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Purpose: To explore, by simulation procedures, the feasibility of characterizing, from sparse data, the concentration-effect relationship of drugs with pharmacodynamic hysteresis., Methods: For computer simulations, the concentration-effect relationship was assumed to be describable by the Sigmoid-Emax equation, the site of drug action was located in a distinct effect compartment (keo = 10 x kelim), and the pharmacokinetics were those of either a linear one- or two-compartment system. In view of the poor estimability of the parameters of the Sigmoid-Emax model under the usual clinical conditions, central compartment post-distributive drug concentrations required to elicit various intensities of effect within the therapeutic range were used as data descriptors. Effect intensities of 5 and 25, or 25 and 50 units (with the "unknown" Emax = 100 units) were targeted in multiple-dose (steady state) trial designs. From these data, drug concentrations required to produce effect intensities of 15 and 50 units were estimated by both log-linear and linear interpolation and the actual effect intensities produced by these concentrations were calculated. These simulations were performed over a wide range of Hill coefficient values (0.5 to 4.0) and dosing intervals (0.1 to 1.5 x elimination t1/2., Results: Acceptable results could be obtained by measuring drug concentrations and effect intensities at or near the end of a dosing interval. The largest deviations of effective concentration estimates (in terms of effect intensity) occurred at a Hill coefficient value of 0.5 and the results were very little affected by changing the dosing interval., Conclusions: Our results demonstrate that effect-controlled clinical trials, with sparse data, of drugs with pharmacodynamic hysteresis for determining concentration-effect relationship in the therapeutic range are feasible in principle.

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.

Since many intravenous anesthetic drugs alter blood flows, physiologically-based pharmacokinetic models describing drug disposition may be time-varying. Using the commercially available programming software MATLAB, a platform to simulate time-varying physiological pharmacokinetic models was developed. The platform is based upon a library of pharmacokinetic blocks which mimic physiological structure. The blocks can be linked together flexibly to form models for different drugs. Because of MATLAB's additional numerical capabilities (e.g. non-linear optimization), the platform provides a complete graphical microcomputer-based tool for physiologic pharmacokinetic modeling.

By regarding sampled tissues in a physiological model as linear subsystems, the usual advantages of flow models are preserved while mitigating two of their disadvantages, (i) the need for assumptions regarding intratissue kinetics, and (ii) the need to simultaneously fit data from several tissues. To apply the linear systems approach, both arterial blood and (interesting) tissue drug concentrations must be measured. The body is modeled as having an arterial compartment (A) distributing drug to different linear subsystems (tissues), connected in a specific way by blood flow. The response (CA, with dimensions of concentration) of A is measured. Tissues receive input from A (and optionally from other tissues), and send output to the outside or to other parts of the body. The response (CT, total amount of drug in the tissue (T) divided by the volume of T) from the T-th one, for example, of such tissues is also observed. From linear systems theory, CT can be expressed as the convolution of CA with a disposition function, F(t) (with dimensions 1/time). The function F(t) depends on the (unknown) structure of T, but has certain other constant properties: The integral integral infinity0 F(t) dt is the steady state ratio of CT to CA, and the point F(0) is the clearance rate of drug from A to T divided by the volume of T. A formula for the clearance rate of drug from T to outside T can be derived. To estimate F(t) empirically, and thus mitigate disadvantage (i), we suggest that, first, a nonparametric (or parametric) function be fitted to CA data yielding predicted values, CA, and, second, the convolution integral of CA with F(t) be fitted to CT data using a deconvolution method. By so doing, each tissue's data are analyzed separately, thus mitigating disadvantage (ii). A method for system simulation is also proposed. The results of applying the approach to simulated data and to real thiopental data are reported.