Comparison of four basic models of indirect pharmacodynamic responses

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)