Introduction

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Phenytoin (diphenylhydantoin) has been used extensively in the treatment of seizure disorders. Although its pharmacokinetics has been well reported both in animals and in humans (Olanow and Finn, 1981; Bauer and Blouin, 1983; Shavit et al., 1984; Jones and Wimbish, 1985; Levine and Chang, 1990) the concentration-anticonvulsant effect profile of phenytoin is not thoroughly understood. Consequently, prediction of the accurate PK-PD relationship for both clinical and preclinical scopes is still a difficult undertaking. This can be attributed largely to the lack of adequate quantitative measures of the effect of AED in vivo (Danhof et al., 1992b). The nonlinear pharmacokinetics of phenytoin represents an additional complicating factor (Theodore, 1992).

To date, the numerous models developed to delineate the anticonvulsant properties of antiepileptic drugs in preclinical investigation, such as the kindling and maximal electroshock models, have limitations which prohibit the assessment of the PK-PD relationship (Rundfeldt et al., 1990; Rundfeldt and Löscher, 1993; Mulzac and Scott, 1993; Dimmock and Baker, 1994). A major limitation is the impossibility to determine repeatedly the anticonvulsant effect intensity within individual rats.

Furthermore, approaches in which the use of antagonists might fully explain the effect of the agonist are not applicable in vivo because of the mechanism of action of phenytoin. The neuropharmacological and biochemical effects of phenytoin are vast. Some of the reported actions of phenytoin in various systems include: (1) changes in the conductance of ionic channels (Jones and Wimbish, 1985); (2) inhibition of calcium uptake and calcium-dependent protein phosphorylation (Twombly et al., 1988); (3) elevation of membrane potential and changes in the amplitudes of synaptic potentials; (4) suppression of bursting activity; (5) increase in cortical levels of -aminobutyric acid (Griffith and Taylor, 1988).

With respect to the pharmacokinetics, it is important to consider that the decay in plasma concentration is not linear. Because the rate at which phenytoin is hydroxylated is dose dependent, elimination can follow both first and zero-order processes, depending on the concentration range. A model with Michaelis-Menten elimination is therefore required to describe the pharmacokinetics of phenytoin (Gibaldi and Perrier, 1982).

In addition, one has to consider that the bulk of PK-PD modeling theory and methodology pertains to linear pharmacokinetics with specific drug-receptor interaction systems (Danhof et al., 1992a, 1993). Mathematical models and methods for such nonlinear systems are much less developed (Ritschel and Hussain, 1984; van Rossum and Burgers, 1984; Gillespie, 1993).

The intent of this report was to develop an integrated approach for the assessment of the time course of the effect of phenytoin by use of the EEG and CSM models. The former is based on the use of quantitative EEG parameters as a measure of the effect on brain electric activity (Mandema and Danhof, 1992). The latter consists of the induction of mild convulsive activity, which is evoked by applying electric pulse trains directly to the cortex. The TLS and TGS can be used as measures of the anticonvulsant effect (Voskuyl et al., 1992). In this way, a realistic estimate of the anticonvulsant effect intensity is obtained (Hoogerkamp et al., 1994).

	Methods

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Study Design

The study protocol was approved by the Ethical Committee for Animal Experimentation. The anticonvulsant activity and the EEG effect of phenytoin were determined in two groups of rats according to a parallel group design. Two groups of male Wistar-derived rats (Sylvius Laboratory Breeding Facility, Leiden, The Netherlands) (225-300 g) were used throughout the study. The animals were housed individually in plastic cages under constant temperature (21°C) and 12-hr light/dark cycle. Laboratory chow (Standard Laboratory Rat, Mouse and Hamster Diets, RMH-TM, Hope Farms, Woerden, The Netherlands) and water were available ad libitum, except during the experimental procedures.

Surgical Procedure

Seven chronic cortical EEG electrodes were implanted in the skull of the animals (Mandema and Danhof, 1990) 1 week before the experiments for the measurement of EEG signals (group I). Implantation of two permanent electrodes over the motor area of the frontoparietal cortex (Voskuyl et al., 1989) allowed the assessment of the anticonvulsant effect (group II). One day before the measurements, indwelling cannulae were implanted into the right jugular vein (for drug administration) and femoral artery (for blood sampling).

Drug Dosage, Blood Sampling and Pharmacokinetics

A 40 mg · kg¹ dose of phenytoin was infused intravenously at a rate of 0.1 ml · min¹ for 5 min. Phenytoin sodium (Sigma Chemical Co., St. Louis, MO) was dissolved in water alkalinized with 0.1 N sodium hydroxide. Arterial blood samples (100 or 200 µl) were collected in heparinized tubes before and 5, 10, 15, 20, 30, 40, 60, 90, 120, 150, 180, 240 and 300 min after drug administration. Blood samples were then centrifuged for 10 min at 5000 rpm and plasma (50 or 100 µl) separated and stored at 30°C until analysis.

EEG Measurements and Cortical Stimulation

Group I. The output from bipolar leads was continuously monitored by a Nihon Kohden EEG recorder. During the course of the experiment, animals were kept in motion in a slow-speed rotating drum (10 rph) to control the vigilance level. Base-line activity was monitored for 30 min. After drug administration, EEG recordings were continued for 5 hr. The frontocentral lead on the left hemisphere was subjected to on-line aperiodic analysis for quantification of the effect. The aperiodic analysis algorithm calculates the amplitudes of each EEG signal on a wave-by-wave basis. The analyzed EEG data were stored on a magnetic floppy disk. The drug-induced change in the total number of waves in the 12.0- to 30.0-Hz frequency band was applied as effect measure.

Group II. The seizure thresholds were determined as described previously (Voskuyl et al., 1989). Convulsive activity was induced by a single train of bipolar pulses (total pulse duration, 2 msec, 50 Hz) of increasing amplitude (0-1000 µA in 15 sec) applied to the electrodes. The TLS and TGS were defined as the minimal current intensity necessary to induce clonic movements of the forelimbs and generalized clonic activity, respectively. Stimulation was continued until the TGS was reached. Seizure activity was induced five times before the infusion started, at intervals of 5 min between each stimulation, to determine the base-line threshold values. Thereafter, drug effect was assessed up to 5 hr after administration, at intervals between stimulations, varying from 5 min immediately after the infusion to 15 min 2 hr later. The effect was determined subsequently by use of a video-recording device. The elevation of the thresholds above their average base line represents the anticonvulsant effect.

Phenytoin Assay

Samples were analyzed by the high-performance liquid chromatography technique essentially in the manner outlined by Ratnaraj et al.(1989). A solution of 1.5 µg mephenytoin (internal standard) in 150 µl acetonitrile was added to a 50- or 100-µl plasma sample. To separate the organic phase, 100 µl saturated NaH₂PO₄ solution were added and then whirl-mixed for 15 sec. After 10 min centrifugation at 5000 rpm, 75 µl were transferred from the supernatant and 25 µl were injected into the chromatographic system. The mobile phase consisted of a mixture of 0.067 M phosphate buffer (pH = 5.6) and acetonitrile in a 70:30 ratio with a flow rate of 1.7 ml · min¹. The high-performance liquid chromatography system consisted of a Kratos solvent delivery system, a WISP-710B automatic sample injector and a Spectroflow 757 Kratos spectrophotometer (wave length, 215 nm). The analytical column was a 25 cm × 4.6 mm i.d. Altex column filled with Ultrasphereô-ODS 5 µ. Data processing was performed by a Chromatopack C-R3A reporting integrator. Phenytoin retention time was 8.0 min. Within-day precision was 1.7% for a 10 µg · ml¹ control sample (n = 8). Limit of detection was 0.25 µg · ml¹ and the assay was linear in the range from 1 to 100 µg · ml¹.

Protein Binding

Residual blood was collected by aorta puncture after completion of the experiments and centrifuged for 10 min at 5000 rpm. Plasma was separated and stored at 30°C until assay. The protein binding was determined for each individual animal by ultrafiltration at 37°C, with use of the Amicon Micropartition System (Amicon Division, Danvers, MA). Three 0.5-ml aliquots of a plasma sample were spiked with phenytoin to a concentration of 10, 50 and 100 µg · ml¹. Total plasma concentration was measured by the described method in a 50-µl sample of the spiked plasma. Separation of free drug from protein-bound drug was carried out at 37°C by filtration of a 400-µl plasma through a YMT ultrafiltration membrane (Amicon) at 1090 × g for 10 min. The ultrafiltrate was then analyzed for free drug concentrations.

Data Analysis

The pharmacokinetics and pharmacodynamics of phenytoin were quantified for each individual rat. First, a two-compartment model with Michaelis-Menten elimination was used to describe the plasma concentration-time profile (Gibaldi and Perrier, 1982):

(1)

(2)

with the error model

(3)

where dC₁/dt is the rate of decline of drug concentration at time t, V₁ the distribution volume, V_max the theoretical maximum rate of the process, K_m the Michaelis-Menten constant and k_ij the transfer rate constant from compartment i to j; 1 and 2 refer to the first and second compartments, respectively. C_mi is the ith measured concentration and C_pi is the predicted concentration according to the PK model. The model was programmed into SIMULINK (The MathWorks Inc., Natick, MA) and a fifth-order Runge-Kutta method was used for integration. The data were fitted to the model by use of the nonlinear least squares routine fmins in MATLAB (The MathWorks Inc., Natick, MA), which uses the simplex method for the minimization. The log-transform is approximately equivalent to a constant CV model.

The hysteresis was collapsed with a hysteresis minimization routine written for MATLAB based on the COLAPS program described previously (Veng-Pedersen et al., 1991). C_e was calculated by SIMULINK according to the following link model (see fig. 1):

(4)

where *C_p indicates convolution of the concentration in the central compartment.

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Schematic representation of the fitting model used for kinetics and hysteresis minimization.

The sigmoid E_max model was used to describe the relationship between drug concentration and EEG effect (Holford and Sheiner, 1982):

(5)

where E(C_e) is the observed effect at concentration C, E₀ is the base-line effect value, E_max is the maximal effect, EC₅₀ is the concentration at half-maximal effect and n is a constant expressing the shape of the concentration-effect relationship.

Finally, based on the sigmoid E_max model we have derived an equation to describe the exponential profile of the anticonvulsant effect. This was performed under the assumption that both EC₅₀ and E_max values are very high and cannot be determined experimentally, without lesion of the brain or animal harm. When drug concentrations are small in relation to EC₅₀, the equation tends to a constant value in the denominator. In practice, the combined parameter E_max/EC₅₀ⁿ may be used to describe drug effect in the range observed:

(6)

Assuming that E_max/EC₅₀ⁿ = Bⁿ, the equation can be rewritten as:

(7)

where E(C_e) is the observed effect at concentration C, E₀ is the base-line effect value, B represents the quotient between E_max and EC₅₀ and n is a constant expressing the steepness of the curve.

In both cases the pharmacokinetic model was used to generate drug concentrations at the times of effect measurement. The equations were fitted to the data by the nonlinear least squares regression routine in MATLAB. After applying the Bartlett's test for nonhomogeneity of variances, statistical analysis was carried out by a one-way analysis of variance or the nonparametric Kruskal-Wallis test.

	Results

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Pharmacokinetics

The kinetic disposition of phenytoin followed a two-compartment model with Michaelis-Menten elimination. The averaged concentration profile is plotted against time in figure 2. V_max and K_m presented somewhat higher values in group II (table 1). Because protein binding was similar in both groups, the lower values of volume of distribution apparently compensated for such differences, without additional consequences for biophase equilibration and pharmacodynamics.

View larger version (12K): [in this window] [in a new window]   Fig. 2.   Time course of phenytoin plasma concentration (n  7) after i.v. infusion of 40 mg · kg1 phenytoin. The markers denote the mean ± S.E.. The solid line represents the fit to all individual data. The bars indicate the duration of infusion.

Hysteresis

The effect onset was characterized by a temporal delay relative to plasma concentrations in both groups. As shown in figure 3, the hysteresis was minimized successfully by the link model. k_e0 values of the same magnitude were obtained for the EEG and anticonvulsant effects.

View larger version (13K): [in this window] [in a new window]   Fig. 3.   The hysteresis between plasma concentration and EEG effect of an individual rat is normalized after minimization with a monoexponential conductance function. The same is observed for the hysteresis between plasma concentration and the anticonvulsant effect (TGS). The arrow indicates the time sequence of the observations.

Pharmacodynamics

Group I. Intravenous administration of phenytoin induced changes in both amplitudes and TNW in the beta frequency band (12.0-30.0 Hz) of the EEG spectral power. The increase in TNW was selected as the EEG effect measure (fig. 4). Because an E_max value was reached, the concentration-EEG effect relationship could be characterized by the sigmoid E_max model (fig. 5).

View larger version (15K): [in this window] [in a new window]   Fig. 4.   Time course of averaged EEG () and anticonvulsant (TGS, ) effects (n  7) after i.v. administration of phenytoin (40 mg · kg1). Plots show changes relative to base-line values and the markers indicate the mean ± S.E.. The TLS () was not affected by drug administration. The solid bars represent the duration of infusion.

View larger version (13K): [in this window] [in a new window]   Fig. 5.   PK-PD relationships of phenytoin for individual rats in the EEG and CSM. , Relationship between phenytoin concentrations and the EEG effect measure derived after i.v. administration. The solid line represents the best fit of the actual data to the sigmoid Emax model. , Relationship between phenytoin concentrations and the anticonvulsant effect. The solid line represents the best fit to the exponential equation.

Group II. The anticonvulsant effect of phenytoin was reflected by the elevation of the TGS without any significant alteration in the TLS. As depicted in figure 4, the effect-time course profile followed a pattern remarkably similar to the changes observed in the EEG. However, fitting these data to the sigmoid E_max model was not possible. It seems that E_max cannot be reached at the administered dose. The exponential equation 7 was used to describe the nonlinear profile of the anticonvulsant effect (fig. 5). The pharmacokinetic and pharmacodynamic parameters generated from the PK-PD modeling are summarized in table 1.

	Discussion

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In this study we demonstrate the application of an integrated PK-PD approach to characterize the biophase equilibration kinetics and the concentration-effect relationship of phenytoin both in the EEG and in the cortical stimulation models.

The nonlinear pharmacokinetic profile of phenytoin, described by a two-compartment model with Michaelis-Menten elimination, presented high variability. Our data agree with published data, however (Jones and Wimbish, 1985; Itoh et al., 1988). K_m (Michaelis constant) and V_max (maximum metabolic rate) estimates in different populations range from 1.2 to 24.2 µg · ml¹ and 108 to 568 µg · min¹, respectively (Rambeck et al., 1979). The nonlinear phase of decay in plasma concentration (concentrations greater than the K_m values) persisted up to 2 hr after administration in both groups (fig. 2). Because the effect predominated over the same time span, modeling of the concentration-effect profile occurred essentially in the nonlinear phase. Plasma protein binding presented only minor variations within the concentration range investigated. The free fraction ranged from 25 to 30%, which is consistent with data published previously (Levine and Chang, 1990).

To exert its anticonvulsant effect, phenytoin needs to reach its site of action in the central nervous system. Phenytoin in the unbound form distributes into transcellular fluids and is present in various tissue compartments, including liver, fat, muscle and brain (Jones and Wimbish, 1985). In principle, one could expect peak brain concentrations after i.v. administration to be reached immediately, because of the high lipophilicity of phenytoin and the relatively high blood flow to the brain. However, previous studies reported that maximum concentrations in brain were observed 6 min after a 2-min i.v. infusion was completed (Ramsay et al., 1979). Such a difference coincides with the delay to the onset of effect and to maximal effect observed in both models investigated.

The temporal delay (hysteresis) between plasma concentrations and effect appears to be a characteristic of PK-PD modeling of several drugs active in the central nervous system (Mandema et al., 1991; Danhof et al., 1992a). The current study does not permit us to establish whether distribution is the major determinant of the observed hysteresis. However, the rationale for this delay is easily understood if one assumes that the resulting pharmacological effect or response is preceded by drug distribution to the site of action. Thus far, there is no consistent report demonstrating the role of other factors in the biophase equilibration of phenytoin which are known to cause hysteresis, such as coupling mechanisms and effectuation process that follow the drug-receptor interaction. The hysteresis can be modeled mostly by the effect-compartment approach, which postulates the existence of a hypothetical effect compartment linked to the plasma site by a first-order process (k_e0). Our approach is based on the assumption that distribution kinetics between plasma and effect site is linear and that the same effect-site concentration always evokes the same response, independent of time. This assumption may not hold when interactive metabolites are formed or when there is development of acute tolerance. However, it has been demonstrated that main metabolites of phenytoin have little or no antiepileptic activity (Jones and Wimbish, 1985). Moreover, there is no evidence of the development of tolerance toward the EEG or anticonvulsant effects of phenytoin in these models.

The successful minimization of hysteresis under the assumption of an effect compartment indicates that plasma (central compartment) concentration can reflect the biophase concentration properly (fig. 3). Furthermore, because the resulting k_e0 values for the EEG and anticonvulsant effects do not differ significantly, one may suggest that the biophase for both effects is pharmacokinetically indistinguishable. In fact, this can be correlated with anatomophysiological findings. The anatomical substrate (somatosensory cortex) for assessment of both effects is the same. Furthermore, studies on the brain regional distributions of specific [³H]phenytoin binding have demonstrated that the cortex is a major binding site (Wong and Teo, 1988).

Regarding the pharmacodynamics, the assessment of the anticonvulsant action is a complex issue. Therefore, useful, accurate measures of the anticonvulsant effect intensity for PK-PD studies are scarce, despite the numerous animal models of epilepsy. Quantitative pharmaco-EEG on the basis of aperiodic analysis has fulfilled most of the requirements for PK-PD modeling. In previous studies it has been successfully used to describe the effect of benzodiazepines (Mandema et al., 1992; Danhof and Mandema, 1992). Application of this technique to antiepileptic drugs has not been reported, however. For benzodiazepines a clear correlation has been established between the EEG effect and the anticonvulsant effect in the pentylenetetrazole model (Mandema et al., 1991). Whether this is also the case for phenytoin remains to be determined. To date, it is well known that phenytoin increases levels of -aminobutyric acid in rat cerebral cortex and enhances its uptake (Wong and Teo, 1988). In addition, phenytoin was recently shown to potentiate the increase in the amplitude of cortical high frequency (20-30 Hz) background activity induced by N-methyl-D-aspartate antagonists. This EEG response is considered to be caused by the antagonistic effect exerted by phenytoin on the release of glutamate or on the N-methyl-D-aspartate receptor-linked channels (Popoli et al., 1994). The existing data do not permit the conclusion that the observed EEG effects are relevant to the anticonvulsant action of phenytoin. Further investigation is still required to establish a correlation between the EEG effect and the pharmacological mechanisms involved. Notwithstanding, the primary merit of such a parameter is to allow PK-PD modeling of the effect according to the sigmoid E_max model, providing meaningful pharmacodynamic estimates, i.e., E_max and EC₅₀. Moreover, it is worth noting that in vivo PK-PD modeling of a drug with nonlinear kinetics by the sigmoid E_max model has not been reported thus far.

In contrast to the EEG response, the pharmacodynamic endpoint in the CSM is a direct measure of the anticonvulsant action of phenytoin. Particularly important is the fact that the CSM is one of the few models that allow a graded, reproducible and clinically relevant measure of the antiepileptic effect in an individual animal (Hoogerkamp et al., 1994). In addition, the pharmacological meaning of each threshold has been investigated in previous studies (Voskuyl et al., 1992). Analogous to the difference in efficacy in the pentylenetetrazole and maximal electroshock screening models, the threshold for localized seizure activity has been shown to reflect the capacity of a drug to block the onset or triggering of seizure activity but the threshold for generalized seizure activity to encompass the capacity of a drug to prevent propagation of the seizure activity. Thus, the elevation of the TGS without alteration in the TLS agrees with the postulated mechanisms of action of phenytoin, which involve inhibition of the propagation of seizure activity.

The PK-PD relationship presented a nonlinear pattern with a steep increase of the effect at the concentration range of 15 to 25 µg · ml¹ (fig. 5). As in previous studies E_max could not be measured. This seems to be a common feature of the method for all the antiepileptic drugs (Hoogerkamp et al., 1994). Such a phenomenon might be explained by the impossibility of more frequent measurement of the effect at the early distribution phase. Furthermore, because the current that was applied to the cortex does not discriminate between inhibitory or excitatory systems, another hypothesis to consider is the triggering and overlapping of different mechanisms which distort the actual effect profile at higher current intensity. This has been partially investigated in a comparison between the concentration-anticonvulsant effect profiles of antiepileptic drugs in the pentylenetetrazole model and in the CSM. The results indicated that the mechanisms by which seizure activity is evoked in these models are responsible for the differences in effect pattern (Dingemanse et al., 1990). This does not diminish the quality and accuracy of the information obtained from the thresholds, however. In terms of modeling, such a nonlinear profile can be fitted by either an exponential function, as the one we have applied here, or by the log-linear model, which is a simplification of the sigmoid E_max model. However, the log-linear model does not explain the effect in the absence of the drug and requires the assumption of a threshold for concentrations to produce a significant effect (Holford and Sheiner, 1981).

In fact, the parameters derived from this approach seem to provide a realistic insight into the anticonvulsant effect of phenytoin. Despite the practical constraints mentioned above, both EC₅₀ values in the EEG model and the concentration range of effective anticonvulsant action in the CSM are of the same magnitude as the therapeutic levels in humans. Correcting for protein binding, the EEG effect occurred in the range of 1.8 to 6.0 µg · ml¹ whereas a significant elevation of the TGS was observed between 1.75 and 10 µg · ml¹. This is consistent with plasma concentrations yielding effective therapeutic responses in humans (Wolf, 1993; Yoshida et al., 1993).

In conclusion, our results show that the use of concomitant PK-PD modeling provided independent, accurate information about the transport of phenytoin to the site of action, understanding about the nature of the observed effects and the underlying concentration-effect relationship. Application of this methodology represents an important step forward in the comprehension of the pharmacodynamics of drugs with nonlinear pharmacokinetics.