Send reprint r.qu.sts to: Arthur K. Cho, Ph.D., Department of Pharmacology,tk�iversity of California-Los Angeles School of Medicine, Los Angeles, CA 90024-1735.

�ic �9JPCDE PCE PCA

FIG. l.Structures.

125

0090-9556/93/2 10I-0125S02.00/ODRUG METABOLISM AND DisrosITloNCopyright © 1993 by The American Society for Pharmacology and Experimental Therapeutics

Vol.21,No. IPriniedi,, U.S.A.

A PHARMACOKINETIC STUDY OF PHENYLCYCLOHEXYLDIETHYLAMINE

An Analog of Phencyclidine

A. K. CHO, M. HIRAMATSU, DEBRA A. SCHMITZ, E. M. LANDAW, A. S. CHANG, S. RAMAMURTHY, AND

D. J. JENDEN

Departments of Pharmacology (A.K.C., M.H., D.A.S., A.S.C., SR., D.J.J.) and Biomathematics (E.M.L., D.J.J.), University of California-Los Angeles,

School of Medicine

(Received May 27, 1 992; accepted September 1 , 1992)

ABSTRACT:

The pharmacokinetics of three phencyclidine analogs-phenylcy-

clohexyl-diethylamine (PCDE), phenylcyclobuxylethylamine (PCE),and phenylcyclohexylamine (PCA)-were determined in rats after

intravenous administration of each drug. Because PCE and PCA aremajor metabolltes of PCDE, their plasma levels were also measured

after administration of PCDE. Similarly, PCA concentration was de-

termined after administration of PCE. The data were combined and

analyzed by nonlinear regression procedures using compartmental

and noncompartmental models to determine the kinetic parameters

of PCDE metabolism. The object was to estimate the kinetic con-

slants for the metabolic sequence, PCDE to PCE to PCA. A 6-

compartment model (two pools for each analyte) that included sat-

urable components for the conversion of PCDE to PCE and PCE to

PCA gave the best fit to the combined data. Despite large uncertain-

ties for some microparameters, useful estimates were obtained forclearances, distribution volumes, and fraction of PCDE or PCE con-

veiled to PCE and PCA in vivo under nonsaturating conditions. The

estimated fraction of PCDE converted to PCA and the apparent Km

value for the conversion of PCDE to PCE were comparable to values

obtained in vftro with microsomal preparations, suggesting that met-

abolic studies In vitro provide reasonable predictors of the biotrans-

formation process in vivo for this class of compounds.

In a previous study of PCP ‘ analogs, PCDE (fig. 1), a ring-

opened analog, was found to have very little affinity for the MK801 binding site on the NMDA receptor, the purported site ofaction for these compounds (1). In contrast, the actions of PCDE

in vivo were comparable to those of PCP itself (2, 3). One

explanation for the discrepancy between actions of the com-pound in vitro and in vivo was the conversion of PCDE to anactive metabolite (3). The proposed active metabolite is PCE, acompound slightly more potent than PCP itself (2, 3). PCE is

converted to PCA, a compound with very low affinity for the

NMDA receptor binding site and a correspondingly low activityin vivo (2, 3). The conversion of PCDE to PCE and PCA is

therefore an important process in the pharmacology of PCDE.We describe herein results of a pharmacokinetic study of the

conversion of PCDE to PCE then to PCA in the rat, the mostcommon behavioral subject. In the study, equimolar doses ofPCDE, PCE, or PCA were administered separately to threegroups ofrats, and plasma concentrations ofall three compoundswere measured in each rat at specified times after administration.

The plasma concentration data were analyzed by nonlinearregression techniques using various pharmacokinetic and non-compartmental models to assess the relationships between thesequential conversion and alternate pathways, and to examine

different approaches for the analysis of such data.

This study was supported by U.S. Public Health Serv�e Grants CA-16042

(E.M.L.), DA 02431 (A.K.C.), and MH 17691 (D.J.J.).I Abbreviations used are: PCP, phencyd�e; PCDE, phenylcyclohexyldiethy-

amine; PCE, phenylcyc$ohexylethylamine; PCA, phenylcyclohexylamine; NMDA, N-

methyl-o-aspartate; CV, coefficient of variation; AIC, Akaike information criterion;

SC, Schwarz criterion.

Materials and Methods

PCDE and PCE were obtained from the Research Technology Branch

of the National Institute on Drug Abuse (Rockville, MD). RCA wassynthesized by published methods (4). Deutenum-labeled internal stand-ard for PCDE was synthesized by reduction of N-acetyl-phenylcycloh-

exylethylamine with lithium aluminum deuteride, and the internal stand-ard for PCA was obtained from 2H5-bromobenzene carried through theprocedure of Maddox et a!. (5). The purity of each compound was

confirmed by elemental analysis, OC, and MS.Animals. Male Sprague-Dawley rats weighing 260 to 330 g (Charles

River Breeding Laboratories, Wilmington, MA) were used in the exper-iments. Vascular-Access-Ports, model SLA, from Norfolk Medical Prod-

ucts (Skokie, IL) were implanted 24 hr before the experiment by proce-

dures described previously (6). These ports allow sequential collection ofblood from the jugular vein of a conscious and moving animal. In the

experiment, the ports were flushed with heparinized saline, the druginjected, and the port again flushed with heparinized saline. Serial blood

samples were taken at 5, 10, 20, 30, 60, 120, 180, 300, and 420 mm afteradministration. In each collection, 0.6 ml of blood was collected and set

aside before collection of the actual sample (0.5 ml). The 0.6 ml wasthen reinjected and the port washed by an additional 0.5 ml of saline.The blood samples were centrifuged at 15,000 rpm for 3 mm and theplasma stored at -80#{176}Cuntil assayed. The three compounds were ad-ministered to separate groups of animals as the hydrochloride salts insaline at doses of 35.7 Mmol� kg’.

Plasma Analysis. Internal standards in 60% perchloric acid (0. 1 ml)were added to 0.2 ml ofplasma, mixed, and centrifuged. The supernatantwas transferred to a 20 ml culture tube containing 1 ml of 1.5 M sodium

FIG. 2. Compartmental mode/for the serial conversion ofPCDE to PCE

toPCA.

126 CHO ET AL.

carbonate (pH 9.5) and 5 ml ofglass distilled dichloromethane (Burdickand Jackson, Muskegon, MI). The mixture was shaken for 10 mm and

centrifuged at 2000 rpm to separate the layers. The organic layer wastransferred to a 12 ml conical tube, and most of the solvent was

evaporated under a stream of nitrogen. The residue, about 0. 15 ml, wastransferred to an autosampler vial (Wheaton Glass Co., Milville, NJ) for

GC/MS analysis.A Hewlett-Packard 597lA GC/MS system, operating in the selected

ion mode at 70 eV, was used to analyze the samples. The GC contained

a methyl silicone (0.33 Mm film thickness) capillary column that was

12.5 m in length and 0.2 mm in internal diameter. The chromatographwas heated with a temperature ramp of80 to 2l0C with a rate of 3YC/

mm. The temperatures of the injection port, transfer line, and mass

analyzer were l90, 280, and 180C, respectively (3) The m/z values forthe internal standards used in the selected ion monitoring mode weremhz = 190 for PCDE (PCDEd2) and I 37 for PCA (PCAd5). PCDEd2was used as the internal standard for PCE. The m/z values used tomonitor analytes were 188, 160, and 132 for PCDE, PCE, and PCA,respectively. Concentrations were determined from standard curves thatwere run with each analysis. Recoveries of amines from spiked plasma

samples were more than 90% and varied by less than 10%.Data Analysis. Plasma levels of the three analytes varied over a range

of more than three orders of magnitude, and it was necessary to assessthe error structure of the data prior to evaluation of specific pharmaco-kinetic models. Analysis of replicate assay data demonstrated that meas-

urement error variability had a nearly constant CV (approximately 6%for all three analytes). Interindividual variability was assessed for each

compound at each sample time by the variance of measurements across

rats. Log-log plots of the variance against the mean yielded slopes notmarkedly different from 2.0 for each of the three compounds, and therewere no significant differences among the three straight line fits. Thisindicated that the population standard deviation was also proportional

to the mean (CV approximately 30%). Because a logarithmic transfor-mation yields a more homogeneous variance than the raw data when

CVs are constant (7), all subsequent least squares analyses used constantunit weights (i.e. were unweighted), with the logarithm ofthe concentra-tion as the dependent variable. Because the three analytes did not appearto differ in their error structure, identical constant weights were used for

each compound for those regressions involving simultaneous fitting ofmore than one analyte.

Compartmental Analysis ofPooled Data. Because of the known irre-versible conversion sequence among the three compounds and an ap-

parent biexponential decay curve for each compound alone, the basicmodel likely to provide a reasonable fit to the data consists of threesequential central compartments (PCDE, PCE, and PCA), each with

reversible entry into a peripheral compartment with first-order kinetics(fig. 2). The system ofdifferential equations for this model is (fig. 2):

-(k10 + k12 + k14)q + k..1q4dt

d�2 -(km + k23 + k25)q2 + k,2q1 + k52q5

� = -(k� + k�)q3 + k23q2 +

� = k�4q� -, = k25q2 -

d�j6 k�q3 - /c63q6,

where q1, q2, and q3 are the quantities of PCDE, PCE, and PCA,respectively, in the central compartments; q4, q3, and q6 are their respec-tive quantities in the peripheral compartments; and the k,1 are thefractional transfer or conversion coefficients from compartment i to

This block diagram is described by the system ofdifferential equationsineq. I.

compartmentj. Note that k1�q1 represents the metabolic flux for conver-

sion of PCDE to centrally appearing PCE and k23q2 represents the flux

for conversion of PCE to centrally appearing PCA. Also the “leaks” k10,

k�, and k� represent all remaining irreversible metabolic and excretory

pathways for clearance of the analytes. Thus we assume that all irrevers-

ible formation and elimination steps occur exclusively in those tissues

kinetically associated with the central pool. We note that the lumpedconstant k10 includes any portion oftotal PCDE elimination kinetics due

to the formation of PCE that undergoes further irreversible elimination

without ever having appeared in the systemic circulation. Similarly, anyportion of PCE elimination due to conversion to PCA that does not

appear in the systemic circulation is included in the lumped constant

k�. Plasma concentrations (the dependent variables, assumed to repre-

sent samples from the central pool) at time t are given by c,(t) =

where V1, V2, and V3 are the central volumes of distribution for PCDE,

PCE, and PCA. With the observed concentrations in nM units and V1 in

units ofliter. � the initial (Ja&� all zero for each injection except q1(0)

= 35,700 nmol.kg’ for the PCDE injection data, or q2(0) = 35,700

nmol.kg’ for the PCE injection, or q3(0) = 35,700 nmoI.kg� for thePCA injection.

Because of the large number of parameters in the compartmental

model, the limited number ofrats studied for each injection, and the fact

that each rat could be injected with only one compound, we concluded

that a population modeling approach would be problematic and electedto use a “naive” pooled-data method (8, 9). That is, we fitted a single

compartmental model simultaneously to the data from all three sets of

injection experiments to estimate mean population parameters. This is

in contrast to the noncompartmental estimates, described subsequently,

based on fits of simpler models to individual data for each rat. The

nonlinear regression program BMDPAR (10) was used with the DIFEQ

feature to fit a numerical solution of the differential equation model tothe data from all experiments simultaneously. The basic system describedin eq. 1 was fitted to the data, and F tests for nested models were used

to compare this to fits of simpler models (i.e. with peripheral compart-

( 1) ments removed) or to fits of more complex models (i.e. saturable kineticsas described in Results for one or more metabolic conversions). To

compare fits among several candidate models we also used the AIC [AIC

= N.ln(RSS) + 21’] and SC [SC = N.ln(RSS) + ln(N).Pj, where Nis the

number of data points, RSS is the residual sum of squares, and P is the

number of estimable model parameters (1 1, 12). Each criterion may be

considered a measure of parsimony, and the model having the smallest

criterion value is considered “best” (13). Because eq. 1 can be solvedanalytically, we compared the BMDPAR fits of the basic model with

those using the analytic solution and program BMDP3R (10). The

parameter estimates and standard errors were very similar for thesecomparisons, and only BMDPAR fits are reported.

Functions ofparameters and their standard errors were also estimated.

(5)

PHARMACOKINETICS OF A PCP ANALOG 127

With subscripts 1, 2, and 3 denoting PCDE, PCE, and PCA respectively,

total clearances are

CL1 = V1(k,� + k,,+), i = 1, 2

CL3 V3k�.

The fraction ofcentral PCDE converted to centrally appearing PCE (f...

2) is equivalent in concept to the fraction oftotal clearance of PCDE that

furnishes PCE to the systemic circulation (14) and is given by

J-.2 k2/(k0 + k2).

The fraction of PCE converted to centrally appearing PCA is

f2-.3 k23/(k� + k23).

If we assume that the appearance of PCA from administered PCDE

arises only from the metabolism of centrally appearing PCE, then the

fraction ofPCDE eventually converted to centrally appearing PCA is f...3 = fI_.2 . f2..3. Finally, the apparent steady-state distribution volume ( Vi,)

is defined as the steady-state mass of analyte in the whole system (i.e.

central plus peripheral compartments) divided by the plasma concentra-tion ofanalyte. With steady-state maintained by a constant flux of analyteentering only the central pool, the predicted ratio ofperipheral compart-ment mass to central compartment mass is k14/k�1 for PCDE, k25/k52 forPCE, and k�/k�3 for PCA. It follows then that

v,_r3=v1(l +��)

Clearances, conversion fractions, and distribution volumes were alsocomputed for fits to subsequent models that included saturable kinetics

for the conversion of PCDE to PCE and/or PCE to PCA (see eqs. 13-16and accompanying discussion). For these more complex models, the k12

and k23 terms in eqs. 2-4 were replaced by the corresponding ratio of the

metabolic conversion flux to the amount of parent compound in thelimit of vanishingly small concentrations; these limiting ratios are de-noted ki�2 and k�3. Therefore estimated clearances and metabolic conver-sion fractions for saturable models are meant to apply when concentra-tions of analytes remain well below their Michaelis (“half-saturation”)constants.

IndividualMultiexponential Fits and NoncompartmentalAnalysis. Tocomplement the pooled-data compartmental analyses, we used alternate“noncompartmental” methods for linear systems to analyze individualrat data. For PCA injection experiments, a multiexponential model c3(t)

= �A�exp(-X,t) was fitted to the PCA concentration data for each rat,

and the area under the curve (AUC), area under the moment curve(AUMC), central volume, and total clearance were estimated:

AUC = � A,/X,

AUMC = � A,/X�

V3 = 35,700/s A,

CL3 35,700/AUC. (9)

Letting MRT’#{176}�and MRT”� denote the lower and upper bounds ofthe mean residence time for PCA in the body given that it starts in

plasma, their estimates are (15, 16):

MRT’#{176}”�= AUMC/AUC (10)

MR1”� = �

We note that the true MRT = MRT’#{176}”�’ when elimination occurs

exclusively from the central pool (as assumed in the basic compartmental

model ofeq. 1), and true MRT = MRT”� for the opposite extreme-acatenary model with elimination exclusively from the most peripheral

pool. As V�, = CL. MRT, bounds on the steady-state volume of distri-

bution can be computed to test the sensitivity of V�, estimates to as-

sumptions about elimination sites. These lower and upper bounds on(2) the true distribution volume are:

�‘=CL3.MRD� (11)

�/�eT = CL3 . MRT�T

For PCE injection data, a multiexponential model for PCE and a

second multiexponential model for metabolite PCA (constrained to equal(3) zero at time 0) were fitted to the data for each rat. Similarly for PCDE

injection data, models were fitted to the parent PCDE ‘and metabolite

PCE data for each rat; PCA concentrations were not used in these

(4) noncompartmental analyses. Constrained biexponential, triexponential,

and polynomial exponential models were tried for the metabolite curves,and no model fitted better than a difference of two exponentials; noattempt was made to constrain the time constants for the fit for the

metabolite curve to match the time constants for the parent compound.

Central volumes, clearances, bounds for MRT, and bounds for steady-

state distribution volumes were estimated by computations analogous tothose used for PCA. As the standard errors for each noncompartmentalparameter were roughly constant across rats, population means were

estimated by unweighted averages of the point estimates, and precision

ofeach such mean was measured by the usual SEM. Additionally, giventhat the dose in moles/kg was identical for all three analytes, a bioavail-

ability calculation was used to estimate the population mean fraction ofPCDE converted to centrally appearing PCE and mean fraction of PCE

converted to centrally appearing PCA:

fI-.2 AUC12/AUC22 (12)

f2-.3 AUC23/AUC33,

where AUC� denote the average across rats of the AUC for analyte jgiven analyte i injected. The validity of eqs. 12 depends on the usual

linearity and stationarity assumptions plus an equivalent source con-straint (15) between analyte injected intravenously and that produced

metabolically and appearing centrally. Finally, eqs. 12 and the model-

specific counterparts in eqs. 3 and 4 underestimate the fractional for-

mation of a metabolite if any portion of formed metabolite undergoes

irreversible elimination (e.g. further metabolism or direct secretion intobile) prior to first appearance in the systemic circulation (14).

A biexponential model (N = 2) was used in all cases for fining thedecay curve for each parent compound, because higher order models did

not improve the fit. Therefore, assuming the compartmental model of

eq. 1 is correct, for each rat receiving a PCDE injection k14, k.�, and (k10

+ k2) were estimated from the fit to the parent compound; similarly k25,

(6) k52, and (k20 + k23) were estimated for each rat receiving a PCE injection,

and k�, /(63, and k� for each rat receiving PCA. Again, population mean

estimates were made by simple unweighted averages across rats. Finally,(7) population mean estimates for k0, k12, k�, and k23 were made using the

relationships in eqs. 3 and 4 and the population mean estimates for (k10+ k2), (k20 + k23), f1�.2, and f2...3. Standard errors for those population

(8) means derived as functions of other population mean estimates were

computed by the delta method.

Results

Compartmental Analysis. The linear 6-compartment modeldescribed in Materials and Methods was fitted to pooled data

from six experiments in which PCDE, PCE, or PCA was admin-istered and the concentrations of metabolites and parent com-

pound were measured. Groups of 5-6 rats were studied acrosstime for each combination ofanalyte injected and analyte meas-

ured, resulting in N = 277 usable data points. Parameter esti-

mates and their asymptotic standard errors (expressed as per-centage ofCV) for this basic model are listed in the first column

of table 1, and derived clearances, conversion fractions, and

TABLE 1

Summary ofmicroparameter estimates (% CV)

Model INo saturation

Model 2PCE -� PCA

Saturation

Model 3PCDE -. PCEPCE -‘ PCASaturation

Derived fromF�its to mdi-vidual Rats

RSS 49.77 41.17 40.56 -

No. of parameters 14 15 16 -

AIC 1110.3 1059.8 1057.6 -

SC 1161.1 1114.2 1115.6 -

k0 (min’) 0.0142(27.9%)

0.00905(22.7%)

0.00964(24.3%)

0.0106

(36.6%)k4 (min�) 0.0733

(24.9%)

0.0445

(31.6%)0.0552

(28.1%)0.0486

(7.2%)k41 (min�) 0.0184

(17.8%)

0.0198

(22.2%)

0.0176

(19.0%)

0.0191

(12.2%)

k2 0.0309

(16.0%)0.0167

(15.7%)0.0258#{176}

(26.9%)0.0214

(18.7%)V�1(nmol.min�.kg’) - - 780

(45.5%)

-

KMI(nM) 13172

(57.8%)

k� (min�) 0.00413(24.3%)

0.00543(22.4%)

0.00660

(22.9%)

0.00529

(65.1%)

k25 (min�) 0.00968

(46.4%)

0.0234

(30.8%)

0.0315

(28.1%)

0.05 18(19.8%)

k52 (min’)

k23

0.01045

(47.9%)0.00668

(13.7%)

0.0129

(24.7%)0.0163”

(17.5%)

0.0137

(21.1%)0.02 1 1”

(20.7%)

0.0227

(10.3%)0.0216

(22.8%)Vmax2 (nmol.min’.kg’) - 171.4

(17.5%)156.2

(16.7%)

-

K,� (nM) 2886(23.7%)

2445(23.3%)

k� (min�) 0.0128(16.9%)

0.0181(15.7%)

0.0187(15.9%)

0.0164(12.9%)

k� (min�) 0.0286(52.5%)

0.0415(35.1%)

0.0422(34.6%)

0.0617(23.8%)

/(63 (min’) 0.0234(40.1%)

0.0215(27.4%)

0.0209(26.4%)

0.0398(15.0%)

V1 (liter.kg’)

V2(liter.kg’)

1.49

(20.9%)5.47

(1 1.2%)

2.74

(17.9%)3.65

(13.1%)

2.29

(21.0%)3.02

(15.6%)

2.29(5.8%)2.54

(18.6%)

V3 (liter.kg’) 4.67(17.8%)

3.34(16.9%)

3.25(17.0%)

3.82(10.4%)

where

a k�.

steady-state distribution volumes are listed in the first column oftable 2.

The full 6-compartment model was distinctly better fitting (14)than any simpler model lacking one or more peripheral corn-partments (p < l06 for all F tests). However, for a subset of the The two estimable parameters replacing k23 are V,,�,2 and K,,,�,

data corresponding to early times after PCE administration, there respectively, the maximum flux (mass/time/kg body weight) andwere systematic positive deviations of the observed PCE data Michaelis constant for the conversion of PCE to PCA. This

and negative deviations of observed PCA data from their fitted resulted in a significant improvement in the fit (F1262 = 54.7; pvalues. This suggested that conversion of PCE to PCA may be < 10-6), and estimates are presented in the second column of

saturable, and an expanded model was fitted in which all flux tables 1 and 2. The Michaelis constant for PCE to PCA conver-terms k23q2 in eq. 1 for conversion of PCE to PCA were replaced sion in vivo was 2886 ± 683 (SE) nM. Assuming PCE concen-by trations in the linearizing range (i.e. well below the Michaelis

constant), the plasma clearance for all three analytes under thisk�3q2

(13) model were 0.060 - 0.079 liter. min� . kg’, and the estimatedq2/ V2 clearance for PCE (0.0792 ± 0.0059 liter. min’ .kg’) was larger

1 + -i--- than that based on model 1 (0.059 1 ± 0.0040). The fraction of

128 CHO ET AL.

I .4 Vmax2K23 �,

TABLE 2

Summary ofderived parameter estimates (%CV)

Model 3 Derived fromModel 2 PCDE -0Model 1 PCE -� PCA PCE -‘ PCA Fits to Indi-No saturation vidual RatsSaturation Saturation K51 v(i + KM:VI � K�V2)�

and the flux for PCE to PCA isCL1 (liter.min’ .kg�)

CL2 (liter. min� . kf’)

CL3 (liter.min’ .kg’)

J�-.2

f2-.3

v�,:�7 �iter.kg’

V�cr (liter.kg�)

v�er (liter.kg’)

I/UPPCf (liter.kg�)Lu

VI�r (liter.kg’)

I/UPPCT (liter.kg�)3,3

Vma,�2q1

might be competitive substrates for the same enzyme system, so

_________________________________________ that the flux for PCDE to PCE is

Vmazi q(17)

0.0673 0.0706 0.0813 0.0703(7.0%) (6.1%) (9.5%) (5.1%)

0.0591 0.0792 0.0839 0.0557(6.8%) (7.2%) (8.0%) (14.9%) - (18)

q1 q2(7.0%) (6.3%) (6.2%) (5.4%) K� v2(�+ KMI V1 K� V2J0.0599 0.0604 0.0609 0.0598 _____ _____0.685 0.648 0.728 0.657

(7.4%) (6.4%) (7.4%) (1 8.9%) This modification was not significantly better than model 2

0.618 0.750 0.762 0.769 (F261 = 0.84, p = 0.4) and is not displayed. The plotted final(10.2%) (6.7%) (6.3%) (19.4%) fits for model 3 are nearly indistinguishable from those for model

7.46 8.9 1 9.47 8.25 2, and the former are displayed with means ± SE ofthe observed(12.6%) (10.8%) (1 1.3%) (5.7%) datain fig. 3 forinjectionsofPCDE, PCE, and PCA, respectively.

10.54 10.26 9.96 7.55 A formal goodness-of-fit test indicated that the lack of fit mean

(14.6%) (10.6%) (10.2%) (13.5%) squared error is about 1.9 times larger than the mean squared

10.37 9.78 9.8 1 9.38 replicate error (F38.223 = 1 .89, p = 0.002). There was no gross(12.5%) (1 1.6%) (1 1.6%) (3.6%) systematic misfitting in the residuals, and this moderate lack of

- - - 12.14(7 0%) fit may be a result of the usual problem associated with ignoring

. interindividual variability in the naive pooled-data method.- - - 10.25

However, this last interpretation raises the possibility that the(14.4%)

- - - 1 1.07 significantly improved fits for the saturation model may also be(4.9%) artifacts of the pooled-data fit.

Comparisons with Individual Fits and Noncompartmental Re-

sults. Biexponential models were fitted to individual rat data,PCE converted to centrally appearing PCA (again assuming

and point estimates were averaged across rats, as discussed inconcentrations below saturation) was 0.750 ± 0.050 using model Materials and Methods, for noncompartmental estimates of2, in contrast to 0.618 ± 0.063 for model 1; the fraction of PCDE clearance, conversion fractions of PCDE to PCE and PCE to

converted to centrally appearing PCE was similar for both models �A and steady-state distribution volumes. These are listed in(0.648 ± 0.042 for model 2 vs. 0.685 ± 0.05 1 for model 1). the last column of table 2 and, despite being based on a linear

Finally, the estimated central volumes for PCDE, PCE, and PCA systems analysis, tend to agree more closely with derived esti-

(2.7 ± 0.5, 3.7 ± 0.5, and 3.3 ± 0.6 liter. kg’) were more similar mates from the best-fitting saturable compartmental models 2

to each other than those for model 1 (1.5 ± 0.3, 5.5 ± 0.6, and and 3. Additionally, assuming that the basic linear compartmen-

4.7 ± 0.8 liter. kg�). tal model of fig. 2 is correct, mean population microparameters

A similar deviation of the data from the fitted model at early and central volumes were estimated and are listed in the last

times following the injection of PCDE led to evaluation of a column of table 1 . The most striking result is that the central

third model in which additionally the flux from PCDE to PCE volume estimates tend to be in much better agreement with the

is saturable, with k12q1 terms being replaced by saturable models than with the model 1 estimates.

Of the parameters that could be estimated on each individualk�q1

( 15) rat, the central volumes and clearances tended to have the lowestq1/V1 estimation variability, permitting simple assessments ofthe mag-

1 + � nitude of population variability. For example, the sample stand-

ard deviation of the point estimates of CL1, CL2, and CL3 were,whererespectively, 0.008 1 (N = 5 rats), 0.0204 (N = 6), and 0.0072

k4 Vm�,i (16) liter. min’ . kg’ (N = 5), whereas the median asymptotic stand-12K

MI V1 ard errors for individual clearance estimates were, respectively,0.0034, 0.0043, and 0.0040 liter#{149}min’ .kg�. Thus of the total

This resulted in a borderline improvement in fit over the variance among the point estimates, only about 18%, 4%, andsecond model in which only PCE to PCA is saturable (F,26 = � 1 % could be accounted for as being due to estimation variabil-

3.95; p = 0.048). The estimates for this third model are presented ity, suggesting that the majority of the observed clearance varia-

in the third column of tables 1 and 2. The Michaelis constant bility represents true population heterogeneity. In contrast, thefor PCE to PCA in vivo was 13170 ± 7610 nM, and the sample standard deviations for central volumes V1, V2, and V3

remaining estimates are generally close to those for model 2. were 0.30 (N = 5), 1.16 (N = 6), and 0.90 liter. kg’ (N = 5),

AIC and SC in table 1 are measures of parsimony for model with the median ofthe estimation variances being approximately

discrimination, each a function of the residual sum of squares 100%, 39%, and 190% of the variance of the point estimates.

plus a penalty term increasing with the number of parameters.Discussion

The AIC picked model 3 and the SC picked model 2 as best,both by a small margin, in agreement with the marginal improve- The sequential conversion of PCDE to PCE and then to PCA

ment of model 3 over model 2. is a major metabolic pathway. In a study with microsomes in

Finally the possibility was considered that PCDE and PCE vitro, the sequence accounted for 57% ofthe metabolic products

PHARMACOKINETICS OF A PCP ANALOG 129

PCDE PCE PCA

Injected I :�PCDE

PCE

PCA

130 CHO ET AL.

Measured

I I I I U

0 100 200 300 400

urn.

4.

C

.2S� 3..

U I U U I

0 100 200 300 400Tim.

I I I I I

0 100 200 300 400

lime

4.C

0S

� 3,

C

8-S 2I!

1�

4.

C

.2S� 3.C

if

0 100 200 300 400

lime

I

I I I I I0 100 200 300 400

Time

FIG. 3. Model 3 (saturable conversion ofPCDE to PCE and PCE to PCA).

U U I

0 100 200 300 400

Tim.

For each compound injected (left; dose = 35,700 nmol. kg’) and each compound measured after that injection (top), solidlines indicate predicted

log1�(concentration) from the model. Concentration is in nM, time is in mm. Circles represent means of the observed log concentrations; in almostall cases, the standard error bars for the means are covered by the plot symbols.

of PCDE (1). The corresponding in vivo estimate for central

appearance of PCA from PCDE from our study is the product

f-.2�f2-.3 (i.e. 55.5 ± 5.7 (SE) % for model 3 or 5 1 ± 14% fromthe linear noncompartmental analysis). The good agreementamong these estimates suggests that elimination in vivo of un-changed analyte is a negligible fraction of total clearance ofPCDE and PCE, and that nearly all of the PCE and PCA

produced metabolically is available to the systemic circulation.

Other studies report that only 10% of administered PCE is

excreted unchanged (17). PCDE is much less polar than PCE

and may resemble PCP, of which only 2% is excreted as un-

changed drug. Thus, these compounds are extensively metabo-lized. The metabolic sequence studied (i.e. the oxidative metab-olism of the amine portion of the multiring compound) is aquantitatively important pathway. In the case of PCP, the reac-tion leads to the carboxylic acid (18-20), the dominant excretionproduct in many species. The analogous reaction of PCDE,

however, is a metabolic activation. The metabolite, PCE, has anaffinity for the NMDA receptor that is comparable to that ofPCP, and produces a response in vivo that is 3 to 5 times greater

than that of PCP (21). Separate studies with PCDE and other

analogs indicate that PCE must contribute to PCDE actions (.3).The kinetic parameters of PCDE metabolism are estimated

here from the combined kinetics of the parent compound and

its two metabolites. Although some microparameter estimateshad large standard errors, the values for individual clearances,conversion fractions, and volumes of distribution were more

precise. Chakrabarthi and Law (1 7) have compared the phar-macokinetics of PCE and PCP after intravenous doses of radio-

labeled drugs. These workers reported a rate constant for totalelimination of 0.020 min’ for PCE, in fair agreement with ourestimate of M3 + k20 (0.0277 ± 0.0050 min’) using the presentdata.

Using model 3, estimated steady-state distribution volumeswere ofsimilar size among the three analytes (9.5 - 10 liter.kg�)

and at least 3-fold greater than central volumes. This similarityamong the distribution volumes suggests that all three com-

pounds have ready and comparable access to body compart-ments. One assumption for these model-based estimates of dis-tribution volume is that eliminating tissues are associated exclu-

PHARMACOKINETICS OF A PCP ANALOG 131

sively with the central pool. We have no direct evidence to eitherrefute or support this standard assumption, but comparison of

the noncompartmental upper and lower bounds for the true

distribution volume (last column, bottom oftable 2) suggests theestimates are not very sensitive to violations of this assumption.

In particular, the ratio of the upper bound to lower bound was

only 1.5, 1.4, and 1.2 for PCDE, PCE, and PCA, with Vf’�

corresponding to the “worst-case” extreme of elimination exclu-sively non-central and j,lowcr corresponding to the standard cen-

tral elimination assumption.

The saturation models gave apparent Michaelis constants forPCDE to PCE of 13 iM and for PCE to PCA, 2.4 tiM. Thecorresponding value for microsomal metabolism of PCDE was38 �M (1), a value that is in reasonable agreement when the 58%CV for the in vivo constant is considered. The large volumes of

distribution, associated with ratios k14/k�1 and k25/k52 exceedingunity, suggest that high tissue levels ofthe drug might be achievedrelative to plasma. PCP has been shown to have brain/plasma

ratios that range from four (22) to six (23), depending on thedosage schedule. The concentrations of the compounds in the

liver at early time points could therefore substantially exceed KM,

accounting for the apparent saturation, and because levels in

plasma would be lower than in liver, KM would be underesti-mated.

It is also possible that the kinetics in each rat are truly linearbut the apparent saturation is due to our data-analytic approachin the presence of significant variation of kinetic parameters

across rats. Because it was not possible to collect complete datasets following administration of all three compounds to eachindividual rat, we used a pooled-data analysis that lumps inter-

individual variation with measurement error. Nevertheless, there

is moderately good agreement between the derived pooled-data

estimates of volumes, clearances, and conversion fractions andthe corresponding linear noncompartmental estimates using fitsto individual rats. Even if saturation does occur, most of the

observed concentrations (beyond early times) were probably lowenough to be in the linearizing range, accounting for the agree-ment between our two approaches and providing additional

confidence in the validity ofthese derived estimates. Quantifyingpopulation variability was not a primary goal of this study, butwe note that the variance in individual clearance estimates acrossrats most probably represents true population heterogeneity,because estimation variability is a small fraction ofthis variance.

On the other hand, the observed variance among central volumeestimates may be due primarily to estimation error.

It is worth noting that the compartmental analyses in thiswork utilized simultaneously all ofthe available data, specificallyincluding plasma concentrations of PCDE, PCE, and PCA fol-lowing administration of PCDE, and plasma concentrations of

both of the metabolites after administration of each. Attemptsto fit similar models to individual data sets obtained after ad-ministration of only one of the analytes were less successful,

frequently failed to converge, and always yielded larger variances

of the parameter estimates when they did converge. These find-ings highlight the desirability of fitting pharmacokinetic modelsto a comprehensive data set rather than using a piecemeal fittingprocedure to individual data sets, at least in catenary models of

the kind considered here. Finally, the generally good agreement

between the results of the two data-analytic approaches used in

this investigation suggests that unless the assessment of popula-tion heterogeneity is a major objective of a study, the errors

involved in lumping population variability with estimation error

may be less important than the linearity assumptions generallyimplicit in a noncompartmental approach, particularly if the

nonlinearity significantly affects a larger data domain than in

our present experiments.

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