Journal of Pharmaeokinetics and Biopharmaceutics, Vol. 18, No. 1, 1990

Saturable Rate of Cefatrizine Absorption After Oral Administration to Humans Bruno G. Reigner, !'4 W i l l i a m Couet, 2 Jean-Paul Guedes, 3 Jean-Bernard Fourtillan, 2 and Thomas N. Tozer ~ Received April 18, 1989--Final September 11, 1989 This study examined the absorption kinetics of cefatrizine, an amino-fl-lactam antibiotic, after oral administration of a single 500-rag dose to 12 healthy volunteers. Plasma concentrations were determined by high performance liquid chromatography. The plots of the percentage of drug unabsorbed and the apparent rate of cefatrizine absorption as a function of time showed, first, a delay and, then, an almost constant rate of absorption with a tendency to move toward first-order kinetics at the end of the process. Three compartmental models incorporating a lag time and first-order elimination kinetics, but differing in their input rate, were used for analysis of the time course of cefatrizine plasma concentrations. The model with first-order absorption kinetics was clearly inadequate. The results were improved with the model for which the rate of absorption is constant, but a model incorporating saturable absorption kinetics of the Michaelis-Menten type improved the fit further. This last model was statistically superior to the constant-rate input model in 6 out of 12 subjects, according to the likelihood-ratio method. Because of the innovative feature of the model incorporating the Michaelis-Menten equation, simulations of the effect of altering the model parameters and the dose administered on the concentration-time profile, were performed. Different hypotheses which might explain why cefatrizine absorption kinetics fits the MichaelisMenten equation were examined. The observation of saturable absorption kinetics is consistent with a carrier-mediated transport previously reported to occur in the gastrointestinal tract of rats.

KEY WORDS: cefatrizine; Michaelis-Menten equation; saturable absorption rate.

INTRODUCTION

The oral absorption of drugs in man is often approximated by first-order kinetics (1). A constant rate of absorption (zero-order kinetics) is more uncommon, but has been described for drugs such as hydroflumethiazide t Department of Pharmacy, School of Pharmacy, University of California, San Francisco, California 94143, U.S.A. 2CEMAF, 144 rue de la Gibauderie, 86000 Poitiers, France. 3Lyc6e Descartes, 37000 Tours, France. 4To whom correspondence should be addressed. 17 0090-466x/90/0200-0017506.00/09 1990plenum PublishingCorporation

18

Reigner, Couet, Guedes, Fourtillan, and Tozer

(2), ampicillin (3), 8-methoxypsoralen (4), and cyclosporine (5). KrugerThiemer (6) proposed the use of the Michaelis-Menten equation to describe saturable rate of absorption, but did not apply it to experimental data. To our knowledge, this paper is the first of such applications in vivo to man. Cefatrizine, 7-[R-(- )-2 amino-(p-hydroxyphenyl) acetamido-)-3-[1H1,2,3-triazole-4(5)-ylthiomethyl]3-cephem-4-carboxylic acid, is an oral semisynthetic cephalosporin with a broad antibacterial spectrum against most strains of clinically important Gram-positive and Gram-negative bacteria (7,8). Several pharmacokinetic studies of this drug have been conducted (9-11). After oral administration of a single dose (500 mg), the absorption is fast (time of the peak concentration, t. . . . occurs between 1 and 2 hr) and nearly complete (F = 0.75); the mean values of the peak concentration, Cmax, and the area under the plasma concentration versus time curve, A UC, are about 8 mg 9 L -1 and 28 mg 9 L - 1 9 hr, respectively. Cefatrizine elimination occurs mostly by the renal route; 60 to 80% of the administered dose is excreted unchanged in urine. The mean values of the half-lives in subjects with normal renal function have been reported to be 0.98 + 0.24 hr (11) and 1.78 + 0.06 hr (9). Adding sampling times before and around the expected time of the peak and using a specific assay method (high performance liquid chromatography), we have studied cefatrizine pharmacokinetics in healthy volunteers after oral administration of 500 mg. The results of noncompartmental analysis have been recently published (12). Preliminary compartmental analysis with a classical model for drug absorption and disposition revealed difficulties in fitting the absorption phase, suggesting the need for reevaluation of the absorption. Moreover, studies in the rat have shown that aminocephalosporins are absorbed from the small intestine (13) and several authors have suggested carrier-mediated transport in the rat (14) as well as in man (15) because of saturability in its rate of absorption. The aim of the study was to examine the absorption kinetics of cefatrizine in man. Since the rate of cefatrizine absorption appears to be saturable, a model incorporating a Michaelis-Menten type absorption is proposed and compared to more classical models of drug input, with respect to their fit of the cefatrizine concentration versus time after a single oral dose. MATERIAL AND METHODS The clinical protocol and the analytical methods have been previously published (12). Briefly, the study was conducted in 6 female and 6 male volunteers between 20 and 26 years of age. All were found to be healthy by routine clinical and laboratory examinations within a 10-day period

Saturable Rate of Cefatrizine Absorption

19

preceding the study. A 500-mg dose of cefatrizine capsule (Cefaperos, Laboratoires Allard, France) was given to each volunteer. All subjects, fasted since 10 p.m. of the previous day, swallowed the capsule with 200 ml of tap water. A standardized meal was served 2 hr after drug administration. The study was previously reviewed and approved by the local Ethics Committee. Blood samples were taken from an antecubital vein just prior to dosing and 0.25, 0.50, 0.75, 1, 1.25, 1.50, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 10, and 12hr after drug administration. All samples were collected using heparinized tubes (Vacutainer, Becton Dickinson). Plasma was separated by centrifugation and transferred into plastic tubes. All samples were stored at - 80~ until assayed. Plasma concentrations of cefatrizine were measured by reversed-phase liquid chromatography (HPLC) with UV detection at 254 rim.

Pharmacokinetic Analysis Cefatrizine absorption kinetics was analyzed by the Wagner-Nelson method (16) in which the percentage of cefatrizine unabsorbed (100 minus the percentage absorbed) was determined with time. The percentage absorbed was used to estimate the apparent rate of cefatrizine absorption according to the equation ( ~ X a / 2 x t ) / F = D[(percentage absorbed),,+ 1-(percentage absorbed), ] 1 0 0 " (//+1 --

ti)

(1) where Xa is the amount absorbed, F is the bioavailability, D is the dose and [(percentage absorbed),,+,- (percentage absorbed),,] is the difference between the percentages absorbed at two consecutive sampling times ti and ti+l. The time course of the absorption rate relative to bioavailability was graphically represented by a plot of ( A X a / A t ) / F against the midpoint of each interval, (ti + t~+1)/2. Three distinct compartmental models, incorporating a delay of absorption (lag time, t~ag) and first-order elimination kinetics, were used for the data-fitting of the plasma concentrations of cefatrizine against time. The models as shown in Fig. 1, differ in their absorption components. After absorption begins, the M1 model is mathematically equivalent (17) to F. D . ka (e_k. c _ e -kSt') C = V ( k ~ - k)

(2)

20

Reigner, Couet, Guedes, Fourtillan, and Tozer

Absorpti~h.[

Aa,Ca

(Va)

"1

tl a g

A,C "

I

(V)

I

CL v

Model

](inetie Nature of ,~bsorvtion Sten

M1 M0 MM

First-order Zero-order Michaelis-Menten

Fig. 1. Generalized scheme and specific models for the absorption and disposition of cefatrizine. Three models, differing in the nature of their absorption processes, are indicated. The amounts (Aa, A), concentrations (Ca, C) of drug and the apparent volumes of distribution (Va, V) of the two compartments (absorption site and body, respectively) are presented. Clearance from the body compartment (CL) and a delay (Gg) in the absorption are also indicated.

where k a is the absorption rate constant, k is the elimination rate constant (CL/V) and t' is the difference between the time since drug administration and tlag. The M0 model is equivalent (17) to the following equations: From time tlag to the end of the absorption

C - F- . D ( 1 - e - k t') r'V'k

(3)

After the absorption is over C

F.D _ _ z'V'k

(e-k(r-~)_e-k- c)

(4)

where ~r is the duration of absorption. In the MM model, the rate of absorption, dAa/dt, is

dAa dt

Ca Km+ Ca

Vma x 9

(5)

and the rate of change of drug in body, dA/dt, is

dA Vmax"Ca dt - K m + Ca

CL. C

(6)

where Vmaxis the maximum rate of absorption and Km is the value of Ca at which the absorption rate is one.half the maximum. Since cefatrizine is

Saturable Rate of Cefatrizine Absorption

21

only measured in plasma, the model must be expressed in terms of C. This is accomplished by dividing Eqs. (5) and (6) by V and letting C a ' = Va . C a / V , K m - ' - Va . K~n/ V and V~ax= Vmax/ V. Then, the model differential equations are dCa' dt

V'max" Ca' -

(7)

K ~ + Ca'

dC

V ' a x " Ca'

CL

dt

K'm + Ca'

V

9C

(8)

The initial conditions are Ca'(O) = F . D ~ V and C(0) = 0. As no explicit solutions are available for this set of differential equations, the Runge-Kutta-Fehlberg numerical integration method (18) was used to estimate the values of C with time. The estimations of individual parameters with each model were performed by nonlinear regression analysis using the program P h a r m (19). For comparison, the same minimization algorithm (20) was used with the three models. A weighted least squares (WLS) method was used to estimate the parameters by minimizing the value of the objective function OwLs: N OWLS ~-" E W/( Y//- y~/r)2 i=1

(9)

where N is the number of data points (time, concentration), W~ is the weighting factor, Y~is the measured concentration and Y/is the theoretical concentration (21). The weighting factor has been chosen according to the analytical repeatability; since the variance of the measured concentration at different levels was not constant or proportional to the theoretical concentration, the intermediate weight of 1/Y/was used. The weighted residuals against time and Y/were examined to evaluate the goodness of fit and the suitability of the weighting factor (22). Precision in the estimation of the individual parameters was evaluated with the standard deviation and the coefficient of variation calculated from the covariance matrix (21). The M0 and MM kinetic models were compared by visual inspection and formally, according to the likelihood ratio method previously described by Sheiner (23). Briefly, the test value, AO, is defined in this particular case as

0 = N, In [ OWLs(R)/OWLs(F) ]

(10)

where OWLs(R) and OwLs(F) are the objective functions of the reduced (M0) and the full (MM) models, respectively. The value of AO is assumed to follow a X2(1 dO distribution under the null hypothesis. If the value of

22

Reigner, Couet, Guedes, Fourtillan, and Tozer

AO is greater than X2(1 df), the null hypothesis (in this case,. M0 model) is rejected in favor of the alternative hypothesis (full model, i.e., MM model). The individual values of Cmax, t . . . . AUC, and tl/2 were calculated for the M0 and MM models. With the M0 model, the values were derived from the equations (17) tma x = tlag + "r

F.D

Cmax - - - - - - - - ~ '/" k "

(11) (1 - e -k'~" )

AUC : F. D / ( k . V)

(12)

(13)

Cmax and tmaxfor the MM model were computed numerically. Integration of the differential equations yielded F. D / ( k . V) for the AUC, as expected for a model with a linear disposition. The half-lives were obtained from tl/2 = In 2/k.

Statistieal Comparisons The mean values of C . . . . t . . . . AUC, and t~/2 calculated with the M0 and MM models were compared by a two-way analysis of variance (ANOVA). The 95% probability confidence interval of the relative difference between the means was calculated according to the equation: [ mM0--~-~MM'] " l O 0 • mMM

J

(14) /

mMM

where m is the mean, SD is the estimate of the standard deviation of the difference, and t(n - 2) is the Student's t value for (n - 2) degrees of freedom. The value of SD is

SD: 24 2/

(15)

where S2Ris the residual error from ANOVA and n is the number of subjects (24). RESULTS AND DISCUSSION After oral administration, the decline of the concentration was clearly a straight line on a log-concentration vs. time plot in 12 out of 12 subjects. This observation confirms the data published by Gaver and Deeb (10). Such profiles suggest that a one-compartment model is appropriate to describe cefatrizine pharmacokinetics. However, when Pfeffer et al. (11) infused cefatrizine in healthy volunteers over 30 min, the decline of the average concentration was biexponential. A two-compartment model fits the average data and therefore, suggests that the rate of cefatrizine absorption should

Saturable Rate of Cefatrizine Absorption

23

be analyzed with the Loo-Riegelman method (25). Since cefatrizine was not administered intravenously to the subjects in our study, we could not perform this method. Furthermore, analysis of the average data in Pfeffer's publication (11) to assess the importance of the more rapid (distribution) phase in cefatrizine disposition showed that distribution is very rapid and relatively unimportant as the exponential term describing the distribution phase tends toward zero so quickly with time, that it makes virtually no contribution to the estimated plasma concentration after oral administration. In addition, the two-compartment model with first-order input was observed to fit the data no better than the M0 and MM models as determined by an increase in the objective function [Eq. (9)]. Consequently, we considered the one-compartment model a reasonable approximation of cefatrizine pharmacokinetics after oral administration. Therefore, the Wagner-Nelson method was used to analyze cefatrizine absorption. Percentage of drug unabsorbed against time obtained by the WagnerNelson method is shown in Fig. 2A. Simple visual inspection of the plots of these data suggests that there is a time lag of 20 to 40 min before the absorption process begins and that the subsequent linear decline reflects zero-order kinetics with passage toward a first-order process in a few of the subjects at low values. Beyond the time lag, these profiles exhibit a form described by Wagner (26) as "hockey sticks" which are consistent with Michaelis-Menten kinetics (26). A plot of the apparent rate of cefatrizine absorption against time (Fig. 2B) confirms the previous interpretation. After the lag phase, the rate is generally constant until the end of the absorption is approached. Here, the rate declines by a first-order process in several subjects. To calculate the absorption parameters, absorption models could have been fit to percentage unabsorbed values with time as performed recently with nitrofurantoin (27) and quinidine (28). With the Wagner-Nelson method (16), no model is assumed for the absorption process, but an estimate of k is required. This estimation, however, is influenced by the choice of the number of points to be included in the terminal phase (logarithm of concentration vs. time). An alternative approach consists of testing a model which simultaneously takes absorption and elimination of the drug into account. The parameter values of the model are fit to the experimental concentration-time data. As revealed by simple visual inspection of fitted versus observed concentrations against time, the classical M1 model is inadequate (cf. example in Fig. 3A). The residuals are not randomly distributed which confirms that M1 model is not suitable for these data (22). As suggested by Fig. 2, zero-order absorption kinetics may be more appropriate for cefatrizine. The fit of the M0 model was much better than that of the M1 model in all

24

Reigner, Couet, Guedes, Fourtillan, and Tozer

,oo

A "o G) o J~ r-

60

40'

Q.

20'

O' 0.0

0.5

1.0

1.5

2.0

2.5

3.0

g 400t =~ 3oot ~ 200] g~

'~176 0.0

I

0.5

I

1 .0

I

1 .5

2.0

, 2.5

I

3.0

Hours Fig. 2. Panel A: Percentage of cefatrizine remaining to be absorbed against time for each of the 12 subjects. Panel B: Rate of absorption relative to bioavailability against midpoint time, calculated from Eq. (1), for the same subjects.

subjects as illustrated for the data of the same subject (Fig. 3B). Furthermore, the objective function is lower with M0 model than with M1 model, which confirms the superiority of the M0 model. The MM model provided almost perfect fit to the data of all subjects. This conclusion, illustrated in Fig. 3C, was confirmed by a further reduction of the objective function. However, the difference between the M0 and MM models is small and it is difficult to show the superiority of either model.

Saturable Rate of Cefatrizine Absorption

25

7"

e

9

A

o

g

8 "r-

C

9

,

1

9

,

2

9

r

3

9

,

.

4

,

5

9

,

6

9

,

7

9

,

8

Hours Fig. 3. Cefatrizine concentrations in plasma (O) with time in one subject. The curves (solid lines) result from the fit of the parameters of the three models to the experimental data. Panel A: M1 model, Panel B: M0 model, and Panel C: MM model.

Reigner, C met, Guedes, Fourtillan, and Tozer

26

The superpositioning of simulated M0 and MM model curves on the experimental data, however, shows some difference in that the peak has discontinuity with the M0 model but is smooth with the MM model. This difference is only apparent in about half of the subjects. Formal comparison using the statistical likelihood-ratio test confirms the visual observations; the difference is statistically significant (P < 0.05) with 6 out of 12 subjects. A significant difference appears to occur when there are experimental concentrations exactly at the peak time. Thus, more information (samples) near the peak may allow better discrimination between the models. In statistical terms, the experiment failed sometimes to show the superiority of the MM model, but with another experimental design, this alternative hypothesis might be accepted. The mean + SEM values of the pharmacokinetic parameters estimated directly by the nonlinear regression with the M0 and MM models are presented in Table I. Model parameters in individual subjects were estimated with precision (coefficients of variation from the covariance matrix lower than 10%) except with K'm, for which the coefficients of variation were about 50%. The lower variability in K " estimation is observed with the subjects for whom the difference between the M0 and MM models is significant. Absorption parameters have been used to simulate the rate of absorption as a function of time for the three models (Fig. 4A). The shape of the curve for the MM model is intermediate between those of the other two models. From Eq. (5), it appears that the rate of absorption approaches the first-order kinetics (M1 model) if Km is large compared to the concentration at the absorption site; conversely, if K m is small, the rate remains independent of the concentration and close to Vmax, a condition equivalent to zero-order kinetics. These conclusions are illustrated in Fig. 4B. As observed in Fig. 2B, the absorption rate of cefatrizine is almost constant and there is a tendency to move toward first-order kinetics at the end of the process,

Table I. Mean • Values of the Pharmacokinetic Parameters Estimated by the Nonlinear Regression Analysis With the M0 and M M Models Parameters

Ca'(O) ( m g . L - l ) ~"(hr) V~ax(mg 9 hr -1 - L -~) K ~ ( m g . L -1) tla~ (hr) k (hr-~)

M0 model

M M model

10.6• 1.44 • 0.07 Not applicable Not applicable 0.34 • 0.04 0.49 • 0.02

10.7• Not applicable 9.2• 1.1 +0.4 0.35 • 0.04 0.49 • 0.02

Saturable Rate of Cefatrizine Absorption

800

9

600

9

27

A

M0

400

200

"~

"

5 0 0 "1

,0ol 3~176 t

t 0

3

Hours Fig. 4. Panel A: Simulation of the rate-time profiles of the three absorption models. The parameters of the three models are as follows: M1, k ~ - 1.39hr-1; M0, ~'= 1.44hr; MM, V~a ~= 9 . 1 6 m g . h r - L . L -z, K ~ = l . 1 2 m g - L -z, Ca'(O)=10.Tmg. L -1, and tjag= 0.34 hr for the three models. The MM and M0 models parameters are the mean values obtained from fitting these models to the individual subjects. The simulated k a value for the M1 model was chosen to be the same as the mean input of the M0 model (1/k~ = r/2). Panel B: Simulation of the MM model in which the rate of absorption with time is shown as a function of the K ~ value. The values of other parameters are V~, x= 9.16 mg 9 hr -1 9 L -1, Ca'(O) = 10.7 mg 9 L -1, and tj~e = 0.34 hr. The Krm values are 0.28 (1), 0.56 (2), 1.12 (3), 2.24 (4), and 4.48 mg 9 L -~ (5).

28

Reigner, Couet, Guedes, Fourtillan, and Tozer

as expected with Michaelis-Menten absorption. The extent of saturation of the absorption process can be appreciated from calculation of the ratio K'/Ca'(O). This index, equal to ( V'ax -- Ro)/Ro from rearrangement of Eq. (7), is small if Ro (equal to dCa'(O)/dt) is close to V'max. In this case, the process is almost completely saturated at time zero and apparently zeroorder kinetics continues until the absorption is nearly finished. The mean value of K'm/Ca'(O) in all subjects was 0.11 (range: 0.004 to 0.4). The six highest values were observed with the subjects for whom the MM model is statistically superior. These results confirm that cefatrizine is absorbed at an almost constant rate after a time lag of about 30 min following oral dosing with a capsule. The M0 model, which is a simplification of the MM model ( K m equal to zero), may be used practically to analyze cefatrizine data after oral administration of 500 mg. This simplification is analogous to that for ethanol elimination. The kinetics of ethanol biotransformation are expressed in terms of the Michaelis-Menten model, but the zero-order model has a broad application for the disposition of this compound (17). The averages of the classical pharmacokinetic values (C . . . . t . . . . A UC, and tl/2) have been compared by a two-way analysis of variance to evaluate the differences between the M0 and MM models (Table II). The mean values are similar, although the differences sometimes reach a significant

Table II. Statistical Comparisons of the Mean Values of Pharmacokinetic Values Obtained With the M0 and M M Models Confidence interval of the relative M0 model difference a

M M model Cmax(mg 9 L -1)

tmax(hr)

7.02+0.44

7.55+0.42

i

i

P < 0.001

1.81•

1.78•

I AUC(mg. L -~ 9 hr)

tl/2(hr)

-3.7%;0.3%

I

ns

21.56• 1.05

21.63 + 1.04

I

I

P

Saturable rate of cefatrizine absorption after oral administration to humans.

This study examined the absorption kinetics of cefatrizine, an amino-beta-lactam antibiotic, after oral administration of a single 500-mg dose to 12 h...
883KB Sizes 0 Downloads 0 Views