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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.

The objectives of this investigation were to characterize the disposition of fentanyl and alfentanil in 14 tissues in the rat, and to create physiological pharmacokinetic models for these opioids that would be scalable to man. We first created a parametric submodel for the disposition of either drug in each tissue and then assembled these submodels into whole-body models. The disposition of fentanyl and alfentanil in the heart and brain and of fentanyl in the lungs could be described by perfusion-limited 1-compartment models. The disposition of both opioids in all other examined tissues was characterized by 2- or 3-compartment models. From these models, the extraction ratios of the opioids in the various tissues could be calculated, confirming the generally lower extraction of alfentanil as compared to fentanyl. Assembly of the single-tissue models resulted in a wholebody model for fentanyl that accurately described its disposition in the rat. A similar assembly of the tissue models for alfentanil revealed non-first-order elimination kinetics that were not apparent in the blood concentration data. Michaelis-Menten parameters for the hepatic metabolism of alfentanil were determined by iterative optimization of the entire model. The parametric models were finally scaled to describe the disposition of fentanyl and alfentanil in humans.

Physiologically based pharmacokinetic modeling procedures employ anatomical tissue weight, blood flow, and steady tissue/blood partition data, often obtained from different sources, to construct a system of differential equations that predict blood and tissue concentrations. Because the system of equations and the number of variables optimized is considerable, physiologic modeling frequently remains a simulation activity where fits to the data are adjusted by eye rather than with a computer-driven optimization algorithm. We propose a new approach to physiological modeling in which we characterize drug disposition in each tissue separately using constrained numerical deconvolution. This technique takes advantage of the fact that the drug concentration time course, CT(t), in a given tissue can be described as the convolution of an input function with the unit disposition function (UDFT) of the drug in the tissue, (i.e., CT(t) = (Ca(t)QT)*UDFT(t) where Ca(t) is the arterial concentration, Q tau is the tissue blood flow and * is the convolution operator). The obtained tissue until disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug infected into the tissue in the absence of recirculation. From the UDF, a parametric model for the intratissue disposition of each tissue can be postulated. Using as input the product of arterial concentration and blood flow, this submodel is fit separately utilizing standard nonlinear regression programs. In a separate step, the entire body is characterized by reassembly of the individuals submodels. Unlike classical physiologic modeling the fit for a given tissue is not dependent on the estimates obtained for other tissues in the model. Additionally, because this method permits examination of individual UDFs, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat.

Traditionally, physiological pharmacokinetic models assume that arterial blood flow to tissue is the rate-limiting step in the transfer of drug into tissue parenchyma. When this assumption is made the tissue can be described as a well-stirred single compartment. This study presents the tissue washout concentration curves of the two opioid analgesics fentanyl and alfentanil after simultaneous 1-min iv infusions in the rat and explores the feasibility of characterizing their tissue pharmacokinetics, modeling each of the 12 tissues separately, by means of either a one-compartment model or a unit disposition function. The tissue and blood concentrations of the two opioids were measured by gas-liquid chromatography. The well-stirred one-compartment tissue model could reasonably predict the concentration-time course of fentanyl in the heart, pancreas, testes, muscle, and fat, and of alfentanil in the brain and heart only. In most other tissues, the initial uptake of the opioids was considerably lower than predicted by this model. The unit disposition functions of the opioids in each tissue could be estimated by nonparametric numerical deconvolution, using the arterial concentration times tissue blood flow as the input and measured tissue concentrations as the response function. The observed zero-time intercepts of the unit disposition functions were below the theoretical value of one, and were invariably lower for alfentanil than for fentanyl. These findings can be explained by the existence of diffusion barriers within the tissues and they also indicate that alfentanil is less efficiently extracted by the tissue parenchyma than the more lipophilic compound fentanyl. The individual unit disposition functions obtained for fentanyl and alfentanil in 12 rat tissues provide a starting point for the development of models of intratissue kinetics of these opioids. These submodels can then be assembled into full physiological models of drug disposition.

We have developed a computer-controlled infusion pump to achieve rapidly and then maintain stable plasma thiopental concentrations in rats. Initially we derived the parameters of a triexponential pharmacokinetic model for thiopental, administered as a brief infusion to 10 rats, using nonlinear regression and standard pharmacokinetic equations. These parameters were incorporated into the pharmacokinetic model of a computer-controlled infusion pump. In a second group of animals this device was used to maintain three consecutive target thiopental concentrations ranging from 5 to 100 micrograms/ml in a stepwise fashion. Arterial blood gases were kept normal through controlled ventilation when necessary. The plasma thiopental concentrations in this second group of animals were generally higher than the target concentrations. The bias in pump performance (median prediction error) was +25%, and the inaccuracy (median absolute prediction error) was 26%. We fit the parameters of a three-compartment model to the plasma thiopental concentrations observed in the second group of animals. This produced a second set of thiopental pharmacokinetic parameters with the unique characteristic of having been derived from a computer controlled infusion study. These parameters were tested prospectively with a computer-controlled infusion pump in a third group of animals. This second set of thiopental pharmacokinetic parameters performed better, with a median prediction error of 0% and a median absolute prediction error of 15%. This study shows that it is possible to achieve rapidly and maintain steady plasma thiopental concentrations in the rat. Our results suggest that it is feasible to derive robust pharmacokinetic parameters from unusual drug dosing approaches, such as employed by a computer-controlled infusion pump.(ABSTRACT TRUNCATED AT 250 WORDS)

We have developed a chronically instrumented rat model that uses changes in electroencephalographic wave forms to estimate continuously the degree of central nervous system (CNS) depression induced by thiopental. Such changes were subject to aperiodic signal analysis, a technique that breaks down the complex EEG into a series of discreet neurologic "events" which are then quantitated as waves/sec. We thus obtained a continuous measure of CNS drug effect. In addition we continuously recorded central arterial blood pressure and heart rate and monitored ventilatory status using arterial blood gas determinations. We also determined, with frequent arterial blood sampling, the distribution and elimination of thiopental in individual animals. The time lag occurring in the curve representing arterial concentration of thiopental vs. EEG effect suggests that arterial plasma is not kinetically equivalent to the EEG effect site. Application of semiparametric pharmacodynamic modeling techniques enabled us to estimate equilibration rate constant (Keo) for concentrations of thiopental between arterial plasma and the effect site. The half-life for equilibration of thiopental with the EEG (CNS) effect was less than 80 sec. Knowledge of the rate of equilibration permitted characterization of the relationship between the steady state plasma concentrations and CNS effect of thiopental, as measured by activation and slowing of the EEG. At concentrations of thiopental below 5 micrograms/ml, EEG activity was 180% higher than during the baseline awake state. Thiopental produced an activated EEG over more than 20% of the concentration-effect relationship. Further increases in the concentration of thiopental at the site of effect depressed EEG activity progressively until complete suppression of the EEG signal occurred (at which time, the concentration was approximately 80 micrograms/ml). This report describes our model and its application to the assessment of the pharmacodynamics of thiopental as manifested by changes on the EEG.

Methods based on moment analysis are described which permit the calculation of the fundamental parameters of reversible drug/metabolite systems. These parameters include the four essential clearances of reversible and irreversible elimination, the central and steady-state distributional volumes, and the sojourn times or turnover rates of the metabolic pair. Additional parameters unique to interconversion systems are developed which describe the properties of metabolic entrapment ("recycled fraction"), conservation ("exposure enhancement"), and equilibrium resulting from reversible metabolism ("Percent parent drug at steady-state"). Parameters obtained by these methods are compared to those generated by conventional mammillary analysis. The influence of perturbation of essential parameters on the response of mammillary descriptors and the state of the interconversion system are simulated. The interconversion analysis is applied to disposition data for methylprednisolone and methylprednisone in the rabbit. Mammillary methods underestimate the metabolic clearance of these two steroids by 30%, while steroid turnover is underestimated by 100%. The steady-state volumes of distribution of the two steroids are overestimated by 10 and 61%. Additional literature data for disposition of several corticosteroids in various species and disease states are reanalyzed. Examination of cortisol/cortisone disposition in thyroid disorders reveals that mammillary methods detect the overall acceleration of steroid elimination in hyperthyroidism, but fail to reveal a 50% reduction in metabolite backconversion and decreased metabolic cycling. These moment analysis methods should facilitate characterization of the pharmacokinetics of the increasing array of reversible drug/metabolite systems.

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.