first-order kinetics

**Definition:** Rate of elimination = k × C (k = elimination rate constant, C = plasma concentration). As concentration falls, the absolute amount eliminated per unit time falls, but the fraction eliminated stays constant. Elimination is not saturated; metabolic/excretory capacity far exceeds drug load.

**Key equations:** - Half-life: t1/2 = 0.693 / k = (0.693 × Vd) / CL. Half-life is constant and independent of dose/concentration. - k = CL / Vd. - Clearance (CL) is constant: CL = rate of elimination / C. - Concentration over time: C(t) = C0 × e^(−kt). - Plot: concentration vs. time is a curved exponential decay; log concentration vs. time is a straight line with slope −k/2.3.

**Clinical pearls:** - Time to steady state ≈ 4–5 half-lives, independent of dose or dosing interval. Likewise, ~94–97% of the drug is eliminated after 4–5 half-lives. - After each half-life: 50% → 25% → 12.5% → 6.25% → 3.1% remaining. - Steady-state concentration (Css) is proportional to dose (doubling the dose doubles Css). This gives predictable, linear dose-concentration relationships. - Loading dose = (Cp × Vd)/F; maintenance dose = (CL × Css × τ)/F. Loading dose depends on Vd, maintenance dose depends on CL. - Changes in Vd or CL alter half-life: increased Vd lengthens t1/2; increased CL shortens t1/2. Renal or hepatic disease reduces CL, prolongs t1/2, and requires dose adjustment.

**Contrast with zero-order kinetics:** - Zero-order: constant AMOUNT eliminated per unit time (rate independent of concentration) because the enzymes are saturated. Concentration declines linearly; half-life is NOT constant (it increases as concentration rises). Drugs: Phenytoin (at high doses; transitions to zero-order within therapeutic range), Ethanol, Aspirin (at toxic doses), as well as Theophylline, Warfarin (mnemonic "PEA, a WThe" — Phenytoin, Ethanol, Aspirin; also Warfarin, Theophylline sometimes listed). - Zero-order elimination causes disproportionate rises in plasma concentration with small dose increases, leading to toxicity. - Many first-order drugs convert to zero-order kinetics (Michaelis-Menten/mixed-order) at toxic/overdose concentrations when enzymes saturate.

**Board-style takeaways:** - "Constant fraction/percentage per unit time" = first order; "constant amount per unit time" = zero order. - Half-life constant = first order. - Most drugs at therapeutic doses follow first-order kinetics. - Weak acid/base drugs: urinary pH manipulation (alkalinize urine for salicylates/phenobarbital; acidify for amphetamines/PCP) alters clearance but elimination remains first-order.