Comparison of four basic models of indirect pharmacodynamic responses

The time of maximum effect for model selection in pharmacokinetic-pharmacodynamic analysis applied to frusemide

AIMS

Both indirect-response models and effect-compartment models are used to describe the pharmacodynamics of drugs when there is a delay in the time course of the pharmacological effect in relation to the concentration of the drug. The aim of this study was to investigate whether the time of maximum response after single-dose administration at different dose levels could be used to distinguish between these models and to select the most appropriate pharmacokinetic-pharmacodynamic model for frusemide.

METHODS

Three doses of frusemide, 10, 25 and 40 mg were given as rapid intravenous infusions to five healthy volunteers. Urine samples were collected for 5 h after dosing. Volume and sodium losses were isovolumetrically replaced with an intravenous rehydration fluid. Diuresis and natriuresis were modelled for all three doses simultaneously, applying both an indirect-response model and an effect-compartment model with the frusemide excretion rate as the pharmacokinetic input.

RESULTS

The observed time of maximum diuretic and natriuretic response significantly increased with dose. This increase was well predicted by the indirect-response model, whereas the modelling with the effect-compartment model led to a poor prediction of the peaks. There was no difference between the observed and predicted time of maximum diuretic and natriuretic response using the indirect-response model, whereas the time of maximum response predicted by the effect-compartment model was significantly earlier than the time observed for the 25 mg (P < 0.05) and 40 mg (P < 0.05) doses.

CONCLUSIONS

The time of maximum response to frusemide was better described using an indirect-response model than an effect-compartment model. Studying the time of maximum response after administration of different single doses of a drug may be used as a selective tool during pharmacokinetic-pharmacodynamic modelling.

Physiological indirect effect modeling of the antilipolytic effects of adenosine A1-receptor agonists

The relationship between blood concentrations of the adenosine A1-receptor agonist N6-(p-sulfophenyl) adenosine (SPA) and its effect on both plasma nonesterified fatty acid (NEFA) and glycerol release was described on the basis of an integrated pharmacokinetic-pharmacodynamic model. An indirect response model rather than a hypothetical "link" model was used to account for the delayed response. For that purpose an empirical solution to the differential equation describing the physiological indirect response model is presented. The model-estimated rate constant for the output of the glycerol response was compared to the elimination rate constant after exogenous administration of glycerol. In a crossover designed study, chronically cannulated male Wistar rats were subjected to either SPA administration (120 microgram/kg for 15 min) for measurement of the effects on glycerol, or glycerol administration for determination of glycerol pharmacokinetics. Glycerol pharmacokinetics was determined in the presence of a stable level of SPA (171 +/- 6 ng/ml) to suppress endogenous glycerol levels completely. The indirect response model adequately described the relationship between SPA concentrations and plasma glycerol levels. The PD parameter estimates for EC50, EMAX, and Hill factor were 23 +/- 2 ng/ml, 74 +/- 3% (change from baseline), and 3.3 +/- 0.5, respectively. These values were not different from those obtained when analyzing the data on basis of the differential equation directly. Furthermore, the EC50 values for the reduction in glycerol or NEFA levels were identical (23 +/- 2 and 21 +/- 3 ng/ml, respectively) indicating that both PD endpoints reflect the same physiological process. The concentration-time profile after administration of glycerol could be described best on the basis of a biexponential function. The value for kout in the PK/PD model (0.19 +/- 0.03 min-1) corresponded very well to the terminal elimination rate constant determined after i.v. administration of glycerol (0.25 +/- 0.03 min-1). In conclusion, the antilipolytic effects of adenosine A1-receptor agonists can be described by the indirect suppression model. The rate constant describing the delay between concentration and glycerol effect was shown to be a true reflection of the removal of glycerol.

A population model for the follicular growth in women treated with follicle stimulating hormone

PURPOSE

To develop a pharmacodynamic model that can describe the time course of follicular growth and to investigate the influence, if any, of covariates on the parameters of the model.

METHODS

A population pharmacodynamic analysis was performed on total follicular volume data obtained after in vitro fertilisation and embryo transfer with urinary or recombinant human follicle stimulating hormone (FSH) treatment. A growth model in which the increase in total follicular volume with time is a function of several possible components was chosen.

RESULTS

In the final population pharmacodynamic model, increase in total follicular volume (TFV) was described by the equation: dTFV/dt = Emax.TFV/(TFV + TFV50) + constant, in which Emax, TFV50, and constant were 508 mm3/hr (interindividual variability 72%), 12,900 mm3 (66%), and 1.43 mm3/hr (91%), respectively. Growth was positively correlated to baseline estradiol levels, so that Emax and TFV50 changed 0.52% for every picomolar change from the median baseline estradiol value of 100 pmol/L. Growth was negatively correlated to pretreatment FSH levels, so that individuals with a median FSH (6.7 IU/L) were expected to have a fivefold higher total follicular volume at day 10 after the start of treatment, compared to individuals at the high end of the pretreatment FSH range (12 IU/L). No relationship between FSH concentration and follicular growth was found. The urinary versus recombinant origin of the drug did not influence the ovarian response.

CONCLUSION

Women with high endogenous levels of FSH respond less to standard doses of exogenous FSH. Women with higher baseline levels of estradiol have larger expected follicular growth rates.

Determination of parameters responsible for pharmacokinetic behavior of TCDD in female Sprague-Dawley rats

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) is the most toxic member of a class of planar and halogenated chemicals. Improvements in exposure assessment of TCDD require scientific information on the distribution of TCDD in target tissues and cellular responses induced by TCDD. Since 1980, several physiologically based pharmacokinetic (PBPK) models for TCDD and related compounds have been reported. Some of these models incorporated the induction of a hepatic binding protein in response to interactions of TCDD, the Ah receptor, and DNA binding sites and described the TCDD disposition in a biological system for certain data sets. Due to the limitations of the available experimental data, different values for the same physical parameters of these models were obtained from the different studies. The inconsistencies of the parameter values limit the application of PBPK models to risk assessment. Therefore, further refinement of previous models is necessary. This paper develops an improved PBPK model to describe TCDD disposition in eight target tissues. The interaction of TCDD with the Ah receptor and with hepatic inducible CYP1A2 were also incorporated into the model. This model accurately described the time course distribution of TCDD following a single oral dose of 10 microg/kg, as well as the TCDD concentration on Day 3 after six different doses, 0.01, 0.1, 0.3, 1, 10, and 30 microg TCDD/kg, in target tissues. This study extends previous TCDD models by illustrating the validity and the limitation of the model and providing further confirmation of the potential PBPK model for us in optimal experimental design and extrapolation across doses and routes of exposure. In addition, this study demonstrated some critical issues in PBPK modeling.

Pharmacokinetic-pharmacodynamic modelling of the anti-lipolytic and anti-ketotic effects of the adenosine A1-receptor agonist N6-(p-sulphophenyl)adenosine in rats

1. The purpose of this study was to develop and validate an integrated pharmacokinetic-pharmacodynamic model for the anti-lipolytic effects of the adenosine A1-receptor agonist N6-(p-sulphophenyl)adenosine (SPA). Tissue selectivity of SPA was investigated by quantification of haemodynamic and anti-lipolytic effects in individual animals. 2. After intravenous infusion of SPA to conscious normotensive Wistar rats, arterial blood samples were drawn for determination of blood SPA concentrations, plasma non-esterified fatty acid (NEFA) and beta-hydroxybutyrate levels. Blood pressure and heart rate were monitored continuously. 3. The relationship between the SPA concentrations and the NEFA lowering effect was described by the indirect suppression model. Administration of SPA at different rates and doses (60 microg kg[-1] in 5 min and 15 min, and 120 microg kg[-1] in 60 min) led to uniform pharmacodynamic parameter estimates. The averaged parameters (mean+/-s.e., n=19) were Emax: -80+/-2% (% change from baseline), EC50: 22+/-2 ng ml(-1), and Hill factor: 2.2+/-0.2. 4. In another group, given 400 microg kg(-1) SPA in 15 min, pharmacodynamic parameters for both heart rate and anti-lipolytic effect were derived within the same animal. The reduction in heart rate was directly related to blood concentration on the basis of the sigmoidal Emax model. SPA inhibited lipolysis at concentrations lower than those required for an effect on heart rate. The EC50 values (mean+/-s.e., n=6) were 131+/-31 ng ml(-1) and 20+/-3 ng ml(-1) for heart rate and NEFA lowering effect, respectively. 5. In conclusion, the relationship between blood SPA concentrations and anti-lipolytic effect was adequately described by the indirect suppression model. For SPA a 6 fold difference in potency was observed between the effects on heart rate and NEFAs, indicating some degree of tissue selectivity in vivo.

Comparison of a direct and indirect population pharmacodynamic model: application to recombinant human erythropoietin in athletes

Basic physiologic indirect response models have been proposed to account for the pharmacodynamics of drugs that act by way of inhibition or stimulation of the production or loss of endogenous substances or mediators. In this work, these models were applied to account for the effects of recombinant human erythropoietin (rHuEpo) in man. Indeed, rHuEpo induces a delayed increase of serum soluble transferrin receptors (sTfr) and a delayed decrease in ferritin (fr) concentrations. The purpose of the present study was to compare two pharmacodynamic approaches to relate serum erythropoietin (Epo) concentrations to the effect of rHuEpo on sTfr, and fr, the "indirect effect" and the "effect compartment" models. However, due to the average lag time of about 50 hr between the first intake of rHuEpo and the onset of the measurable effects, a delay function was incorporated into the "indirect response models" to describe the relationship between the Epo plasma concentrations and the endogenous receptors or mediators affected by the drug and responsible for the effects on sTfr and fr. There are no real differences in the descriptive features of the two models used. For these reasons, the indirect model seems more appropriate because it supplies a possible mechanistic interpretation of the physiological process.

Mathematical formalism for the properties of four basic models of indirect pharmacodynamic responses

Four basic models for characterizing indirect pharmacodynamic responses were proposed previously and applied using differential equations. These models consider inhibition or stimulation by drug of the production or loss of mediators or response variables. This report develops partially integrated solutions for these models which allow more detailed examination of the roles of model parameters and pharmacokinetic functions in affecting the time course of drug effects. Because of the nonlinear Hill function, the solutions are represented by means of definite integrals containing kinetic and dynamic functions. These solutions allow a qualitative examination, using calculus, of how response is controlled by Dose, IC50 or SC50, Imax or Smax, and kout for drugs exhibiting monotonic or biphasic disposition. Characteristics of the response curves that were identified include shape, maximum or minimum, and changes with the above parameters and time. These relationships, together with simulation studies, provide a fundamental basis for understanding the temporal aspects of the basic indirect response models.

Characterization of four basic models of indirect pharmacodynamic responses

Four basic models of indirect pharmacodynamic responses were characterized in terms of changing dose, Imax or Smax, and IC50 or SC50 to examine the effects of these fundamental drug properties on response profiles. Standard pharmacokinetic parameters were used for generating plasma concentration, and response-time profiles using computer simulations. Comparisons to theoretical expectations were made. In all four models, the maximum response (Rmax) (inhibition or stimulation) and the time of its occurrence (TRmax) were dependent on the model, dose, Imax or Smax, and IC50 or SC50 values. An increase in dose or a decrease in IC50 or SC50 by the same factor produced, as theoretically expected, identical and superimposable pharmacodynamic response patterns in each of the models. Some parameters (TRmax, ABEC) were nearly proportional to log dose, while others (Rmax, CRmax) were nonlinear. Assessment of expected response signature patterns as demonstrated in this report may be helpful in experimental designs and in assigning appropriate models to pharmacodynamic data.

Pharmacokinetic-pharmacodynamic modelling of DP-1904, a novel thromboxane synthetase inhibitor in rabbits, based on an indirect response model

A new imidazole derivative, DP-1904, produces a selective, potent and long-acting inhibition of thromboxane A2 (TXA2) syntheses and platelet aggregation. This study was designed to investigate the pharmacokinetics and pharmacodynamics (PK/PD) of DP-1904. DP-1904 disappeared from plasma with a half-life of 20 min after i.v. dosing, and the bioavailability after oral dosing was approximately 70%. The level of serum TXB2, which is a pharmacological marker for thromboxane synthetase inhibition, was measured to characterize the pharmacodynamics of DP-1904. A marked reduction of serum TXB2 was exhibited within 1 h after both i.v. and oral doses, reflecting the rapid onset of action of DP-1904. Serum TXB2 returned to the basal level much more slowly after oral dosing than after i.v. dosing, due to the longer half-life after oral dosing. An Emax model was employed to fit the pharmacological data after oral dosing, and IC50 and Emax values were estimated to be 5.0 ng/ml and 81%, respectively. In order to test its predictability, the PK/PD model was then used to predict a pharmacological profile after i.v. dosing; good agreement between the observed and predicted values was achieved. Thus, the present modelling procedure may be useful for optimizing the therapeutic regimens of DP-1904.

Pharmacodynamic modeling of furosemide tolerance after multiple intravenous administration

OBJECTIVE

Physiologic indirect-response models have been proposed to account for the pharmacodynamics of drugs with an indirect mechanism of action, such as furosemide. However, they have not been applied to tolerance development. The aim of this study was to investigate the development of tolerance after multiple intravenous dosing of furosemide in healthy volunteers.

METHODS

Three repetitive doses of 30 mg furosemide were given as rapid intravenous infusions at 0, 4, and 8 hours to eight healthy volunteers. Urine samples were collected for a period up to 14 hours after the first dose. Volume and sodium losses were isovolumetrically replaced with an oral rehydration fluid.

RESULTS

Tolerance was demonstrated as a significant decrease in diuretic and natriuretic response over time. Total mean diuresis was 35% lower (p < 0.01) and total mean natriuresis was 52% lower (p < 0.0001) after the third dose of furosemide compared with the first dose. However, there were considerable interindividual variations in the rate and extent of tolerance development for both diuresis and natriuresis. Pharmacokinetic-pharmacodynamic modeling of tolerance development was performed with use of an indirect-response model with an additional "modifier" compartment. This model gave an accurate description of the diuretic and natriuretic data after multiple dosing of furosemide and enabled the estimation of a lag-time for tolerance and a rate constant for tolerance development. Physiologic counteraction was demonstrated as a significant increase in plasma active renin levels (p < 0.00001) and a decrease in atrial natriuretic peptide levels (p < 0.005) during the day, concomitantly with the development of a negative sodium balance. This may be viewed as physiologic reflections of the modifier in our model.

CONCLUSION

Indirect-response models may be successfully applied for tolerance modeling of drugs after multiple dosing.

Use of an indirect pharmacodynamic stimulation model of MX protein induction to compare in vivo activity of interferon alfa-2a and a polyethylene glycol-modified derivative in healthy subjects

Interferon alfa-2a was chemically modified by the covalent attachment of a polyethylene glycol (PEG) moiety to enhance its circulating half-life and to reduce its immunogenicity. A comparative evaluation of the pharmacokinetics of the PEG-modified interferon alfa-2a showed a greater than twofold increase in the circulating half-life as a result of this chemical modification. An indirect physiologic response model was developed to characterize the time course of the MX protein response after subcutaneous administration of single ascending doses of either interferon alfa-2a or PEG-interferon alfa-2a in healthy volunteers. Analysis of the pharmacokinetic-pharmacodynamic relationship suggested that the PEG-modified interferon alfa-2a could not be administered less than twice weekly and therefore offered little therapeutic advantage over its unmodified counterpart, which is administered three times weekly. These results were consistent with findings in phase II trials. This study substantiates the usefulness of pharmacodynamic modeling as a tool for the development of dose recommendations and for the early selection of drug candidates in the drug development process.

Artificial neural networks as a novel approach to integrated pharmacokinetic-pharmacodynamic analysis

A novel model-independent approach to analyze pharmacokinetic (PK)-pharmacodynamic (PD) data using artificial neural networks (ANNs) is presented. ANNs are versatile computational tools that possess the attributes of adaptive learning and self-organization. The emulative ability of neural networks is evaluated with simulated PK-PD data, and the power of ANNs to extrapolate the acquired knowledge is investigated. ANNs of one architecture are shown to be flexible enough to accurately predict PD profiles for a wide variety of PK-PD relationships (e.g., effect compartment linked to the central or peripheral compartment and indirect response models). Also, an example is given of the ability of ANNs to accurately predict PD profiles without requiring any information regarding the active metabolite. Because structural details are not required, ANNs exhibit a clear advantage over conventional model-dependent methods. ANNs are proved to be robust toward error in the data and perturbations in the initial estimates. Moreover, ANNs were shown to handle sparse data well. Neural networks are emerging as promising tools in the field of drug discovery and development.

Pharmacokinetic-pharmacodynamic relationships for benzodiazepines

This article reviews the literature on the plasma concentration-effect relationships for benzodiazepines, in humans and in experimental animals. Only literature that explicitly links pharmacokinetics to pharmacodynamics is included. The following questions are evaluated. Can concentration-effect relationships be demonstrated? If so, are these relations stable? Are the influences of specific factors such as age and disease on these relationships established? It is clear that, when studies are conducted and interpreted appropriately, relations can be found for a wide range of benzodiazepine effects. These include objective measures such as electroencephalography, semisubjective measures such as psychomotor performance, and subjective measures such as mood/sedation scales. A generally applicable model of the relationship which will allow prediction of effect is, however, not yet established. The relationship appears to be dependent on route and rate of administration, because of factors such as distributional delay, formation of active metabolites and, probably, acute tolerance. Furthermore, intra- and interindividual variability is considerable, probably due to varying experimental conditions and intrinsic interindividual differences. The limited data available on factors influencing the plasma concentration-effect relationships for benzodiazepines demonstrate clear changes in the pharmacodynamics after multiple doses, suggesting the development of tolerance, and a subsensitivity in patients with panic disorder. The influence of factors such as age, disease and drug interactions on the pharmacokinetic-pharmacodynamic relationship remains less clear.

Population pharmacodynamics: strategies for concentration-and effect-controlled clinical trials

OBJECTIVE

To explore and evaluate various strategies for drug concentration-and effect-controlled clinical trials, respectively, in the context of studies of population pharmacodynamics (concentration-effect relationships).

METHODS

The relative utility of drug concentration- and pharmacologic effect-controlled, randomized clinical trials with two or three concentration-effect measurements for each subject has been explored by computer simulation. The basis for these simulations was a sigmoid-Emax (maximum effect) pharmacodynamic model with Emax = 100%, EC50 (drug concentrations required to produce an effective intensity of 50%) = 10 concentration units, gamma = 2, and no hysteresis. Emax and gamma were held constant whereas EC50 was assumed to be log-normally distributed with a 26% coefficient of variation of the natural lognormalized data. A smaller random variability and variability due to measurement error also were incorporated in the simulations. To explore the implications of variable and unknown Emax and gamma values, the suitability of linear and log-linear interpolation procedures for two-point concentration-effect data in different regions of the sigmoid-Emax curve was compared.

RESULTS

Pharmacologic effect-controlled clinical trials with 300 hypothetical subjects and targeted effect intensities of 25% and 75% yielded very good estimates of drug concentrations required to produce effect intensities of 35%, 50%, and 65%, whereas concentration-controlled trials yielded much poorer estimates. Moreover, the concentration-controlled trials, despite optimum choice of targeted concentrations, yielded a large number of data points with poor information content (effect intensities of < 15% or > 85%). Determinations based on targeted effect intensities of 25% and 75% yielded better estimates of individual EC50 values than those targeted for 25% and 50% or 50% and 75% effect intensity. Results were not significantly improved by adding a third measurement (targeted to 50% effect) to the 25% and 75% effect design. Estimations of drug concentrations required to produce an effect intensity of 50%, based on log-linear interpolation of exact concentration-effect data at 25% and 75%, yielded exact results independent of gamma value (0.5-8.0) whereas linear interpolation produced large overestimates at gamma = 0.5 or 1.0 but satisfactory estimates at gamma > or = 2.0. Similar calculations for an effect intensity of 15% based on exact concentration-effect data at 5% and 25% yielded reasonably good estimates by both methods of interpolation over a wide range of gamma values. A review of the clinical literature showed that gamma values are usually 2 or higher.

CONCLUSIONS

Population pharmacodynamic studies of reversibly acting drugs without pharmacodynamic hysteresis or time dependency (e.g., tolerance) can be successfully conducted using a pharmacologic effect-controlled randomized clinical trial design with only two properly selected target effect intensities per subject.

Tolrestat pharmacokinetic and pharmacodynamic effects on red blood cell sorbitol levels in normal volunteers and in patients with insulin-dependent diabetes

OBJECTIVES

To examine the effect of diabetes mellitus on the pharmacokinetics of tolrestat and to investigate its effect on red blood cell sorbitol levels according to a new pharmacodynamic model for this class of drugs.

METHODS

Single and multiple doses of tolrestat (200 mg/twice a day) were administered to 12 patients with insulin-dependent (type I) diabetes and 12 healthy volunteers in an open parallel trial.

RESULTS

Tolrestat disposition was characterized by first-order absorption and biexponential disposition: In normal subjects the terminal disposition half-life (t1/2) was 13 +/- 3 hours (mean +/- SD) and the apparent oral clearance (CL/F) was 48 +/- 9 ml/hr/kg, similar to the values in patients with type I diabetes mellitus (t1/2 = 14 +/- 4 hours; CL/F = 55 +/- 10 ml/hr/kg). Red blood cell sorbitol concentrations, which declined because of tolrestat's inhibition of aldose reductase, were characterized by an indirect-response model including a 50% inhibition constant (IC50) for production of sorbitol by aldose reductase. The removal of sorbitol (kout) was slower in patients with diabetes. The plasma IC50 averaged 2.0 +/- 1.3 micrograms/ml in normal subjects and 2.5 +/- 1.9 micrograms/ml in patients with diabetes. IC50 values expressed in free (unbound) concentrations (fu = 0.64%), which ranged from 12 to 16 ng/ml, were similar to the in vitro IC50 for inhibition of sorbitol accumulation in human red blood cells.

CONCLUSIONS

Tolrestat pharmacokinetics were similar in normal subjects and in patients with diabetes; however, the patients with diabetes had higher baseline sorbitol levels (11 versus 5 nmol/ml for normal subjects) and slower sorbitol efflux rates. The proposed biochemically realistic, dynamic model characterized well the red blood cell sorbitol response patterns after administration of single and multiple doses of tolrestat.

Concentration-effect relationship of levodopa in patients with Parkinson's disease

Studies on the concentration-effect relationship of levodopa in Parkinson's disease have established that: (1) in patients with a fluctuating response to levodopa, concentration-effect profiles are steeper and markedly shifted to the right (i.e. potency is decreased) compared with those patients whose symptoms are adequately controlled; (2) with controlled-release (CR) preparations, the concentration-effect relationship indicates a decreased potency compared with conventional immediate-release (IR) preparations; and (3) coadministration of a dopamine receptor agonist (even at a subclinical dose) enhances the potency of levodopa. These findings support some current hypotheses on the origin of, and the pathophysiological process underlying, response fluctuations. In patients with response fluctuations, metabolism of levodopa and storage of dopamine in the striatum are reduced. Levodopa is decarboxylated in the extracellular space, with the result that dopamine is released directly to the effect site. Thus, without dopamine storage acting as a buffer between levodopa metabolism and dopaminergic effect, the decline in motor response closely follows the decrease in levodopa concentrations. Even small fluctuations of levodopa concentrations around the EC50 value (the concentration threshold necessary to produce a motor response) might be followed by response fluctuations. Patients with Parkinson's disease who do not have response fluctuations exhibit a residual capacity of production and storage of endogenous dopamine; thus, lower amounts of 'exogenous' dopamine (formed by decarboxylation of levodopa) are required. The storage buffer is responsible for a time lag between decline in peripheral plasma concentrations of levodopa and dopamine-induced motor response. Low doses of a dopamine receptor agonist increase the basal tonus of the striatum, but do not reach the threshold concentration for triggering a motor response. Because of the dichotomic character of the motor response, patients do not switch from an 'off' (not responding) phase to an 'on' (responding) phase. However, lower amounts of exogenous dopamine released in the synaptic cleft will be necessary to induce response. To date, pharmacokinetic-pharmacodynamic modelling does not give a clear answer as to whether response fluctuations are additionally induced by receptor desensitisation or inhibition of the active transport of levodopa across the blood-brain barrier by the main metabolite of levodopa, 3-O-methyldopa. Nevertheless, there is some evidence that higher plasma concentrations of levodopa are required for similar motor effects when CR preparations are compared with IR preparations. Attempts have been made to establish therapeutic drug monitoring of levodopa in patients with response fluctuations. The interindividual variability of EC50 values in single studies is relatively low (10% to a maximum of 50%), which might allow specification of a 'population' threshold plasma concentration (i.e. a minimal effective plasma concentration required to obtain clinical effects). However, considering the short elimination half-life of levodopa, it seems doubtful whether such target drug concentrations can be maintained as steady-state. A marked prolongation of the dosage interval with CR preparations might be limited by the higher threshold concentrations of levodopa necessary to maintain clinical effects.

Pharmacokinetics and receptor-mediated pharmacodynamics of corticosteroids

The corticosteroids, such as prednisolone and methylprednisolone, provide diverse antiinflammatory and immunosuppressive effects which typically show responses with slow onset and prolonged duration. This report summarizes modeling efforts which are successful in describing such steroid effects. Clinical effects with such a pattern, including adrenal suppression and altered trafficking of basophils and helper T-cells, can be related to plasma drug concentrations by models containing an inhibition function and differential equations for controlling input and disposition of the response variable. Some responses have circadian-controlled inputs which add time-dependent complexities to the models. Kinetic/dynamic data for several corticosteroid effects yield IC50 values which agree well with receptor KD values. A relationship of linear AUC of effect versus log AUC of steroid in plasma is found with these models over a large range of doses. Gene-mediated effects of corticosteroids are initiated by receptor-binding which causes a cascade effect altering DNA transcription, RNA, mRNA and proteins or enzymes accounting for drug effects. Models for such behavior have been developed in animals for hepatic tyrosine aminotransferase (TAT) enzyme activity. Studies with methylprednisolone formulated in liposomes show tissue sequestration of steroid, prolonged receptor-binding and extended inhibition of splenocyte proliferation. The data and models usually show good correspondence of the AUC of receptor occupancy with the AUC of pharmacologic response.

Pharmacokinetic-pharmacodynamic (PK-PD) modelling in non-steady-state studies and arterio-venous drug concentration differences

In conducting a non-steady-state pharmacokinetic (PK)-pharmacodynamic (PD) study there is potential for the observed effect (E) vs time, and venous plasma drug concentration (C) vs time, profiles to display temporal displacement with respect to each other. This is most frequently observed when there exists a distributional nonequilibrium across the effect organ giving rise to hysteresis, i.e. observed C preceding E in the time domain, with the resulting potential for a counterclockwise loop to be generated in the observed E vs C plot (when data are connected in time-order). Such temporal displacement does not afford direct prediction of the steady-state E vs C PD relationship. When an arterio-venous (A-V) difference exists across the tissues of the blood sampling compartment (i.e. the arm), and this arises solely from an elimination process then drug concentration in the respective peripheral arterial plasma and venous plasma compartments will be in equilibrium at all times during a non-steady-state PK experiment. If there are no other sources of temporal displacement in the relationship between E and C then the observed E vs C plot will be a direct predictor of the steady-state E vs C PD relationship. In contrast when the A-V difference is of a distributional nature then proteresis, i.e. observed E preceding C in the time domain, will arise with the potential for the generation of a clockwise loop in the observed E vs C relationship. Simulated error-incorporated E vs time, and C vs time, data was analysed by semi-parametric implementation of an effect-compartment link-model that affords accurate steady-state E vs C PD predictions (without the requirement of sampling arterial blood) from data that incorporates the concurrent presence of: (i) distributional nonequilibrium across the effect organ, and (ii) distributional A-V non-equilibrium. Accurate steady-state E vs C PD predictions were achieved irrespective of the comparative magnitudes of the two nonequilibria, i.e. whether the rate of equilibration across the effect organ was faster than, or slower than, the rate of equilibration across the arm (resulting in a clockwise or counterclockwise loop in the observed E vs C plot, respectively), or indeed if one or other of the nonequilibria is essentially absent. When the rate of equilibration across the effect organ is slower than the rate of A-V equilibration (i.e. counterclockwise loop generated in the observed E vs C plot) then the need to model for the underlying A-V nonequilibrium is redundant, i.e. accurate steady-state E vs C PD predictions can be achieved with implementation (strictly incorrectly) of a more simple link parameterised solely to model for distributional nonequilibrium across the effect organ.(ABSTRACT TRUNCATED AT 400 WORDS)