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 (Emax), 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 (Emax) 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.
The log-linear model assumes that the effect is directly proportional to the logarithm of drug concentration.
The effect, E, is given by the following equation. Here, S represents the effect generated by a unit drug concentration, C represents the plasma drug concentration, and E0 means the baseline effect.
When the maximum effect, Emax, is between 20 and 80%, the plot of the logarithm of drug concentration versus effect appears nearly linear.
Notably, the model cannot predict the Emax or the effect at zero drug concentration.
However, it is used to predict the concentration–effect relationship for drugs such as warfarin and propranolol.
For instance, the plot of the log plasma concentration of propranolol and the percentage block of exercise-induced tachycardia is linear for both IV and oral routes.
As a result, increasing propranolol concentration effectively reduces exercise-induced tachycardia, with the IV route showing a more pronounced and consistent response.
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