Time Course of Plasma Concentration and Effect

After the administration of a drug, its concentration in plasma rises, reaches a peak, and then declines gradually to the starting level, due to the processes of distribution and elimination (p. 46). Plasma concentration at a given point in time depends on the dose administered. Many drugs exhibit a linear relationship between plasma concentration and dose within the therapeutic range (dose-linear kinetics (A) note different scales on ordinate). However, the same does not apply to drugs whose elimination processes are already sufficiently activated at therapeutic plasma levels so as to preclude further proportional increases in the rate of elimination when the concentration is increased further. Under these conditions, a smaller proportion of the dose administered is eliminated per unit of time. 

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 dose dependence of the time course of the drug effect is exploited when the duration of the effect is to be prolonged by administration of a dose in excess of that required for the effect. This is done in the case of penicillin G (p. 268), when a dosing interval of 8 h is being recommended, although the drug is eliminated with a half-life of 30 min. This procedure is, of course, feasible only if supramaximal dosing is not associated with toxic effects. 

Futhermore it follows that a nearly constant effect can be achieved, although the plasma level may fluctuate greatly during the interval between doses. 

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 

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The concentration-effect relationship of many biotech drugs, however, cannot be described by direct link PK/PD models, but is characterized by a temporal dissociation between the time courses of plasma concentration and effect. In this case, concentration maxima would occur before effect maxima, effect intensity would... 

Under non-steady-state conditions, time courses of plasma concentration and effect may dissociate. Thus, to characterize fully the time course of drug action under nonsteady-state conditions, PK and PD have to be adequately linked to predict the relationship of PD effect vs. drug concentration in plasma. This link is provided by the following four attributes in the integrated PK/PD models. 

Time course of drug concentration and effect Plasma half-life and steady-state concentration Therapeutic monitoring... 

However, there are other major factors in determining the dosing regimen, such as the nature of the concentration-response relationship for both efficacy and toxicity (therapeutic window) and commercial/ compliance factors. There are additional reasons why caution should be applied in assuming an efficacy-time profile from a given plasma concentration-time profile. Some reasons why the time course of drug concentration and effect may differ are given in Table 5.1. 

Relating the Time-Course of Plasma Concentrations to the Time-Course of Effect A critical decision to be made after the first human study is whether the compound s speed of onset and duration of action are likely to be consistent with the desired clinical response. Speed of onset is clearly of interest for treatments which are taken intermittently for symptoms rehef, for example, acute treatments for migraine, analgesics, or antihistamines for hay fever. Duration of action phase I is particularly important when the therapeutic effect needs to be sustained continuously, such as for anticonvulsants. The first information on the probable time course of action often comes from the plasma pharmacokinetic profile. However, it has become increasingly evident that the kinetic profile alone may be misleading, with the concentration-time and the effect-time curves being substantially different. Some reasons for this, with examples, include... 

Appearance in systemic fluids In addition to the method of administering the test substance, the second critical aspect of a technique is the sampling procedure for quantitating the extent and/or rate of absorption. With in vivo methods the least invasive techniques entail the collection of blood, urine, or breath samples for determining the appearance of the absorbed test substance (and its metabolites) in body fluids. Comparing the time course of plasma concentrations or excretory rates in urine or breath after oral administration with the results after intravenous administration may permit quantitation of the extent of absorption of the test substance and the rate constant of this process [20]. This approach is relatively imprecise and may be confounded by numerous factors such as the rsf pass effect, the enterohepatic circulation of the agent, and the status of elimination processes such as hepatic and... 

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. 

The methodology to predict the time course of drug concentration in plasma after administration is well described and well accepted as a pharmacokinetic principle. Today, pharmacokinetic principles are used routinely to estimate and manage dosing of medications for their safe and effective use. Such knowledge is useful not only in designing clinical trials for a new molecular entity, but also in day-to-day clinical practice (Box 5.1). 

As is implicit from all the above, the measured concentration in plasma is directly linked to the observed effect for these simple mechanistic, pharmacokinetic-dynamic models. Accordingly, these models are called direct-link models since the concentrations in plasma can be used directly in (10.6) and (10.7) for the description of the observed effects. Under the assumptions of the direct-fink model, plasma concentration and effect maxima will occur at the same time, that is, no temporal dissociation between the time courses of concentration and effect is observed. An example of this can be seen in the direct-fink sigmoid Emax model of Racine-Poon et al. [418], which relates the serum concentration of the anti-immunglobulin E antibody CGP 51901, used in patients for the treatment of seasonal allergic rhinitis, with the reduction of free anti-immunglobulin E. 

Time course of PHY concentration in plasma and brain was compared after 650 ptg/kg dose i.m. and oral and 100 pig/kg after i.v. administration as shown in Figure 5.5. BuChE activity in plasma and AChE activity in brain was also compared after these doses. The figure shows the pharmacokinetic and pharmacodynamic effects of PHY. PHY does not reach an effective concentration in the brain after oral administration because of its first-pass effect. However, it is an effective pretreatment drug after i.v. and i.m. routes of administration. 

The dose-concentration-effect relationship is defined by the pharmacokinetic and pharmacodynamic characteristics of a drug. Pharmacokinetics comprises all processes that contribute to the time course of drug concentrations in various body fluids, generally blood or plasma, that is, all processes affecting drug absorption, distribution, metabolism, and excretion. In contrast, pharmacodynamics characterizes... 

Onset/Duration The extent and time course of BP reduction by minoxidil do not correspond closely to its plasma concentration. When minoxidil is administered chronically, once or twice a day, the time required to achieve maximum effect on BP is inversely related to the size of the dose. Thus, maximum effect is achieved on 10 mg/day within 7 days, on 20 mg/day within 5 days and on 40 mg/day within 3 days. 

Figure 13.8. Effects of route and sustained release formulation on the time course of human growth hormone concentration in plasma. Shown is the average time course of human growth hormone (hGH) in plasma after intravenous (0.02mg/kg) and subcutaneous (0.1 mg/kg) administration in humans. Arrows indicate weekly subcutaneous dosing of hGH in solution. A single dose of the same protein formulated in polylactide-co-glycolide (PLG) microspheres (0.75 mg/kg) given subcutaneously sustains human growth hormone levels in plasma for at least one month.

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... 

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