Journal of Pharmacokinelics and Biopharmaceulics, Vol. 4, No. 5, 1976
Hemodialyzer Clearancesof Gentamicin, Kanamycin, Tobramycin, Amikacin, Ethambutol, Procainamide, and Flucytosine, with a Technique for Planning Therapy T. Graham Christopher, 2 A n d r e w D. Blair, 2 Arden W. Forrey, 2 and Ralph E. Cutler 2
Received Nov. 4, 1975--Final May 3, 1976
Hemodialyzer clearance studies have been undertaken on the following drugs: gentamicin, kanamycin, tobramycin, amikacin, ethambutol, procainamide, and flucytosine. The following hemodialyzers were tested: Dow model4, Kiil, Travenol UF II, and the Extracorporeal EX-03. The studies were predominantly undertaken in vitro, permitting direct comparison between drug clearances on the same dialyzer. Protein binding studies for gentamicin, kanamycin, procainamide, and ethambutol are also reported. Nomograms to facilitate the prediction of drug dosage regimens in dialysis patients are included. KEY WORDS: dialysis; drugs; renal failure; gentamicin; kanamycin; tobramycin; amikacin; ethambutol; procainamide; flucytosine.
INTRODUCTION
Hemodialyzer clearance values have been reported for many drugs and different types of hemodialyzers. Many of these reports have included measurements of only a single dialyzer or have relied on changes in the drug This work was supported in part by a grant from the General Clinical Research Centers Program (RR- 133) of the Division of Research Resources, National Institutes of Health, and by a research contract (2-2219) from the Artificial Kidney-Chronic Uremia Program of the National Institute of Arthritis, Metabolism, and Digestive Diseases, National Institutes of Health. 1 . . . . This paper was presented m .part at the American Sooety of Nephrology meeting, 1974. 2University of Washington, School of Medicine, Department of Medicine, Harborview Medical Center, Seattle, Washington 98104. 427 9 1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.
428
Christopher, Blair, Forrey, and Cutler
concentration decay curves in patients during hemodialysis for the estimation of dialyzer clearances. In many cases, the measurements have taken place in patients taking overdoses of drugs or under nonstandard conditions. This study represents a comparison between different models of hemodialyzers and different drugs under controlled laboratory and clinical conditions. Comparisons between laboratory clearance measurements and those made during the dialysis of patients have been made for some of these drugs. This report discusses dialysance measurements for the Dow model 4 hollow fiber kidney, the standard 1.0-m 2 Kiil, the Extracorporeal EX-03, and the Travenol Ultraflow II, standard model. Drugs which have been studied include gentamicin, kanamycin, ethambutol, procainamide, amikacin (BB-K8), tobramycin, 5-flucytosine, and two comparative marker molecules, creatinine and 169yb-D.T.P.A. The last compound is 603 daltons and has a hemodialyzer clearance similar to that of phosphate. Two nomograms intended to simplify the administration of drugs to dialysis patients are presented. These nomograms are based on a one-compartment model of dialysis. It should be noted that the word "clearance" is used interchangeably with "dialysance" for reasons which are explained in the text. This is done purposely to facilitate clinical utilization of the data. MATERIALS AND METHODS Dialysis Methods
Laboratory dialyzer studies were undertaken with the double-loop recirculating system illustrated in Fig. 1. A standard dialysate solution (Renalyte-86, diluted 35 : 1 with deaerated, deionized water) was employed, both as blood simulant and in the dialysate compartment. Two reservoirs were prepared, each of 2 liters. The blood simulant was circulated through the dialyzer from one reservoir at 200 ml/min, using a blood pump. The dialysate was recirculated through the dialyzer in a countercurrent manner
Blood
E~
J
Dialyzer
F
Pomp Rewarmer Calibrated Flask
Fig. 1. Diagram of dialysate loop.
Hemodialyzer Clearances of Various Drugs
429
at 460 ml/min from another 2-liter reservoir. Both reservoirs were continuously agitated by magnetic stirrers. No "negative" transmembrane pressure was applied to the dialyzer. The transmembrane pressures were thus developed solely by the hydrodynamic characteristics of the blood and dialysate compartments of each dialyzer. In the coil dialyzers, the recirculating dialysate volume was 7 liters. This represents the volume of the holding tank for the dialyzer cartridge. The dialysate was circulated transversely across the coils at the standard recirculating dialysate flow rate (Drake Willock unit). At the commencement of the experiment, the test drug, together with 1/x Ci of 169yb-D.T.P.A. and/or 300 mg creatinine, was thoroughly mixed in the blood side reservoir with the blood pump turned off. At zero time, the blood pump was started. Samples from both the blood and dialysate reservoirs were taken at 5-min intervals for 2-389hr, depending on the drug dialysance. The concentration differences between compartments were measured as a function of time. Experiments with gentamicin and 14C-ethambutol were undertaken in a test dialysis in patients with stable chronic renal failure requiring hemodialysis, and without acute intercurrent illness. Clearances were measured by a similar technique to that described for the in vitro experiments. A closed recirculating dialysate loop was used with a total volume of 1.0-1.5 liters. Dialysate was recirculated at 500 ml/min with no ultrafiltration pressure. Blood flow was held constant at 200 ml/min by a blood pump. Drug clearances in different experiments were measured by dialyzing drug either from the dialysate loop to the patient or from the patient to the dialysate. In the gentamicin studies, the drug was dialyzed into the patient. In the ethambutol experiments in patients, the clearance measurements were undertaken in both directions. In this latter study, the blood-todialysate experiment was commenced 1 hr after the parenteral administration of ~4C-ethambutol in order to minimize the likelihood of the presence of ethambutol metabolites, which may be expected to progressively accumulate. In all studies, creatinine clearance was estimated by determining the creatinine accumulation in the dialysate loop. Blood samples were collected at 30-min intervals during the 2-hr experiment, and dialysate samples at 10-min intervals. Serum drug concentrations were used for all computations. Assay
Assay for ethambutol was made possible by the availability of 14Cethambutol prepared by Lederle Laboratories; 14C-labeled samples were counted by standard liquid scintillation methods. One milliliter plasma samples and dialysate samples were prepared in 1 ml Protosol and 15 ml Aquasol, and were counted in a Packard Tricarb
430
Christopher, Blair, Forrey, and Cutler
scintillation counter. Settings were optimized for 14C. The samples were quench-corrected by comparison with standards made up with varying amounts of hemoglobin to give a range of color-quenched standards. The samples were compared to AES ratio, and the DPMs were calculated by comparing the unknown samples to a computer-assisted least-squares regression line constructed from the quench standards. 169yb-D.T.P.A. concentrations were determined by gamma-ray spectrometer in a nuclear Chicago gamma counter. Creatinine concentrations in Renalyte-86 and plasma were determined by a Technicon Auto Analyzer II method, utilizing the Jaff6 reaction (1). In vivo flucytosine samples were analyzed by a high-pressure liquid chromatographic assay previously reported (2). A spectrophotometric assay was developed for the flucytosine in vitro samples. Nine standard flucytosine sample concentrations ranging from 0 to 20 mg/liter were measured at 280 nm with each assay. The spectrophotometer response was fitted by a first-degree polynomial using an unweighted least-squares technique. Predicted values for each sample concentration and the 95% confidence limits were computed. Laboratory dialysis studies of kanamycin, gentamicin, tobramycin, or amikacin were assayed by allowing the individual drug in Renalyte-86 to react with fluorescamine (Fluram, Roche Diagnostics, Nutley, New Jersey) by a modification of the method reported by Udenfriend et al. (3). Five microliters of 0.1 M borate buffer ( p H 9.7) was added to 1 ml of sample and mixed thoroughly. One milliliter of fluorescamine in 1,4-dioxan (30 mg/dl) was added to this mixture with rapid mixing on a vortex mixer. The resulting fluorescence, which was stable for 6 hr, was measured in a Turner model 430 fluorometer using 397-nm and 476-nm excitation and emission settings, respectively. These samples were compared to fresh standard solutions prepared identically. The results from the fluorescamine assay of the aminoglycoside antibiotics were treated in a similar fashion to those for flucytosine. The standards for the fluorescamine assay were linear from 0 to 5 mg/liter, which was the range used in this study. Above 5 mg/liter, the curve did not behave in a linear fashion because of fluorescence quenching~ Assays for gentamicin in patient studies were undertaken using the adenylating enzymatic method of Smith et al. (4), as modified by our laboratory (5). Procainamide concentrations from the in vitro experiments were measured by an autoanalyzer assay modified from the Bratton-Marshall (6) reaction normally used for para-aminohippurate. Plasma protein binding studies were undertaken by two techniques: (a) ultrafiltration of the drug dissolved in human plasma using Amicon Centriflo
Hemodialyzer Clearances of Various Drugs
431
cones (7), and (b) the column elution method of Hummel and Dreyer (8), as modified by Forrey et al. (7). Data Calculation
The equilibration of a test drug or creatinine between the dialysate and blood compartments, in both the in vitro and in vivo experiments, follows a monoexponential curve if the volumes of the reservoirs are held approximately constant. This is because the time constant for drug mixing within the compartments is much shorter than the time constant for equilibration between the compartments (9,10). A nonlinear least-squares curve-fitting program was employed to measure the overall time constant (K) for equilibration between compartments, using either equation 1 or equation 2. 3 The intercept of the ordinate at time T = 0, which is equal to ACo in equation 1 and Ct + B in equation 2, was used to confirm the dose of the drug and the volume of the injected compartment. The fitted asymptote, G, permitted measurement of the total volume of the system. The computed value for the time constant of equilibration K then permitted the dialysance D to be derived from equation 3, where Vo and V/~ represent the loop volumes. ACt = AC0 exp { - K T }
(1)
where the concentrating difference between compartments becomes zero at infinite time. G = Cr + B exp { - K T }
(2)
where the final equilibrium concentration Cf is found at infinite time. K = VD + VB D
(3)
VoV~ The term "dialysance" is used when recirculating systems are employed and thus the dialysate inlet concentrations are not zero. "Dialysance" is defined in equation 4, which shows how this reduces to a clearance in single-pass systems. In that situation, the dialysate inlet concentration, Co, equals 0 (equation 5). D = S / ( CB CL =
-
-
Co)
S/C.
3please see the Appendix for definitions of terms.
(4) (5)
Christopher, Blair, Forrey, and Cutler
432
Tablel. In Vitro Dialyzer Clearance Values (ml/min) Dow
Kiil
EX-03
UF II
24 + 2.26 25 • 5.0 18 • 2.1 27 + 2.3 52 • 1.5 65 • 3.4 113• 31 • 2.8 106 • 10
24 • 0.9 21 • 0.56 14 • 1.0 18 • 2.5 34 • 5.3 44 + 0.8 55• 24 • 1.9 60 • 6.4
30 • 1.7 28 • 3.0 23 • 3.8 27 • 0.7 42 + 0.95 59 • 1.6 85• 33 • 2.3 90 + 11
29 • 3.0 30 • 3.6 27 • 4.2 32 + 4.2 51 • 1.0 71 • 0.46 92+5.6 41 • 6.1 97 • 21
Drug a
Gentamicin Kanamycin Amikacin Tobramycin Ethambutol Procainarnide Flueytosine 169yb-D.T.P.A.
Creatinine a
Plasma protein binding has been measured for these drugs and has been shown to be < 10 go. '
"
9
O
I n the e x p e r i m e n t s described here, dialysance was m e a s u r e d . H o w e v e r , as can b e seen f r o m e q u a t i o n s 4 a n d 5, this is identical to the dialyzer c l e a r a n c e u n d e r single-pass conditions.
RESULTS T a b l e I shows the results of p l a s m a p r o t e i n b i n d i n g studies a n d clearance m e a s u r e m e n t s for different dialyzers in vitro. E a c h c l e a r a n c e value listed is the m e a n a n d s t a n d a r d d e v i a t i o n of at least t h r e e c l e a r a n c e e x p e r i m e n t s m e a s u r e d f r o m c o n c e n t r a t i o n decay curves as discussed. A c o m p a r i s o n of the p a t i e n t a n d l a b o r a t o r y clearance studies for g e n t a m i c i n , e t h a m b u t o l , a n d flucytosine is s h o w n in T a b l e II.
DISCUSSION T h e l a b o r a t o r y c l o s e d - l o o p m e t h o d that we have d e s c r i b e d here m a y be c o m p a r e d with clinical studies we have p r e v i o u s l y d e s c r i b e d (11) a n d
Table II. Comparison Between Patient and Laboratory Clearance Values (ml/min) Gentamicina
Dow Kiil
Ethambutolb
Flueytosinec
In vivo
In vitro
In vivo
In vitro
In vivo
In vitro
24 24
51
52 28
117
113
24
Christopher et al. (11). bChristopher et al. (19). CBlock et al. (15).
Hemodialyzer Clearances of Various Drugs
433
provides certain clearcut advantages, together with some disadvantages. These advantages include the following: 1. The avoidance of protein-containing solutions. Serum proteins have multiple effects on dialysis. These include solute binding, and adsorption to the nonbiological interfaces (12,13), thus changing the physiochemical properties of these interfaces. The contamination of membrane surfaces by proteins either makes it necessary for the membranes to be cleaned between dialyses, which may change the permeability characteristics of the membrane, or requires the use of a new dialyzer for each experiment. By avoiding protein-containing solutions, it is therefore possible to undertake repeated studies on the same dialyzer using different drugs without deterioration of performance. 2. An increase in data collection capability. Studies in dialysis patients are significantly hampered by the number of blood samples tolerable. This tends to reduce the number of data points which can be collected per experiment and may significantly degrade the quality of the data. 3. The measurement of mass balance. The presence of a closed system permits repeated verification of the total quantity of drug in the system, facilitating identification of spurious data points. The disadvantages of the in vitro technique are also evident. Thus the laboratory experiment, because of its freedom from the complications induced by red cells, serum proteins, and heparin administration during dialysis, may v~ot truly reflect the conditions seen during an actual dialysis. Thus protein contamination of dialyzer surfaces may induce a timedependent alteration of dialyzer function during a dialysis. The measurement of a dialyzer clearance with a homogeneous fluid also may not predict its performance with a multicompartment fluid such as blood. In the studies which we are reporting here, the laboratory experiments were undertaken repeatedly with the same dialyzers. We employed two marker molecules, both to verify the stability of dialyzer performance and for comparison with clinical results. These markers were creatinine and 169yb-D.T.P.A., which has a clearance similar to that of phosphate. The use of the two-compartment closed model with curve-fitting procedures provided a satisfactory analytical technique. Data analysis difficulties are encountered if significant ultrafiltration occurs, as this adds a convective flux of solute across the dialyzer and/or superimposes a constant rate of dilution of one compartment and concentration of the other compartment. This makes it necessary to use partial differential equations for data analysis and a more complex procedure for curve fitting. However, this was minimized by
434
Christopher, Blair, Forrey, and Cutler
keeping negative pressure across the dialyzer low. We are currently studying additional techniques by which this source of error can be further minimized. In the patient studies, we also employ a loop dialysis experiment. This permits us to avoid the use of A-V difference techniques for clearance measurement and to maintain the quality of measurement of clearance, while at the same time permitting a short experiment to be undetaken. As is well known, the A-V clearance method is based on the relationship Clearance -
QB ( CBi -- CBe )
CBi
(6)
This technique is satisfactory if the value (CBi - CBe) is large with respect to the error in the assay. However, in many situations, there may be a 5-10% error in the assay which may be greater than the magnitude of (CBi - Cne). ThUS very large errors in the estimation of clearance may result. Further complications are encountered because of the disequilibrium which may occur between the red cell and plasma (14). During the passage of blood through a dialyzer, substances may be trapped within red cells only to be re-equilibrated in the circulation. Thus blood collected from the venous effluent of a dialyzer will be undergoing a gradual re-equilibration of drug between the plasma and cells. If these cells are not rapidly separated, the final estimation for the dialyzer clearance will be lower than its true value. This problem is minimized by the dialysate loop method outlined in this article, since the rate of drug transport is estimated from the rate of change of dialysate concentrations of the drug. Currently, we utilize a Dow hollow fiber kidney, model 4, for all clinical studies. This dialyzer is chosen because of the somewhat lower ultrafiltration rate with it and because of its uniformity with'respect to clearance measurement. In general, the results obtained for gentamicin, ethambutol, and flucytosine show very good correlation between the laboratory and the patient studies in spite of the theoretical problems outlined. We are continuing our research in this area in order to determine whether all of our laboratory measurements can adequately predict results in patients. The data in Table I demonstrate that the aminoglycoside antibiotics are all rather poorly dialyzed relative to creatinine. Amikacin is not as well dialyzed as tobramycin or kanamycin. The results also demonstrate the much greater efficiency of the coil-type dialyzers and the Dow model 4 when compared with the standard Kiil. CLINICAL IMPLICATIONS The effect of intermittent dialysis on drug therapy adds a new dimension to the problems of drug administration in renal disease and almost
Hemodialyzer Clearances of Various Drugs
435
makes it mandatory for dialysis physicians to understand the principles of pharmacokinetics. The most useful concept in drug therapy in renal disease is that of the drug half-life. During parenteral drug therapy, one can selectively administer either one-half of a loading dose every half-life or three-quarters of a loading dose every two half-lives, etc. The selection of the dosage schedule is then based on the tolerable maximum and minimum drug concentrations. For those drugs dependent solely on renal function for their excretion, it has been shown that the half-life is proportional to the reciprocal of the glomerular filtration rate, and thus directly proportional to the serum creatinine (16-18). When hemodialysis is added to this situation, the half-life will be proportional to the reciprocal of the sum of all routes of clearance and the serum creatinine is no longer valid.
11/2 -
-
0.693 V CLm + CLr + CLD
(7)
Thus the plasma half-life for the patient on dialysis may need to be considered separately from the plasma half-life between dialyses. Furthermore, as the scheduling and duration of a dialysis treatment will be selected on clinical grounds alone, it will be difficult to predict the plasma concentrations for the drug without utilizing pharmacokinetic models. Previous experience has demonstrated the validity of a one-compartment pharmacokinetic model in regular thrice-weekly dialysis for gentamicin (10, 23). The major difficulty which remains is the effect of a change of dialysis schedule, a relatively common occurrence in patients treated in dialysis centers. As indicated earlier (11), this can cause a significant alteration in drug doses. We have therefore devised two nomograms which can be used for any drug-dialyzer combinations and for any dialysis schedule. The nomograms are based on a one-compartment model of dialysis in which drug concentration is given by
Ct= Coexp [ - - ~ 7]
(8)
Using these nomograms and tables of data as illustrated in Table III, drug concentration, either on or off dialysis, can be predicted; however, to simplify the utilization of the method, it is advisable to have a standardized drug administration pattern. It has proved to be clinically expedient that if a drug is significantly removed by dialysis then a dose of the drug will be given either before or after dialysis, with additional treatments at other times, if these are necessary. The size of dose which should be given must be based on an estimate of the residual drug in the patient at the time of administration.
436
Christopher, Blair, Forrey, and Cutler Table IIL PharmacokineticParameters for PlanningDrug Therapy a
Drug
Volume of distribution (ml/kg body weight)
Gentamicin (11)c Kanamycin (20) Amikacin (20) Tobramycin Flucytosine Procainamide (22) Ethambutol (19)
250 250 250 250 569 2000 800
Nonrenalb clearance (ml/min) 2 2 2 2 2 200 90
aTo obtain total clearance, add the nonrenal clearance to the estimated dialyzer
clearance and renal clearance. bEstimated from the literature. CReferencenumbers are given in parentheses.
Th~ nomogram (Fig. 2) permits the computation of drug half-life for renal failure patients either on or off dialysis. Several scales have been provided to encompass a wide range of kinetic parameters. This nomogram is used in conjunction with a second nomogram (Fig. 3) which also has paired scales that can be used to predict the residual concentration of a drug from the half-life and the time interval after administration. The model assumes that rapid absorption has occurred and thus is better for parenteral therapy. However, in patients with slow drug excretion, all forms of drug administration more closely approximate this model. It should be noted that the nomograms in Figs. 2 and 3 may be used for any drugs. For this reason, several paired scales have been included in each nomogram. Scales with similar letters should be used. The use of scales A - B would yield erroneous results. The most practical method to calculate drug therapy is to consider that an intravenous loading dose of a drug has been given immediately after a dialysis. Using the nomogram in Fig. 3 and knowledge of the drug half-life between dialyses, it is possible to predict the concentration of the drug prior to the next dialysis. If the drug half-life is considerably shorter than the interdialysis intervals, then the same nomogram (Fig. 3) can be used to select a dosage administration schedule which will permit several doses to be given so that the blood concentration does not fall below a desired minimum value, and so that a final dose can be given at the commencement of the next dialysis. This returns the concentration to its desired predialysis value and facilitates the computation of the postdialysis dose. Thus, in all patients, a predialysis dose and a postdialysis dose of a drug are planned.
437
Hemodialyzer Clearances of Various Drugs 0 I0 15 I 0 2O 15 4O 20 I0 5O 25 6O 30 15 r 7O 35 4020 8O I 9 0 45 g I00 5025 l l O 55 120 6 0 30 ~5 130 t 4 0 ~o 35 150 75 160 80 40 f70 8 5 180 9 0 4 5 190 9 5 2OO 100 50 2 1 0 105 22O I IO ~.r 230115 -' 24012060" 250125 F E O
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? - 5 5 0 I00 244896 234692 224488 214284 204080 I 93876 I 83672 '17 34 68 ~16 3 2 6 4 '15 3 0 6 0 14 2 8 5 6 "13 2 6 5 2 2448 II 2 2 4 4 I 0 20 4 0 9 18 36 8 16 32 7 1428 6 1224 5 I0 2 0 16 4 8 12 :3 6 4 8 I 2 4 0 0 0 D E F
.,~
~ o E O
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Fig. 2. Nomogram relating drug half-life, distribution volume, and plasma clearance (one-compartment model).
As an example of this technique, consider the administration of a drug whose concentration should not fall below 30% of the initial loading concentration. The drug has a nondialyzed half-life of 7 hr and the interdialysis interval is 48 hr. Using scale C of the nomogram (Fig. 3), it can be seen that the dosage interval should not be greater than every 12 hr or the plasma concentration will fall below one-third of the initial value. As this time interval is a .convenient fraction of the desired 48-hr interdialysis period, the drug could be given as two-thirds of the loading dose every 12 hr, which would result in optimal predialysis concentrations. Subsequently, if the half-life of the drug during dialysis is known, it is possible to calculate a suitable dose of drug which, at the end of dialysis, will again restore full blood concentrations. In order to simplify the determination of plasma half-life, the nomogram in Fig. 2 can be used in conjunction with Table III. Table III shows the estimated volumes of distribution and nonrenal clearances for the drugs
438
Christopher, Blair, Forrey, and Cutler 0 4 8
I
3 .J
"T
E
12 16 2O 24 28 32 36 4O 44 48 52 56 60 64 68 72 76 80 84 88 92 96 I00 c
2
4 6 8
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16
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18 20 22
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24
12
28 30 32 34 36 38
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I
2
4
0 A
0 B
0 C
~:
I o J ~) "~ -> $
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Fig. 3. Nomogramfor calculatingresidualdrug concentrationfromknowndrug half-life and elapsedtime.
listed. From the patient's total body weight, the total volume of distribution of a drug can be estimated. Using this value, and estimating the total plasma clearance (which may need to include the clearance due to dialysis), the plasma half-life can' be computed using Fig. 2. In some situations, the addition of the dialyzer clearance to the plasma clearance will not greatly alter the total plasma clearance, and thus will not greatly alter the plasma half-life. In this situation, the effect of dialysis may be neglected. Table III shows clearly that the clearance of gentamicin may be increased by a factor of 10 by hemodialysis. However, the plasma clearance of procainamide is increased only 25% by dialysis. During dialysis, procainamide half-life in a 70-kg person might be minimally reduced from 789hr to 6 hr. Thus the importance of the dialyzer clearance of a drug must be assessed by the relative increase in plasma clearance due to dialysis and the duration of the dialysis, not by the absolute magnitude of the change in clearance. The same
Hemodialyzer Clearances of Various Drugs
439
principle holds for the efficiency of hemodialysis in the treatment of drug intoxication. The importance of knowing the specific drug-handling characteristics of a dialyzer when making dialysis predictions may be seen from an example. A typical aminoglycoside antibiotic has no plasma protein binding (21) and has a volume of distribution of approximately 25% of the total body weight. The plasma clearance values calculated from Table III suggest that a 6-hr dialysis with a coil dialyzer in a 70-kg patient will result in a final drug concentration which is approximately 53% of the starting concentration. In order to remove the same amount of drug with a Kiil, approximately 9 hr of dialysis will be required. If, on the other hand, a 6-hr Kiil dialysis is administered, the final drug concentration will be approximately 65 % of the initial value. Thus a 6-hr Kiil hemodialysis in a patient with no other route for aminoglycoside elimination could remove 35% of the dose, whereas a 6-hr treatment with a more efficient dialyzer under similar circumstances could remove 47% of the drug. In a repetitive dosing regimen, these differences could cause the peak blood concentrations in the Kiil dialysis patient to be 30% higher than in the patient receiving treatment by a coil dialyzer. In general, the practice of dialyzing patients to maintain a predialysis creatinine concentration below 12 mg/dl will minimize these differences. However, if the treatment times for all dialyzers are equalized, then it can be seen that in borderline undertreatment or overtreatment situations this phenomenon may be important. SUMMARY
The data presented show that quite marked differences in drug clearance can be expected from different dialyzers. Those drugs which are entirely dependent on dialysis for their elimination may thus demonstrate considerable differences in half-life, depending on the dialyzer employed. The management of hemodialysis patients in whom there are many changing variables, including body size, dialysis schedule, drug metabolism, and desirable blood concentration, is particularly difficult. In order to simplify this process, two nomograms have been provided which will facilitate the optimizations of the drug therapeutic regimen to the particular clinical situation which may be encountered. APPENDIX
B = a constant determined by the initial conditions of the experiment. C = solute concentration measured in the reservoir (in either blood or dialysate).
Christopher, Blair, Forrey, and Cutler
440
A C = concentration difference between blood and dialysate in the reservoir, i.e., the difference between c o m p a r t m e n t concentrations. K = time constant obtained from curve-tilting procedure. D = dialysance of the dialyzer. Q = flow rate (blood or dialysate). S = rate of drug transport across dialyzer. T = time. V = c o m p a r t m e n t volume. CL = clearance. Subscripts: 0 = at time 0. t = at time t. f = final (at T = ~ ) . i = dialyzer inlet. e = dialyzer outlet. B = blood side. D = dialysate side. CLm = metabolic clearance. CLr = renal clearance. C L o = dialyzer clearance.
ACKNOWLEDGMENTS E X - 0 3 and EX-23 dialyzers were kindly supplied by Extracorporeal Corporation. U F II was kindly supplied by Travenol Corporation.
REFERENCES 1. R. J. Henry. Clinical Chemistry Techniques and Principles, Harper and Row, New York, 1965, p. 288. 2. A. D. Blair, A. W. Forrey, B. T. Meijsen, and R. E. Cutler. Assay of 5-flucytosine and furosemide by high pressure liquid chromatography. J. Pharm. Sci. 64:1334-1339 (1975). 3. S. Udenfriend, S. Stein, P. Bohlen, W. Dairman, W. Leimgruber, and M. Weigele. Fluorescamine; a reagent for assay of amino acids, peptides, proteins, and nrimary amines in the picomole range. Science 178:871-872 (1972). 4. D. H. Smith, C. Van Otto, and A. L. Smith. A rapid chemical assay for gentamicin. New Engl. J. Med. 286:583-586 (1972). 5. A. W. Forrey, A. D. Blair, M. O'Neill, R. E. Cutler, and T. G. Christopher. Enzymatic assay for gentamicin (letter to editor). New Engl. J. Med. 288:108 (1973). 6. A. C. Bratton and E. K. Marshall. A new coupling component for sulfanilamide determinations. J. Biol. Chem. 128:537-550 (1939). 7. A. W. Forrey, B. Kimpel, A. D. Blair, and R. E. Cutler. Furosemide concentrations in serum and urine, and its binding by serum proteins as measured fluorometrically. Clin. Chem. 20:152-158 (1974). 8. J. P. Hummel and W. J. Dreyer. Measurement of protein binding phenomena by gel filtration. Biochim. Biophys. Acta 63:532-534 (1962).
Hemodialyzer Clearances of Various Drugs
441
9. C. P. Ramos, T. G. Christopher, C. J. Maurer, B. H. Scribner, and A. L. Babb. Mass transfer resistance determination of slowly dialyzed molecules with applications to the p H dependence of phosphate dialysis. Trans. Am. Soc. A m f . Intern. Org. 16:150--154 (1970). 10. C. M. Collins, G. Buffaloe, and K. C. Kuruvila. Dialysate closed loop method for in vivo determination of middle molecular weight clearances. Proc. Clin. Dial. Transplant. Forum 3:234-241 (1973). 11. T. G. Christopher, D. Korn, A. D. Blair, A. W. Forrey, M. A. O'Neill, and R. E. Cutler. Gentamicin pharmacokinetics during hemodialysis. Kidney Int. 6:38-44 (1974). 12. R. C. Dutton, R. E. Baier, R. L. Dedrick, and R. L. Bowman. Initial thrombus formation on foreign surfaces. Trans. Am. Soc. Arttf. Intern. Org. 14:57-62 (1968). 13. L. A. Jacobs, E. Klopp, and V. L. Gott. Studies on the fibrinolytic removal of thrombus from prosthetic surfaces. Trans. Am. Soc. Artif. Intern. Org. 14:63-67 (1968). 14. A. L. Babb, R. P. Popovich, P. L. Farrell, and C. R. Blagg. The effect of erythrocyte mass transfer rates on solute clearance measurements during hemodialysis. Proc. Eur. Dial Transplant. Assoc. 9:303-321 (1972). 15. E.R. Block, J. E. Bennett, L. G. Livoti, W. J. Klein, R. R. MacGregor, and L. Henderson. Flucytosine and amphotericin B hemodialysis effects on the plasma concentration and clearance. Ann. Intern. Med. 80:613-617 (1974). 16. R. E. Cutler and B. M. Orme. Correlation of serum creatinine concentration and kanamycin half-life: Therapeutic implication. J. Am. Med. Assoc. 21}9:539-542 (1969). 17. R. E. Cutler, A. M. Gysetynck, W. P. Fleet, and A. W. Forrey. Correlation of serum creatinine concentration and gentamicin half-life. J. Am. Med. Assoc. 219:1037-1041 (1972). 18. M. C. McHenry, T. L. Gavan, R. W. Gifford, N. A. Geurkink, R. A. Van Ommen, M. A. Town, and J. G. Wagner. Gentamicin dosages for renal insufficiency; adjustments based on endogenous creatinine clearance and serum creatinine concentration. Ann. Intern. Med. 74:192-197 (1971). 19. T. G. Christopher, A. D. Blair, A. W. Forrey, and R. E. Cutler. Kinetics of ethambutol elimination in renal disease. Proc. Dial. Transplant. Forum 3:96-101 (1973). 20. J.T. Clarke, R. D. Libke, C. Regamey, and W. M. Kirby. Comparative pharmacokinetics of amikacin and kanamycin. Clin. Pharm. Ther. 15:610-616 (1974). 21. R. C. Gordon, C. Regamey, and W. M. Kirby. Serum protein binding of the aminoglycoside antibiotics. Antimicrob. Agents Chemother. 2:214-216 (1972). 22. K. J. Simons, R. H. Levy, R. E. Cutler, and T. G. Christopher. Dependence of procainamide clearance on renal function in humans. Paper presented at APhA Academy of Pharmaceutical Sciences meeting, New Orleans, November 1974. 23. M. Danish, R. Schultz, and W. J. Juslco. Pharmacokinetics of gentamicin and kanamycin during hemodialysis. Antimicrob. Agents Chemother. 6:841-847 (1974).
Hemodialyzer Clearancesof Gentamicin, Kanamycin, Tobramycin, Amikacin, Ethambutol, Procainamide, and Flucytosine, with a Technique for Planning Therapy T. Graham Christopher, 2 A n d r e w D. Blair, 2 Arden W. Forrey, 2 and Ralph E. Cutler 2
Received Nov. 4, 1975--Final May 3, 1976
Hemodialyzer clearance studies have been undertaken on the following drugs: gentamicin, kanamycin, tobramycin, amikacin, ethambutol, procainamide, and flucytosine. The following hemodialyzers were tested: Dow model4, Kiil, Travenol UF II, and the Extracorporeal EX-03. The studies were predominantly undertaken in vitro, permitting direct comparison between drug clearances on the same dialyzer. Protein binding studies for gentamicin, kanamycin, procainamide, and ethambutol are also reported. Nomograms to facilitate the prediction of drug dosage regimens in dialysis patients are included. KEY WORDS: dialysis; drugs; renal failure; gentamicin; kanamycin; tobramycin; amikacin; ethambutol; procainamide; flucytosine.
INTRODUCTION
Hemodialyzer clearance values have been reported for many drugs and different types of hemodialyzers. Many of these reports have included measurements of only a single dialyzer or have relied on changes in the drug This work was supported in part by a grant from the General Clinical Research Centers Program (RR- 133) of the Division of Research Resources, National Institutes of Health, and by a research contract (2-2219) from the Artificial Kidney-Chronic Uremia Program of the National Institute of Arthritis, Metabolism, and Digestive Diseases, National Institutes of Health. 1 . . . . This paper was presented m .part at the American Sooety of Nephrology meeting, 1974. 2University of Washington, School of Medicine, Department of Medicine, Harborview Medical Center, Seattle, Washington 98104. 427 9 1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.
428
Christopher, Blair, Forrey, and Cutler
concentration decay curves in patients during hemodialysis for the estimation of dialyzer clearances. In many cases, the measurements have taken place in patients taking overdoses of drugs or under nonstandard conditions. This study represents a comparison between different models of hemodialyzers and different drugs under controlled laboratory and clinical conditions. Comparisons between laboratory clearance measurements and those made during the dialysis of patients have been made for some of these drugs. This report discusses dialysance measurements for the Dow model 4 hollow fiber kidney, the standard 1.0-m 2 Kiil, the Extracorporeal EX-03, and the Travenol Ultraflow II, standard model. Drugs which have been studied include gentamicin, kanamycin, ethambutol, procainamide, amikacin (BB-K8), tobramycin, 5-flucytosine, and two comparative marker molecules, creatinine and 169yb-D.T.P.A. The last compound is 603 daltons and has a hemodialyzer clearance similar to that of phosphate. Two nomograms intended to simplify the administration of drugs to dialysis patients are presented. These nomograms are based on a one-compartment model of dialysis. It should be noted that the word "clearance" is used interchangeably with "dialysance" for reasons which are explained in the text. This is done purposely to facilitate clinical utilization of the data. MATERIALS AND METHODS Dialysis Methods
Laboratory dialyzer studies were undertaken with the double-loop recirculating system illustrated in Fig. 1. A standard dialysate solution (Renalyte-86, diluted 35 : 1 with deaerated, deionized water) was employed, both as blood simulant and in the dialysate compartment. Two reservoirs were prepared, each of 2 liters. The blood simulant was circulated through the dialyzer from one reservoir at 200 ml/min, using a blood pump. The dialysate was recirculated through the dialyzer in a countercurrent manner
Blood
E~
J
Dialyzer
F
Pomp Rewarmer Calibrated Flask
Fig. 1. Diagram of dialysate loop.
Hemodialyzer Clearances of Various Drugs
429
at 460 ml/min from another 2-liter reservoir. Both reservoirs were continuously agitated by magnetic stirrers. No "negative" transmembrane pressure was applied to the dialyzer. The transmembrane pressures were thus developed solely by the hydrodynamic characteristics of the blood and dialysate compartments of each dialyzer. In the coil dialyzers, the recirculating dialysate volume was 7 liters. This represents the volume of the holding tank for the dialyzer cartridge. The dialysate was circulated transversely across the coils at the standard recirculating dialysate flow rate (Drake Willock unit). At the commencement of the experiment, the test drug, together with 1/x Ci of 169yb-D.T.P.A. and/or 300 mg creatinine, was thoroughly mixed in the blood side reservoir with the blood pump turned off. At zero time, the blood pump was started. Samples from both the blood and dialysate reservoirs were taken at 5-min intervals for 2-389hr, depending on the drug dialysance. The concentration differences between compartments were measured as a function of time. Experiments with gentamicin and 14C-ethambutol were undertaken in a test dialysis in patients with stable chronic renal failure requiring hemodialysis, and without acute intercurrent illness. Clearances were measured by a similar technique to that described for the in vitro experiments. A closed recirculating dialysate loop was used with a total volume of 1.0-1.5 liters. Dialysate was recirculated at 500 ml/min with no ultrafiltration pressure. Blood flow was held constant at 200 ml/min by a blood pump. Drug clearances in different experiments were measured by dialyzing drug either from the dialysate loop to the patient or from the patient to the dialysate. In the gentamicin studies, the drug was dialyzed into the patient. In the ethambutol experiments in patients, the clearance measurements were undertaken in both directions. In this latter study, the blood-todialysate experiment was commenced 1 hr after the parenteral administration of ~4C-ethambutol in order to minimize the likelihood of the presence of ethambutol metabolites, which may be expected to progressively accumulate. In all studies, creatinine clearance was estimated by determining the creatinine accumulation in the dialysate loop. Blood samples were collected at 30-min intervals during the 2-hr experiment, and dialysate samples at 10-min intervals. Serum drug concentrations were used for all computations. Assay
Assay for ethambutol was made possible by the availability of 14Cethambutol prepared by Lederle Laboratories; 14C-labeled samples were counted by standard liquid scintillation methods. One milliliter plasma samples and dialysate samples were prepared in 1 ml Protosol and 15 ml Aquasol, and were counted in a Packard Tricarb
430
Christopher, Blair, Forrey, and Cutler
scintillation counter. Settings were optimized for 14C. The samples were quench-corrected by comparison with standards made up with varying amounts of hemoglobin to give a range of color-quenched standards. The samples were compared to AES ratio, and the DPMs were calculated by comparing the unknown samples to a computer-assisted least-squares regression line constructed from the quench standards. 169yb-D.T.P.A. concentrations were determined by gamma-ray spectrometer in a nuclear Chicago gamma counter. Creatinine concentrations in Renalyte-86 and plasma were determined by a Technicon Auto Analyzer II method, utilizing the Jaff6 reaction (1). In vivo flucytosine samples were analyzed by a high-pressure liquid chromatographic assay previously reported (2). A spectrophotometric assay was developed for the flucytosine in vitro samples. Nine standard flucytosine sample concentrations ranging from 0 to 20 mg/liter were measured at 280 nm with each assay. The spectrophotometer response was fitted by a first-degree polynomial using an unweighted least-squares technique. Predicted values for each sample concentration and the 95% confidence limits were computed. Laboratory dialysis studies of kanamycin, gentamicin, tobramycin, or amikacin were assayed by allowing the individual drug in Renalyte-86 to react with fluorescamine (Fluram, Roche Diagnostics, Nutley, New Jersey) by a modification of the method reported by Udenfriend et al. (3). Five microliters of 0.1 M borate buffer ( p H 9.7) was added to 1 ml of sample and mixed thoroughly. One milliliter of fluorescamine in 1,4-dioxan (30 mg/dl) was added to this mixture with rapid mixing on a vortex mixer. The resulting fluorescence, which was stable for 6 hr, was measured in a Turner model 430 fluorometer using 397-nm and 476-nm excitation and emission settings, respectively. These samples were compared to fresh standard solutions prepared identically. The results from the fluorescamine assay of the aminoglycoside antibiotics were treated in a similar fashion to those for flucytosine. The standards for the fluorescamine assay were linear from 0 to 5 mg/liter, which was the range used in this study. Above 5 mg/liter, the curve did not behave in a linear fashion because of fluorescence quenching~ Assays for gentamicin in patient studies were undertaken using the adenylating enzymatic method of Smith et al. (4), as modified by our laboratory (5). Procainamide concentrations from the in vitro experiments were measured by an autoanalyzer assay modified from the Bratton-Marshall (6) reaction normally used for para-aminohippurate. Plasma protein binding studies were undertaken by two techniques: (a) ultrafiltration of the drug dissolved in human plasma using Amicon Centriflo
Hemodialyzer Clearances of Various Drugs
431
cones (7), and (b) the column elution method of Hummel and Dreyer (8), as modified by Forrey et al. (7). Data Calculation
The equilibration of a test drug or creatinine between the dialysate and blood compartments, in both the in vitro and in vivo experiments, follows a monoexponential curve if the volumes of the reservoirs are held approximately constant. This is because the time constant for drug mixing within the compartments is much shorter than the time constant for equilibration between the compartments (9,10). A nonlinear least-squares curve-fitting program was employed to measure the overall time constant (K) for equilibration between compartments, using either equation 1 or equation 2. 3 The intercept of the ordinate at time T = 0, which is equal to ACo in equation 1 and Ct + B in equation 2, was used to confirm the dose of the drug and the volume of the injected compartment. The fitted asymptote, G, permitted measurement of the total volume of the system. The computed value for the time constant of equilibration K then permitted the dialysance D to be derived from equation 3, where Vo and V/~ represent the loop volumes. ACt = AC0 exp { - K T }
(1)
where the concentrating difference between compartments becomes zero at infinite time. G = Cr + B exp { - K T }
(2)
where the final equilibrium concentration Cf is found at infinite time. K = VD + VB D
(3)
VoV~ The term "dialysance" is used when recirculating systems are employed and thus the dialysate inlet concentrations are not zero. "Dialysance" is defined in equation 4, which shows how this reduces to a clearance in single-pass systems. In that situation, the dialysate inlet concentration, Co, equals 0 (equation 5). D = S / ( CB CL =
-
-
Co)
S/C.
3please see the Appendix for definitions of terms.
(4) (5)
Christopher, Blair, Forrey, and Cutler
432
Tablel. In Vitro Dialyzer Clearance Values (ml/min) Dow
Kiil
EX-03
UF II
24 + 2.26 25 • 5.0 18 • 2.1 27 + 2.3 52 • 1.5 65 • 3.4 113• 31 • 2.8 106 • 10
24 • 0.9 21 • 0.56 14 • 1.0 18 • 2.5 34 • 5.3 44 + 0.8 55• 24 • 1.9 60 • 6.4
30 • 1.7 28 • 3.0 23 • 3.8 27 • 0.7 42 + 0.95 59 • 1.6 85• 33 • 2.3 90 + 11
29 • 3.0 30 • 3.6 27 • 4.2 32 + 4.2 51 • 1.0 71 • 0.46 92+5.6 41 • 6.1 97 • 21
Drug a
Gentamicin Kanamycin Amikacin Tobramycin Ethambutol Procainarnide Flueytosine 169yb-D.T.P.A.
Creatinine a
Plasma protein binding has been measured for these drugs and has been shown to be < 10 go. '
"
9
O
I n the e x p e r i m e n t s described here, dialysance was m e a s u r e d . H o w e v e r , as can b e seen f r o m e q u a t i o n s 4 a n d 5, this is identical to the dialyzer c l e a r a n c e u n d e r single-pass conditions.
RESULTS T a b l e I shows the results of p l a s m a p r o t e i n b i n d i n g studies a n d clearance m e a s u r e m e n t s for different dialyzers in vitro. E a c h c l e a r a n c e value listed is the m e a n a n d s t a n d a r d d e v i a t i o n of at least t h r e e c l e a r a n c e e x p e r i m e n t s m e a s u r e d f r o m c o n c e n t r a t i o n decay curves as discussed. A c o m p a r i s o n of the p a t i e n t a n d l a b o r a t o r y clearance studies for g e n t a m i c i n , e t h a m b u t o l , a n d flucytosine is s h o w n in T a b l e II.
DISCUSSION T h e l a b o r a t o r y c l o s e d - l o o p m e t h o d that we have d e s c r i b e d here m a y be c o m p a r e d with clinical studies we have p r e v i o u s l y d e s c r i b e d (11) a n d
Table II. Comparison Between Patient and Laboratory Clearance Values (ml/min) Gentamicina
Dow Kiil
Ethambutolb
Flueytosinec
In vivo
In vitro
In vivo
In vitro
In vivo
In vitro
24 24
51
52 28
117
113
24
Christopher et al. (11). bChristopher et al. (19). CBlock et al. (15).
Hemodialyzer Clearances of Various Drugs
433
provides certain clearcut advantages, together with some disadvantages. These advantages include the following: 1. The avoidance of protein-containing solutions. Serum proteins have multiple effects on dialysis. These include solute binding, and adsorption to the nonbiological interfaces (12,13), thus changing the physiochemical properties of these interfaces. The contamination of membrane surfaces by proteins either makes it necessary for the membranes to be cleaned between dialyses, which may change the permeability characteristics of the membrane, or requires the use of a new dialyzer for each experiment. By avoiding protein-containing solutions, it is therefore possible to undertake repeated studies on the same dialyzer using different drugs without deterioration of performance. 2. An increase in data collection capability. Studies in dialysis patients are significantly hampered by the number of blood samples tolerable. This tends to reduce the number of data points which can be collected per experiment and may significantly degrade the quality of the data. 3. The measurement of mass balance. The presence of a closed system permits repeated verification of the total quantity of drug in the system, facilitating identification of spurious data points. The disadvantages of the in vitro technique are also evident. Thus the laboratory experiment, because of its freedom from the complications induced by red cells, serum proteins, and heparin administration during dialysis, may v~ot truly reflect the conditions seen during an actual dialysis. Thus protein contamination of dialyzer surfaces may induce a timedependent alteration of dialyzer function during a dialysis. The measurement of a dialyzer clearance with a homogeneous fluid also may not predict its performance with a multicompartment fluid such as blood. In the studies which we are reporting here, the laboratory experiments were undertaken repeatedly with the same dialyzers. We employed two marker molecules, both to verify the stability of dialyzer performance and for comparison with clinical results. These markers were creatinine and 169yb-D.T.P.A., which has a clearance similar to that of phosphate. The use of the two-compartment closed model with curve-fitting procedures provided a satisfactory analytical technique. Data analysis difficulties are encountered if significant ultrafiltration occurs, as this adds a convective flux of solute across the dialyzer and/or superimposes a constant rate of dilution of one compartment and concentration of the other compartment. This makes it necessary to use partial differential equations for data analysis and a more complex procedure for curve fitting. However, this was minimized by
434
Christopher, Blair, Forrey, and Cutler
keeping negative pressure across the dialyzer low. We are currently studying additional techniques by which this source of error can be further minimized. In the patient studies, we also employ a loop dialysis experiment. This permits us to avoid the use of A-V difference techniques for clearance measurement and to maintain the quality of measurement of clearance, while at the same time permitting a short experiment to be undetaken. As is well known, the A-V clearance method is based on the relationship Clearance -
QB ( CBi -- CBe )
CBi
(6)
This technique is satisfactory if the value (CBi - CBe) is large with respect to the error in the assay. However, in many situations, there may be a 5-10% error in the assay which may be greater than the magnitude of (CBi - Cne). ThUS very large errors in the estimation of clearance may result. Further complications are encountered because of the disequilibrium which may occur between the red cell and plasma (14). During the passage of blood through a dialyzer, substances may be trapped within red cells only to be re-equilibrated in the circulation. Thus blood collected from the venous effluent of a dialyzer will be undergoing a gradual re-equilibration of drug between the plasma and cells. If these cells are not rapidly separated, the final estimation for the dialyzer clearance will be lower than its true value. This problem is minimized by the dialysate loop method outlined in this article, since the rate of drug transport is estimated from the rate of change of dialysate concentrations of the drug. Currently, we utilize a Dow hollow fiber kidney, model 4, for all clinical studies. This dialyzer is chosen because of the somewhat lower ultrafiltration rate with it and because of its uniformity with'respect to clearance measurement. In general, the results obtained for gentamicin, ethambutol, and flucytosine show very good correlation between the laboratory and the patient studies in spite of the theoretical problems outlined. We are continuing our research in this area in order to determine whether all of our laboratory measurements can adequately predict results in patients. The data in Table I demonstrate that the aminoglycoside antibiotics are all rather poorly dialyzed relative to creatinine. Amikacin is not as well dialyzed as tobramycin or kanamycin. The results also demonstrate the much greater efficiency of the coil-type dialyzers and the Dow model 4 when compared with the standard Kiil. CLINICAL IMPLICATIONS The effect of intermittent dialysis on drug therapy adds a new dimension to the problems of drug administration in renal disease and almost
Hemodialyzer Clearances of Various Drugs
435
makes it mandatory for dialysis physicians to understand the principles of pharmacokinetics. The most useful concept in drug therapy in renal disease is that of the drug half-life. During parenteral drug therapy, one can selectively administer either one-half of a loading dose every half-life or three-quarters of a loading dose every two half-lives, etc. The selection of the dosage schedule is then based on the tolerable maximum and minimum drug concentrations. For those drugs dependent solely on renal function for their excretion, it has been shown that the half-life is proportional to the reciprocal of the glomerular filtration rate, and thus directly proportional to the serum creatinine (16-18). When hemodialysis is added to this situation, the half-life will be proportional to the reciprocal of the sum of all routes of clearance and the serum creatinine is no longer valid.
11/2 -
-
0.693 V CLm + CLr + CLD
(7)
Thus the plasma half-life for the patient on dialysis may need to be considered separately from the plasma half-life between dialyses. Furthermore, as the scheduling and duration of a dialysis treatment will be selected on clinical grounds alone, it will be difficult to predict the plasma concentrations for the drug without utilizing pharmacokinetic models. Previous experience has demonstrated the validity of a one-compartment pharmacokinetic model in regular thrice-weekly dialysis for gentamicin (10, 23). The major difficulty which remains is the effect of a change of dialysis schedule, a relatively common occurrence in patients treated in dialysis centers. As indicated earlier (11), this can cause a significant alteration in drug doses. We have therefore devised two nomograms which can be used for any drug-dialyzer combinations and for any dialysis schedule. The nomograms are based on a one-compartment model of dialysis in which drug concentration is given by
Ct= Coexp [ - - ~ 7]
(8)
Using these nomograms and tables of data as illustrated in Table III, drug concentration, either on or off dialysis, can be predicted; however, to simplify the utilization of the method, it is advisable to have a standardized drug administration pattern. It has proved to be clinically expedient that if a drug is significantly removed by dialysis then a dose of the drug will be given either before or after dialysis, with additional treatments at other times, if these are necessary. The size of dose which should be given must be based on an estimate of the residual drug in the patient at the time of administration.
436
Christopher, Blair, Forrey, and Cutler Table IIL PharmacokineticParameters for PlanningDrug Therapy a
Drug
Volume of distribution (ml/kg body weight)
Gentamicin (11)c Kanamycin (20) Amikacin (20) Tobramycin Flucytosine Procainamide (22) Ethambutol (19)
250 250 250 250 569 2000 800
Nonrenalb clearance (ml/min) 2 2 2 2 2 200 90
aTo obtain total clearance, add the nonrenal clearance to the estimated dialyzer
clearance and renal clearance. bEstimated from the literature. CReferencenumbers are given in parentheses.
Th~ nomogram (Fig. 2) permits the computation of drug half-life for renal failure patients either on or off dialysis. Several scales have been provided to encompass a wide range of kinetic parameters. This nomogram is used in conjunction with a second nomogram (Fig. 3) which also has paired scales that can be used to predict the residual concentration of a drug from the half-life and the time interval after administration. The model assumes that rapid absorption has occurred and thus is better for parenteral therapy. However, in patients with slow drug excretion, all forms of drug administration more closely approximate this model. It should be noted that the nomograms in Figs. 2 and 3 may be used for any drugs. For this reason, several paired scales have been included in each nomogram. Scales with similar letters should be used. The use of scales A - B would yield erroneous results. The most practical method to calculate drug therapy is to consider that an intravenous loading dose of a drug has been given immediately after a dialysis. Using the nomogram in Fig. 3 and knowledge of the drug half-life between dialyses, it is possible to predict the concentration of the drug prior to the next dialysis. If the drug half-life is considerably shorter than the interdialysis intervals, then the same nomogram (Fig. 3) can be used to select a dosage administration schedule which will permit several doses to be given so that the blood concentration does not fall below a desired minimum value, and so that a final dose can be given at the commencement of the next dialysis. This returns the concentration to its desired predialysis value and facilitates the computation of the postdialysis dose. Thus, in all patients, a predialysis dose and a postdialysis dose of a drug are planned.
437
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Fig. 2. Nomogram relating drug half-life, distribution volume, and plasma clearance (one-compartment model).
As an example of this technique, consider the administration of a drug whose concentration should not fall below 30% of the initial loading concentration. The drug has a nondialyzed half-life of 7 hr and the interdialysis interval is 48 hr. Using scale C of the nomogram (Fig. 3), it can be seen that the dosage interval should not be greater than every 12 hr or the plasma concentration will fall below one-third of the initial value. As this time interval is a .convenient fraction of the desired 48-hr interdialysis period, the drug could be given as two-thirds of the loading dose every 12 hr, which would result in optimal predialysis concentrations. Subsequently, if the half-life of the drug during dialysis is known, it is possible to calculate a suitable dose of drug which, at the end of dialysis, will again restore full blood concentrations. In order to simplify the determination of plasma half-life, the nomogram in Fig. 2 can be used in conjunction with Table III. Table III shows the estimated volumes of distribution and nonrenal clearances for the drugs
438
Christopher, Blair, Forrey, and Cutler 0 4 8
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E
12 16 2O 24 28 32 36 4O 44 48 52 56 60 64 68 72 76 80 84 88 92 96 I00 c
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~:
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Fig. 3. Nomogramfor calculatingresidualdrug concentrationfromknowndrug half-life and elapsedtime.
listed. From the patient's total body weight, the total volume of distribution of a drug can be estimated. Using this value, and estimating the total plasma clearance (which may need to include the clearance due to dialysis), the plasma half-life can' be computed using Fig. 2. In some situations, the addition of the dialyzer clearance to the plasma clearance will not greatly alter the total plasma clearance, and thus will not greatly alter the plasma half-life. In this situation, the effect of dialysis may be neglected. Table III shows clearly that the clearance of gentamicin may be increased by a factor of 10 by hemodialysis. However, the plasma clearance of procainamide is increased only 25% by dialysis. During dialysis, procainamide half-life in a 70-kg person might be minimally reduced from 789hr to 6 hr. Thus the importance of the dialyzer clearance of a drug must be assessed by the relative increase in plasma clearance due to dialysis and the duration of the dialysis, not by the absolute magnitude of the change in clearance. The same
Hemodialyzer Clearances of Various Drugs
439
principle holds for the efficiency of hemodialysis in the treatment of drug intoxication. The importance of knowing the specific drug-handling characteristics of a dialyzer when making dialysis predictions may be seen from an example. A typical aminoglycoside antibiotic has no plasma protein binding (21) and has a volume of distribution of approximately 25% of the total body weight. The plasma clearance values calculated from Table III suggest that a 6-hr dialysis with a coil dialyzer in a 70-kg patient will result in a final drug concentration which is approximately 53% of the starting concentration. In order to remove the same amount of drug with a Kiil, approximately 9 hr of dialysis will be required. If, on the other hand, a 6-hr Kiil dialysis is administered, the final drug concentration will be approximately 65 % of the initial value. Thus a 6-hr Kiil hemodialysis in a patient with no other route for aminoglycoside elimination could remove 35% of the dose, whereas a 6-hr treatment with a more efficient dialyzer under similar circumstances could remove 47% of the drug. In a repetitive dosing regimen, these differences could cause the peak blood concentrations in the Kiil dialysis patient to be 30% higher than in the patient receiving treatment by a coil dialyzer. In general, the practice of dialyzing patients to maintain a predialysis creatinine concentration below 12 mg/dl will minimize these differences. However, if the treatment times for all dialyzers are equalized, then it can be seen that in borderline undertreatment or overtreatment situations this phenomenon may be important. SUMMARY
The data presented show that quite marked differences in drug clearance can be expected from different dialyzers. Those drugs which are entirely dependent on dialysis for their elimination may thus demonstrate considerable differences in half-life, depending on the dialyzer employed. The management of hemodialysis patients in whom there are many changing variables, including body size, dialysis schedule, drug metabolism, and desirable blood concentration, is particularly difficult. In order to simplify this process, two nomograms have been provided which will facilitate the optimizations of the drug therapeutic regimen to the particular clinical situation which may be encountered. APPENDIX
B = a constant determined by the initial conditions of the experiment. C = solute concentration measured in the reservoir (in either blood or dialysate).
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A C = concentration difference between blood and dialysate in the reservoir, i.e., the difference between c o m p a r t m e n t concentrations. K = time constant obtained from curve-tilting procedure. D = dialysance of the dialyzer. Q = flow rate (blood or dialysate). S = rate of drug transport across dialyzer. T = time. V = c o m p a r t m e n t volume. CL = clearance. Subscripts: 0 = at time 0. t = at time t. f = final (at T = ~ ) . i = dialyzer inlet. e = dialyzer outlet. B = blood side. D = dialysate side. CLm = metabolic clearance. CLr = renal clearance. C L o = dialyzer clearance.
ACKNOWLEDGMENTS E X - 0 3 and EX-23 dialyzers were kindly supplied by Extracorporeal Corporation. U F II was kindly supplied by Travenol Corporation.
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9. C. P. Ramos, T. G. Christopher, C. J. Maurer, B. H. Scribner, and A. L. Babb. Mass transfer resistance determination of slowly dialyzed molecules with applications to the p H dependence of phosphate dialysis. Trans. Am. Soc. A m f . Intern. Org. 16:150--154 (1970). 10. C. M. Collins, G. Buffaloe, and K. C. Kuruvila. Dialysate closed loop method for in vivo determination of middle molecular weight clearances. Proc. Clin. Dial. Transplant. Forum 3:234-241 (1973). 11. T. G. Christopher, D. Korn, A. D. Blair, A. W. Forrey, M. A. O'Neill, and R. E. Cutler. Gentamicin pharmacokinetics during hemodialysis. Kidney Int. 6:38-44 (1974). 12. R. C. Dutton, R. E. Baier, R. L. Dedrick, and R. L. Bowman. Initial thrombus formation on foreign surfaces. Trans. Am. Soc. Arttf. Intern. Org. 14:57-62 (1968). 13. L. A. Jacobs, E. Klopp, and V. L. Gott. Studies on the fibrinolytic removal of thrombus from prosthetic surfaces. Trans. Am. Soc. Artif. Intern. Org. 14:63-67 (1968). 14. A. L. Babb, R. P. Popovich, P. L. Farrell, and C. R. Blagg. The effect of erythrocyte mass transfer rates on solute clearance measurements during hemodialysis. Proc. Eur. Dial Transplant. Assoc. 9:303-321 (1972). 15. E.R. Block, J. E. Bennett, L. G. Livoti, W. J. Klein, R. R. MacGregor, and L. Henderson. Flucytosine and amphotericin B hemodialysis effects on the plasma concentration and clearance. Ann. Intern. Med. 80:613-617 (1974). 16. R. E. Cutler and B. M. Orme. Correlation of serum creatinine concentration and kanamycin half-life: Therapeutic implication. J. Am. Med. Assoc. 21}9:539-542 (1969). 17. R. E. Cutler, A. M. Gysetynck, W. P. Fleet, and A. W. Forrey. Correlation of serum creatinine concentration and gentamicin half-life. J. Am. Med. Assoc. 219:1037-1041 (1972). 18. M. C. McHenry, T. L. Gavan, R. W. Gifford, N. A. Geurkink, R. A. Van Ommen, M. A. Town, and J. G. Wagner. Gentamicin dosages for renal insufficiency; adjustments based on endogenous creatinine clearance and serum creatinine concentration. Ann. Intern. Med. 74:192-197 (1971). 19. T. G. Christopher, A. D. Blair, A. W. Forrey, and R. E. Cutler. Kinetics of ethambutol elimination in renal disease. Proc. Dial. Transplant. Forum 3:96-101 (1973). 20. J.T. Clarke, R. D. Libke, C. Regamey, and W. M. Kirby. Comparative pharmacokinetics of amikacin and kanamycin. Clin. Pharm. Ther. 15:610-616 (1974). 21. R. C. Gordon, C. Regamey, and W. M. Kirby. Serum protein binding of the aminoglycoside antibiotics. Antimicrob. Agents Chemother. 2:214-216 (1972). 22. K. J. Simons, R. H. Levy, R. E. Cutler, and T. G. Christopher. Dependence of procainamide clearance on renal function in humans. Paper presented at APhA Academy of Pharmaceutical Sciences meeting, New Orleans, November 1974. 23. M. Danish, R. Schultz, and W. J. Juslco. Pharmacokinetics of gentamicin and kanamycin during hemodialysis. Antimicrob. Agents Chemother. 6:841-847 (1974).
