Pharmacokinetic–Pharmacodynamic Relationship: Dose to Pharmacological Effect

A drug’s dosage and pharmacokinetic properties determine how quickly it acts, how intense its effects are, and how long it lasts. Higher doses increase drug concentration at receptor sites, producing a hyperbolic curve when pharmacologic response is plotted against drug dose. Converting this scale to a log-linear format results in a sigmoidal curve, better representing dose–response relationships.

For drugs following a one-compartment model, the pharmacologic response is directly proportional to the logarithm of the drug’s plasma concentration. The effect, E, of drug concentration, C, follows a mathematical equation that can be rearranged to solve for log C. However, after intravenous (IV) administration, drug concentration is calculated differently. Substituting pharmacokinetic parameters into the equation reveals a new expression with a slope of km/2.3.

The slope represents the linear decline of the drug's effect over time. Drugs with a higher m value require more frequent dosing to counteract rapidly decreasing responses. This is crucial for maintaining therapeutic efficacy, particularly for drugs with short half-lives.

For example, in controlled clinical pharmacology studies, intravenous administration of lysergic acid diethylamide (LSD) has been used to examine time-dependent drug effects. In these studies, the log concentration of LSD and the performance score—a quantitative measure of pharmacologic effect—decline linearly over time. This pattern is characteristic of many centrally acting drugs, in which effect duration depends on elimination half-life, as well as receptor desensitization and redistribution.

Understanding these relationships is essential for optimizing dosing regimens. Clinicians must balance drug potency, duration of action, and frequency of administration to achieve therapeutic effects while minimizing adverse reactions.