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Effect of Alteration of Cerebrospinal Fluid Bulk Flow on Nicotine Cerebrospinal Fluid Exit Transfer Kinetics
Effect of Alteration of Cerebrospinal Fluid Bulk Flow on Nicotine Cerebrospinal Fluid Exit Transfer Kinetics M. D. KAROL", P. VENG-PEDERSEN~, R. E. BRASHEAR§, AND R. E. DEATLEY~ Received June 2, 1986, from the *College of Pharmacy, Universit of Arizona, Tucson, AZ 85721,the *Colle e of Pharmacy, University of Iowa, Iowa City, /A, and the &Indiana University School of Medicine, Indhapolis, IN. Accepted for publication Anuary 27, 1988. ~~~~~~~~~
Abstract 0 This study was undertaken to determine if a compound which alters the bulk flow of cerebrospinal fluid (CSF) alters the elimination kinetics of a compound in the CSF. Acetazolamide was chosen as the CSF bulk flow-alteringagent. It produces a relatively large
effect on the flow process, affecting both choroidal and extrachoroidal CSF production, and has been shown to affect CSF flow following iv administration.The compound monitored was nicotine. Acetazolamide was administered orally for one week before and intravenously during the experiment. Nicotine was administered by a bolus injection directly into the CSF via the cisterna magna. The results indicate that the introduction of acetazolamide into the general circulation increases the rate of removal of nicotine from the CSF. Subjects receiving acetazolamide had elevated CSF pressures. The increase in CSF pressure associated with the administration of acetazolamide suggests pressure as a possible factor in the observed increase in the rate of removal of nicotine.
Numerous compounds exert their pharmacological effect by action within the central nervous system (CNS).' Under various circumstances, altering the cerebrospinal fluid (CSF) pharmacokinetics to obtain elevated or lowered drug levels may be desirable. This may be done by altering either the kinetics of uptake or elimination to or from the CSF, respectively. Although many studies have investigated methods of altering CSF levels by affecting the uptake kinetics, relatively few studies have investigated factors which affect the exit processes. Table I summarizes studies which have investigated those factors in vivo, and perhaps the most significant is the alteration of the exit kinetics of benzylpenicillin.2 Benzylpenicillin is used for the treatment of CNS infections. As such, maintenance of high CNS concentrations is desirable. This has been accomplished by the coadministration of probenecid. By competitively inhibiting the exit transport process, elevated CNS benzylpenicillin levels are obtained. Cerebrospinal fluid continuously drains via the arachnoid villi into the venous system.3-6Previous studies indicate that bulk flow accounts for -16% of the CSF elimination kinetics of theophylline.6 Although the impact of bulk flow on the total elimination kinetics will be different for various compounds, it would seem rational to hypothesize that compounds which alter the rate of bulk flow would produce changes in CSF concentrations. Drugs which diffuse readily would be affected only minimally. On the other hand, the same change in bulk flow should have a greater impact on compounds which diffuse slowly since the flow process would comprise a greater portion of the total CSF elimination process. This study is concerned with the investigation of these phenomena; specifically, whether o r not the introduction of an agent which alters bulk flow will produce detectable changes in the CSF elimination kinetics of a drug. Numerous compounds inhibit the process of bulk flow. Table 11, adapted from Segal and Pollay7 summarizes the percent inhibition seen following administration of each of OO22-3~9/88/07OO-0571$0 1 .OO/O 0 1988, American Pharmaceuticai Association
the agents. Of all agents, acetazolamide appeared to be the most suitable for this work. It produces a relatively large effect on the flow process, as much as 90%, and has been shown to affect flow following iv administration. Pollay et al. have shown that acetazolamide produces a decrease in CSF secretion rate from -50 to 5 pL/min in isolated perfused sheep choroid plexus.8 Inhibition of bulk flow currents in the brain perivascular spaces by acetazolamide has also been dem~nstrated.~ Maren has compared the relative amounts needed in the systemic circulation and cisternal fluid for complete inhibition. In the case of systemic circulation, an unbound plasma concentration of -10 pg/mL in CSF is needed.g Extrachoroidal fluid production is also affected by acetazolamide. In this case, acetazolamide appears to be an effective inhibitor only when given systemically.1° Thus, it may be possible to obtain a greater effect following systemic administration since acetazolamide affects both choroidal and extrachoroidal production by this route. In addition to these qualities, the fact that acetazolamide is administered chronically makes the study of its effects clinically relevant since the coadministration of acetazolamide with any CNS active drug may alter that CNS concentration of the drug. The objective of this study was to investigate the effect of a bulk flow-altering agent on the kinetics of CSF elimination of a drug in the CSF. To achieve this objective, numerous compounds could be selected. A desirable quality of such a compound is that it tends t o pass through membranes rapidly. For such a compound, the bulk flow process comprises a relatively small portion of the CSF exit kinetics. If an impact of bulk flow alteration can be demonstrated for such an agent, then it is most likely of importance for slower diffusing drugs as well. A compound which diffuses through membranes rapidly is nicotine." In addition, nicotine may be of interest for the following reasons. Nicotine produces much of its pharmacological effect via action in the CNS" and, although it is rarely if ever administered as a drug per se, -60 million persons in the United States alone take nicotine into their systems by smoking cigarettes. Among the CNS effects of nicotine is the potential to elevate blood pressure. Although in some portions of the population smoking does not appear to have this effect, males aged 17 to 44 years who smoke one to two packs of cigarettes per day have been shown to have an occurrence of hypertension that is 75% higher than males of the same age who have never smoked.12 Four of the eight agents listed in Table 11, including the chosen test compound acetazolamide, have an antihypertensive action. In light of the blood pressure elevating potential of nicotine, an interesting therapeutic question is raised. Will a person who has nicotine-induced hypertension and then receives one of the antihypertensive agents in Table I1 have a resulting pressure that is higher or lower than before the antihypertensive? On one hand, the antihypertensive should lower elevated blood pressure but, on the other hand, it may potentiate the effects of nicotine by decreasing the Journal of Pharmaceutical Sciences / 571 Vol. 77,No. 7,July 1988
Table I-In
Vivo Blood-Cerebrospinal Fluid and Blood-Brain Barrier Exit Transport Studies
Subject Number
Compound
Cat a Rabbita
3-7
Cat a Rabbita Dog
3-7
Penicillin P-Aminosalicylic acid Iodide
9
Benzyl Penicillin
RabbitC
2-4
Rabbitd
3
Rabbit
8-9
Rabbit’
2-6
Goatg Rabbit”
5-9
20
P-Arninosalicylic acid Insulin lnulin Sucrose Manitol Highly lipid soluble compounds Low lipid soluble compounds Diocrast Iodide
Input Site Left lateral ventricle
Delivery
Transport Type
Site
Perfusion Cisterna magna
Left lateral Perfusion Cisterna ventricle magna Right ventricle Perfusion Cisterna rnagna Perfusion Cisterna magna Injection Urine, cisterna magna Lateral Injection Urine Cisterna cerebral ventricle magna Cisterna Injection Cisterna Whole magna brain Cisterna Spinal magna cord VentriculoPerfusion Perfusate cisternal and blood lntraperitoneal Injection Blood and cisternal CSF
Left lateral ventricle Lateral ventricle
Weak carboxyl acid carrier
Inhibitor Added Salicylate Probenecid
Interaction and/or Conclusion Clearance, CSF concentration
Carrier mediated Salicylate Probenecid P-Aminosalicylic Active carrier acid Probenecid
No effect
Active carrier
None
Self-inhibition
Flow
CSF pressure varied
Rate is blood pressure dependent
Flow
None
Similar rate of removal for all three compounds
Flow
None
Enter and exit rapidly Enter slowly
Self-saturation Competitive inhibition
Exit rapidly Flow and active P-Arninophipurate Competitive inhibitor carrier PhenosulfonSelf-saturation phihalen Perchlorate Active carrier 25-Fold increase in relative CSF levels relative to blood
a Spector, R.; Lorenzo, A. V. J. Pharmacol. Exp. Ther. 1974, 188 (I), 55-65. Dixon, R. L.; Owens, E. S.; Rall, D. P. J. Pharm. Sci. 1969, 58 (9), 1106-1 109. ‘Spector, R.; Lorenzo, A. V. J. Pharmacol. Exp. Ther. 1973, 185 (3)642-648. dDustan, H. P. US. Dept. of Health and Human Services,
NIH PublicationNo. 80-2016 (1980). Prockop, L. D.; Schanker, L. S.; Brodie B. 8. Sciencel961, 134, 1424. ‘Mayer, S.; Maickel, R. P.; Brodie, B. 6. J. Pharrnacol. Exp. Ther. 1959, 127, 205-211. gPappenheimer,J. R.; Heisey, S. R.; Jordan, E. F. Am. J. Physiol. 1961,200 (I), 1-10, hBecker, 6. Am. J. Physiol. 1961, 201 (S),1149-1 151. ’ Includes: antipyrine, aniline, aminopyrine, 4-aminoantipyrine,thioperital. ’Includes: acetarnilide, barbital, N-acetyl-4-arnino-antipyrine,salicylic acid.
Table ICCompounds That Inhibit Bulk Flow Compound
Inhibition of Flow, %
Acetazolamide Ouabain Dinitrophenol Amphotericin B Spironolactone Ethacrynic acid Amiloride Furosemide Vasopressin
35-90 40-90 45-60 70 70 60 50 45 50
rate of bulk flow and, therefore, the rate of removal of nicotine out of the CNS. In order to meet the primary goal of this study, experiments were conducted to determine whether or not the bulk flow inhibitor acetazolamide alters the rate of elimination of nicotine from the CSF. Since the study is concerned only with exit transport out of the CSF, a kinetic approach using only CSF data was taken. The approach is based on a comparison of derivatives for CSF elimination profiles before and after treatment with acetazolamide by two methods of analysis. The “autonomic” method of analysis provides a visual basis of comparison of treatment and control data. It is based on a comparison of derivatives for CSF elimination profiles. The approach is not based on classical compartmental modeling, thereby reducing the number of assumptions. This, along with the fact that tissues that constitute the blood-brain 572 ,’Journal of PharmaceuticalSciences Vol. 77. No. 7, July 1988
barrier in dogs apparently do not differ significantly from those of the human,I3 should aid in the extrapolation of results to human.
Experimental Section Procedure-All dogs were anesthetized with intravenous sodium pentobarbital (30 mglkg; Abbott Laboratories; nembutal sodium solution, 50 mglmL). Supplemental doses were given as needed during the remainder of the experiment. A 16-gauge catheter was percutaneously placed in the left lateral saphenous vein for acetazolamide infusion and supplemental anesthesia doses. A second catheter was surgically placed in a femoral artery, with the tip terminating in the aorta in the proximity of the heart for monitoring arterial blood pressure (Beckman R511A physiograph, B & H type 4-3270121 Physiological Pressure Transducer). All dogs were ventilated with a Harvard Apparatus Respiration Pump (model 607). Stroke volume was initially set t o 280 mL, with a rate of 14 mlimin. Respiration was monitored with a bellows pneumograph as a gauge of depth of anesthesia and t o provide a timing signal for respiratoryassociated variations in blood pressure and CSF pressure. An 18gauge needle was percutaneously placed in the cisterna magna for injection of nicotine. This needle was removed and a second needle was put in its place for sampling from the CSF. Cerebrospinal fluid (CSF) pressure was monitored with a pressure transducer connected to a stopcock a t the end of the CSF needle, permitting continuous pressure monitoring except when samples were drawn. Arterial blood samples were taken to assure proper ventilation. Samples were checked for pH, pa02, p,COz, and percent O2saturation with conventional electrodes (Instrumentation Laboratories, Lexington, MA). Exhaled levels of COP were continuously monitored as percent with a medical gas analyzer.
Each dog served as its own control. Thus, acetazolamide was administered in only half of the experiments. For the noncontrol portion, each dog received 250-mg oral doses of acetazolamide (Lederle, Diamox) daily for one week before the experiment. At the beginning of the procedure, a loading dose of 6 mg/kg was administered to increase blood levels from the trough of the last oral dose to the desired level. This was followed by a continuous infusion a t a rate of 10 pgkgimin throughout the duration of the experiment to maintain the desired level. To aid in extrapolation of results to humans and increase clinical relevance, all doses of acetazolamide were based on those found in humans during chronic therapy. A total of five dogs received nicotine injections into the CSF via the cisterna magna. In three of the dogs, the control portion of the experiment was performed before the experiment involving acetazolamide. In the other two, the acetazolamide portion was done first. In either case, a minimum of a one-week rest period was allotted between procedures on any given dog. All five dogs received -9.4 pg (3.0 pCi) of nicotine in both control and acetazolamide procedures. Approximately 30 pL of ['4Clnicotine in ethanol (New England Nuclear; I4C label in the number two position of the pyrrolidine ring; 0.1 mCi/mL of ethanol; specific activity 51.7 mCi/mmol) was pipetted (Drummond Microdispenser No. 275). Solution from the pipette was then placed directly into a preweighed 1-mL syringe. By determining the difference in weight, the actual amount placed in the syringe was determined. In a second 1-mL syringe was placed 0.3 mL of synthetic CSF (Table 111). Both syringes were placed on a three-way stopcock. The third connection was placed in the CSF needle which terminated in the cisterna magna. At time zero, the plunger of the nicotinecontaining syringe was depressed, forcing the nicotine into the CSF. This was then followed by a flush of the nicotine syringe with a portion of the synthetic CSF in the second syringe. The nicotine syringe, then containing only a residue of nicotine and some of the synthetic CSF, was depressed, forcing the diluted residue into the dog. The flush procedure was repeated until the total 0.3 mL of synthetic CSF was injected. The entire injection and flush procedure required <30 s. Samples of 0.2 mL of CSF were drawn from the cisterna magna starting a t 6 min. A total of 30 samples, evenly distributed over a period of 3 h, were taken. Samples were placed directly into preweighed empty liquid scintillation vials. The actual amount of sample was determined by difference in weight. Samples were stored under refrigeration until the time of assay. All samples were assayed by liquid scintillation. To each sample vial, 10 mL of aqueous counting scintillant (ACS; Amersham, IL) was added. A standard of 12.3 mg (14.2 pL) of ['4C]toluene (17810.8 dpm) in 10 mL of ACS and a blank of only ACS were also counted for each experimental run. The quantity of 14C was calculated based on the efficiency determined from the standard. Background was subtracted from all counts. Based on the specific activity of 51.7 mCi/ mmol (supplied by New England Nuclear) and the molecular weight of 162.23, the quantity of nicotine present was calculated.14 Counts were assumed to be indicative of the quantity of nicotine present, since nicotine is not metabolized in the brain.lS Counts were done on an Isocapi300 liquid scintillation counter (Searle Analytic, Inc.). Pharmacokinetic Analysis-Assessment of Acetazolamide Effect-The primary objective of the study was to determine if the introduction of the bulk flow inhibitor acetazolamide alters the CSF elimination kinetics of nicotine. In the presence of a bulk flow inhibitor, a decrease in total exit transport would be expected. To assess if a change in exit transport rate occurred, a comparison of data before and after administration of the inhibitor was done. A simple comparison of raw CSF concentration versus time data was felt to be inadequate. Although it would reflect differences in rate of Table Ill-Synthetic
Cerebrospinal Fluid Compositiona
Component
NaCl KCI CaCI, MgCb NaHPO, NaHCO, a
Solution made to volume with sterile water.
Molarity
0.1295 0.0030 0.0015 0.0014 0.0005 0.0025
removal, this technique is sensitive to variation in volume of distribution, quantity of drug injected, and small variations in the time between injection and sampling. A better technique is to compare derivatives. A comparison of derivatives more directly addresses the question of the impact of acetazolamide on exit rate. Two derivative comparisons are possible, derivative versus time and derivative versus concentration. Comparison of derivative versus time is sensitive to the same factors as a comparison of concentration versus time. A difference in volume of distribution or dose between experimental runs would produce different concentrations a t the same point in time, even if the underlying kinetics were unchanged. Since the derivative is dependent on concentration, differences in derivatives a t the same point in time may be due solely to a change in either dose administered or volume of distribution between experiments. On the other hand, comparison of derivative versus concentration is immune to these factors. This autonomic approach does not assume that doses are equal nor does it require that the volume of distribution be the same in the pre- and post-acetazolamide experiments. Furthermore, since comparison is based on concentration and not time, the method is insensitive to lag time associated with injection, since only the time difference between samples needs to be known. An autonomic approach is appropriate under any circumstances where the rate of elimination is solely a function of concentration. In other words:
where g is any function defining the rate of elimination at a given concentration. Previous work indicates that the exit transport of theophylline from the CSF may be adequately described by the following:
where: k is a diffusion constant, V, is the apparent volume of distribution in the CSF, f i s the fraction offree (unbound) drug, C is the drug concentration, and Q is the CSF bulk flow rate (subscript 2 refers to the CSF?. This shows that the assumption is reasonable for drugs administered via the CSF. It is not a requirement, however, that drugs exit by first-order processes, but only that the rate of removal be a function of the CSF concentration. For example, MichaelisMenten elimination in such a system is solely a function of C(t),and therefore conforms to the requirements of eq 1:
dC(t) - ---Vm,,C dt
K m +C
(3)
Assessment of the effect of acetazolamide on the elimination kinetics from the CSF is a two step process: nonlinear regression and derivative comparison. In the first step, a function is fitted to the CSF concentration-time data by nonlinear regression. Since the approach is model independent, any function which approximates the data well is suitable for the analysis. In the case of the nicotine study, a sum of three exponentials was used to approximate the CSF concentration-time profile. All curves were fitted by linear regression using the interactive program FUNFIT.I6 Comparison of derivatives for the pre- and post-acetazolamide functions was done by computer according to the following algorithm (see Figure 1). The first step was to select a n appropriate time point, T,to evaluate the pre,-acetazolamide concentration function, C(t),and derivative function C(t).The first time point was typically the time of the first sample. Exceptions occurred in cases where the postacetazolamide concentration-time curve did not extend to sufficiently high concentrations. In such cases, comparison of derivatives a t the same concentration was not possible since the concentration on the pre-acetazolamide curve did not exist on the post-acetazolamide curve. When this was the case, the initial time point was incremented in 1-min steps until a n appropriate time point was located. Subsequent evaluations were done at times incremented by 6 min, since this was the time of separation between samples. Journal of Pharmaceutical Sciences / 573 Vol. 77, No. 7, July 1988
Pre-acetazolamide
.
I I
Pas t-acetazalamide
I
Figure 1-Derivative Comparison. Given T on the pre-acetazolamide curve, c ( T ) is located. The same concentration on the post-acetazofais located, and the corresponding time, T,, is mide curve /C,(T~)] determined. Derivatives of the pre- and post-acetazolamidecurves are determined at time T and T,, respectively, and compared.
Once an appropriate time point, was selected, both C ( t ) and C(t) were evaluated, giving C ( T )and C ( d , respectively. Since the functional form was known explicitly, its derivative could be encoded directly in the program. The technique was to compare the derivatives of the pre- and postacetazolamide treatment functions at the same concentration. This necessitated the determination of the time point (7.1 where the postacetazolamide function [C,(t)lhad the same concentration as the preacetazolamide function IC(t)l. In other words, it was necessary to find Ca-’ LC(rl1, the inverse of Ca(~,).The inverse function cannot be stated explicitly and therefore requires the use of a numerical technique. This was done by first setting the difference of the postacetazolamide function [C,(t)l and the desired concentration [c(T)] equal to zero:
0 = C,(t)
-
C(7)
(4)
Then, the Brent algorithm of the IMSL library,l7 a n algorithm designed to locate the zeros of a function, was used. The next step was to calculate the derivative of the post-acetazola, by solution of eq 4. mide function [C,(t)l a t the time point, T ~ found As was the case for the pre-acetazolamide function, this function was also encoded an& evaluated directly since its functional form was explicitly known. At this point in the algorithm, the derivatives corresponding to the same concentration for both pre- and postacetazolamide functions were calculated. Difference and percent difference in derivatives were then taken. Percent difference was defined relative to the pre-treatment curve as shown in eq 5:
-‘
10
10 - 3
:3 -2 YG/L
10
NICOTINE.
~‘
Figure 2- Negative derivative versus concentration for cerebrospinal fluid nicotine, shown on log-log scales. Same subject as shown in Figure 4. Pre- and post-acetazolamide functions represented by solid and dashed lines, respectively.
.Icoo
-
.OBOO
-
1 -
. z
ZZ
2
y
.0600-
-a W >
c
> .OYOO0 W
--
Ln c
I
-
.0200-
z
W
z
U
.MODlL W
The value of T was then incremented by 6 min and the process was repeated. Log-Linear Approach-The above approach provides a n excellent graphic representation (Figures 2 and 3) of the phenomena of interest. It does assume that the kinetics behave autonomically with regard to the concentration of drug in CSF. As seen in Figure 4, elimination of nicotine from the CSF does not follow simple firstorder kinetics. Although this in itself is not sufficient to claim that exit is not a function of only concentration, it is recognized that this fundamental assumption may possibly be violated. It is for this reason, in conjunction with the fact that the autonomic approach does not readily lend itself to statistical workup, that the following alternative analytic approach was also used. In a system where the change in concentration with time follows a log-linear relationship, the derivative of concentration is dependent only on concentration. This is apparent from the fact that in such a system the logarithmic derivative is also equal to the ratio of the derivative of concentration to concentration:
(6) 574 / Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
5 a -.0200
1
lo-*
,
. ....,., . . ......, 10”
10”
,
NICOTINE.
,
.,..,., 10-1
MG/L
,
. ...,.., 10
,
.
..-..l
10
’
Figure 3-Difference in pre- and post-acetazolamide derivatives as determined at same concentrations versus concentration for cerebrospinal fluid nicotine. Key: dog 1 (x); dog 2 (diamond); dog 3 (arrow); dog 4 (X);and dog 5 (z).
Rearrangement of eq 6 gives:
C(t) = -aC(t)
(7)
showing that the derivative is solely dependent on Concentration. Each set of data demonstrated log-linear behavior in the early portion of the experiment, a t high concentrations (Figure 4). In light of the previous discussion, adherence to the requirement that the rate of elimination from the CSF be only a function of concentration can be guaranteed if analysis is limited to the log-linear portion of
A 0 .a
I
50 .a
I
I
150.0
HINd%t
I
200 .o
Flgure 4- Least-squares fit of a triexponential to cerebrospinal fluid nicotine data in a representative subject. Pre-acetazolarnidedata and fitted equation represented by circles and solid line, respectively. Postacetazolarnide data and fitted equation represented by triangles and dashed line, respectively.
the data. Under such circumstances, a change in the kinetics is reflected in the rate constant (a),thereby simplifying the analysis. Limiting the analysis to the portion of the data where log-linear behavior was seen, corresponding rate constants for control and postacetazolamide treatments were compared via a paired t test.18 The above autonomic method has the advantage that the entire time course of the compound is used in the analysis. It does, however, require the assumption that elimination from the sampled site be autonomic, and it does not readily lend itself to statistical workup. On the other hand, the log-linear approach does not require the assumption, but does not utilize the entire time course of the compound. Integrity of Sampled System-The integrity of the sampled system was checked by monitoring CSF pressure via a pressure transducer connected to the needle terminating in the cisterna magna. Two tests were done to compare the initial pressure to the pressure at the end of 3 h of sampling. The first was an absolute difference test consisting of a paired t test to determine if there was any detectable change in pressure. The second test was done to determine if the change in pressure was of importance when compared with CSF pressure variations normally seen. In a normal healthy subject, CSF pressure oscillates with respiration in the same manner as blood pressure. In these experiments, a CSF pressure change of 3 cm of water was observed due to respiration alone. Therefore, a paired t test was done, comparing the mean difference in pressure versus a change of 3 cm, to determine if the change was large enough to be of concern when compared with normal pressure changes.
Results and Discussion The goal of the study was to determine if a compound which alters the bulk flow of cerebrospinal fluid alters the elimination kinetics of a compound in the CSF. To determine this, nicotine was delivered directly into the CSF via a needle in the cisterna magna. The compound was administered twice, once as a control and once in the presence of acetazolamide, a flow inhibitor shown to reduce flow from 35 to 90%. Assessment of Acetazolamide Effect on Nicotine-Nicotine data showed curvature when plotted on log-linear scales (Figure 4).It is directly apparent that more than one expo-
nential is necessary for an approximating function. A biexponential was attempted and was demonstrated to be inadequate. The resulting function consistently overestimated concentration in the middle and underestimated concentration a t the end of the concentration-time profile. Therefore, a triexponential equation was fitted to the nicotine data. No trend of error was observed, and the sum of squares of error was less than that of the biexponential. Both the control and post-acetazolamide sets of data were fitted: Table IV shows the sum of squares of error and correlation coefficients for these fittings, and Figure 4 shows the data and fitted curves for nicotine control and nicotine following acetazolamide for dog 2. Once appropriate approximating functions were obtained, a comparison of derivatives for the pre- and post-acetazolamide functions was done based on the algorithm previously described. Figure 5 shows the derivatives for dog 2 of the preand post-acetazolamide functions in the nicotine experiment. As shown in Figure 4,the concentrations in this experiment change by as much as 1000 fold. As such, a simple linear scale for concentration tends to emphasize the higher concentrations. Likewise, the smaller derivatives associated with the low concentrations are difficult to see. For this reason the functions of Figure 5 were also plotted on log-log scales (Figure 2). The difference in the derivative and the percent difference in the derivative for all dogs undergoing nicotine experimentation are shown in Figures 3 and 6 , respectively. Inspection of Figure 5 indicates that nicotine in the presence of acetazolamide is removed from the CSF faster than in the absence of the flow inhibitor (control subject). In all other subjects, the same trend was seen for high concentrations, although some subjects did demonstrate convergence of control and post-acetazolamide functions a t low concentration levels. Figures 5 and 2 show the derivatives directly and also indicate that a t a given concentration, the CSF elimination of nicotine is greater in the presence of acetazolamide. In some of the subjects, the two functions of Figure 2 crossed at low concentrations; this was consistent with the observed convergence of the concentration-time profile. Figure 3 indicates that the effect of acetazolamide was to increase the rate of elimination of nicotine from the CSF a t high concentrations for all subjects. At low concentrations, the effect oscillates near zero, with some dogs responding positively and some negatively. Inspection of Figure 5 shows that a simple difference in derivative may not be the best way of representing the effect of acetazolamide. As concentration decreases, the derivative decreases for both control and post-acetazolamide functions. As such, the difference also decreases, apparently in proportion to the derivative. For this reason, percent difference in derivative was also included in the analysis. Figure 6 shows the percent difference in the derivative and Table IV-Sum of Squares of Error (SS) and Correlation Coefficients (r) for Nlcotlne Data Fltted to a Trlexponentlal
Dog
Number of Points
ss
r
29 29 29 29 28
0.00594 0.01630 0.00015 0.04891 0.03566
0.9965 0.9912 0.9983 0.9977 0.9983
29 28 29 27 28
0.01446 0.00330 0.00114 0.00283 0.08911
0.9948 0.9984 0.9996 0.9989 0.9990
Control 1 2 3 4 5
Post-acetazolamide 1 2 3 4 5
Journal of Pharmaceutical Sciences / 575 Vol. 77,No. 7,July 1988
-
150.0
z I
z \
-I
2
.100.0
W
>
c U
>
cc W
0
+50.0
2
I
z
wo.0
u z
W
E LLI LL LL
0
=-so.o W
Figure 5-Negative derivative versus concentration for cerebrospinal fluid nicotine, shown on linear scales. Same subject as shown in Figure 4. Pre- and post-acetazolarnide functions represented by solid and dashed lines, respectively.
0 E W
a.
-1oo.c 0
indicates that, a t higher concentrations, this difference is positive and approaches a constant value for all five dogs tested. A positive difference indicates that acetazolamide increased the rate of CSF elimination of nicotine. Table V shows the results of the log-linear analysis which indicates a significant (p < 0.05) change in the mean of 0.03408 in the positive direction. This indicates that acetazolamide increased the rate of nicotine removal from the CSF. Changes apparent from inspection of the results obtained via the autonomic approach show an increase in the rate of nicotine removal from the CSF as well. It would seem that not only did acetazolamide alter the CSF elimination kinetics of nicotine, but that the alteration was in a direction that was not anticipated. Work by other researchers indicates that acetazolamide decreases flow by 35 to 90%. Previous work by this author indicates that a portion of the CSF elimination kinetics of theophylline is mediated by bulk flow. It would be anticipated, therefore, that the CSF elimination rate of nicotine would decrease in the presence of acetazolamide. Although at low concentration the percent difference does go in a negative direction for some of the subjects, the majority of the differences are positive, and, at the higher concentrations, all the differences are positive and approach a constant percent difference. Acetazolamide is a carbonic anhydrase inhibitor with the capability of decreasing blood pH.19 The nicotine molecule has two tertiary nitrogens, one on a pyridine ring, with a pK,, of 6.16, and the other on a pyrrolidine ring, with a pK, of 10.96. The pH of dog CSF2O is normally 7.37. At this pH, the pyridine ring nitrogen will be primarily unionized and the pyrrolidine ring nitrogen will be almost completely ionized. One of the pK, values is close to physiologic pH, and a small change in pH due to acetazolamide could potentially alter the degree of ionization of nicotine enough to significantly change its membrane transport kinetics. The mean change in blood pH was -0.05, but was not shown to be significant (Tables VI and VII). If the pH change had been significant, this factor would not have explained or contributed to the results obtained. A decrease in pH would have increased the 576 /Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
0.200
1
0.400
NICOTINE.
0.600
3.800
1 .ooo
YG/L
Figure 6- Percent difference in pre- and post-acetazolamide derivatives as determined at same concentrations versus concentration for cerebrospinal fluid nicotine. Key: dog 1 (x); dog 2 (diamond); dog 3 (arrow); dog 4 (F);and dog 5 (z). Table V-Initial
Phase Exponential Term'
Dog
Control
Post-Acetazolamide
1 2 3 4 5
0.08130 0.08240 0.08585 0.07446 0.07043
0.09821 0.01803 0.04572 0.03977 0.02732
Difference --0.01698 0.06436 0.04012 0.03977 0.04311
Mean
0.03408 0.03031 2.514b
SD t Test a
Expressed in rnin
'. bNS, p > 0.05.
Table VI-Physiological Parameters before and after Acetazolamide Treatment'
Control 1 2 3 4 5
7.38 7.39 7.40 7.40 7.43
40 41 41 39 41
93 85 82 97 89
96 96 96 97 97
5.4 5.0 5.0 4.0 5.0
40 41 45 43 39
89 79 70 90 94
95 95 93 95 97
4.0 4.7 5.0 4.0 4.0
Post-acetazolamide 1
2 3 4 5
7.31 7.40 7.37 7.26 7.40
a Dogs 4 and 5 underwent acetazolarnide experiment before control, all others underwent the control portion first. bPercent O2 saturation.
Table VII-Difference in Arterial pH between Control and Acetazolamide Experiments'
Table IX-Cerebrospinal Fluid Pressure' and Mean Pressure before and after 3 h of Sampling
Dog
pH Difference
1 2 3 4 5
-0.07 0.01 -0.03 -0.14 -0.03
Mean
-0.05 -0.06 -2.04'
Dog
Initial
Terminal ~~
SD t Test
aMinus sign implies a decrease in pH following acetazolamide treatment. bNS, p > 0.05. degree of ionization of the nicotine molecule and a decrease in nicotine transport would have been expected. In actuality, acetazolamide increased the rate of nicotine removal from the CSF. Each dog served as its own control. As such, each dog was exposed to the rigor of experimentation twice, once as a control and once following acetazolamide. As a check on the effect of previous experimentation two of the five dogs underwent the acetazolamide procedure first. This included dogs 4 and 5, denoted as X and Z on Figure 6 . Inspection of Figure 6 indicates that previous experimentation apparently produced no bias in the results. Cerebrospinal fluid pressure was monitored (Tables VIII and 1x1, and two comparisons were made. The first was a simple absolute difference to determine if a change in pressure had taken place, and the second was a relative test to see if the change was greater than the change normally seen upon respiration. Results of the comparison indicate that for the control set of data, there was a significant change in pressure, but this change was not statistically greater than that due to respiration. The post-acetazolamide set of data Table VIII-Cerebrospinal Fluid Pressure' and Change In Pressure followlng 3 h of Sampling
Initial
Terminal
Difference
2 4 5 6 7 8 9
10.2 7.6 7.7 3.0 7.9 8.0 12.0
9.1 2.7 4.0 0.1 2.0 4.2 8.8
1.1 4.9 3.7 2.9 5.9 3.8 3.2
Mean SD t Test, Absolute t Test, Relative
8.1
4.4
3.6 1.5 6.3 1.1
4 5 7 9
12.1 12.8 16.1 15.0
1.9 1.o 2.0 8.0
10.2 11.8 14.1 7.0
Mean SD f Test, Absolute t Test, Relative
14.0
3.2
10.7 3.0 7.3 5.2
Dog
Before Acetazolamide 2 4 5 6 7 8 9
10.2 7.6 7.7 3.0 7.9 8.0 12.0
9.1 2.7 4.0 0.1 2.0 4.2 8.8
Mean
8.1
4.4
4 5 7 9
12.1 12.8 16.1 15.0
1.9 1.o 2.0 8.0
Mean
14.0
3.2
After Acetazolamide
t Test
3.78
0.57'
a Pressure in cm H20. Dogs 6 and 8 did not survive to undergo acetazolamide treatment; post-acetazolamide pressure was not available for dog 2. 'NS, p > 0.05.
indicated a significant change in pressure, both absolute and relative (Table VIII). Further analysis (Table IX) shows that the terminal CSF pressure for the control and post-acetazolamide animals do not differ. On the other hand, initial pressures were significantly elevated following the administration of acetazolamide. This would tend to imply that acetazolamide causes an elevation in CSF pressure and that the difference seen is not due to an abnormally low pressure at the end of sampling, but to an unusually high pressure at the beginning of the procedure. The elevated pressure is contrary to current reports in the literature which indicate a decrease in bulk flow from 35 to 90% due to acetazolamide. It is, however, consistent with the increase in nicotine removal seen in these experiments following acetazolamide administration.
Conclusions
Before Acetazolamide
After Acetazolamide
'Pressure in cm H20. bDogs 6 and 8 did not survive to undergo acetazolamidetreatment; post-acetazolamide pressure not available for dog 2. 'NS, p > 0.05.
The results indicate that the introduction of acetazolamide into the general circulation increases the rate of removal of nicotine from the CSF. Although low concentrations showed variability, a t high levels the effect was nearly constant for all subjects. The effect of a decrease in pH by acetazolamide on the degree of ionization of the compound was considered. Under such conditions, the ionic character of nicotine would increase and presumably decrease the transport rate; this is contrary to the observed effect. Results were consistent regardless of the sequence of experimentation: either control or post-acetazolamide first. Subjects receiving acetazolamide had elevated CSF pressures. It is concluded that acetazolamide increases the rate of removal of nicotine from the CSF. This effect is apparently not due to a change in ionization of nicotine due to possible pH alteration. The increase in CSF pressure associated with the administration of acetazolamide suggests pressure as a possible factor in the increased rate of removal of nicotine from the CSF.
References and Notes 1. Meyers, F. H.; Jawetz, E.; Goldfien, A. Review ofMedical Pharmacology; Lang Medical Publications: Los Altos, CA. 2. Abraham, E. P.; Chain, E.; Fletcher, C.; Gardner, A,; Heatley, N.; Jennings, M.; Florey, H. Lancet 1941,241, 177. Journal of Pharmaceutical Sciences i 577 Vol. 77, No. 7, July 1988
3. Hill, A. E. Proc. Roy. SOC.Lond. B 1975,190,99-114. 4. Hill, A. E. Proc. Ro Soc Lond. B 1975,190,115-134. 5. Davson, H.; Luck, 8:P. i.Physiol. 1957,137,279-293. 6. Karol, M. D.;Vena-Pedersen. P.: Brashear.’ R. E. J. Pharmacokinet. Biopharm. f983,11(3),’ 273-287. 7. Se al, M.B ; Pollay, M.; Exp. Eye Res. Suppl. 1977,25,127-148. 8. Pofiay, M.; Stevens, A.; Estrada, E.; Kaplan, R. J.Appl. Physzol. 1972 32,612-617. 9. In Fluid Environment ofthe Brain; Cserr, H.; Fenstermacher, J.; Fenel, V., Eds.; Academic: New York, 1975. 10. Curl, F.; Pollay, M. Exp. Neurol. 1968,20,558-574. 11. Sivette, H.; Hoff, E. C.; Larson, P. S.; Haag, 3. H. Pharmacol. Rev. 1962,14,137-173. 12. Wilson, R. W. Cigarette Smoking and Health Characteristics; Public Health Service Publication No. 1000-Series 10,No. 34, Washington, D.C., 1967.
578 /Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
13. Oldendorg, W. H. Ann. Rev. Pharmacol. Toxicol. 1974,14,239248. 14. The Merck Index; Merck: NJ, 1983;p. 6367. 15. Russell. M. A. H. Drug Metab. Rev. 1978.8f1). 29-57. 16. Veng-Pedersen, P.J.?harmacokinet. Biopharm. 1977,5, 513531. 17. IMSL (International Mathematics and Statistics Libra ) ZBRENT, GNB Building, 7500 Bellair Boulevard, Houston, 18. Mendenhall, W. Introduction to Probability and Statistics; Duxbury: Belmont, CA, 1979;p. 297. 19. Goodman, L.S.;Gilman, A. The Pharmacological Basis of Therapeutics; MacMillan: New York, 1975. 20. Biological Handbooks: Blood and Other Body Fluids; Dittmer, D. S., Ed.; Federation of American Societies for Experimental Biology: Washington, D.C., 1961.
’%:
Abstract 0 This study was undertaken to determine if a compound which alters the bulk flow of cerebrospinal fluid (CSF) alters the elimination kinetics of a compound in the CSF. Acetazolamide was chosen as the CSF bulk flow-alteringagent. It produces a relatively large
effect on the flow process, affecting both choroidal and extrachoroidal CSF production, and has been shown to affect CSF flow following iv administration.The compound monitored was nicotine. Acetazolamide was administered orally for one week before and intravenously during the experiment. Nicotine was administered by a bolus injection directly into the CSF via the cisterna magna. The results indicate that the introduction of acetazolamide into the general circulation increases the rate of removal of nicotine from the CSF. Subjects receiving acetazolamide had elevated CSF pressures. The increase in CSF pressure associated with the administration of acetazolamide suggests pressure as a possible factor in the observed increase in the rate of removal of nicotine.
Numerous compounds exert their pharmacological effect by action within the central nervous system (CNS).' Under various circumstances, altering the cerebrospinal fluid (CSF) pharmacokinetics to obtain elevated or lowered drug levels may be desirable. This may be done by altering either the kinetics of uptake or elimination to or from the CSF, respectively. Although many studies have investigated methods of altering CSF levels by affecting the uptake kinetics, relatively few studies have investigated factors which affect the exit processes. Table I summarizes studies which have investigated those factors in vivo, and perhaps the most significant is the alteration of the exit kinetics of benzylpenicillin.2 Benzylpenicillin is used for the treatment of CNS infections. As such, maintenance of high CNS concentrations is desirable. This has been accomplished by the coadministration of probenecid. By competitively inhibiting the exit transport process, elevated CNS benzylpenicillin levels are obtained. Cerebrospinal fluid continuously drains via the arachnoid villi into the venous system.3-6Previous studies indicate that bulk flow accounts for -16% of the CSF elimination kinetics of theophylline.6 Although the impact of bulk flow on the total elimination kinetics will be different for various compounds, it would seem rational to hypothesize that compounds which alter the rate of bulk flow would produce changes in CSF concentrations. Drugs which diffuse readily would be affected only minimally. On the other hand, the same change in bulk flow should have a greater impact on compounds which diffuse slowly since the flow process would comprise a greater portion of the total CSF elimination process. This study is concerned with the investigation of these phenomena; specifically, whether o r not the introduction of an agent which alters bulk flow will produce detectable changes in the CSF elimination kinetics of a drug. Numerous compounds inhibit the process of bulk flow. Table 11, adapted from Segal and Pollay7 summarizes the percent inhibition seen following administration of each of OO22-3~9/88/07OO-0571$0 1 .OO/O 0 1988, American Pharmaceuticai Association
the agents. Of all agents, acetazolamide appeared to be the most suitable for this work. It produces a relatively large effect on the flow process, as much as 90%, and has been shown to affect flow following iv administration. Pollay et al. have shown that acetazolamide produces a decrease in CSF secretion rate from -50 to 5 pL/min in isolated perfused sheep choroid plexus.8 Inhibition of bulk flow currents in the brain perivascular spaces by acetazolamide has also been dem~nstrated.~ Maren has compared the relative amounts needed in the systemic circulation and cisternal fluid for complete inhibition. In the case of systemic circulation, an unbound plasma concentration of -10 pg/mL in CSF is needed.g Extrachoroidal fluid production is also affected by acetazolamide. In this case, acetazolamide appears to be an effective inhibitor only when given systemically.1° Thus, it may be possible to obtain a greater effect following systemic administration since acetazolamide affects both choroidal and extrachoroidal production by this route. In addition to these qualities, the fact that acetazolamide is administered chronically makes the study of its effects clinically relevant since the coadministration of acetazolamide with any CNS active drug may alter that CNS concentration of the drug. The objective of this study was to investigate the effect of a bulk flow-altering agent on the kinetics of CSF elimination of a drug in the CSF. To achieve this objective, numerous compounds could be selected. A desirable quality of such a compound is that it tends t o pass through membranes rapidly. For such a compound, the bulk flow process comprises a relatively small portion of the CSF exit kinetics. If an impact of bulk flow alteration can be demonstrated for such an agent, then it is most likely of importance for slower diffusing drugs as well. A compound which diffuses through membranes rapidly is nicotine." In addition, nicotine may be of interest for the following reasons. Nicotine produces much of its pharmacological effect via action in the CNS" and, although it is rarely if ever administered as a drug per se, -60 million persons in the United States alone take nicotine into their systems by smoking cigarettes. Among the CNS effects of nicotine is the potential to elevate blood pressure. Although in some portions of the population smoking does not appear to have this effect, males aged 17 to 44 years who smoke one to two packs of cigarettes per day have been shown to have an occurrence of hypertension that is 75% higher than males of the same age who have never smoked.12 Four of the eight agents listed in Table 11, including the chosen test compound acetazolamide, have an antihypertensive action. In light of the blood pressure elevating potential of nicotine, an interesting therapeutic question is raised. Will a person who has nicotine-induced hypertension and then receives one of the antihypertensive agents in Table I1 have a resulting pressure that is higher or lower than before the antihypertensive? On one hand, the antihypertensive should lower elevated blood pressure but, on the other hand, it may potentiate the effects of nicotine by decreasing the Journal of Pharmaceutical Sciences / 571 Vol. 77,No. 7,July 1988
Table I-In
Vivo Blood-Cerebrospinal Fluid and Blood-Brain Barrier Exit Transport Studies
Subject Number
Compound
Cat a Rabbita
3-7
Cat a Rabbita Dog
3-7
Penicillin P-Aminosalicylic acid Iodide
9
Benzyl Penicillin
RabbitC
2-4
Rabbitd
3
Rabbit
8-9
Rabbit’
2-6
Goatg Rabbit”
5-9
20
P-Arninosalicylic acid Insulin lnulin Sucrose Manitol Highly lipid soluble compounds Low lipid soluble compounds Diocrast Iodide
Input Site Left lateral ventricle
Delivery
Transport Type
Site
Perfusion Cisterna magna
Left lateral Perfusion Cisterna ventricle magna Right ventricle Perfusion Cisterna rnagna Perfusion Cisterna magna Injection Urine, cisterna magna Lateral Injection Urine Cisterna cerebral ventricle magna Cisterna Injection Cisterna Whole magna brain Cisterna Spinal magna cord VentriculoPerfusion Perfusate cisternal and blood lntraperitoneal Injection Blood and cisternal CSF
Left lateral ventricle Lateral ventricle
Weak carboxyl acid carrier
Inhibitor Added Salicylate Probenecid
Interaction and/or Conclusion Clearance, CSF concentration
Carrier mediated Salicylate Probenecid P-Aminosalicylic Active carrier acid Probenecid
No effect
Active carrier
None
Self-inhibition
Flow
CSF pressure varied
Rate is blood pressure dependent
Flow
None
Similar rate of removal for all three compounds
Flow
None
Enter and exit rapidly Enter slowly
Self-saturation Competitive inhibition
Exit rapidly Flow and active P-Arninophipurate Competitive inhibitor carrier PhenosulfonSelf-saturation phihalen Perchlorate Active carrier 25-Fold increase in relative CSF levels relative to blood
a Spector, R.; Lorenzo, A. V. J. Pharmacol. Exp. Ther. 1974, 188 (I), 55-65. Dixon, R. L.; Owens, E. S.; Rall, D. P. J. Pharm. Sci. 1969, 58 (9), 1106-1 109. ‘Spector, R.; Lorenzo, A. V. J. Pharmacol. Exp. Ther. 1973, 185 (3)642-648. dDustan, H. P. US. Dept. of Health and Human Services,
NIH PublicationNo. 80-2016 (1980). Prockop, L. D.; Schanker, L. S.; Brodie B. 8. Sciencel961, 134, 1424. ‘Mayer, S.; Maickel, R. P.; Brodie, B. 6. J. Pharrnacol. Exp. Ther. 1959, 127, 205-211. gPappenheimer,J. R.; Heisey, S. R.; Jordan, E. F. Am. J. Physiol. 1961,200 (I), 1-10, hBecker, 6. Am. J. Physiol. 1961, 201 (S),1149-1 151. ’ Includes: antipyrine, aniline, aminopyrine, 4-aminoantipyrine,thioperital. ’Includes: acetarnilide, barbital, N-acetyl-4-arnino-antipyrine,salicylic acid.
Table ICCompounds That Inhibit Bulk Flow Compound
Inhibition of Flow, %
Acetazolamide Ouabain Dinitrophenol Amphotericin B Spironolactone Ethacrynic acid Amiloride Furosemide Vasopressin
35-90 40-90 45-60 70 70 60 50 45 50
rate of bulk flow and, therefore, the rate of removal of nicotine out of the CNS. In order to meet the primary goal of this study, experiments were conducted to determine whether or not the bulk flow inhibitor acetazolamide alters the rate of elimination of nicotine from the CSF. Since the study is concerned only with exit transport out of the CSF, a kinetic approach using only CSF data was taken. The approach is based on a comparison of derivatives for CSF elimination profiles before and after treatment with acetazolamide by two methods of analysis. The “autonomic” method of analysis provides a visual basis of comparison of treatment and control data. It is based on a comparison of derivatives for CSF elimination profiles. The approach is not based on classical compartmental modeling, thereby reducing the number of assumptions. This, along with the fact that tissues that constitute the blood-brain 572 ,’Journal of PharmaceuticalSciences Vol. 77. No. 7, July 1988
barrier in dogs apparently do not differ significantly from those of the human,I3 should aid in the extrapolation of results to human.
Experimental Section Procedure-All dogs were anesthetized with intravenous sodium pentobarbital (30 mglkg; Abbott Laboratories; nembutal sodium solution, 50 mglmL). Supplemental doses were given as needed during the remainder of the experiment. A 16-gauge catheter was percutaneously placed in the left lateral saphenous vein for acetazolamide infusion and supplemental anesthesia doses. A second catheter was surgically placed in a femoral artery, with the tip terminating in the aorta in the proximity of the heart for monitoring arterial blood pressure (Beckman R511A physiograph, B & H type 4-3270121 Physiological Pressure Transducer). All dogs were ventilated with a Harvard Apparatus Respiration Pump (model 607). Stroke volume was initially set t o 280 mL, with a rate of 14 mlimin. Respiration was monitored with a bellows pneumograph as a gauge of depth of anesthesia and t o provide a timing signal for respiratoryassociated variations in blood pressure and CSF pressure. An 18gauge needle was percutaneously placed in the cisterna magna for injection of nicotine. This needle was removed and a second needle was put in its place for sampling from the CSF. Cerebrospinal fluid (CSF) pressure was monitored with a pressure transducer connected to a stopcock a t the end of the CSF needle, permitting continuous pressure monitoring except when samples were drawn. Arterial blood samples were taken to assure proper ventilation. Samples were checked for pH, pa02, p,COz, and percent O2saturation with conventional electrodes (Instrumentation Laboratories, Lexington, MA). Exhaled levels of COP were continuously monitored as percent with a medical gas analyzer.
Each dog served as its own control. Thus, acetazolamide was administered in only half of the experiments. For the noncontrol portion, each dog received 250-mg oral doses of acetazolamide (Lederle, Diamox) daily for one week before the experiment. At the beginning of the procedure, a loading dose of 6 mg/kg was administered to increase blood levels from the trough of the last oral dose to the desired level. This was followed by a continuous infusion a t a rate of 10 pgkgimin throughout the duration of the experiment to maintain the desired level. To aid in extrapolation of results to humans and increase clinical relevance, all doses of acetazolamide were based on those found in humans during chronic therapy. A total of five dogs received nicotine injections into the CSF via the cisterna magna. In three of the dogs, the control portion of the experiment was performed before the experiment involving acetazolamide. In the other two, the acetazolamide portion was done first. In either case, a minimum of a one-week rest period was allotted between procedures on any given dog. All five dogs received -9.4 pg (3.0 pCi) of nicotine in both control and acetazolamide procedures. Approximately 30 pL of ['4Clnicotine in ethanol (New England Nuclear; I4C label in the number two position of the pyrrolidine ring; 0.1 mCi/mL of ethanol; specific activity 51.7 mCi/mmol) was pipetted (Drummond Microdispenser No. 275). Solution from the pipette was then placed directly into a preweighed 1-mL syringe. By determining the difference in weight, the actual amount placed in the syringe was determined. In a second 1-mL syringe was placed 0.3 mL of synthetic CSF (Table 111). Both syringes were placed on a three-way stopcock. The third connection was placed in the CSF needle which terminated in the cisterna magna. At time zero, the plunger of the nicotinecontaining syringe was depressed, forcing the nicotine into the CSF. This was then followed by a flush of the nicotine syringe with a portion of the synthetic CSF in the second syringe. The nicotine syringe, then containing only a residue of nicotine and some of the synthetic CSF, was depressed, forcing the diluted residue into the dog. The flush procedure was repeated until the total 0.3 mL of synthetic CSF was injected. The entire injection and flush procedure required <30 s. Samples of 0.2 mL of CSF were drawn from the cisterna magna starting a t 6 min. A total of 30 samples, evenly distributed over a period of 3 h, were taken. Samples were placed directly into preweighed empty liquid scintillation vials. The actual amount of sample was determined by difference in weight. Samples were stored under refrigeration until the time of assay. All samples were assayed by liquid scintillation. To each sample vial, 10 mL of aqueous counting scintillant (ACS; Amersham, IL) was added. A standard of 12.3 mg (14.2 pL) of ['4C]toluene (17810.8 dpm) in 10 mL of ACS and a blank of only ACS were also counted for each experimental run. The quantity of 14C was calculated based on the efficiency determined from the standard. Background was subtracted from all counts. Based on the specific activity of 51.7 mCi/ mmol (supplied by New England Nuclear) and the molecular weight of 162.23, the quantity of nicotine present was calculated.14 Counts were assumed to be indicative of the quantity of nicotine present, since nicotine is not metabolized in the brain.lS Counts were done on an Isocapi300 liquid scintillation counter (Searle Analytic, Inc.). Pharmacokinetic Analysis-Assessment of Acetazolamide Effect-The primary objective of the study was to determine if the introduction of the bulk flow inhibitor acetazolamide alters the CSF elimination kinetics of nicotine. In the presence of a bulk flow inhibitor, a decrease in total exit transport would be expected. To assess if a change in exit transport rate occurred, a comparison of data before and after administration of the inhibitor was done. A simple comparison of raw CSF concentration versus time data was felt to be inadequate. Although it would reflect differences in rate of Table Ill-Synthetic
Cerebrospinal Fluid Compositiona
Component
NaCl KCI CaCI, MgCb NaHPO, NaHCO, a
Solution made to volume with sterile water.
Molarity
0.1295 0.0030 0.0015 0.0014 0.0005 0.0025
removal, this technique is sensitive to variation in volume of distribution, quantity of drug injected, and small variations in the time between injection and sampling. A better technique is to compare derivatives. A comparison of derivatives more directly addresses the question of the impact of acetazolamide on exit rate. Two derivative comparisons are possible, derivative versus time and derivative versus concentration. Comparison of derivative versus time is sensitive to the same factors as a comparison of concentration versus time. A difference in volume of distribution or dose between experimental runs would produce different concentrations a t the same point in time, even if the underlying kinetics were unchanged. Since the derivative is dependent on concentration, differences in derivatives a t the same point in time may be due solely to a change in either dose administered or volume of distribution between experiments. On the other hand, comparison of derivative versus concentration is immune to these factors. This autonomic approach does not assume that doses are equal nor does it require that the volume of distribution be the same in the pre- and post-acetazolamide experiments. Furthermore, since comparison is based on concentration and not time, the method is insensitive to lag time associated with injection, since only the time difference between samples needs to be known. An autonomic approach is appropriate under any circumstances where the rate of elimination is solely a function of concentration. In other words:
where g is any function defining the rate of elimination at a given concentration. Previous work indicates that the exit transport of theophylline from the CSF may be adequately described by the following:
where: k is a diffusion constant, V, is the apparent volume of distribution in the CSF, f i s the fraction offree (unbound) drug, C is the drug concentration, and Q is the CSF bulk flow rate (subscript 2 refers to the CSF?. This shows that the assumption is reasonable for drugs administered via the CSF. It is not a requirement, however, that drugs exit by first-order processes, but only that the rate of removal be a function of the CSF concentration. For example, MichaelisMenten elimination in such a system is solely a function of C(t),and therefore conforms to the requirements of eq 1:
dC(t) - ---Vm,,C dt
K m +C
(3)
Assessment of the effect of acetazolamide on the elimination kinetics from the CSF is a two step process: nonlinear regression and derivative comparison. In the first step, a function is fitted to the CSF concentration-time data by nonlinear regression. Since the approach is model independent, any function which approximates the data well is suitable for the analysis. In the case of the nicotine study, a sum of three exponentials was used to approximate the CSF concentration-time profile. All curves were fitted by linear regression using the interactive program FUNFIT.I6 Comparison of derivatives for the pre- and post-acetazolamide functions was done by computer according to the following algorithm (see Figure 1). The first step was to select a n appropriate time point, T,to evaluate the pre,-acetazolamide concentration function, C(t),and derivative function C(t).The first time point was typically the time of the first sample. Exceptions occurred in cases where the postacetazolamide concentration-time curve did not extend to sufficiently high concentrations. In such cases, comparison of derivatives a t the same concentration was not possible since the concentration on the pre-acetazolamide curve did not exist on the post-acetazolamide curve. When this was the case, the initial time point was incremented in 1-min steps until a n appropriate time point was located. Subsequent evaluations were done at times incremented by 6 min, since this was the time of separation between samples. Journal of Pharmaceutical Sciences / 573 Vol. 77, No. 7, July 1988
Pre-acetazolamide
.
I I
Pas t-acetazalamide
I
Figure 1-Derivative Comparison. Given T on the pre-acetazolamide curve, c ( T ) is located. The same concentration on the post-acetazofais located, and the corresponding time, T,, is mide curve /C,(T~)] determined. Derivatives of the pre- and post-acetazolamidecurves are determined at time T and T,, respectively, and compared.
Once an appropriate time point, was selected, both C ( t ) and C(t) were evaluated, giving C ( T )and C ( d , respectively. Since the functional form was known explicitly, its derivative could be encoded directly in the program. The technique was to compare the derivatives of the pre- and postacetazolamide treatment functions at the same concentration. This necessitated the determination of the time point (7.1 where the postacetazolamide function [C,(t)lhad the same concentration as the preacetazolamide function IC(t)l. In other words, it was necessary to find Ca-’ LC(rl1, the inverse of Ca(~,).The inverse function cannot be stated explicitly and therefore requires the use of a numerical technique. This was done by first setting the difference of the postacetazolamide function [C,(t)l and the desired concentration [c(T)] equal to zero:
0 = C,(t)
-
C(7)
(4)
Then, the Brent algorithm of the IMSL library,l7 a n algorithm designed to locate the zeros of a function, was used. The next step was to calculate the derivative of the post-acetazola, by solution of eq 4. mide function [C,(t)l a t the time point, T ~ found As was the case for the pre-acetazolamide function, this function was also encoded an& evaluated directly since its functional form was explicitly known. At this point in the algorithm, the derivatives corresponding to the same concentration for both pre- and postacetazolamide functions were calculated. Difference and percent difference in derivatives were then taken. Percent difference was defined relative to the pre-treatment curve as shown in eq 5:
-‘
10
10 - 3
:3 -2 YG/L
10
NICOTINE.
~‘
Figure 2- Negative derivative versus concentration for cerebrospinal fluid nicotine, shown on log-log scales. Same subject as shown in Figure 4. Pre- and post-acetazolamide functions represented by solid and dashed lines, respectively.
.Icoo
-
.OBOO
-
1 -
. z
ZZ
2
y
.0600-
-a W >
c
> .OYOO0 W
--
Ln c
I
-
.0200-
z
W
z
U
.MODlL W
The value of T was then incremented by 6 min and the process was repeated. Log-Linear Approach-The above approach provides a n excellent graphic representation (Figures 2 and 3) of the phenomena of interest. It does assume that the kinetics behave autonomically with regard to the concentration of drug in CSF. As seen in Figure 4, elimination of nicotine from the CSF does not follow simple firstorder kinetics. Although this in itself is not sufficient to claim that exit is not a function of only concentration, it is recognized that this fundamental assumption may possibly be violated. It is for this reason, in conjunction with the fact that the autonomic approach does not readily lend itself to statistical workup, that the following alternative analytic approach was also used. In a system where the change in concentration with time follows a log-linear relationship, the derivative of concentration is dependent only on concentration. This is apparent from the fact that in such a system the logarithmic derivative is also equal to the ratio of the derivative of concentration to concentration:
(6) 574 / Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
5 a -.0200
1
lo-*
,
. ....,., . . ......, 10”
10”
,
NICOTINE.
,
.,..,., 10-1
MG/L
,
. ...,.., 10
,
.
..-..l
10
’
Figure 3-Difference in pre- and post-acetazolamide derivatives as determined at same concentrations versus concentration for cerebrospinal fluid nicotine. Key: dog 1 (x); dog 2 (diamond); dog 3 (arrow); dog 4 (X);and dog 5 (z).
Rearrangement of eq 6 gives:
C(t) = -aC(t)
(7)
showing that the derivative is solely dependent on Concentration. Each set of data demonstrated log-linear behavior in the early portion of the experiment, a t high concentrations (Figure 4). In light of the previous discussion, adherence to the requirement that the rate of elimination from the CSF be only a function of concentration can be guaranteed if analysis is limited to the log-linear portion of
A 0 .a
I
50 .a
I
I
150.0
HINd%t
I
200 .o
Flgure 4- Least-squares fit of a triexponential to cerebrospinal fluid nicotine data in a representative subject. Pre-acetazolarnidedata and fitted equation represented by circles and solid line, respectively. Postacetazolarnide data and fitted equation represented by triangles and dashed line, respectively.
the data. Under such circumstances, a change in the kinetics is reflected in the rate constant (a),thereby simplifying the analysis. Limiting the analysis to the portion of the data where log-linear behavior was seen, corresponding rate constants for control and postacetazolamide treatments were compared via a paired t test.18 The above autonomic method has the advantage that the entire time course of the compound is used in the analysis. It does, however, require the assumption that elimination from the sampled site be autonomic, and it does not readily lend itself to statistical workup. On the other hand, the log-linear approach does not require the assumption, but does not utilize the entire time course of the compound. Integrity of Sampled System-The integrity of the sampled system was checked by monitoring CSF pressure via a pressure transducer connected to the needle terminating in the cisterna magna. Two tests were done to compare the initial pressure to the pressure at the end of 3 h of sampling. The first was an absolute difference test consisting of a paired t test to determine if there was any detectable change in pressure. The second test was done to determine if the change in pressure was of importance when compared with CSF pressure variations normally seen. In a normal healthy subject, CSF pressure oscillates with respiration in the same manner as blood pressure. In these experiments, a CSF pressure change of 3 cm of water was observed due to respiration alone. Therefore, a paired t test was done, comparing the mean difference in pressure versus a change of 3 cm, to determine if the change was large enough to be of concern when compared with normal pressure changes.
Results and Discussion The goal of the study was to determine if a compound which alters the bulk flow of cerebrospinal fluid alters the elimination kinetics of a compound in the CSF. To determine this, nicotine was delivered directly into the CSF via a needle in the cisterna magna. The compound was administered twice, once as a control and once in the presence of acetazolamide, a flow inhibitor shown to reduce flow from 35 to 90%. Assessment of Acetazolamide Effect on Nicotine-Nicotine data showed curvature when plotted on log-linear scales (Figure 4).It is directly apparent that more than one expo-
nential is necessary for an approximating function. A biexponential was attempted and was demonstrated to be inadequate. The resulting function consistently overestimated concentration in the middle and underestimated concentration a t the end of the concentration-time profile. Therefore, a triexponential equation was fitted to the nicotine data. No trend of error was observed, and the sum of squares of error was less than that of the biexponential. Both the control and post-acetazolamide sets of data were fitted: Table IV shows the sum of squares of error and correlation coefficients for these fittings, and Figure 4 shows the data and fitted curves for nicotine control and nicotine following acetazolamide for dog 2. Once appropriate approximating functions were obtained, a comparison of derivatives for the pre- and post-acetazolamide functions was done based on the algorithm previously described. Figure 5 shows the derivatives for dog 2 of the preand post-acetazolamide functions in the nicotine experiment. As shown in Figure 4,the concentrations in this experiment change by as much as 1000 fold. As such, a simple linear scale for concentration tends to emphasize the higher concentrations. Likewise, the smaller derivatives associated with the low concentrations are difficult to see. For this reason the functions of Figure 5 were also plotted on log-log scales (Figure 2). The difference in the derivative and the percent difference in the derivative for all dogs undergoing nicotine experimentation are shown in Figures 3 and 6 , respectively. Inspection of Figure 5 indicates that nicotine in the presence of acetazolamide is removed from the CSF faster than in the absence of the flow inhibitor (control subject). In all other subjects, the same trend was seen for high concentrations, although some subjects did demonstrate convergence of control and post-acetazolamide functions a t low concentration levels. Figures 5 and 2 show the derivatives directly and also indicate that a t a given concentration, the CSF elimination of nicotine is greater in the presence of acetazolamide. In some of the subjects, the two functions of Figure 2 crossed at low concentrations; this was consistent with the observed convergence of the concentration-time profile. Figure 3 indicates that the effect of acetazolamide was to increase the rate of elimination of nicotine from the CSF a t high concentrations for all subjects. At low concentrations, the effect oscillates near zero, with some dogs responding positively and some negatively. Inspection of Figure 5 shows that a simple difference in derivative may not be the best way of representing the effect of acetazolamide. As concentration decreases, the derivative decreases for both control and post-acetazolamide functions. As such, the difference also decreases, apparently in proportion to the derivative. For this reason, percent difference in derivative was also included in the analysis. Figure 6 shows the percent difference in the derivative and Table IV-Sum of Squares of Error (SS) and Correlation Coefficients (r) for Nlcotlne Data Fltted to a Trlexponentlal
Dog
Number of Points
ss
r
29 29 29 29 28
0.00594 0.01630 0.00015 0.04891 0.03566
0.9965 0.9912 0.9983 0.9977 0.9983
29 28 29 27 28
0.01446 0.00330 0.00114 0.00283 0.08911
0.9948 0.9984 0.9996 0.9989 0.9990
Control 1 2 3 4 5
Post-acetazolamide 1 2 3 4 5
Journal of Pharmaceutical Sciences / 575 Vol. 77,No. 7,July 1988
-
150.0
z I
z \
-I
2
.100.0
W
>
c U
>
cc W
0
+50.0
2
I
z
wo.0
u z
W
E LLI LL LL
0
=-so.o W
Figure 5-Negative derivative versus concentration for cerebrospinal fluid nicotine, shown on linear scales. Same subject as shown in Figure 4. Pre- and post-acetazolarnide functions represented by solid and dashed lines, respectively.
0 E W
a.
-1oo.c 0
indicates that, a t higher concentrations, this difference is positive and approaches a constant value for all five dogs tested. A positive difference indicates that acetazolamide increased the rate of CSF elimination of nicotine. Table V shows the results of the log-linear analysis which indicates a significant (p < 0.05) change in the mean of 0.03408 in the positive direction. This indicates that acetazolamide increased the rate of nicotine removal from the CSF. Changes apparent from inspection of the results obtained via the autonomic approach show an increase in the rate of nicotine removal from the CSF as well. It would seem that not only did acetazolamide alter the CSF elimination kinetics of nicotine, but that the alteration was in a direction that was not anticipated. Work by other researchers indicates that acetazolamide decreases flow by 35 to 90%. Previous work by this author indicates that a portion of the CSF elimination kinetics of theophylline is mediated by bulk flow. It would be anticipated, therefore, that the CSF elimination rate of nicotine would decrease in the presence of acetazolamide. Although at low concentration the percent difference does go in a negative direction for some of the subjects, the majority of the differences are positive, and, at the higher concentrations, all the differences are positive and approach a constant percent difference. Acetazolamide is a carbonic anhydrase inhibitor with the capability of decreasing blood pH.19 The nicotine molecule has two tertiary nitrogens, one on a pyridine ring, with a pK,, of 6.16, and the other on a pyrrolidine ring, with a pK, of 10.96. The pH of dog CSF2O is normally 7.37. At this pH, the pyridine ring nitrogen will be primarily unionized and the pyrrolidine ring nitrogen will be almost completely ionized. One of the pK, values is close to physiologic pH, and a small change in pH due to acetazolamide could potentially alter the degree of ionization of nicotine enough to significantly change its membrane transport kinetics. The mean change in blood pH was -0.05, but was not shown to be significant (Tables VI and VII). If the pH change had been significant, this factor would not have explained or contributed to the results obtained. A decrease in pH would have increased the 576 /Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
0.200
1
0.400
NICOTINE.
0.600
3.800
1 .ooo
YG/L
Figure 6- Percent difference in pre- and post-acetazolamide derivatives as determined at same concentrations versus concentration for cerebrospinal fluid nicotine. Key: dog 1 (x); dog 2 (diamond); dog 3 (arrow); dog 4 (F);and dog 5 (z). Table V-Initial
Phase Exponential Term'
Dog
Control
Post-Acetazolamide
1 2 3 4 5
0.08130 0.08240 0.08585 0.07446 0.07043
0.09821 0.01803 0.04572 0.03977 0.02732
Difference --0.01698 0.06436 0.04012 0.03977 0.04311
Mean
0.03408 0.03031 2.514b
SD t Test a
Expressed in rnin
'. bNS, p > 0.05.
Table VI-Physiological Parameters before and after Acetazolamide Treatment'
Control 1 2 3 4 5
7.38 7.39 7.40 7.40 7.43
40 41 41 39 41
93 85 82 97 89
96 96 96 97 97
5.4 5.0 5.0 4.0 5.0
40 41 45 43 39
89 79 70 90 94
95 95 93 95 97
4.0 4.7 5.0 4.0 4.0
Post-acetazolamide 1
2 3 4 5
7.31 7.40 7.37 7.26 7.40
a Dogs 4 and 5 underwent acetazolarnide experiment before control, all others underwent the control portion first. bPercent O2 saturation.
Table VII-Difference in Arterial pH between Control and Acetazolamide Experiments'
Table IX-Cerebrospinal Fluid Pressure' and Mean Pressure before and after 3 h of Sampling
Dog
pH Difference
1 2 3 4 5
-0.07 0.01 -0.03 -0.14 -0.03
Mean
-0.05 -0.06 -2.04'
Dog
Initial
Terminal ~~
SD t Test
aMinus sign implies a decrease in pH following acetazolamide treatment. bNS, p > 0.05. degree of ionization of the nicotine molecule and a decrease in nicotine transport would have been expected. In actuality, acetazolamide increased the rate of nicotine removal from the CSF. Each dog served as its own control. As such, each dog was exposed to the rigor of experimentation twice, once as a control and once following acetazolamide. As a check on the effect of previous experimentation two of the five dogs underwent the acetazolamide procedure first. This included dogs 4 and 5, denoted as X and Z on Figure 6 . Inspection of Figure 6 indicates that previous experimentation apparently produced no bias in the results. Cerebrospinal fluid pressure was monitored (Tables VIII and 1x1, and two comparisons were made. The first was a simple absolute difference to determine if a change in pressure had taken place, and the second was a relative test to see if the change was greater than the change normally seen upon respiration. Results of the comparison indicate that for the control set of data, there was a significant change in pressure, but this change was not statistically greater than that due to respiration. The post-acetazolamide set of data Table VIII-Cerebrospinal Fluid Pressure' and Change In Pressure followlng 3 h of Sampling
Initial
Terminal
Difference
2 4 5 6 7 8 9
10.2 7.6 7.7 3.0 7.9 8.0 12.0
9.1 2.7 4.0 0.1 2.0 4.2 8.8
1.1 4.9 3.7 2.9 5.9 3.8 3.2
Mean SD t Test, Absolute t Test, Relative
8.1
4.4
3.6 1.5 6.3 1.1
4 5 7 9
12.1 12.8 16.1 15.0
1.9 1.o 2.0 8.0
10.2 11.8 14.1 7.0
Mean SD f Test, Absolute t Test, Relative
14.0
3.2
10.7 3.0 7.3 5.2
Dog
Before Acetazolamide 2 4 5 6 7 8 9
10.2 7.6 7.7 3.0 7.9 8.0 12.0
9.1 2.7 4.0 0.1 2.0 4.2 8.8
Mean
8.1
4.4
4 5 7 9
12.1 12.8 16.1 15.0
1.9 1.o 2.0 8.0
Mean
14.0
3.2
After Acetazolamide
t Test
3.78
0.57'
a Pressure in cm H20. Dogs 6 and 8 did not survive to undergo acetazolamide treatment; post-acetazolamide pressure was not available for dog 2. 'NS, p > 0.05.
indicated a significant change in pressure, both absolute and relative (Table VIII). Further analysis (Table IX) shows that the terminal CSF pressure for the control and post-acetazolamide animals do not differ. On the other hand, initial pressures were significantly elevated following the administration of acetazolamide. This would tend to imply that acetazolamide causes an elevation in CSF pressure and that the difference seen is not due to an abnormally low pressure at the end of sampling, but to an unusually high pressure at the beginning of the procedure. The elevated pressure is contrary to current reports in the literature which indicate a decrease in bulk flow from 35 to 90% due to acetazolamide. It is, however, consistent with the increase in nicotine removal seen in these experiments following acetazolamide administration.
Conclusions
Before Acetazolamide
After Acetazolamide
'Pressure in cm H20. bDogs 6 and 8 did not survive to undergo acetazolamidetreatment; post-acetazolamide pressure not available for dog 2. 'NS, p > 0.05.
The results indicate that the introduction of acetazolamide into the general circulation increases the rate of removal of nicotine from the CSF. Although low concentrations showed variability, a t high levels the effect was nearly constant for all subjects. The effect of a decrease in pH by acetazolamide on the degree of ionization of the compound was considered. Under such conditions, the ionic character of nicotine would increase and presumably decrease the transport rate; this is contrary to the observed effect. Results were consistent regardless of the sequence of experimentation: either control or post-acetazolamide first. Subjects receiving acetazolamide had elevated CSF pressures. It is concluded that acetazolamide increases the rate of removal of nicotine from the CSF. This effect is apparently not due to a change in ionization of nicotine due to possible pH alteration. The increase in CSF pressure associated with the administration of acetazolamide suggests pressure as a possible factor in the increased rate of removal of nicotine from the CSF.
References and Notes 1. Meyers, F. H.; Jawetz, E.; Goldfien, A. Review ofMedical Pharmacology; Lang Medical Publications: Los Altos, CA. 2. Abraham, E. P.; Chain, E.; Fletcher, C.; Gardner, A,; Heatley, N.; Jennings, M.; Florey, H. Lancet 1941,241, 177. Journal of Pharmaceutical Sciences i 577 Vol. 77, No. 7, July 1988
3. Hill, A. E. Proc. Roy. SOC.Lond. B 1975,190,99-114. 4. Hill, A. E. Proc. Ro Soc Lond. B 1975,190,115-134. 5. Davson, H.; Luck, 8:P. i.Physiol. 1957,137,279-293. 6. Karol, M. D.;Vena-Pedersen. P.: Brashear.’ R. E. J. Pharmacokinet. Biopharm. f983,11(3),’ 273-287. 7. Se al, M.B ; Pollay, M.; Exp. Eye Res. Suppl. 1977,25,127-148. 8. Pofiay, M.; Stevens, A.; Estrada, E.; Kaplan, R. J.Appl. Physzol. 1972 32,612-617. 9. In Fluid Environment ofthe Brain; Cserr, H.; Fenstermacher, J.; Fenel, V., Eds.; Academic: New York, 1975. 10. Curl, F.; Pollay, M. Exp. Neurol. 1968,20,558-574. 11. Sivette, H.; Hoff, E. C.; Larson, P. S.; Haag, 3. H. Pharmacol. Rev. 1962,14,137-173. 12. Wilson, R. W. Cigarette Smoking and Health Characteristics; Public Health Service Publication No. 1000-Series 10,No. 34, Washington, D.C., 1967.
578 /Journal of Pharmaceutical Sciences Vol. 77, No. 7, July 1988
13. Oldendorg, W. H. Ann. Rev. Pharmacol. Toxicol. 1974,14,239248. 14. The Merck Index; Merck: NJ, 1983;p. 6367. 15. Russell. M. A. H. Drug Metab. Rev. 1978.8f1). 29-57. 16. Veng-Pedersen, P.J.?harmacokinet. Biopharm. 1977,5, 513531. 17. IMSL (International Mathematics and Statistics Libra ) ZBRENT, GNB Building, 7500 Bellair Boulevard, Houston, 18. Mendenhall, W. Introduction to Probability and Statistics; Duxbury: Belmont, CA, 1979;p. 297. 19. Goodman, L.S.;Gilman, A. The Pharmacological Basis of Therapeutics; MacMillan: New York, 1975. 20. Biological Handbooks: Blood and Other Body Fluids; Dittmer, D. S., Ed.; Federation of American Societies for Experimental Biology: Washington, D.C., 1961.
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