Pharmacodynamic variability may exceed pharmacokinetic variability (see Figure 8-1). The drug dose or concentration that produces a pharmacological effect differs widely among patients. Similarly, pharmacological effects can vary widely among patients with a comparable plasma concentration of drug.

The principles of dosage regimen design discussed above rely heavily on the existence of a functional relationship between the concentration at an effect site and the intensity of the response produced. Many observed processes in nature behave according to the sigmoid relationship shown in Figure 8-7. At a low dose or concentration, only a marginal effect is produced. As drug dose or concentration increases, the intensity of effect (E) increases until a maximum effect (Emax) is achieved. This response is observed as a plateau in the sigmoid dose-effect curve (see Figure 8-7). Further dosage increases do not produce a greater effect.

FIGURE 8-7. The sigmoid maximum effect (Emax) pharmacodynamic model relates concentration (C) to intensity of effect (E).

EC50 is the concentration that produces half of the Emax, and n is an exponent that relates to the shape of the curve.

The sigmoid dose-effect relationship in Figure 8-7 has practical applications to psychopharmacology. The increase in drug response that results from an increase in dosage depends on the shape and steepness of the theoretical dose-response curve for each patient and the starting point on the curve when a dosage is changed. At low doses or concentrations, a substantial dose increase may be necessary to achieve an effect. In a linear part of the relationship, dosage increases should result in proportional increases in effect. In the higher dose or concentration range, a further increase will not produce a significant increase in effect because of diminishing returns. This phenomenon is likely caused by the saturation of enzyme-binding sites or receptors by drug molecules above a critical concentration.

The general equation shown in Figure 8-7 describes the sigmoid relationship between concentration and response (i.e., intensity of effect). The response is usually measured as a percentage change or the difference from the baseline effect. C is the drug concentration, and EC50 is the effective concentration that produces half of the Emax. Theoretically, n is an integer reflecting the number of molecules that bind to a specific drug receptor. Practically, it is a parameter that determines the sigmoid shape of the concentration-effect relationship. Pharmacokinetic-pharmacodynamic models have found wide application in psychopharmacology—for example, relating concentration to electroencephalogram parameters, psychomotor reaction times, and subjective effects from drugs of abuse (Dingemanse et al. 1988).

Drugs rarely have a single pharmacological effect or interact with only a single receptor population or molecular target. Drugs generally have affinity for multiple receptors; therefore, several theoretical concentration-effect relationships can exist for a given drug. Dose-response curves are shown in Figure 8-8 for a drug that produces a therapeutic effect and mild and severe toxicity. The greater the separation between the curves for therapeutic and toxic effects, the more safely the drug can be administered in increasing doses to achieve therapeutic goals. Estimates of these interrelationships are made in preclinical animal studies and Phase I human studies for drugs in development. In clinical practice, the degree of separation between these curves and their steepness will show both inter- and intraindividual variability. Concurrent medical illness may predispose patients to side effects by effectively causing a shift to the left in one or both of the concentration-toxicity curves. This narrows the range over which doses can be safely administered without incurring adverse effects. The EC50 in Figure 8-8 produces negligible toxicity. Increasing the concentration with a dosage increase to gain an increased response can only be accomplished at the expense of mild toxicity. As the dosage and concentration increase, therapeutic effects approach a plateau, and small increments in concentration result in a disproportionate change in toxicity.

FIGURE 8-8. Concentration-effect curves for a drug that produces a therapeutic effect and mild (A) and severe (B) toxicity.

FIGURE 8-8. Concentration-effect curves for a drug that produces a therapeutic effect and mild (A) and severe (B) toxicity.

Concentration {arbitrary units)

Copyright © American Psychiatric Publishing, Inc., or American Psychiatric Association, unless otherwise indicated in figure legend, All rights reserved.

The concentration is shown for a therapeutic effect that produces 50% of the maximum effect (EC50).

The pharmacodynamic relationships considered above are most reproducible when pharmacological effects are direct and closely related to plasma concentration. In Figure 8-9, the concentration-effect relationship is shown as a function of drug concentration changes over time. In Figure 8-9A, the changes in effect are almost superimposable with the increase and decrease in concentration. This type of relationship often reflects a direct action of the drug with a single receptor. This straightforward relationship is generally not observed in psychopharmacology.

FIGURE 8-9. Theoretical relationships of drug concentration versus intensity of effect.

Drug concentration changes occur in the direction of the arrow. Effects superimposable on concentration changes (A) suggest a direct and reversible interaction between drug and receptor, a clockwise hysteresis curve (B) suggests the development of tolerance, and a counterclockwise curve (C) suggests an indirect effect or the presence of an active metabolite.

In Figure 8-9B, the response has begun to diminish with time before concentration begins to decline. This type of plot is known as a clockwise hysteresis curve. The observed effect may be explained by the development of tolerance. The time course of tolerance to psychoactive drug effects varies from minutes to weeks. Acute tolerance to some euphoric effects of cocaine can occur following a single dose (Foltin and Fischman 1991). Tolerance to the sedative effects of various drugs may take weeks. The mechanisms operative in the development of tolerance include acute depletion of a neurotransmitter or cofactor, homeostatic changes in receptor sensitivity from blockade of various transporters, or receptor agonist or antagonist effects. Ultimately, cellular responses to chronic treatment with drugs can alter gene transcription factors as mediators of physical and psychological aspects of tolerance (Nestler 1993).

A time delay in response occurs when effects are increasing and are maintained despite decreasing plasma drug concentration (see Figure 8-9C). This results in a counterclockwise hysteresis curve. A pharmacokinetic explanation of this lag in response may involve a delay in reaching the critical drug MEC at the effect site until the plasma concentration has already begun to decline. Alternatively, response may depend on multiple "downstream" receptor effects. This theory likely accounts for the counterclockwise hysteresis curve observed between plasma drug concentration and growth hormone response in plasma after an intravenous alprazolam challenge (Osman et al. 1991). Response may increase despite a decreasing drug concentration when a metabolite contributes to the observed effects. To overcome these complications, kinetic dynamic models can incorporate an "effect"

compartment (see Figure 8-1). The effect site equilibrates with plasma after a finite time, which can be assigned a half-life. Models can also incorporate the presence of metabolites (Dingemanse et al. 1988).

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