- Email: [email protected]
Vurea are linked
Peritoneal Dialysis Indices: Weekly CrCl and Weekly Kt/Vurea Are Linked Michael J. Flanigan, MD ● Peritoneal dialysis uses a biological ‘‘membrane,’’ the peritoneum, to control solute movement between the patient and the dialysate. Equilibrium thermodynamic models predict that the movement of small molecules across the peritoneum will be restricted in proportion to their permeability indices, the available membrane surface area, and the solute concentration gradient between plasma water and dialysate. During peritoneal dialysis, the membrane surface area, dialysate flow, and solute concentration gradients are quite similar for small solutes such as creatinine and urea. Hence, the clearances of creatinine and urea should be proportional to one another in a ratio equal to that of their membrane permeabilities; if that ratio is known, a peritoneal creatinine clearance could be derived for any known peritoneal urea clearance, and vice versa. Analysis of patient data supports this hypothesis and suggests that if disparate normalization procedures are avoided, peritoneal dialysis patients without residual renal function will have difficulty consistently attaining the weekly normalized creatinine clearance of H60 L/1.73 m2 recommended by the National Kidney Foundation– Dialysis Outcomes Quality Indicators (NKF-DOQI) without achieving a weekly Kt/Vurea of H2.5. r 1998 by the National Kidney Foundation, Inc. INDEX WORDS: Peritoneal dialysis; CAPD; peritoneal equilibration test; Kt/V; creatinine clearance.
T
HE National Cooperative Dialysis Study confirmed that patient health is effected by hemodialysis dose.1 It subsequently has become stylish to define the minimal dialysis dose consistent with a favorable clinical outcome as adequate. This has resulted in the use of Kt/V as both a measure of the delivered dialysis dose and a description of the dialysis prescription’s appropriateness or ‘‘adequacy.’’2 Since patients not on dialysis can have excellent health, any dialysis adequacy index intended to describe the dialysis prescription’s appropriateness should incorporate both the delivered dialysis dose and the residual renal function. Presently, two dialysis adequacy indices, a weekly normalized urea clearance (wKt/Vurea) ⱖ2.0 and a weekly normalized creatinine clearance (wCrCl) ⱖ60 L/1.73 m2/wk, derived by combining dialysis and residual renal function clearance measurements, are proposed as the minimum standards for peritoneal dialysis prescriptions.3 During both hemodialysis and peritoneal dialysis, the transport of small molecules across the dialysis membrane can be described using classic equilibrium thermodynamic principles. In such a paradigm, the transmembrane movement of small molecular weight solutes is governed by chemical activity or concentration gradients, membrane surface area, and the membrane-specific conductance. During peritoneal dialysis, the ‘‘membrane surface area’’is reasonably constant when fill volumes exceed 15 mL/kg, and the mass transfer area coefficient (MTaC) can be used to describe the capacity for transmembrane solute movement.4 MTaC ⫽ [VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CB ⫺ CD)i] ⫺ ln[VDf ⴱ (CB ⫺ CD)f]6
Since virgin peritoneal dialysate does not contain organic materials other than dextrose, and because dialysis time, dialysate volume, and membrane surface area are equivalent for the transfer of all small molecular weight solutes, the relative rates of urea and creatinine transfer will be proportional to the ratio of their peritoneal conductances or permeabilities, a ratio equal to the urea MTaC to creatinine MTaC ratio. MTaCurea MTaCcrt ⫽
[VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CureaB ⫺ CureaD)i] ⫺ ln[VDf ⴱ (CureaB ⫺ CureaD)f]6 [VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CcrtB ⫺ CcrtD)i] ⫺ ln[VDf ⴱ (CcrtB ⫺ CcrtD)f]6
MTaCurea MTaCcrt ⫽
5ln[VDi ⴱ (CureaB)i] ⫺ ln[VDf ⴱ (CureaB ⫺ CureaD)f]6 5ln[VDi ⴱ (CcrtB)i] ⫺ ln[VDf ⴱ (CcrtB ⫺ CcrtD)f]6
For simplification, the serum concentration of urea and creatinine change minimally during a
From the Department of Medicine, University of Iowa College of Medicine, Iowa City, IA. Received June 16, 1997; accepted in revised form September 12, 1997. Address reprint requests to Michael J. Flanigan, MD, Department of Medicine, T-305-GH, University of Iowa Hospitals and Clinics, 200 Hawkins Dr, Iowa City, IA 52240. E-mail: [email protected]
r 1998 by the National Kidney Foundation, Inc. 0272-6386/98/3103-0012$3.00/0
American Journal of Kidney Diseases, Vol 31, No 3 (March), 1998: pp 495-501
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dialysis exchange and the ratio can be reduced to MTaCurea MTaCcrt
⫽
[CD /CB]f urea [CD /CB]f crt
and the relative membrane conductances for creatinine and urea are fixed in proportion to the ratio of their peritoneal equilibration test (PET) results. Dialysis clearance (K) is determined by the membrane MTaC and dialysate flow (QD): Kmax ⫽
[QD ⴱ MTaC] [QD ⫹ MTaC]
Since urea and creatinine are removed simultaneously during peritoneal dialysis, the dialysate flow (QD) is equal for both clearance measurements and the relative clearances remain fixed in proportion to the ratio of the MTaCs, which correspond to the PET-derived (D/Pcreatinine)/(D/Purea) ratio. Among our patients, the mean PET D/Pcreatinine ratio is 72% (95% confidence interval, 69% to 75%) of the mean D/Purea index. This value is similar to that reported in other pediatric and adult studies.5-7 Since the ratio of the creatinine MTaC to the urea MTaC equals the creatinine to urea PET ratio, any measured dialysate creatinine clearance should also equal 72% of a simultaneously measured dialysis urea clearance. Using the following parameters based on our adult peritoneal dialysis patients, mean body surface area (BSA) ⫽ 1.77 m2, mean V ⫽ 0.54 ⫻ weight, mean weight ⫽ 68.7 kg, and t ⫽ 60 minutes ⫻ 24 hr/d ⫻ 7 d/wk ⫽ 10,080 min/wk. We conclude that a 70-kg peritoneal dialysis patient with a BSA of 1.73 m2 and a wKt/Vurea of 2.0 would have a urea clearance of approximately 7.5 mL/min and a dialysate creatinine clearance of approximately 5.4 mL/min or 54 L/wk. If wKt/Vurea ⫽ 2.0, then Kurea ⫽ 2.0 ⫻ (V/t) and Kurea ⫽ 2.0 ⫻ [(70 kg ⫻ 540 mL/kg)/(1 wk ⫻ 10,080 min/wk)] ⫽ 7.5 mL/min. Because CrCl ⫽ 0.72 ⫻ Kurea, CrCl ⫽ 0.72 ⫻ Kurea ⫽ 0.72 ⫻ 7.5 mL/min ⫽ 5.4 mL/min and wCrCl ⫽ 5.4 mL/min ⫻ 10,080 min/wk ⫻ 1 L/1,000 mL ⫽ 54.4 L/1.73 m2 BSA/wk. In our patients the ratio of V/Wt ⫽ 0.54 ⫾ 0.059. Thus, for a wKt/Vurea of 2, we would expect 95% of wCrCl measurements to fall between 48 and 61 L/1.73 m2 BSA/wk. A similar analysis indicates that to regularly obtain a wCrCl of 60 L/1.73 m2 BSA/wk, the typical
peritoneal dialysis patient would need either a wKt/V of 2.0 and residual renal function or a dialysis prescription delivering a wKt/Vurea of ⱖ2.5 (95% confidence interval, wKt/Vurea ⫽ 2.0 to 3.0). Such a dialysis prescription would require a daily continuous ambulatory peritoneal dialysis (CAPD) outflow volume of approximately 200 mL/kg body weight or 14 L/d for a 70-kg person. MATERIALS AND METHODS To determine whether these presumptions had clinical relevance, we assessed 182 simultaneously determined dialysate wKt/Vurea and wCrCl measurements from the 58 home peritoneal dialysis patients described in Table 1. Descriptive statistics and comparative data were derived using Microsoft Excel version 5.0 for the Macintosh and P ⱕ 0.05 (two-tailed) was considered significant. Data are presented as the mean values ⫾ 1 SD; ANOVA was used to compare multiple values and least-squares regression analyses was used to determine associations between wKt/Vurea and wCrCl. Describing dialysis efficiency as a wKt/V or wCrCl requires normalization to body size. This is done by dividing the daily mass urea removal (Kt) by the patient’s presumed urea distribution space (V) and multiplying the patient’s daily creatinine clearance by 1.73/the patient’s presumed BSA. These normalized clearances are then converted to weekly values by multiplying by 7. Traditionally, V is derived using the Watson approximation8 and BSA is calculated using the DuBois and DuBois9 or Hume and Weyers10 equation. The Watson approximation for total body water (V) is based on height in centimeters (H), weight in kilograms (W), and age in years (A): Male V ⫽ 2.447 ⫹ 0.1074 ⴱ H ⫹ 0.3362 ⴱ W ⫺ 0.09516 ⴱ A Female V ⫽ ⫺2.097 ⫹ 0.1069 ⴱ H ⫹ 0.2466 ⴱ W Table 1. Patient Characteristics
Sex (M/F) Age (yr) Weight (kg) Height (cm) D/P ratio (Crt:urea) V Watson (L) BSA DuBois (m2) V/Wt Watson (L/kg) BMI (wt/ht2)
Mean ⫾ SD
Range
25/33 48.6 ⫾ 19.3 68.7 ⫾ 28.3 163.5 ⫾ 15.5 0.72 ⫾ 0.13 35.4 ⫾ 8.0 1.74 ⫾ 0.32 0.54 ⫾ 0.10 25.3 ⫾ 5.5
6-80 16.8-120.5 114-193 0.38-0.99 15.7-56.4 0.74-2.33 0.38-1.16 12.9-43.2
NOTE. The patient demographics are those of a heterogeneous population. Ages range from 8 to 80 years and body weights range from 17 to 120 kg. The BMI is commensurate with national data. Seven percent of these patients might be considered ‘‘undernourished,’’ with a BMI of less than 20, while 20% had a BMI ⱖ30.
COUPLED CLEARANCES
497
The DuBois approximation of BSA (in m2) is derived from the height in centimeters (H) and the weight in kilograms (W):
in liters (V): Male V ⫽ (BSA ⫺ 0.3539) ⴱ 27.49 Female V ⫽ (BSA ⫺ 0.1780) ⴱ 21.11
BSA ⫽ 0.007184 ⴱ H0.725 ⴱ W0.425 To avoid introducing a systematic discrepancy into the normalization processes, we elected to derive both V and BSA from the same information. Hume and Weyers10 originally reported that derivations of V based on BSA were similar to those measured with tritiated water and proposed a method of using BSA to approximate total body water. Thus, Hume and Weyers’ conversion permits both weekly urea (wKt/V) and creatinine clearance (wCrCl) to be normalized using identical anthropometric data. Because the DuBois and DuBois9 report on BSA published in 1916 had been validated for relatively few subjects, we questioned whether a contemporary survey of later 20th century subjects might provide different BSA results. A literature search disclosed a contemporary survey of BSA measurements conducted on 400 subjects, including children and adults.11 We compared this approximation with that of DuBois and DuBois and found an excellent correlation (Gehan BSA ⫽ 1.034 * DuBois BSA ⫺ 0.02; r2 ⫽ 0.99). Since the Gehan formula had been assessed on a more contemporary population and because it included both adults and children, we believed it would offer a more robust method of estimating BSA and used it to estimate BSA for each patient. The Hume equation then converted these BSA estimates into urea distribution volumes (V). The Gehan approximation of BSA in square meters based on height in centimeters (H) and weight in kilograms (W) is BSA ⫽ 0.02350 ⴱ H0.42246 ⴱ H0.51456 Hume derived V using both direct anthropometric measures: Male V ⫽ 0.1928 ⴱ H ⫹ 0.2968 ⴱ W ⫺ 14.0129 Female V ⫽ 0.3445 ⴱ H ⫹ 0.1838 ⴱ W ⫺ 35.2701 and by converting BSA in square meters to total body water
RESULTS
Four anthropometric estimates of V (Watson, Hume–anthropometric, Hume conversions of the DuBois, and Gehan BSA estimates) are compared and contrasted to one another in Table 2. While the four V estimates were not different from one another by ANOVA (P ⫽ 0.868), Fig 1 reveals that Watson volumes (V) deviate substantially from the remaining anthropometric and BSA estimated Vs when applied to small individuals (weight ⬍60 kg). Figure 2 suggests that these deviations are principally the result of excessive volume estimates for patients younger than 30 years. Among patients larger than 60 kg, the Watson V was uniformly 1% to 3% below that provided by the Hume direct anthropometric V or BSA conversions of the DuBois and DuBois or Gehan data. Clinical measurements of 182 simultaneous 24-hour dialysate creatinine and urea clearances in 58 patients permitted the calculation of 58 sets of mean values for the dialysis indices wKt/Vurea and wCrCl. These quantification indices were then plotted and a regression analyses performed. A semilogarithmic relationship was chosen to relate the fractional mass removal term wKt/Vurea to the classical clearance measure wCrCl and is displayed in Fig 3. This analysis
Table 2. Anthropometric Estimates of Total Body Water or Urea Distribution Volume (V)
V (L)* Minimum V (L) Maximum V (L) V/Wt (L/kg)* V/Wt, female* V/Wt, male* Minimum V/Wt Maximum V/Wt
Watson
Hume
DuBois
Gehan
35.4 ⫾ 8.0 15.7 56.4 0.54 ⫾ 0.10 0.49 ⫾ 0.07 0.59 ⫾ 0.11 0.38 1.16
35.5 ⫾ 8.8 9.6 55.5 0.53 ⫾ 0.07 0.50 ⫾ 0.07 0.57 ⫾ 0.05 0.37 0.77
35.3 ⫾ 8.8 10.6 54.4 0.53 ⫾ 0.06 0.50 ⫾ 0.06 0.56 ⫾ 0.04 0.38 0.69
36.1 ⫾ 9.1 10.7 57.7 0.54 ⫾ 0.06 0.51 ⫾ 0.06 0.58 ⫾ 0.04 0.40 0.68
NOTE. Total body water or urea distribution volume (V) may be estimated by the methods of Hume and Weyers or Watson. Additionally, DuBois and Gehan estimates of BSA can be converted to V estimates using the Hume method. In this population, the V estimates are not different from one another (ANOVA, P ⫽ 0.868), but the Watson formula resulted in unusual body composition estimates for small individuals in whom V/Wt sometimes exceeded 100% of actual weight and the Watson V was consistently 2% to 4% smaller than the values derived from the Weyers, Hume, and Gehan methods when patients weighed more than 50 kg. *Data expressed as mean value ⫾ 1 SD.
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MICHAEL J. FLANIGAN
Fig 1. Deviation from Watson V. Hume used both direct anthropometric data and BSA estimates to derive total body water or urea distribution volumes (V). These values are expressed as a proportion of total body weight (V/weight ⫺ L/kg) and are compared with the V/weight estimates derived using the Watson formula. The difference between the Watson and Hume anthropometric or BSA determined V/weight values is expressed on the vertical axis and exceeds 10% of actual body weight for patients weighing less than 60 kg. Among larger patients, the Watson V tends to underestimate the total body water predicted by Hume and Weyers.
exhibits a distribution consistent with that predicted by thermodynamic considerations. DISCUSSION
We evaluated the relationship between various derivations of V and, similar to Tzamaloukas and Murata12 and Wong et al,13 concluded that the method used to estimate V impacts the reported wKt/V and wCrCl values. Normalized measurements are sensitive to the methods used to determine BSA and urea distribution volume (V); thus, to highlight the interdependence of the two dialysis indices, wCrCl and wKt/Vurea, we chose to use a single set of anthropometric data
to determine both normalization values. This permitted us to highlight the thermodynamic interdependence of wCrCl and wKt/Vurea. Had we used the Watson method to calculate V and then converted those estimates into BSA values rather than using the Gehan method, we might have changed the absolute wKt/Vurea and wCrCl values but would have reached an identical conclusion about the relationship of the two measurements. During peritoneal dialysis, small molecule transport depends on the MTaC, dialysate flow (QD), and ultrafiltration. The relative removal of any two small molecules remains proportional to
Fig 2. Deviation from Watson V. The Watson derived urea distribution volume (V) varies from those calculated for the same patients using either the Hume anthropometric estimate (derived directly from sex, height, and weight) or conversion of a DuBois or Gehan BSA value primarily as a result of aberrant V estimates in younger individuals. Since the Watson formula was not originally validated in children, it is possible that it overestimates V in smaller individuals.
COUPLED CLEARANCES
499
Fig 3. Peritoneal dialysis—relationship of creatinine clearance to Kt/Vurea. Paired measurements of dialysis performance were made by collecting 24-hour dialysis samples from 58 stable home peritoneal dialysis patients. The mean wCrCl and weekly wKt/Vurea values for each patient are plotted and a regression analysis performed. These data are consistent with the thermodynamic predictions derived from the ratio of 4hour PET values for creatinine and urea, thus confirming the prediction of coupled clearances.
their MTaC ratio under almost all conditions, and this proportionality constant can be determined from PET data. Confirming this hypothesis are the clinical findings of 182 paired dialysis indices (wCrCl and wKt/Vurea) that match the thermodynamic predictions relating urea and creatinine mass removal. Furthermore, because the creatinine to urea PET ratio is 0.72 ⫾ 0.13 to 1.0, obtaining a normalized weekly creatinine clearance ⱖ60 L/1.73 m2/wk will not be a practical
goal for peritoneal dialysis patients who lack residual renal function. Unless patients have residual renal function or we use disparate normalization processes to convert urea and creatinine clearances into dialysis indices, wCrCl and wKt/Vurea will be proportional to one another. The exception to this involves dialysis prescriptions with extremely long dwell times. When the dialysate dwell time exceeds 8 hours, it is possible to achieve virtual
Fig 4. Dialysate equilibration curves. The dialysate to plasma (D/P) ratios of urea and creatinine are plotted against dwell time.6 The D/P ratio for urea begins to approach unity after 8 hours, but creatinine equilibration will be delayed beyond 12 hours. During this transition interval, 8 to 16 hours, mass balance predictions will be dialysate flow dependent and relatively MTaC insensitive. Thus, during very long-dwell peritoneal dialysis session, the ratio of MTaCcrt to MTaCurea is a less accurate predictor of the ratio of creatinine to urea in the dialysate and subsequent clearances. Even so, variations from the MTaC projection are unlikely to exceed 10% unless the average dialysate dwell times exceed 8 hours.
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MICHAEL J. FLANIGAN
Fig 5. Relationship of wCrCl to Kt/Vurea. The regression equations and lines for paired wCrCl and wKt/Vurea data are plotted for three peritoneal dialysis prescriptions. CAPD patients perform four to five exchanges of convenience daily and are instructed that each exchange should have a minimum dwell time of 4 hours. CCPD prescriptions consist of five 2-hour nocturnal exchanges and a single 14-hour daytime exchange, and peritoneal dialysis-plus prescriptions use four 2-hour nocturnal exchanges and two 8-hour daytime exchanges each day.
equilibration of dialysate and plasma urea while creatinine continues to concentrate within the peritoneal fluid. This is illustrated in Fig 4, in which two PET curves, blood urea nitrogen and creatinine, are displayed on a common time axis.6 Sometime between 6 and 8 hours, the curves begin to converge. While MTaC values reflect membrane function, net urea and creatinine transfer are becoming more dependent on dialysate flow and less dependent on membrane transfer as the dwell time approaches 8 hours. After 8 hours, the plasma to dialysate urea concentration gradient dissipates, and urea moves into and out of the peritoneum at almost equal rates, while creatinine, which is not in equilibrium, continues to accumulate in the peritoneum. During this interval, the PET ratio will not accurately predict the ratio of urea to creatinine mass removal, and the creatinine clearance to urea clearance ratio changes from 0.72:1.0 to approach 1:1. Thus, when significant amounts of dialysate have a peritoneal residence time ⱖ8 hours, the creatinine clearance approaches the urea clearance and a wKt/Vurea of 2 approaches a wCrCl of 60 L/1.73 m2/wk rather than the more typical 55 L/1.73 m2/wk. This finding is further illustrated in Fig 5, in which the regression curves and correlation coefficients (r2) for CAPD, continuous cyclic peritoneal dialysis (CCPD), and peritoneal dialysis-plus prescriptions are presented. The CAPD data have greater variability (smaller r2) about the predicted regression line than do the paired data from CCPD and peritoneal dialysis-plus prescriptions. This happens because CAPD pre-
scriptions have longer average dwell times than do CCPD prescriptions and because the prolonged dwells have greater variability than those of the peritoneal dialysis-plus prescription. The cumulative result of these two processes, prolonged dwell times of variable duration, is to increase the range of wCrCl values associated with a specific wKt/Vurea. The mean wCrCl still will not vary from expected by more than 10% unless the average dwell time exceeds 8 to 10 hours. REFERENCES 1. Parker TF: Role of dialysis dose on morbidity and mortality in maintenance hemodialysis patients. Am J Kidney Dis 24:981-989, 1994 2. Barth RH: Urea modeling and Kt/V: A critical appraisal. Kidney Int 41:S252-S260, 1993 (suppl) 3. National Kidney Foundation-DOQI: Clinical Practice Guidelines for Peritoneal Dialysis Adequacy. Madison, WI, Medical Education Institute, 1997 4. Flanigan MJ, Lim VS, Pflederer TA: Tidal peritoneal dialysis: Kinetics and protein balance. Am J Kidney Dis 22:700-707, 1993 5. Warady BA, Alexander SR, Hossil S, Vonesh E, Geary D, Watkins S, Salusky IB, Kohaut EC: Peritoneal transport function in children receiving long-term dialysis. J Am Soc Nephrol 7:2385-2391, 1996 6. Twardowski ZJ, Nolph KD, Prowant BF, Moore HL: Efficiency of high volume low frequency continuous ambulatory peritoneal dialysis (CAPD). ASAIO Trans 29:53-57, 1983 7. 1996 Peritoneal Dialysis–Core Indicators Study. (Data collection results available from Diane Frankenfield at HCFA/HSQB/CCMI) 8. Watson PE, Watson ID, Batt RD: Total body water volumes for adult males and females estimated from simple anthropometric measurements. Am J Clin Nutr 33:27-39, 1980
COUPLED CLEARANCES
9. DuBois D, DuBois EF: Clinical calorimetry: A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 17:863-871, 1916 10. Hume R, Weyers E: Relationship between total body water and surface area in normal and obese subjects. J Clin Pathol 24:234-238, 1971 11. Gehan EA, George SL: Estimation of human body
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surface area from height and weight. Cancer Chemother Rep 54:225-235, 1970 12. Tzamaloukas AH, Murata GH: Body surface area and anthropometric body water in patients on continuous peritoneal dialysis. Perit Dial Int 15:284-285, 1995 13. Wong KC, Xiong DW, Kerr PG, Borovnicar DJ, Stroud DB, Atkins RC, Strauss BJG: Kt/V in CAPD by different estimations of V. Kidney Int 48:563-569, 1995
T
HE National Cooperative Dialysis Study confirmed that patient health is effected by hemodialysis dose.1 It subsequently has become stylish to define the minimal dialysis dose consistent with a favorable clinical outcome as adequate. This has resulted in the use of Kt/V as both a measure of the delivered dialysis dose and a description of the dialysis prescription’s appropriateness or ‘‘adequacy.’’2 Since patients not on dialysis can have excellent health, any dialysis adequacy index intended to describe the dialysis prescription’s appropriateness should incorporate both the delivered dialysis dose and the residual renal function. Presently, two dialysis adequacy indices, a weekly normalized urea clearance (wKt/Vurea) ⱖ2.0 and a weekly normalized creatinine clearance (wCrCl) ⱖ60 L/1.73 m2/wk, derived by combining dialysis and residual renal function clearance measurements, are proposed as the minimum standards for peritoneal dialysis prescriptions.3 During both hemodialysis and peritoneal dialysis, the transport of small molecules across the dialysis membrane can be described using classic equilibrium thermodynamic principles. In such a paradigm, the transmembrane movement of small molecular weight solutes is governed by chemical activity or concentration gradients, membrane surface area, and the membrane-specific conductance. During peritoneal dialysis, the ‘‘membrane surface area’’is reasonably constant when fill volumes exceed 15 mL/kg, and the mass transfer area coefficient (MTaC) can be used to describe the capacity for transmembrane solute movement.4 MTaC ⫽ [VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CB ⫺ CD)i] ⫺ ln[VDf ⴱ (CB ⫺ CD)f]6
Since virgin peritoneal dialysate does not contain organic materials other than dextrose, and because dialysis time, dialysate volume, and membrane surface area are equivalent for the transfer of all small molecular weight solutes, the relative rates of urea and creatinine transfer will be proportional to the ratio of their peritoneal conductances or permeabilities, a ratio equal to the urea MTaC to creatinine MTaC ratio. MTaCurea MTaCcrt ⫽
[VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CureaB ⫺ CureaD)i] ⫺ ln[VDf ⴱ (CureaB ⫺ CureaD)f]6 [VDf /(Tf ⫺ Ti)] ⴱ 5ln[VDi ⴱ (CcrtB ⫺ CcrtD)i] ⫺ ln[VDf ⴱ (CcrtB ⫺ CcrtD)f]6
MTaCurea MTaCcrt ⫽
5ln[VDi ⴱ (CureaB)i] ⫺ ln[VDf ⴱ (CureaB ⫺ CureaD)f]6 5ln[VDi ⴱ (CcrtB)i] ⫺ ln[VDf ⴱ (CcrtB ⫺ CcrtD)f]6
For simplification, the serum concentration of urea and creatinine change minimally during a
From the Department of Medicine, University of Iowa College of Medicine, Iowa City, IA. Received June 16, 1997; accepted in revised form September 12, 1997. Address reprint requests to Michael J. Flanigan, MD, Department of Medicine, T-305-GH, University of Iowa Hospitals and Clinics, 200 Hawkins Dr, Iowa City, IA 52240. E-mail: [email protected]
r 1998 by the National Kidney Foundation, Inc. 0272-6386/98/3103-0012$3.00/0
American Journal of Kidney Diseases, Vol 31, No 3 (March), 1998: pp 495-501
495
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MICHAEL J. FLANIGAN
dialysis exchange and the ratio can be reduced to MTaCurea MTaCcrt
⫽
[CD /CB]f urea [CD /CB]f crt
and the relative membrane conductances for creatinine and urea are fixed in proportion to the ratio of their peritoneal equilibration test (PET) results. Dialysis clearance (K) is determined by the membrane MTaC and dialysate flow (QD): Kmax ⫽
[QD ⴱ MTaC] [QD ⫹ MTaC]
Since urea and creatinine are removed simultaneously during peritoneal dialysis, the dialysate flow (QD) is equal for both clearance measurements and the relative clearances remain fixed in proportion to the ratio of the MTaCs, which correspond to the PET-derived (D/Pcreatinine)/(D/Purea) ratio. Among our patients, the mean PET D/Pcreatinine ratio is 72% (95% confidence interval, 69% to 75%) of the mean D/Purea index. This value is similar to that reported in other pediatric and adult studies.5-7 Since the ratio of the creatinine MTaC to the urea MTaC equals the creatinine to urea PET ratio, any measured dialysate creatinine clearance should also equal 72% of a simultaneously measured dialysis urea clearance. Using the following parameters based on our adult peritoneal dialysis patients, mean body surface area (BSA) ⫽ 1.77 m2, mean V ⫽ 0.54 ⫻ weight, mean weight ⫽ 68.7 kg, and t ⫽ 60 minutes ⫻ 24 hr/d ⫻ 7 d/wk ⫽ 10,080 min/wk. We conclude that a 70-kg peritoneal dialysis patient with a BSA of 1.73 m2 and a wKt/Vurea of 2.0 would have a urea clearance of approximately 7.5 mL/min and a dialysate creatinine clearance of approximately 5.4 mL/min or 54 L/wk. If wKt/Vurea ⫽ 2.0, then Kurea ⫽ 2.0 ⫻ (V/t) and Kurea ⫽ 2.0 ⫻ [(70 kg ⫻ 540 mL/kg)/(1 wk ⫻ 10,080 min/wk)] ⫽ 7.5 mL/min. Because CrCl ⫽ 0.72 ⫻ Kurea, CrCl ⫽ 0.72 ⫻ Kurea ⫽ 0.72 ⫻ 7.5 mL/min ⫽ 5.4 mL/min and wCrCl ⫽ 5.4 mL/min ⫻ 10,080 min/wk ⫻ 1 L/1,000 mL ⫽ 54.4 L/1.73 m2 BSA/wk. In our patients the ratio of V/Wt ⫽ 0.54 ⫾ 0.059. Thus, for a wKt/Vurea of 2, we would expect 95% of wCrCl measurements to fall between 48 and 61 L/1.73 m2 BSA/wk. A similar analysis indicates that to regularly obtain a wCrCl of 60 L/1.73 m2 BSA/wk, the typical
peritoneal dialysis patient would need either a wKt/V of 2.0 and residual renal function or a dialysis prescription delivering a wKt/Vurea of ⱖ2.5 (95% confidence interval, wKt/Vurea ⫽ 2.0 to 3.0). Such a dialysis prescription would require a daily continuous ambulatory peritoneal dialysis (CAPD) outflow volume of approximately 200 mL/kg body weight or 14 L/d for a 70-kg person. MATERIALS AND METHODS To determine whether these presumptions had clinical relevance, we assessed 182 simultaneously determined dialysate wKt/Vurea and wCrCl measurements from the 58 home peritoneal dialysis patients described in Table 1. Descriptive statistics and comparative data were derived using Microsoft Excel version 5.0 for the Macintosh and P ⱕ 0.05 (two-tailed) was considered significant. Data are presented as the mean values ⫾ 1 SD; ANOVA was used to compare multiple values and least-squares regression analyses was used to determine associations between wKt/Vurea and wCrCl. Describing dialysis efficiency as a wKt/V or wCrCl requires normalization to body size. This is done by dividing the daily mass urea removal (Kt) by the patient’s presumed urea distribution space (V) and multiplying the patient’s daily creatinine clearance by 1.73/the patient’s presumed BSA. These normalized clearances are then converted to weekly values by multiplying by 7. Traditionally, V is derived using the Watson approximation8 and BSA is calculated using the DuBois and DuBois9 or Hume and Weyers10 equation. The Watson approximation for total body water (V) is based on height in centimeters (H), weight in kilograms (W), and age in years (A): Male V ⫽ 2.447 ⫹ 0.1074 ⴱ H ⫹ 0.3362 ⴱ W ⫺ 0.09516 ⴱ A Female V ⫽ ⫺2.097 ⫹ 0.1069 ⴱ H ⫹ 0.2466 ⴱ W Table 1. Patient Characteristics
Sex (M/F) Age (yr) Weight (kg) Height (cm) D/P ratio (Crt:urea) V Watson (L) BSA DuBois (m2) V/Wt Watson (L/kg) BMI (wt/ht2)
Mean ⫾ SD
Range
25/33 48.6 ⫾ 19.3 68.7 ⫾ 28.3 163.5 ⫾ 15.5 0.72 ⫾ 0.13 35.4 ⫾ 8.0 1.74 ⫾ 0.32 0.54 ⫾ 0.10 25.3 ⫾ 5.5
6-80 16.8-120.5 114-193 0.38-0.99 15.7-56.4 0.74-2.33 0.38-1.16 12.9-43.2
NOTE. The patient demographics are those of a heterogeneous population. Ages range from 8 to 80 years and body weights range from 17 to 120 kg. The BMI is commensurate with national data. Seven percent of these patients might be considered ‘‘undernourished,’’ with a BMI of less than 20, while 20% had a BMI ⱖ30.
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The DuBois approximation of BSA (in m2) is derived from the height in centimeters (H) and the weight in kilograms (W):
in liters (V): Male V ⫽ (BSA ⫺ 0.3539) ⴱ 27.49 Female V ⫽ (BSA ⫺ 0.1780) ⴱ 21.11
BSA ⫽ 0.007184 ⴱ H0.725 ⴱ W0.425 To avoid introducing a systematic discrepancy into the normalization processes, we elected to derive both V and BSA from the same information. Hume and Weyers10 originally reported that derivations of V based on BSA were similar to those measured with tritiated water and proposed a method of using BSA to approximate total body water. Thus, Hume and Weyers’ conversion permits both weekly urea (wKt/V) and creatinine clearance (wCrCl) to be normalized using identical anthropometric data. Because the DuBois and DuBois9 report on BSA published in 1916 had been validated for relatively few subjects, we questioned whether a contemporary survey of later 20th century subjects might provide different BSA results. A literature search disclosed a contemporary survey of BSA measurements conducted on 400 subjects, including children and adults.11 We compared this approximation with that of DuBois and DuBois and found an excellent correlation (Gehan BSA ⫽ 1.034 * DuBois BSA ⫺ 0.02; r2 ⫽ 0.99). Since the Gehan formula had been assessed on a more contemporary population and because it included both adults and children, we believed it would offer a more robust method of estimating BSA and used it to estimate BSA for each patient. The Hume equation then converted these BSA estimates into urea distribution volumes (V). The Gehan approximation of BSA in square meters based on height in centimeters (H) and weight in kilograms (W) is BSA ⫽ 0.02350 ⴱ H0.42246 ⴱ H0.51456 Hume derived V using both direct anthropometric measures: Male V ⫽ 0.1928 ⴱ H ⫹ 0.2968 ⴱ W ⫺ 14.0129 Female V ⫽ 0.3445 ⴱ H ⫹ 0.1838 ⴱ W ⫺ 35.2701 and by converting BSA in square meters to total body water
RESULTS
Four anthropometric estimates of V (Watson, Hume–anthropometric, Hume conversions of the DuBois, and Gehan BSA estimates) are compared and contrasted to one another in Table 2. While the four V estimates were not different from one another by ANOVA (P ⫽ 0.868), Fig 1 reveals that Watson volumes (V) deviate substantially from the remaining anthropometric and BSA estimated Vs when applied to small individuals (weight ⬍60 kg). Figure 2 suggests that these deviations are principally the result of excessive volume estimates for patients younger than 30 years. Among patients larger than 60 kg, the Watson V was uniformly 1% to 3% below that provided by the Hume direct anthropometric V or BSA conversions of the DuBois and DuBois or Gehan data. Clinical measurements of 182 simultaneous 24-hour dialysate creatinine and urea clearances in 58 patients permitted the calculation of 58 sets of mean values for the dialysis indices wKt/Vurea and wCrCl. These quantification indices were then plotted and a regression analyses performed. A semilogarithmic relationship was chosen to relate the fractional mass removal term wKt/Vurea to the classical clearance measure wCrCl and is displayed in Fig 3. This analysis
Table 2. Anthropometric Estimates of Total Body Water or Urea Distribution Volume (V)
V (L)* Minimum V (L) Maximum V (L) V/Wt (L/kg)* V/Wt, female* V/Wt, male* Minimum V/Wt Maximum V/Wt
Watson
Hume
DuBois
Gehan
35.4 ⫾ 8.0 15.7 56.4 0.54 ⫾ 0.10 0.49 ⫾ 0.07 0.59 ⫾ 0.11 0.38 1.16
35.5 ⫾ 8.8 9.6 55.5 0.53 ⫾ 0.07 0.50 ⫾ 0.07 0.57 ⫾ 0.05 0.37 0.77
35.3 ⫾ 8.8 10.6 54.4 0.53 ⫾ 0.06 0.50 ⫾ 0.06 0.56 ⫾ 0.04 0.38 0.69
36.1 ⫾ 9.1 10.7 57.7 0.54 ⫾ 0.06 0.51 ⫾ 0.06 0.58 ⫾ 0.04 0.40 0.68
NOTE. Total body water or urea distribution volume (V) may be estimated by the methods of Hume and Weyers or Watson. Additionally, DuBois and Gehan estimates of BSA can be converted to V estimates using the Hume method. In this population, the V estimates are not different from one another (ANOVA, P ⫽ 0.868), but the Watson formula resulted in unusual body composition estimates for small individuals in whom V/Wt sometimes exceeded 100% of actual weight and the Watson V was consistently 2% to 4% smaller than the values derived from the Weyers, Hume, and Gehan methods when patients weighed more than 50 kg. *Data expressed as mean value ⫾ 1 SD.
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Fig 1. Deviation from Watson V. Hume used both direct anthropometric data and BSA estimates to derive total body water or urea distribution volumes (V). These values are expressed as a proportion of total body weight (V/weight ⫺ L/kg) and are compared with the V/weight estimates derived using the Watson formula. The difference between the Watson and Hume anthropometric or BSA determined V/weight values is expressed on the vertical axis and exceeds 10% of actual body weight for patients weighing less than 60 kg. Among larger patients, the Watson V tends to underestimate the total body water predicted by Hume and Weyers.
exhibits a distribution consistent with that predicted by thermodynamic considerations. DISCUSSION
We evaluated the relationship between various derivations of V and, similar to Tzamaloukas and Murata12 and Wong et al,13 concluded that the method used to estimate V impacts the reported wKt/V and wCrCl values. Normalized measurements are sensitive to the methods used to determine BSA and urea distribution volume (V); thus, to highlight the interdependence of the two dialysis indices, wCrCl and wKt/Vurea, we chose to use a single set of anthropometric data
to determine both normalization values. This permitted us to highlight the thermodynamic interdependence of wCrCl and wKt/Vurea. Had we used the Watson method to calculate V and then converted those estimates into BSA values rather than using the Gehan method, we might have changed the absolute wKt/Vurea and wCrCl values but would have reached an identical conclusion about the relationship of the two measurements. During peritoneal dialysis, small molecule transport depends on the MTaC, dialysate flow (QD), and ultrafiltration. The relative removal of any two small molecules remains proportional to
Fig 2. Deviation from Watson V. The Watson derived urea distribution volume (V) varies from those calculated for the same patients using either the Hume anthropometric estimate (derived directly from sex, height, and weight) or conversion of a DuBois or Gehan BSA value primarily as a result of aberrant V estimates in younger individuals. Since the Watson formula was not originally validated in children, it is possible that it overestimates V in smaller individuals.
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Fig 3. Peritoneal dialysis—relationship of creatinine clearance to Kt/Vurea. Paired measurements of dialysis performance were made by collecting 24-hour dialysis samples from 58 stable home peritoneal dialysis patients. The mean wCrCl and weekly wKt/Vurea values for each patient are plotted and a regression analysis performed. These data are consistent with the thermodynamic predictions derived from the ratio of 4hour PET values for creatinine and urea, thus confirming the prediction of coupled clearances.
their MTaC ratio under almost all conditions, and this proportionality constant can be determined from PET data. Confirming this hypothesis are the clinical findings of 182 paired dialysis indices (wCrCl and wKt/Vurea) that match the thermodynamic predictions relating urea and creatinine mass removal. Furthermore, because the creatinine to urea PET ratio is 0.72 ⫾ 0.13 to 1.0, obtaining a normalized weekly creatinine clearance ⱖ60 L/1.73 m2/wk will not be a practical
goal for peritoneal dialysis patients who lack residual renal function. Unless patients have residual renal function or we use disparate normalization processes to convert urea and creatinine clearances into dialysis indices, wCrCl and wKt/Vurea will be proportional to one another. The exception to this involves dialysis prescriptions with extremely long dwell times. When the dialysate dwell time exceeds 8 hours, it is possible to achieve virtual
Fig 4. Dialysate equilibration curves. The dialysate to plasma (D/P) ratios of urea and creatinine are plotted against dwell time.6 The D/P ratio for urea begins to approach unity after 8 hours, but creatinine equilibration will be delayed beyond 12 hours. During this transition interval, 8 to 16 hours, mass balance predictions will be dialysate flow dependent and relatively MTaC insensitive. Thus, during very long-dwell peritoneal dialysis session, the ratio of MTaCcrt to MTaCurea is a less accurate predictor of the ratio of creatinine to urea in the dialysate and subsequent clearances. Even so, variations from the MTaC projection are unlikely to exceed 10% unless the average dialysate dwell times exceed 8 hours.
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Fig 5. Relationship of wCrCl to Kt/Vurea. The regression equations and lines for paired wCrCl and wKt/Vurea data are plotted for three peritoneal dialysis prescriptions. CAPD patients perform four to five exchanges of convenience daily and are instructed that each exchange should have a minimum dwell time of 4 hours. CCPD prescriptions consist of five 2-hour nocturnal exchanges and a single 14-hour daytime exchange, and peritoneal dialysis-plus prescriptions use four 2-hour nocturnal exchanges and two 8-hour daytime exchanges each day.
equilibration of dialysate and plasma urea while creatinine continues to concentrate within the peritoneal fluid. This is illustrated in Fig 4, in which two PET curves, blood urea nitrogen and creatinine, are displayed on a common time axis.6 Sometime between 6 and 8 hours, the curves begin to converge. While MTaC values reflect membrane function, net urea and creatinine transfer are becoming more dependent on dialysate flow and less dependent on membrane transfer as the dwell time approaches 8 hours. After 8 hours, the plasma to dialysate urea concentration gradient dissipates, and urea moves into and out of the peritoneum at almost equal rates, while creatinine, which is not in equilibrium, continues to accumulate in the peritoneum. During this interval, the PET ratio will not accurately predict the ratio of urea to creatinine mass removal, and the creatinine clearance to urea clearance ratio changes from 0.72:1.0 to approach 1:1. Thus, when significant amounts of dialysate have a peritoneal residence time ⱖ8 hours, the creatinine clearance approaches the urea clearance and a wKt/Vurea of 2 approaches a wCrCl of 60 L/1.73 m2/wk rather than the more typical 55 L/1.73 m2/wk. This finding is further illustrated in Fig 5, in which the regression curves and correlation coefficients (r2) for CAPD, continuous cyclic peritoneal dialysis (CCPD), and peritoneal dialysis-plus prescriptions are presented. The CAPD data have greater variability (smaller r2) about the predicted regression line than do the paired data from CCPD and peritoneal dialysis-plus prescriptions. This happens because CAPD pre-
scriptions have longer average dwell times than do CCPD prescriptions and because the prolonged dwells have greater variability than those of the peritoneal dialysis-plus prescription. The cumulative result of these two processes, prolonged dwell times of variable duration, is to increase the range of wCrCl values associated with a specific wKt/Vurea. The mean wCrCl still will not vary from expected by more than 10% unless the average dwell time exceeds 8 to 10 hours. REFERENCES 1. Parker TF: Role of dialysis dose on morbidity and mortality in maintenance hemodialysis patients. Am J Kidney Dis 24:981-989, 1994 2. Barth RH: Urea modeling and Kt/V: A critical appraisal. Kidney Int 41:S252-S260, 1993 (suppl) 3. National Kidney Foundation-DOQI: Clinical Practice Guidelines for Peritoneal Dialysis Adequacy. Madison, WI, Medical Education Institute, 1997 4. Flanigan MJ, Lim VS, Pflederer TA: Tidal peritoneal dialysis: Kinetics and protein balance. Am J Kidney Dis 22:700-707, 1993 5. Warady BA, Alexander SR, Hossil S, Vonesh E, Geary D, Watkins S, Salusky IB, Kohaut EC: Peritoneal transport function in children receiving long-term dialysis. J Am Soc Nephrol 7:2385-2391, 1996 6. Twardowski ZJ, Nolph KD, Prowant BF, Moore HL: Efficiency of high volume low frequency continuous ambulatory peritoneal dialysis (CAPD). ASAIO Trans 29:53-57, 1983 7. 1996 Peritoneal Dialysis–Core Indicators Study. (Data collection results available from Diane Frankenfield at HCFA/HSQB/CCMI) 8. Watson PE, Watson ID, Batt RD: Total body water volumes for adult males and females estimated from simple anthropometric measurements. Am J Clin Nutr 33:27-39, 1980
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9. DuBois D, DuBois EF: Clinical calorimetry: A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 17:863-871, 1916 10. Hume R, Weyers E: Relationship between total body water and surface area in normal and obese subjects. J Clin Pathol 24:234-238, 1971 11. Gehan EA, George SL: Estimation of human body
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surface area from height and weight. Cancer Chemother Rep 54:225-235, 1970 12. Tzamaloukas AH, Murata GH: Body surface area and anthropometric body water in patients on continuous peritoneal dialysis. Perit Dial Int 15:284-285, 1995 13. Wong KC, Xiong DW, Kerr PG, Borovnicar DJ, Stroud DB, Atkins RC, Strauss BJG: Kt/V in CAPD by different estimations of V. Kidney Int 48:563-569, 1995