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.