Pharmacodynamic Models: Logarithmic Concentration–Effect Model

The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (E_max), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (E_max) or the effect at zero drug concentration, limiting its applicability in some pharmacodynamic analyses.

The log-linear model is utilized in the pharmacokinetics and pharmacodynamics of various drugs, including warfarin and propranolol. For propranolol, a ꞵ-adrenergic blocker, the concentration–effect relationship can be demonstrated by plotting the log of plasma concentration against the percentage reduction in exercise-induced tachycardia. This relationship is linear for intravenous (IV) and oral administration routes. Increased propranolol concentrations consistently diminish exercise-induced tachycardia by blocking ꞵ-adrenergic receptors. The response is more consistent and pronounced with IV administration compared to oral routes, likely due to reduced variability in bioavailability and plasma concentration.

This model is a valuable tool for understanding and predicting the concentration–effect relationship for drugs where such linearity is observed in specific effect ranges.