Plasma concentration-effect-time relationships

The effects of different model parameters on the plasma concentration versus time relationship can be demonstrated by mathematical analysis of the previous equations, or by graphical representation of a change in one or more of the variables. Equation (10.95) indicates that the plasma concentration (Cp is proportional to the dose (Av) inversely proportional to the volume of distribution (V)- Thus an increase in Aw or a decrease in Fboth yield an equivalent increase in Cp as illustrated in Figure 10.20. Note that the general shape of the curve, or more specifically the slope of the line for ln(Cp versus t, is not a function of Av or V. Equations (10.98) and (10.99) show that the... 

We can view these plasma drug concentration -effect-time relationships in three-dimensional space, as seen in Fig. 17.4. 

There may be several reasons for this pattern to be observed. One obvious reason is distribution, i.e. the drug needs time to reach its site of action, and the time lag between the measured drug concentration in plasma and the drug effect is due to distributional delay. In order to describe such a plasma concentration-effect relationship, a PK-PD model that allows for drug distribution to the site of action, e.g. the effect compartment model may be used. 

Another situation in which the plasma concentration-effect relationship may be confounded by time is one where there is very rapid development of tolerance to the drug, even within a single dosing cycle. In this case, for a given plasma concentration, drug effect will be lower as concentrations are falling than when they are rising and will produce clockwise hysteresis this has been demonstrated for nicotine. 

Figure 17.5 Relationship between albuterol plasma concentration, effect (measured by the forced expiratory volume in 1 s [FEV]]) and time, (a) Plasma drug concentration versus time (b) effect versus time (c) effectversus plasma drug concentration.

The time course of the effect and of the concentration in plasma are not identical, because the concentration-effect relationships obeys a hyperbolic function (B cf. also p. 54). This means that the time course of the effect exhibits dose dependence also in the presence of dose-linear kinetics (C). 

The hyperbolic relationship be tween plasma concentration and effect explains why the time course of the effect, unlike that of the plasma concentration, cannot be described in terms of a simple exponential function. A half-life can be given for the processes of drug absorption and elimination, hence for the change in plasma levels, but generally not for the onset or decline of the effect... 

The time evolution of plasma drug concentration can be treated by a simple model that assumes first-order absorption and first-order elimination of the drug. If [Dq] is the effective concentration of the drug dose, appearance of drug in the plasma will obey the relationship ... 

When creating a graph of the relationship between the time course of the plasma concentrations of a drug in the body (plotted on the x-axis) and the time course of the observed drug effect (plotted on the y-axis), a loop with a counterclockwise direction may be obtained. This means that there are more than two values of effect that correspond to a single plasma concentration (Fig. 6). The phenomenon is called counterclockwise hysteresis or just hysteresis, provided that the model describes a stimulatory (positive) response. If the drug effect would be inhibitory (negative), the direction of the hysteresis would be clockwise. 

In the simplest case, drug effects are directly related to plasma concentrations, but this does not necessarily mean that effects simply parallel the time course of concentrations. Because the relationship between drug concentration and effect is not linear... 

Much has been published on the extrapolation of in vivo data from animals to humans. These include pharmacokinetic data (e.g. half-lives, plasma concentrations, clearances and rates of metabolism) and pharmacodynamic data (e.g. effective and toxic doses). Two excellent reviews present many examples and insightful discussions on isometric and allometric relationships, time scales, interspecies pharmacokinetic and pharmacodynamic scaling, and physiological models (Boxenbaum and D Souza, 1990 Chappell and Mordenti, 1991). 

Various factors may account for the variability in response to neuroleptics. These include differences in the diagnostic criteria, concurrent administration of drugs which may affect the absorption and metabolism of the neuroleptics (e.g. tricyclic antidepressants), different times of blood sampling, and variations due to the different type of assay method used. In some cases, the failure to obtain consistent relationships between the plasma neuroleptic concentration and the clinical response may be explained by the contribution of active metabolites to the therapeutic effects. Thus chlorpromazine, thioridazine, levomepromazine (methotrime-prazine) and loxapine have active metabolites which reach peak plasma concentrations within the same range as those of the parent compounds. As these metabolites often have pharmacodynamic and pharmacokinetic activities which differ from those of the parent compound, it is essential to determine the plasma concentrations of both the parent compound and its metabolites in order to establish whether or not a relationship exists between the plasma concentration and the therapeutic outcome. 

A pharmacodynamic (PD) model describing the relationship between the observed concentration/exposure measure (e.g. the area under the plasma concentration-time profile AUC) and the observed drug effects on biomarkers, efficacy or safety measurements (or endpoints). Time dependent changes (e.g. development of tolerance) and influence of intrinsic and extrinsic factors should also be reflected in the model. 

In the direct-link model, concentration-effect relationships are established without accounting for the intrinsic pharmacodynamic temporal behavior, and the relationships are valid only under the assumption of effect site, prereceptor equilibrium H3. In contrast, indirect-link models are required if there is a temporal dissociation between the time courses of concentration and effect, and the observed delay in the concentration-effect relationship is most likely caused by a functional delay between the concentrations in the plasma and at the effect site. 

EC90, etc.) and the time lag between the measured rapidly changing plasma concentration and the corresponding steady-state effect at that concentration level. This time-lag parameter is described by the equilibration half-time. Using both these parameters, that is, the expected effect and the time required to obtain the effect, allows investigators to model the effect-concentration relationship when patients are not at steady state. 

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