Kinetics of Kt/V and NPCR - Urea kinetic modeling (UKM) and calculation of a urea Kt/V is the most widely accepted method to quantify the dose of dialysis. The model also provides a measure of protein catabolism rate (PCR) which is equivalent to dietary protein intake in the metabolically stable patient. The calculated Kt/V is proportional to the pre-post dialysis BUN decrease. The single pool Kt/V(spKt/V) is calculated from the pre-dialysis BUN and the post-dialysis BUN obtained 15 sec after the end of dialysis. This delay is carried out to circumvent any access recirculation which might be present which would lower the BUN and result in an erroneous increase in spKt/V.

Equally important is the concept of urea “rebound”. At the end of the dialysis the concentration of BUN is lower in the blood and extracellular fluid than in cells. It requires 30-40 minutes for diffusion of urea to accomplish a uniform concentration (diffusion equilibrium). The difference between the two BUNs is the “rebound”. Therefore, the spKt/V calculated using the end dialysis BUN will be higher than an equilibrated Kt/V (eKt/V) which is calculated from the BUN after post dialysis equilibration. It is the eKt/V which more accurately reflects the effective dose of dialysis. If one understands the concept of Kt/V as representing an accurate picture of dialysis dose in relationship to urea removal and water removal from the total body water, it is a small step further to understand the need to wait until equilibration is completed, so that the values are accurate and we avoid errors in prescription. We would not take a sample of anything without mixing the solution, or shaking to equilibrate the contents--so why not do the equivalent in the dialysis patient? That is - “shaken but not stirred”. The rebound phenomenon and effects on Kt/V and NPCR are illustrated in Fig 1. The BUN at the end of dialysis can be used to calculate the equilibrated BUN value using validated equations or by keeping the patient for 30-60 min to take another blood sample.

Figure 1.  The Kt/V and NPCR are both calculated from the magnitude of BUN decrease during dialysis.  The apparent drop in BUN will always be larger before rebound occurs.  Since spKt/V and spNPCR are calculated from Pre BUN minus Post BUN, while eKt/V and eNPCR are calculated from Pre BUN minus Rebound BUN, spKt/V and spNPCR will always be larger than eKt/V and eNPCR.

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The magnitude of rebound is determined almost entirely by the rate at which the dialysis dose is delivered. The rate of dialysis is the critical influence on the rebound. The “rate of dialysis” is defined by the spKt/V divided by the treatment time (t) which equals K/V (K= the delivered clearance and V= the volume of distribution of urea equivalent to the total body water). The greater the K/V the greater is the rebound. Since most patients are treated at about the same blood flows (300 to 400 mL/min) and with the same dialyzer urea clearance (K), the smallest patients (with small Vs and shorter times) will tend to have the highest ratios of K/V and the highest rebounds. For example, if a little patient is given the same dose of spKt/V over the same time as a large patient the rebound will be identical. That however happens infrequently in clinical therapy and smaller patients are usually treated at higher rates for shorter times and have more rebound.

Dialysis dosing target - These relationships are illustrated in Fig 2A where the ratios eNPCR/spNPCR and eKt/V/spKt/V are each plotted as functions of treatment time t. The Tattersall equation was used to calculate eKt/V over a spKt/V range of 1.3 to 1.7 and independent of volume, dialyzer clearance and urea generation (Gu), with treatment times fixed at six levels ranging from 2.0 to 4.5 hrs.  The Tattersall equation:

eKt/V = spKt/V [t/(t+35)]

Over the ranges calculated, eKt/V is a highly linear function of spKt/V when time is held constant so a family of six lines is seen in Fig 2A. In Fig 2A, the eKt/V dose target of 1.2 is depicted as a horizontal line on the y axis and and the spKt/V dose target of 1.4 as a vertical line on the x axis. The regression lines for different dialysis times are depicted as solid lines for all segments with eKt/V ≥ 1.20 and dashed lines for all segments where eKt/V < 1.20. The two adequacy targets agree only in the left lower portion of the plot where eKt/V < 1.20 and spKt/V < 1.40. Here they define a domain of inadequacy common to both criteria. Some of the regression lines for spKt/V> 1.4 pass through the inadequate zone because of their high rebound with shorter dialysis times.

Figure 2. A – Two definitions of adequate dialysis: eKt/V > 1.20 and spKt/V > 1.40.  Note that a substantial number of adequate doses by the criterion spKt/V > 1.40 are inadequate by the eKt/V > 1.20 criterion.  B – When t varies in the patient population, there must be a family of spKt/V values ranging from 1.35 – 1.58 to assure all doses equivalent to eKt/V equals 1.20.

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In Fig 2B the required spKt/V to achieve eKt/V 1.20 is shown for each treatment time by a vertical arrow to the x axis at the point that each regression line reaches the minimum level for adequate dialysis defined by eKt/V = 1.20. It can be seen that the spKT/V necessary to provide an adequate Kt/V can range from 1.32 to 1.58 over a range of dialysis times to provide an eKt/V of 1.20. Therefore, an eKt/V can be associated with several spKT/V values, depending on the dialysis time. In contrast, a single eKt/V 1.20 target permits determination of the optimal time and spKt/V for each patient in the population. At steady state, the NPCR is calculated from the amount of urea removed which is considered equal to the amount of urea generated (Gu) from protein catabolism (PCR). As noted above the post dialysis BUN is artificially low so if it is used for calculation of NPCR the urea removal will be overestimated since it is the difference between this BUN concentration and the pre dialysis BUN of the next treatment that are used. The NPCR will therefore behave like the Kt/V’s (as above).

Impact of residual renal urea clearance (Kru) on eKt/V and eNPCR - Intermittent hemodialysis is very inefficient. With thrice weekly HD dialyzer urea clearance is being utilized for only 5 to 7% of the week while urea and other solutes are generated continuously. Consequently high dialyzer clearances are used which result in an exponential drop in BUN and very inefficient removal of urea and other solutes in the later part of dialysis. A low continuous clearance is far more efficient because the BUN does not fall to very low levels. This is the reason for a lower total clearance requirement in continuous CAPD. A weekly total Kt/VCAPD of 2.00 is equivalent to eKt/V of 1.2 with thrice weekly hemodialysis. The standard Kt/V (stdKt/V) calculation quantifies the effects of both intermittent and continuous dialysis and provides a dose that applies to all dialysis frequencies and intensities ranging from CAPD, short and long daily HD to twice weekly HD. However, in the specific case of thrice weekly hemodialysis, the residual renal function can be directly expressed as a quantity of eKt/V (abbreviated as eKrt/V) according to equation:

eKrt/V = 4.5 * Kru/V

(with V in liters and Kru in mL/min - the units of the coefficient 4.5 are L/mL/min)

Assuming a V of 30 L, 1 mL/min Kru contributes an additional 4.5 L of urea clearance per dialysis session, which translates into a gain of eKt/V of 0.15 (4.5 L / 30 L =0.15). If a patient has a Kru of 3 mL/min it will add 3 x 0.15 = 0.45 to the eKt/V provided by hemodialysis (abbreviated as eKdt/V), a highly significant addition. With this Kru being present, the total equilibrated dialysis dose (eKdrt/V) will be simply the sum of eKdt/V and eKrt/V, so that Kru of 3 mL/min brings an eKt/V of 1.2 to 1.65

The impact of Kru on total eKdrt/V and eNPCR is illustrated in Fig 3A and 3B. In Fig 3A the Kdrt/V is plotted as a function of Kru for an average size patient and four levels of eKdt/V = .40, .60, .80 and 1.00 (these are the y axis values shown when Kru = 0). As discussed above, eKrt/V is additive to eKdt/V. The UKM program in the FMCNA system can calculate the Kdrt/V for 3 and twice weekly dialysis also.

Figure 3. A – Solution for eKdrt/V as a function of Kru for average patient V = 30L.  It can be observed that in the average size patient, each ml of Kru increases eKdrt/V by about 0.15 units of eKt/V.  B – Solutions for “apparent” NPCR if residual Kru is not included in UKM.  The presence of Kru lowers the pre dialysis BUN which will result in spurious lowering of NPCR calculated if Kru is not included in the modeling equations.  The error will be ~ 4% for each ml/min of Kru in the average sized patient.

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In Fig 3B the impact of KrU on NPCR is illustrated. Using the UKM NPCR values of .6, .8, 1.0 and 1.4 are shown with Kru increasing from 0 to 8 mL/min. The “apparent” eNPCR that would be calculated if Kru was present but not measured and assumed to be zero, are depicted. For example, if the NPCR is 1.0 and unmeasured Kru 3 mL/min is present the apparent eNPCR calculated would fall to .80 and would be interpreted as a marginal protein intake. Thus, residual renal function (when measured and applied) can have a marked impact on eKT/V and eNPCR and will further exaggerate the differences between the single pool and equilibrated measures.

 Conclusions:

1. The optimal dialysis dosing target is eKt/V of 1.20 while the equivalent spKt/V varies over a range depending on treatment time. spKt/V should not be used as a target when steps are taken to assure than it defines a dose equivalent to an adequate eKt/V.
2. Residual renal function will increase equilibrated Kt/V by about 0.15 units per 1 mL/min of residual renal urea clearance in an average sized person. The effect of residual renal function on eKt/V can be easily calculated. 
3. Residual renal function increasing eKt/V will result in a spurious decrease in apparent protein catabolic rate about -4% per mL/min of clearance when the residual renal function is not measured. 
4. Dialysis treatment time and residual renal function (when measured and applied) will alter the differences between spKT/V and eKt/V and thus will alter the percentage of patients achieving each of these goals.

Glossary:

UKM = Urea Kinetic Modeling
K= Dialyzer clearance

t= time on dialysis

V= volume (volume of distribution of urea equivalent to the total body water)

K/V= rate of dialysis (clearance per Liter of body water per unit time)

Kt/V= fractional clearance of body water of urea

sp= single pool

e= equilibrated

eKdt/V= dialysis contribution only to eKt/V
eKdrt/V= dialysis and renal contribution both to eKt/V

stdKt/V= Standard Kt/V= the continuous clearance which is therapeutically equivalent to any schedule (number of dialyses per week) and intensity (eKt/V per dialysis) of intermittent dialysis therapy

PCR= protein catabolic rate Gm/day

nPCR=normalized catabolic rate, gm/Kg normalized body weight/day

enPCR=normalized catabolic rate corrected for rebound

Kru= residual renal function ml/min

Gu=urea generation mg/min (amount of continuous urea generation in dialysis patients)

Bibliography:

I.   eKt/V Rationale and Urea Rebound (effect on spKt/V)

1. Hassaballah AM, Ayadi A, Shaheen MH, Barsoum RS, el-Badry A. Post-dialysis urea rebound. J Egypt Med Assoc 57215-226, 1974
2. Pedrini LA, Zereik S, Rasmy S. Causes, kinetics and clinical implications of post-hemodialysis urea rebound. Kidney Int 34:817-824, 1988
3. Evans JH, Smye SW, Brocklebank JT. Mathematical modelling of haemodialysis in children. Pediatr Nephrol 6:349-353, 1992
4. Albouze G, Yanai M, Calamai M, Testou D, Jungers P, Man NK. Urea rebound and residual renal function in the calculation of Kt/V and protein catabolic rate. Kidney Int 41 (Suppl):S278-S281, 1993
5. Kerr PG, Argiles A, Canaud B, Flavier JL, Mion CM. Accuracy of Kt/V estimations in high-flux haemodiafiltration using per cent reduction of urea: incorporation of urea rebound. Nephrol Dial Transplant 8:149-153,1993
6. Abramson F, Gibson S, Barlee V, Bosch JP. Urea kinetic modeling at high urea clearances: implications for clinical  practice. Adv Ren Replace Ther 1:5-14, 1994
7. Spiegel DM, Baker PL, Babcock S, Contiguglia R, Klein M. Hemodialysis urea rebound: the effect of increasing dialysis efficiency. Am J Kidney Dis 25:26-29, 1995
8. Yamada T, Akiba T, Marumo F. One-compartment urea kinetic modeling is not acceptable for quantifying the adequacy of  hemodialysis: comparison of a one-compartment model with a two-compartment model. Blood Purif 14:128-135, 1996 
9. Leblanc M, Charbonneau R, Lalumiere G, Cartier P, Deziel C. Postdialysis urea rebound: determinants and influence on dialysis delivery in chronic hemodialysis patients. Am J Kidney Dis 27:253-261, 1996
10. Vanholder R, Burgelman M, De Smet R, Voogeleere P, Ringoir S. Two-pool versus single-pool models in the determination of urea kinetic parameters. Blood Purif 14:437-450, 1996
11. Depner T, Beck G, Daugirdas J, Kusek J, Eknoyan G. Lessons from the Hemodialysis (HEMO) Study: An improved measure of the actual hemodialysis dose. Am J Kidney Dis 33:142-149, 1999
12. Marsenic O, Pavlicic D, Bigovic G, Peco-Antic A, Jovanovic O. Effects of postdialysis urea rebound on the quantification of pediatric hemodialysis. Nephron 84:124-129, 2000

II.    Methods to Compute eKt/V 

1. Smye SW, Dunderdale E, Brownridge G, Will E. Estimation of treatment dose in high-efficiency haemodialysis. Nephron  67:24-29, 1994 
2. Pflederer BR, Torrey C, Priester-Coary A, Lau AH, Daugirdas JT. Estimating equilibrated Kt/V from an intradialytic sample: effects of access and cardiopulmonary recirculations. Kidney Int 48:832-837, 1995
3. Daugirdas JT. Simplified equations for monitoring Kt/V, PCRn, eKt/V, and ePCRn. Adv Ren Replace Ther 2:295-304, 1995
4. Tattersall JE, DeTakats D, Chamney P, Greenwood RN, Farrington K. The post-hemodialysis rebound: Predicting and quantifying its effect on Kt/V. Kidney Int 50:2094-2102, 1996 
5. Maduell F, Garcia-Valdecasas J, Garcia H, Hernandez-Jaras J, Siguenza F, del Pozo C, Giner R, Moll R, Garrigos E. Validation of different methods to calculate Kt/V considering postdialysis rebound. Nephrol Dial Transplant 12:1928-1933, 1997 
6. Daugirdas JT, Depner TA, Gotch FA, Greene T, Keshaviah P, Levin NW, Schulman G. Comparison of methods to predict equilibrated Kt/V in the HEMO Pilot Study. Kidney Int 52:1395-1405, 1997
7. Bhaskaran S, Tobe S, Saiphoo C, Moldoveanu A, Raj DS, Manuel MA. Blood urea levels 30 minutes before the end of dialysis are equivalent to equilibrated blood urea. ASAIO J 43:M759-M762, 1997
8. Guh JY, Yang CY, Yang JM, Chen LM, Lai YH. Prediction of equilibrated postdialysis BUN by an artificial neural network in high-efficiency hemodialysis. Am J Kidney Dis 31:638-646, 1998
9. Smye SW, Tattersall JE, Will EJ. Modeling the postdialysis rebound: the reconciliation of current formulas. ASAIO J 45:562-567, 1999
10. Jean G, Charra B, Chazot C, Laurent G. Quest for postdialysis urea rebound-equilibrated Kt/V with only intradialytic urea samples. Kidney Int 56:1149-1153, 1999
11. Fernandez EA, Valtuille R, Willshaw P, Perazzo CA. Using artificial intelligence to predict the equilibrated postdialysis blood  urea concentration. Blood Purif 19:271-285, 2001 
12. Castro MC, Romao JE Jr, Marcondes M. Measurement of blood urea concentration during haemodialysis is not an accurate method to determine equilibrated post-dialysis urea concentration. Nephrol Dial Transplant 16:1814-1817, 2001
13. Daugirdas JT, Greene T, Depner TA, Leypoldt J, Gotch F, Schulman G, Star R; Hemodialysis Study Group. Factors that affect postdialysis rebound in serum urea concentration, including the rate of dialysis: results from the HEMO Study. J Am Soc Nephrol 15:194-203, 2004
14. Ookawara S, Suzuki M, Saitou M, Tabei K. Mathematical analysis of urea rebound in long-term hemodialysis patients. Ther Apher Dial 9:167-172, 2005
15. Prado M, Roa LM, Palma A, Milan JA. Double target comparison of blood-side methods for measuring the hemodialysis dose.  Kidney Int 68:2863-2876, 2005

Pediatric Patients:

1. Smye SW, Evans JH, Will E, Brocklebank JT. Paediatric haemodialysis: estimation of treatment efficiency in the presence of urea rebound. Clin Phys Physiol Meas 13:51-62, 1992
2. Goldstein SL, Sorof JM, Brewer ED. Evaluation and prediction of urea rebound and equilibrated Kt/V in the pediatric hemodialysis population. Am J Kidney Dis 34:49-54, 1999
3. Marsenic O, Peco-Antic A, Jovanovic O. Comparison of two methods for predicting equilibrated Kt/V (eKt/V) using true eKt/V value. Pediatr Nephrol 13:418-422, 1999 
4. Marsenic OD, Pavlicic D, Peco-Antic A, Bigovic G, Jovanovic O. Prediction of equilibrated urea in children on chronic hemodialysis. ASAIO J 46:283-287, 2000
5. Goldstein SL, Brewer ED. Logarithmic extrapolation of a 15-minute postdialysis BUN to predict equilibrated BUN and calculate double-pool Kt/V in the pediatric hemodialysis population. Am J Kidney Dis 36:98-104, 2000
6. Kietkajornkul C, Thirakhupt P, Chulamokha Y, Jaiprong S, Kitpanich S. Assessment of the different methods to predict equilibrated Kt/V in pediatric hemodialysis. J Med Assoc Thai 88 (Suppl 3):S180-S187, 2005

III.  eKt/V and spKt/V For Dialysis Prescriptions 

1. Daugirdas JT, Greene T, Depner TA, Gotch FA, Star RA. Relationship between apparent (single-pool) and true (double-pool)   urea distribution volume. Kidney Int 56:1928-1933, 1999
2. Elangovan L, Shinaberger CS, Kraut JA, Shinaberger JH. HEMO equilibrated Kt/V goals are difficult to achieve in large male patients. ASAIO J 47:235-239, 2001
3. Miwa T, Nakai S, Miwa M, Shinzato T, Segawa K, Maeda K. Which Kt/V is the most valid for assessment of both long mild and short intensive hemodialyses? Nephron 92:827-831, 2002 
4. Kanagasundaram NS, Greene T, Larive AB, Daugirdas JT, Depner TA, Garcia M, Paganini EP; Project for the Improvement of the Care of Acute Renal Dysfunction (PICARD) Study Group. Prescribing an equilibrated intermittent hemodialysis dose in intensive care unit acute renal failure. Kidney Int 64:2298-310, 2003
5. Tang HL, Tsang WK, Yeung S, Chan HW, Tong KL. Solute removal index correlates more with equilibrated Kt/V than with single pool Kt/V in haemodialysis patients. Nephrology (Carlton) 9:39-43, 2004
6. Fernandez EA, Valtuille R, Presedo JM, Willshaw P. Comparison of different methods for hemodialysis evaluation by means of ROC curves: from artificial intelligence to current methods. Clin Nephrol 64:205-213, 2005
7. Leypoldt JK, Cheung AK. Revisiting the hemodialysis dose. Semin Dial 19:96-101, 2006
8. Goldstein SL, Brem A, Warady BA, Fivush B, Frankenfield D. Comparison of single-pool and equilibrated Kt/V values for pediatric hemodialysis prescription management: Analysis from the Centers for Medicare & Medicaid Services Clinical Performance Measures Project. Pediatr Nephrol 21:1161-1166, 2006 

IV. eKt/V Associated Outcomes 

1. Gotch FA, Levin NW, Port FK, Wolfe RA, Uehlinger DE. Clinical outcome relative to the dose of dialysis is not what you think: the fallacy of the mean. Am J Kidney Dis 30:1-15, 1997
2. Wolfe RA, Ashby VB, Daugirdas JT, Agodoa LY, Jones CA, Port FK. Body size, dose of hemodialysis, and mortality. Am J Kidney Dis 35:80-88, 2000
3. Eknoyan G, Beck GJ, Cheung AK, Daugirdas JT, Greene T, Kusek JW, Allon M, Bailey J, Delmez JA, Depner TA, Dwyer JT, Levey AS, Levin NW, Milford E, Ornt DB, Rocco MV, Schulman G, Schwab SJ, Teehan BP, Toto R; Hemodialysis (HEMO) Study Group. Effect of dialysis dose and membrane flux in maintenance hemodialysis. N Engl J Med  347:2010-2019, 2002 
4. O'connor AS, Leon JB, Sehgal AR. The relative predictive ability of four different measures of hemodialysis dose. Am J Kidney Dis 40:1289-1294, 2002 
5. Stosovic M, Stanojevic M, Radovic M, Naumovic R, Jovanovic D, Simic S, Marinkovic J, Stankovic S, Djukanovic LJ. Comparative survival analysis of urea kinetic based indices. Int J Artif Organs 28:566-575, 2005
6. Greene T, Daugirdas J, Depner T, Allon M, Beck G, Chumlea C, Delmez J, Gotch F, Kusek JW, Levin N, Owen W, Schulman G, Star R, Toto R, Eknoyan G; Hemodialysis Study Group. Association of achieved dialysis dose with mortality in the hemodialysis study: an example of "dose-targeting bias". J Am Soc Nephrol 16:3371-3380, 2005