3.2 Dose-Response Relationships
Dose-response curves quantify the relationship between drug concentration and biological effect. They are fundamental to understanding drug potency, efficacy, and safety.
Graded Dose-Response
\( E = \frac{E_{max} \cdot [D]}{EC_{50} + [D]} \)
Hill equation (hyperbolic response)
EC50
Concentration for 50% max effect
Emax
Maximum achievable effect
Hill coefficient
Curve steepness (cooperativity)
Quantal Dose-Response
Population response: proportion of individuals responding at each dose.
ED50
Median effective dose
TD50
Median toxic dose
LD50
Median lethal dose
Therapeutic Index
\( TI = \frac{TD_{50}}{ED_{50}} \)
Higher TI = safer drug. Narrow TI drugs require careful monitoring (warfarin, digoxin, lithium, phenytoin).
Certain Safety Factor: TD1/ED99 - more conservative measure of safety margin.