During the last decade, the application of pharmacokinetic and pharmacodynamic modeling techniques has become an increasingly important aspect of contemporary clinical psychopharmacology (1–5). These techniques have been applied during the process of development of new drug entities as well as for the improved understanding of the clinical actions of drugs that are already marketed. Techniques for the study of drug metabolism in vitro have advanced substantially during the last decade, and now are an integral component of preclinical drug development and the link to subsequent clinical studies of drug metabolism and disposition.
Kinetic-dynamic modeling techniques have been combined with in vitro metabolism procedures and in vitro–in vivo mathematical scaling models to provide insight into the general problem of pharmacokinetic drug interactions in clinical psychopharmacology (6–9). This chapter reviews some advances in pharmacokinetics, pharmacodynamics, and drug metabolism, along with methodologic applications to selected problems in clinical psychopharmacology.
POPULATION PHARMACOKINETICS Principles Pharmacokinetic studies based on a traditional intensivedesign model are usually conducted using carefully selected volunteer subjects, a controlled experimental design, and collection of multiple blood samples. After measurement of drug and metabolite concentrations in all samples, pharma- D. J. Greenblatt, L. L. von Moltke, J. S. Harmatz, and R. I. Shader:
Department of Pharmacology and Experimental Therapeutics, Tufts University School of Medicine, and Division of Clinical Pharmacology, New England Medical Center, Boston, Massachusetts.cokinetic models are applied to determine parameters such as elimination half-life, volume of distribution, and clearance.
During the new drug development process, a series of pharmacokinetic studies are conducted to determine the influence of major disease states or experimental conditions hypothesized to affect drug disposition. Such factors might include age, gender, body weight, ethnicity, hepatic and renal disease, coadministration of food, and various drug interactions.
Classical pharmacokinetic studies can quantitate the effects of anticipated influences on drug disposition under controlled circumstances, but cannot identify the unexpected factors affecting pharmacokinetics. A number of examples of altered drug pharmacokinetics became apparent in the patient care setting only in the postmarketing phase of extensive clinical use. Examples include the digoxin-quinidine interaction, altered drug metabolism due to cimetidine, and the ketoconazole-terfenadine interaction.
Population pharmacokinetic methodology has developed as an approach to detect and quantify unexpected influences on drug pharmacokinetics (10–18). Population pharmacokinetic studies, in contrast to classical or traditional pharmacokinetic studies, focus on the central tendency of a pharmacokinetic parameter across an entire population, and identify deviations from that central tendency in a subgroup of individual patients. One software program widely applied to population pharmacokinetic problems is the nonlinear mixed-effects model (NONMEM).
Analysis of clinical data using a population approach allows pharmacokinetic parameters to be determined directly in patient populations of interest and allows evaluation of the influence of various patient characteristics on pharmacokinetics. Because the number of blood samples that need to be collected per subject is small, this approach is often suitable for patient groups unable to participate in traditional pharmacokinetic studies requiring multiple blood samples (e. g. , neonates, 508 Neuropsychopharmacology:
The Fifth Generation of Progress children, critically ill patients, or individuals who are not able to provide informed consent) (19). In many cases the population approach has yielded pharmacokinetic parameter estimates similar to those delineated in classical pharmacokinetic studies of the same drug. Application: Methylphenidate Pharmacokinetics The population approach is illustrated in a study of methylphenidate (MP) pharmacokinetics in children (20). This is a patient group for whom the multiple-sample pharmacokinetic study design may not be appropriate for ethical and practical reasons.
Participating subjects were 273 children aged 5 to 18 years having a primary diagnosis of attentiondeficit/hyperactivity disorder (ADHD). They had been receiving MP at a fixed dosage level for at least 4 weeks, and were under treatment for at least 3 months. The treating physician for each patient judged MP to be clinically effective. Children meeting the eligibility criteria had an initial screening visit, at which one parent or a legal guardian provided written informed consent, and the child provided assent.
Demographic characteristics were recorded, including the dosage of MP, the usual times for individual doses, and the duration of treatment. The second visit, which followed shortly, was a bloodsampling day. Each child, accompanied by parent or guardian, arrived at the investigator’s office 30 to 60 minutes prior to blood sampling. The time and size of the last MP dose, and of any other medication received that day or during the prior 2 weeks, were recorded. A 5-mL whole blood sample was obtained by venipuncture.
This sample was immediately centrifuged, and a 2-mL aliquot of plasma was removed for subsequent determination of MP concentrations by a liquid chromatography/mass spectroscopy/mass spectroscopy (LC/MS/MS) assay. Analysis of Data The identified independent variables were age, sex, body weight, size of each dose, and time of sample relative to the most recent dose. Since only single samples were available for all but 16 of these children, the contribution of withinsubject variance to overall variability in outcome could not be assessed.
The pharmacokinetic model was a one-compartment model with first-order absorption and first-order elimination, under the assumption that all subjects were at steady state (Fig. 38. 1). The overall model was specifically modified for each of the 273 subjects to incorporate the individually applicable independent variables, as well as the dosage schedule (b. i. d. or t. i. d. ). Individual values of continuous variables (t time sample taken relative to the first dose; C plasma MP concentration) were fitted to a single set of iterated.
FIGURE 38. 1. Population pharmacokinetic model for methylphenidate (MP). A series of data points, each consisting of the time (t) after the first dose of the day and the plasma MP concentration (C) at that time, was available from 273 subjects (one data point per subject). Each of these was linked to that subject’s individual dose schedule, size of each dose, interval between doses, and body weight. These variables were entered into a one-compartment pharmacokinetic model with first-order absorption and first-order elimination, as shown.
Using nonlinear regression, the process yielded ‘‘typical’’ population values of clearance per kilogram body weight, the elimination rate constant (Ke), and the absorption rate constant (Ka). variables using unweighted nonlinear regression (Fig. 38. 1). When the time between first and second doses, or between second and third doses, was not available, the mean value was assigned based on cases in which the data were available. For the b. i. d. dosage, the mean interval was 4. 3 hours. For the t. i. d. dosage, the mean intervals were 4.1 and 3. 7 hours, respectively.
As is customary, clearance was assumed to be proportional to body weight. Results The total daily dose of MP was significantly lower in subjects receiving MP b. i. d. (n 109) compared to subjects on a t. i. d. schedule (n 164); the mean total daily dosages in the two groups were 25 and 39. 3 mg, respectively (p . 001). Within each group, clinicians’ choices of total daily dosages were influenced by body weight, as mean total daily dose increased significantly with higher body weights.
However, the association of body weight with mean plasma concentration was not significant for the b. i. d. dosage group, and of only borderline significance (. 05 p . 1) for the t. i. d group. This finding is consistent with the underlying assumption that clearance is proportional to body weight. Age was significantly correlated with body weight (r2 0. 77). Height and 0. 54, p . 001) and with height (r2 0. 77). body weight also were significantly correlated (r2 An acceptable estimate of absorption rate constant could be derived only for the b.i. d. dosing data.
The iterated pa- 38: Pharmacokinetics, Pharmacodynamics, and Drug Disposition 509 FIGURE 38. 2. Overall relation of observed and predicted plasma methylphenidate concentrations (ng/ml). The r-square value of 0. 43 indicates that the model accounts for 43% of the overall variance in plasma concentrations. (From Shader RI, Harmatz JS, Oesterheld JR, et al. Population pharmacokinetics of methylphenidate in children with attention-deficit hyperactivity disorder. J Clin Pharmacol 1999;39:775–785, with permission. ) FIGURE 38. 3.
Predicted plasma methylphenidate concentration curves for b. i. d. and t. i. d. dosage schedules, based on parameter estimates from the population analysis, together with mean values of input variables (body weight, size of doses, intervals between doses). (From Shader RI, Harmatz JS, Oesterheld JR, et al. Population pharmacokinetics of methylphenidate in children with attention-deficit hyperactivity disorder. J Clin Pharmacol 1999;39:775–785, with permission). rameter estimate was 1. 192/h, corresponding to an absorption half-life of 34. 9 minutes.
This estimate was then fixed, and the entire data set analyzed to determine clearance per kilogram of body weight, and the first-order elimination rate constant. The iterated estimates were 0. 154/h for elimination rate constant, corresponding to an elimination halflife of 4. 5 hours (relative standard error: 23%). For clearance, the estimate was 90. 7 mL/min/kg (relative standard error: 9%). The overall r-square was 0. 43 (Fig. 38. 2). There were no evident differences in pharmacokinetics attributable to gender.
Figure 38. 3 shows predicted plasma MP concentration curves for b. i. d.and t. i. d. dosage schedules, based on the population estimates. Implications Pharmacokinetically based approaches to the treatment of ADHD with MP are not clearly established (21–25). In the present study of prescribing patterns in particular clinical practices, the mean prescribed per dose amount for the whole study population was 0. 335 mg/kg per dose (range 0. 044–0. 568), and 36% of the children received between 0. 25 and 0. 35 mg/kg per dose.
The mean total daily dose was 0. 98 mg/kg/day for the entire sample, and increased significantly in association with larger body weight.
This may reflect the clinicians’ considering body weight in their choice of total daily dosage, or it may be that the dose was titrated according to response, which in turn was influenced by associations among concentration, clearance, and weight.
The pharmacokinetic model explained 43% of the variability in plasma MP concentrations during typical naturalistic therapy. The model fit equally well for both genders. Assuming that clearance is proportional to body weight in the context of intercorrelated age and weight allows age, weight, and daily dosage to be used to predict plasma concentrations of MP during clinical use in children.
These findings support the value of prescribing MP on a weightadjusted basis. Our typical population value of elimination half-life was 4. 5 hours, with a confidence interval of 3. 1 to 8. 1 hours. This estimate somewhat exceeds the usual range of half-life values reported in single-dose kinetic studies of MP (25, 26). This could reflect the relatively small number of plasma samples from the terminal phase of the plasma concentration curve, upon which reliable estimates of beta are dependent.
MP kinetics may also have a previously unrecognized dose-dependent component, in which estimated values of half-life are larger at steady state than following a single dose. 510 Neuropsychopharmacology: The Fifth Generation of Progress The single-sample approach described in this study allows relatively noninvasive assessment of pharmacokinetic parameters in a group of children and adolescents under naturalistic circumstances of usual clinical use, when blood sampling is not otherwise clinically indicated.
This approach in general can be applied to other special populations such as neonates, the elderly, or individuals with serious medical disease. KINETIC-DYNAMIC MODELING Principles Pharmacokinetics is the discipline that applies mathematical models to describe and predict the time course of drug concentrations in body fluids, whereas pharmacodynamics refers to the time course and intensity of drug effects on the organism, whether human or experimental animal (Fig. 38. 4).
Both have evolved as the techniques for measuring drug concentrations, and drug effects have become more accurate and sensitive. Evolving in parallel is kinetic-dynamic modeling, in which the variable of time is incorporated into the relationship of effect to concentration (Fig. 38. 4) (27–32). A concentration-effect relationship is, in principle, the most clinically relevant, because it potentially validates the clinical rationale for measuring drug concentrations in serum or plasma.
A kinetic-dynamic study in clinical psychopharmacology typically involves medication administration (usually under placebo-controlled, double-blind laboratory conditions) followed by quantitation of both drug concentration and clinical effect at multiple times after dosing. Measures of effect FIGURE 38. 4. Schematic relation between pharmacokinetics, pharmacodynamics, and kinetic-dynamic modeling, based on the status of the variables of time (t), concentration (C), and effect (E).
Note that kinetic-dynamic modeling incorporates both pharmacokinetics and pharmacodynamics, with time subsumed into the relation of concentration and effect. necessarily depend on the type of drug under study. For sedative-anxiolytic drugs such as benzodiazepines, effects of interest may include subjective or observer ratings of sedation and mood; semiobjective measures of psychomotor performance, reaction time, or memory; or objective effect measures such as the EEG or saccadic eye movement velocity.
The various measures differ substantially in their relevance to the principal therapeutic actions of the drug, the stability of the measure in terms of response to placebo or changes caused by practice or adaptation, the objective or subjective nature of the quantitative assessment, and the comparability of results across different investigators and different laboratories (Table 38. 1). The extent to which the various pharmacodynamic measures provide unique information, as opposed to being overlapping or redundant, is not clearly established.
Pharmacokinetic and pharmacodynamic relationships initially are evaluated separately, and the relationship of effect versus concentration at corresponding times is examined graphically and mathematically. Effect measures are usually expressed as change scores: the net effect (E) at postdosage time t is calculated as the absolute effect at this time (Et) minus the predose baseline value (Eo), that is, E Eo. Several mathematical relationships between effect Et and concentration (E versus C), often termed ‘‘link’’ models, are of theoretical and practical importance (5,32).
The ‘‘sigmoid Emax’’ model, incorporates a value of Emax, the maximum pharmacodynamic effect, and EC50 is the ‘‘50% effective concentration,’’ the concentration that is associated with half of the maximum effect (Fig. 38. 5). The exponent A reflects the ‘‘steepness’’ of the concentration-response relationship in its ascending portion. The biological importance of A is not established. A concentration-effect relationship that is consistent with the sigmoid Emax model may be of mechanistic importance, because drug-receptor interactions often fit the same model.
The Emax and EC50 values allow inferences about questions such as the relative potency or efficacy of drugs producing the same clinical effect, individual differences in drug sensitivity, the mechanism of action of pharmacologic potentiators or antagonists, and the possible clinical role of new medications. The sigmoid Emax model does not necessarily apply to all concentration-effect data (32). When experimental data are not consistent with the model, the corresponding misapplication of the sigmoid Emax relationship can lead to misleading conclusions about Emax and EC50.
Some data sets are consistent with less complex models, such as exponential or linear equations (Fig. 38. 5); in these cases, the concepts of Emax and EC50 are not applicable. Kinetic-dynamic modeling is further complicated when drug concentrations measured in serum or plasma do not reflect the concentration at the site of action, which is sometimes termed the ‘‘effect site. ’’ This is illustrated by the data described below. 38: Pharmacokinetics, Pharmacodynamics, and Drug Disposition TABLE 38. 1.
PHARMACODYNAMIC ENDPOINTS APPLICABLE TO STUDIES OF GABA-BENZODIAZEPINE AGONISTS Classification (with Examples) Subjective Global clinical ratings; targeted rating scales Semi-objective Psychomotor function tests; memory tests Objective Electroencephalography Relation to Primary Therapeutic Action Effect of Placebo Effect of Adaptation/Practice Need for “Blind” Conditions Approach to Quantitation 511 Close Yes Yes Yes Transformation of ratings into numbers Test outcomes are quantitative May be linked to adverse effect profile Not established Yes Yes Yes No No No Fully objective computer-determined quantitation GABA, ? -aminobutyric acid.
Application: Kinetics And Dynamics Of Intravenous Lorazepam In this study the benzodiazepine derivative lorazepam was administered intravenously according to a complex bolusinfusion scheme (33). On the morning of the study day, a rapid intravenous dose of lorazepam, 2 mg, was administered into an antecubital vein, coincident with the start of a zero-order infusion at a rate of 2 g/kg/h. The infusion continued for 4 hours and then was terminated. Venous blood samples were drawn from the arm contralateral to the site of the infusion prior to drug administration and at multiple time points during 24 hours after the start of lorazepam infusion.
Samples were centrifuged, and the plasma separated and frozen until the time of assay. The EEG was used as the principal pharmacodynamic outcome measure (Table 38. 1). The EEG was recorded prior to lorazepam administration, and at times corresponding to blood samples. EEG data were digitized over the power spectrum from 4 to 30 cycles per second (Hz), and analyzed by fast Fourier transform to determine amplitude in the total spectrum (4 to 30 Hz) and in the beta (12 to 30 Hz) frequency range (33–35). Concentrations of lorazepam in plasma samples were determined by gas-chromatography with electroncapture detection.
Analysis of Data The relative EEG beta amplitudes (beta divided by total, expressed as percent) in the predose recordings were used as the baseline. All values after lorazepam administration were expressed as the increment or decrement over the mean predose baseline value, with values averaged across eight recording sites.
The EEG change values were subsequently used as pharmacodynamic effect (E) measures in kineticdynamic modeling procedures described below. For pharmacokinetic modeling, the relation of plasma lorazepam concentration (C) to time (t) was assumed to be consistent with a two-compartment model (Figs.38. 6 and 38. 7).
Examination of plots of pharmacodynamic EEG effect versus plasma lorazepam concentration (E vs. C) indicated counterclockwise hysteresis (see below), suggesting a delay in equilibration of lorazepam between plasma and the site of pharmacodynamic action in brain. This equilibration effect has been described in previous clinical and experimental studies of lorazepam (34,36–39). Accordingly the relationship was modified to incorporate a distinct ‘‘effect site,’’ at which the hypothetical lorazepam concentration is CE (Fig.38. 6).
The apparent rate constant for drug disappearance from the effect compartment is kEO; this rate constant determines the apparent half-life of drug equilibration between FIGURE 38. 5. Three mathematical relationships between concentration (C) and change in pharmacodynamic effect (E) that are commonly applied in kinetic-dynamic modeling procedures. For the sigmoid Emax model, Emax is maximum pharmacodynamic effect, EC50 is the concentration producing a value of E equal to 50% of Emax, and A is an exponent.
For the exponential and linear models, m is a slope factor. 512 Neuropsychopharmacology: The Fifth Generation of Progress plasma and effect site. Under these assumptions, the relation of E to CE was postulated to be consistent with a sigmoid Emax model (Fig. 38. 5). Results Kinetic variables for lorazepam were similar to those reported in previous single-dose studies of lorazepam pharmacokinetics (34,40–45). Overall mean values were volume of distribution, 1. 7 L/kg; elimination half-life, 14 hours; clearance, 1. 44 mL/min/kg.
The bolus-infusion scheme rapidly produced mean plasma lorazepam concentrations in the range of 18 to 19 ng/mL, values close to the mean predicted value of 24 ng/mL. Lorazepam infusion produced significant increases in EEG beta amplitude throughout the 24-hour duration of the study. The maximum change over baseline was measured at 0. 25 to 0. 75 hours after the initiation of lorazepam dosage, whereas the maximum plasma concentration was measured immediately after the loading dose (Fig. 38. 8). The effect-site model eliminated the hysteresis, with a mean equilibration half-life of 8.
8 minutes (Fig. 38. 9). Implications Maximum EEG effects of lorazepam were significantly delayed following the initial intravenous bolus dose. Previous single-dose pharmacodynamic studies of lorazepam, using the EEG or other methods for quantitation of benzodiaze- FIGURE 38. 6. Schematic representation of the kinetic-dynamic model for the lorazepam study. Intravenous lorazepam was assumed to have kinetic behavior consistent with a two-compartment model: reversible distribution to a peripheral compartment, and first-order elimination (clearance) from the central compartment (rate constant: Ke).
Lorazepam in plasma was postulated to equilibrate with a hypothetical effect site, from which the exit rate constant is KEO. Finally, effect-site concentrations were presumed to be the principal determinant of pharmacodynamic effect, via a kinetic-dynamic link model as shown in Fig. 38. 5. FIGURE 38. 7. Plasma lorazepam concentrations (solid circles) together with the pharmacokinetic function determined by nonlinear regression (solid line), in a representative volunteer subject. Shown are the derived pharmacokinetic variables of elimination half-life (t1/2), volume of distribution (Vd), and clearance (CL).
FIGURE 38. 8. Mean values of plasma lorazepam concentration, and of EEG beta amplitude, during the first hour of the study. Note that pharmacodynamic EEG effects are delayed following the peak value of lorazepam in plasma. 38: Pharmacokinetics, Pharmacodynamics, and Drug Disposition 513 FIGURE 38. 9. Left: Mean values of plasma lorazepam concentration versus pharmacodynamic EEG effect at corresponding times, with arrows indicating the direction of increasing time.
As indicated in Fig. 38.8, the maximum EEG effect is delayed, and does not correspond in time to the maximum plasma concentration. Right: The scheme shown in Fig. 38. 6 was applied to the data points, with the link model being the sigmoid Emax relationship shown in Fig. 38. 5. The data points (closed triangles) are the hypothetical effect site concentrations and pharmacodynamic effect values at corresponding times. The solid line is the link model function determined by nonlinear regression, yielding the indicated values of Emax and EC50.
The overall mean equilibration half-life was 8. 8 minutes.pine effect, consistently demonstrate a delay in attainment of maximum drug effect compared to attainment of peak concentrations in plasma (34,36,37). After rapid intravenous dosage, for example, maximum effects may be delayed for an average of 30 minutes after dosage. Experimental studies of the time-course of whole-brain concentrations of lorazepam, or of the degree of benzodiazepine receptor occupancy, indicate that the delay is attributable to the slow physical entry of lorazepam into brain tissue, probably because of the relatively low lipid solubility of lorazepam (34, 38,39).
The delay was mathematically consistent with a kinetic-dynamic model incorporating a hypothetical ‘‘effect site’’ distinct from the central compartment. The half-life for equilibration between plasma and the effect compartment was approximately 9 minutes. This matches clinical experience indicating that intravenous lorazepam cannot easily be used in situations requiring minute-to-minute titration of sedative or amnestic effects (40).
Nonetheless, intravenous lorazepam can be used for the treatment of status epilepticus, although its onset of action may be somewhat slower than that of intravenous diazepam (46,47). tance for the metabolism and clearance of most drugs used in psychopharmacology and in other areas of clinical therapeutics (6–9,48–55) (Fig. 38. 10). For the CYP isoforms most relevant to human drug metabolism, each has its own distinct pattern of relative abundance, anatomic location, mechanism of regulation, substrate specificity, and susceptibility to inhibition and induction by other drugs or foreign chemicals (Table 38.2).
The expression and in vivo function of at least two CYP isoforms (CYP2D6 and CYP2C19) are regulated by a genetic polymorphism, such that some members of a population fail to express ‘‘normal’’ levels of enzyme or expresses poorly functional protein (56–62). Individuals identified as ‘‘CYP2D6 poor metabolizers,’’ as an example, have very low clearance of drugs that are major substrates for biotransformation by CYP2D6 (such as desipramine, nortriptyline, venlafaxine, tramadol, and dextromethorphan). Such individuals are at risk for developing high and potentially toxic plasma concentrations of these.
CYTOCHROMES P-450 IN PSYCHOPHARMACOLOGY: THE IMPORTANCE OF P-450-3A ISOFORMS The cytochrome P-450 (CYP) superfamily of drug metabolizing enzymes is now established as being of primary imporFIGURE 38. 10. Nomenclature system for the cytochrome P-450 (CYP) superfamily of enzymes. Following the CYP designation, the number-letter-number sequence indicates the family, subfamily, and specific isoform. 514 Neuropsychopharmacology: The Fifth Generation of Progress TABLE 38. 2. OVERVIEW OF HUMAN CYTOCHROMES P-450 CYP Isoform 1A2 2B6 2C9 2C19 Relative Hepatic Abundance 13%.