Real drugs — Digoxin, Warfarin, Gentamicin, Phenytoin and more — animated at their actual PK values. Adjust independent variables (Vd, Cl, ka…) and watch the derived parameters and curves recalculate live.
t½ is a derived variable — it depends on two independent parameters: Volume of Distribution (Vd) and Clearance (Cl). A larger Vd lengthens t½; higher Cl shortens it. t½ alone never tells you why elimination is slow.
The two examples have similar absolute Cl (~5–7 L/h) yet t½ differs 25-fold — because Vd differs 33-fold. This is the core insight: t½ ≠ Cl alone.
Clearance (Cl) is an independent variable — it determines the rate of drug removal at any given concentration: elimination rate = Cl × Cp. Higher Cl → faster removal → steeper slope of the Cp-time curve.
ke = Cl/Vd. The drug examples use their real Vd; the cyan custom curve uses Vd=20 L so you can see Cl's isolated effect on the slope. Note that Propranolol's high Cl still gives a moderate t½ because its Vd is also large.
Vd is the apparent volume that would contain the total drug at the measured plasma concentration. A large Vd means the drug is distributed extensively into tissues — plasma concentration is low relative to the total amount in the body.
The formula shows the consequence directly: for a fixed 100 mg IV dose, a drug with Vd=8 L gives Cp₀=12.5 mg/L; the same dose of a drug with Vd=600 L gives Cp₀=0.17 mg/L — almost undetectable in plasma.
Tmax is when absorption rate equals elimination rate. Cmax is the concentration at that moment. Both depend on the absorption rate constant ka — which formulation engineering can tune without changing the total dose absorbed (AUC).
Slow-release formulations reduce ka → lower Cmax (less peak toxicity), later Tmax (smoother onset), same AUC. Metformin XR reduces GI side effects by flattening the peak — the pharmacokinetic rationale for extended-release formulations.
AUC is the integral of Cp over all time — total drug exposure. For IV: AUC = Dose/Cl. For oral: AUC = F×Dose/Cl. The ratio gives absolute bioavailability F. Bioequivalence requires AUC and Cmax within 80–125% of reference.
AUC is determined by Cl and dose alone — not by Vd. A large Vd lowers Cp at any time point but leaves AUC unchanged. The shaded area under the oral curve represents F×100% of the IV AUC.
In first order kinetics, a constant fraction is eliminated per unit time — pathways are unsaturated. The curve is exponential on a linear axis; it becomes a straight line on a log-linear (semi-log) plot. The slope is −ke = −0.693/t½.
Applying LOG to real plasma samples and fitting a regression line is the standard method for calculating t½ and ke in PK studies. Both drugs below follow first order at therapeutic doses.
In zero order kinetics, a constant amount is eliminated per unit time — because elimination pathways are saturated. Cp declines linearly. There is no fixed t½ — apparent t½ shortens as Cp falls toward km. Toxic accumulation is highly unpredictable.
Even small dose increases produce disproportionately large rises in Cp when pathways are saturated. This is why ethanol intoxication worsens non-linearly with intake, and salicylate toxicity is so dangerous.
When Cp ≫ Km the enzyme is saturated → zero order. As Cp falls below Km the enzyme becomes unsaturated → first order. The transition happens near Cp=Km. Drugs with low Km saturate at therapeutic concentrations — making them non-linear and TDM-mandatory.
Phenytoin's Km (~10 mg/L) falls within its therapeutic range (10–20 mg/L) — so it is nearly always in the saturable zone. Small dose changes produce disproportionate Cp changes, making dose titration treacherous.
Without a loading dose, steady state requires 4–5 half-lives. For Digoxin (t½=48 h), that is ~10 days of subtherapeutic concentrations — clinically unacceptable in heart failure or arrhythmia. A loading dose pre-fills the Vd to the target Css immediately.
LD = Vd × Css / F. The larger the Vd, the larger the LD. Amiodarone's Vd is so large (~4000 L) that a full loading regimen takes a week even at 600 mg/day.
The maintenance dose replaces exactly the drug eliminated each interval τ. Css_avg = MD / (Cl × τ). Dose and Cl determine Css; Vd and t½ determine the fluctuation and time to reach Css. Steady state is always 4–5 t½, regardless of dose.
Peak-trough fluctuation increases as τ/t½ increases. A drug with t½ ≪ τ (Amoxicillin, t½=1h, τ=8h) has very large oscillations — between doses the drug is almost gone. Time above MEC drives antibacterial killing for beta-lactams, making frequent dosing essential.