to those reported by others [6]. In prticulr, the overestimtion of Kt/V ws similr to tht reported by Dugirds, nd the regression of Kt/V Kt/Veq nd K/V ws lso similr. This overestimtion of Kt/V by the single-pool model grees with those found in studies using direct dilysis quntifiction [14, 15]. The rebound lso ffects the clcultion of NPR. y ignoring

7 21 Tttersll et!: Quntifying the post-dilysis rebound >< Vii Vi2 Vi3 Vi4 Vi5 Vi6 Vt Veq VilVi2Vi3Vi4Vi5Vi6 V Veq Fig. 7. The reltionship between V,, nd delivered Kt/V in 58 dilysis tretments without () nd with () correction using the tp equtions. V. clculted from 6 intrdilytic smples (to mimic low Kt/V) nd V5 re shown. V is expressed reltive to V1, clculted conventionlly from pre- nd immedite postdilysis smples for ech tretment. The boxes represent the 1th, 25th, 5th, 75th nd 9th centiles. Tble 6. ffect of timing of the post-dilysis smple nd mrker solute on V with nd without correction using the tp equtions onventionl HD Short HDF V ure V cretinine V ure V cretinine ncorrected V, using 35.7 ref 33.7 ref 35.4 ref 32.1 ref V 34.3 P < P < P < P <.1 V P < P < P < P <.1 Vcq 4.9 P < P < P < P <.1 orrected V1, using, 36.3 ref 36.3 ref 36. ref 35.6 ref V P < P <.5 V P < Vq V13 nd V13 re clculted from intr-dilytic smples to represent delivered Kt/V of pproximtely.7 nd.4. The men V nd probbility of it being the sme s men using n immedite post-dilysis smple (,) in the sme tretment re shown. N = 29. it, the single pool model overestimtes the interdilytic rise in ure concentrtion nd NPR tht is clculted from it. Dilysis dequcy is often determined by the position of the pre-dilysis ure plots on normogrm reltive to the ptient's NPR. ny NPR overestimtion my shift the ptient's plot into the domin defined s representing dequcy. This will tend to msk underdilysis due to inter-comprtment effects. Overestimtion of NPR by the single pool model could prtly explin why NPR mesured in hemodilysis ptients is generlly higher thn in PD ptients [161. Residul renl function is often clculted from n interdilytic urine collection nd the men interdilytic blood concentrtion. lood smples tken immeditely post-dilysis t the strt of the collection nd pre-dilysis t the end of the collection re needed. If the rebound is not tken into ccount, the men interdilytic blood concentrtion will be n underestimte nd renl function will be overestimted. Vlues of tp were reproducible in the sme ptients despite being clculted independently from concentrtions mesured under very different conditions (short HDF nd conventionl HD). The vlue tp quntified the rebound in both tretments. This supports the hypothesis tht tp is property of the ptient nd independent of the dilysis process. The vlue tp is similr to the 36 minute constnt in Dugirds's eqution (eqution 2). The cretinine rebound ws significntly greter thn the ure rebound. The vlue tp, describing the time for solute trnsfer within the ptient ws lmost twice s gret for cretinine s ure. Since diffusion is dependent on moleculr weight nd cretinine hs lmost double the moleculr weight s ure, this suggests tht diffusion plys mjor prt in inter-comprtment mss trnsfer nd the post-dilysis rebound. If the rebound is due to regionl blood flows s hs been suggested [1], thn the rebound should not be solute dependent. remic toxins of higher moleculr weight thn cretinine my be importnt [17]. xtrpolting from the behvior of cretinine, it my be expected tht rebound effects would be even greter for these toxins, but more work is needed to investigte this hypothesis. Vlues for tp vried significntly between ptients. This my reflect quntittive nd qulittive differences in cell membrnes. lterntively, it my reflect vribility in crdic index or other ptient-relted mechnisms such s intr-extrcellulr osmotic fluid shifts [18], chnges in crdic output or perfusion cused by blood volume chnges, crdic disese or vsoctive drugs. This inter-ptient vrition in tp ws greter for ure compred to cretinine. This my be becuse cretinine is more precisely mesured in our lbortory. lterntively, cretinine inter-comprtment effects my be more dependent on diffusion due to its greter moleculr weight. Diffusion depends on the surfce re to volume rtio of the peripherl comprtments tht should not vry much between ptients. re inter-comprtment trnsfer is more dependent on flow, which is likely to be more vrible. men vlue of tp could be used to predict the post-dilysis rebound concentrtion more precisely thn the Smye method in the 29 ptients studied. Individul vrition of the ptient's tp contribute to the errors in the tp method for predicting the rebound. The Smye method is not dependent on these ptient differences but uses third smple to clculte the rebound. It seems tht the errors introduced by the third smple in the Smye

8 Tttersll et l: Quntifying the post-dilysis rebound 211 method re greter thn those resulting from inter-ptient tp vrition. The tp method predicted the ure rebound to within.5 mm (1.4 mgldl) on verge. This imprecision is not much greter thn the imprecision of the ure mesurements themselves. lthough the use of men tp vlue will be resonble prcticl pproch nd represents n improvement over conventionl single-pool nlysis, the individul tp vrition did significntly impct on both the delivered Kt/Veq nd pre-dilysis cretinine in our ptients. The ptients with the longest tp were reltively underdilyzed nd hd higher pre-dilysis cretinine concentrtions. Further study is needed to determine the vribility in tp in lrger number of ptients. If there re ptients with very prolonged tp (for exmple those with ccess recircultion or severe hert filure) ssuming men vlue for tp will be indequte, nd it should be mesured directly using 3-minute post-dilysis smple. These uncertinties in the vlue of tp re reltively more importnt in short dilysis. On-line continuous blood solute concentrtion mesurement using n pproprite sensor should llow very precise clcultion of tp s lrge number of concentrtions would be used to compute the log concentrtion slope. This will llow individul tp vrition to be tken into ccount in the prescription nd quntifiction of dilysis. This pproch lso llows simple prospective predictions of cq nd, by liner projection of the log-slopes. The vlue tp ws lso ble to be used to compenste for the ure rebound in the prescription of dilysis time. The ddition of 3 minutes per unit of Kt/V prescribed lmost completely compensted for the rebound in both conventionl nd short dilyses. Our results indicte tht 35 minutes should hve been dded for complete compenstion. This time increment increses dilysis dose reltively more in short dilyses tht lso hve lrger rebounds. Interestingly, the sme time increment lmost completely corrected the cretinine rebound lso despite the tp vlue being higher for cretinine thn ure. This is becuse cretinine KtIVcq for the conventionl HD ws much lower thn the ure Kt/Veq due to combintion of lower K nd higher rebound. Since the time dded is function of both tp nd Kt/Vq, the higher tp is prtly cnceled out by lower Kt/Vcq. The equtions for correcting using tp returned vlue of V which ws independent of dilysis durtion, Kt/Veq, smple timing nd mrker solute. lthough we prescribed Kt/Veq I in ll tretments, we were ble to reproduce the effect of lower Kt/V by clculting V using intrdilytic smples. The expected error in ssocited with low delivered Kt/V ws corrected by the tp equtions. In theory, the eqution should lso correct V, downwrds when Kt/Veq is greter thn one. Further study employing high delivered Kt/Veq is needed to test this spect of the correction. The V., correction eqution overcorrected V11, clculted using smple tken within the first 2 minutes of dilysis. This is not surprising since the pproximtions inherent in this pproch brek down when t < tp. The vlue for the corrected V ws very close to, but significntly lower thn the vlue returned by the Wtson formul. This my be becuse hemodilysis ptients re reltively dehydrted t the end of dilysis nd hve less muscle mss thn the norml subjects studied by Wtson. Reported dt from the S Renl Dt System indictes tht hemodilyses deliver on verge 28% lower Kt/V thn prescribed [191. Our results suggest tht if dilysis is delivered over 15 minutes, Kt/V will overestimte Kt/Veq by pproximtely 2%, prtly msking the underdelivery. In the qulity ssurnce of the dilysis process, 3% shortfll in the delivery of Kt results in 3% higher thn expected V. nfortuntely, if delivered KtfVcq is less thn 1, the rebound effects tend to reduce V. [7], prtly opposing the rise in V due to the underdelivery of Kt. Our results suggest tht if Kt/V of.7 is delivered over 15 minutes, V, will underestimte V by 8%. pproprite corrections (such s the tp equtions) re needed for nd Kt/V to revel the true extent of the tretment filure. The vlue tp is cliniclly convenient method for quntifying inter-comprtment trnsfer in dilysis ptients. nlike other pproches, tp cn be clculted directly from time nd concentrtion mesurements. It mkes no ssumptions of the mechnism of the inter-comprtment trnsfer (diffusion or blood flow). No difficult to mesure prmeter such s V, K, crdic index or inter-comprtment mss trnsfer rte is needed. We hve shown tht tp is independent of the rte nd durtion of dilysis nd cn be mesured reproducibly under different conditions. Our results suggest tht Kt/Veq my be relibly clculted using the tp method without the need for third or delyed blood smple. The tp correction equtions re bsed on concentrtion nd time mesurements only nd re therefore unffected by errors in K or V. The tp method hs dditionl dvntges in tht it cn lso be used to compenste for the rebound in the prescription of dilysis time, correct the errors in V returned by single-pool equtions, nd it cn predict the post-rebound concentrtion for clcultion of rebound-corrected NPR nd residul renl function. We suggest tht hemodilyses re prescribed nd monitored using conventionl single-pool kinetic modeling but corrected using the tp method. lthough vlue for tp = 35 should be sufficient for most ptients, we suggest tht tp is mesured infrequntly in ll ptients using 3-minute post-dilysis smple. If tp is much greter thn 35, ccess recircultion should be suspected. Ptients who consistently hve high tp vlues should hve this higher vlue used insted of 35 in the correction equtions. cknowledgments This study ws funded by Fresenius G, Germny nd the Lister Kidney Foundtion. The uthors thnk Lurie Grred nd Stephen Smye for ssistnce in the nlysis. Reprint requests to Dr. J.. Tttersll, Renl nit, Lister Hospit4 Stevenge, Herts, nglnd SGJ 4, nited Kingdom. ppendix qution 1. Predicting the equilibrted post-dilysis concentrtion (eq) using the Smye method. cqox( \ mt qution 2. The Dugirds eqution for predicting KtIVeq. KtIVcq = KtJV Kt/VSP 36 X +.3

9 212 Tttersll et!: Quntifying the post-dilysis rebound qution 3. lculting tp from concentrtion mesurements only. ln(. } \t / tp t >< 2. WTSON P, WTSON I, r R: Totl body wter volumes for dult mles nd femles estimted from simple nthropometric mesurements. m J lin Nutr 33:27, 198 /c \ 3. Popovici-i RP, HLVINK DJ, OMR J, MONRIF JW, DHRD /q \ Orgns 21:18-115, 1975 keq) 4. PNDRINI PR, ZRK S, RSMY S: uses, kinetics nd clinicl implictions of post-hemodilysis ure rebound. Kidney mt 34: , SHNDITZ D, POLSHGG HD, LVIN NW, u G, MORRIS T, KRMR M, DGIRDS JT: rdio-pulmonry recircultion in dil- qution 4. Predicting the equilibrted post-dilysis concentrtion (eq) using the tp method. JF: The consequences of physiologicl resistnce on metbolite removl from the ptient-rtificil kidney system. Trns m Soc rtif ysis; n under-recognized phenomenon. SIO J 38:M194M199, RMSON F, GISON S, RL V, oscii JP: re kinetioc modelceq = x ling t high ure clernces: Implictions for clinicl prctice. dv Ren \/ Replce Ther 1:514, GOTH F: Kinetic modelling in hemodilysis, in linicl Dilysis (3rd ed), edited by NISSON, FIN, GNTIL, New York, ppleton nd qution 5. orrecting the error in Kt/V using tp. Lnge, HRLDSSON : Higher Kt/V is needed for dequte dilysis if the Kt/V = Kt/V x tretment time is reduced. Nephrol Dil Trnsplnt 1: , eq sp t+tp SMY SW, DNDRDL, ROWNRIDG, WILL : stimtion of qution 6. orrecting the error in the single-pool V (V). The tretment dose in high-efficiency hemodilysis. Nephron 67:2429, 1994 expression ln(/1) is pproximtely equivlent to Kt/V.. 1. DGIRDS JT, SHNDITZ D: Overestimtion of hemodilysis dose + tp depends on dilysis efficiency by regionl blood flow model but not by V = x conventionl two-pool kinetic nlysis.sioj4i:m719m724, TrIRSLL J, GRNWOOD RN, FRRJNGTON K: Inter-comprt- + tp X ln- j X + tn ment diffusion nd crdio-pulmonry recircultion in long nd short dilyses. Jm Soc Nephrol 5:53, GRNWOOD RN, LDRIDG, GOLDSTIN L, KR LRI, TTLL WR: ssessment of rterio-venous fistule from pressure nd ther- ml dilution studies. lin Nephrol 23:189197, LND JM, LTMN DG: Sttisticl methods for ssessing greement between two mthods of clinicl mesurements. Lncet 1:3731, FLNIGN MJ, FNGMN J, LiM VS: Quntitting hemodilysis: \ comprison of three kinetic models.m J Kidney Dis 17:29532, 1991 qution 7. orrecting the error in the equilibrted V (Veq). The expression ln(1/ ) is pproximtely equivlent to Kt!V.. '-1 V = Veq>( + tp X ln 15. TSNG HK, LONRD F, LFVOR GS, ORTLL 5: re dynmics during nd immeditely fter dilysis. SJO J 8:25 126, 1985 qution 8. Prescribing dilysis time, tking the rebound into 16. LINDHOLM, RGSTROM J: Nutritionl spects of PD, in ontinuous mbultory Peritonel Dilysis, edited by GOKL R, dinburgh, ccount. hurchill Livingstone, 1986, pp R L, PoPovicH RP, HRISTOPHR TG, SRINR H: The iv \ genesis of the squre-meter hour hypothesis. Trns m Soc r/if = desired Kt/Veq>< + tp j Orgns 17:8191, 1971 \K / 18. THWS, DNR HJ, HYrN H, SHLZ W: Theroeticl pproch nd clinicl ppliction of kinetic modelling in dilysis. Nephrol Dil References Trnsplnt 6:18192, HLD PJ, PORT FK, GRI J, GYLIN DS, LVIN NW, GOD L: 1. GOTH F, SRGNT J: Mechnistic nlysis of the Ntionl Hemodilysis prescription nd delivery in the.s.: Results from the oopertive Dilysis Study (NDS). Kidney mt 28:526534, 1985 SRDS cse mix study. Jm Soc Nephrol 2:328, 1991