This simulator traces plasma drug concentration over time using a one-compartment pharmacokinetic model. For an intravenous bolus it applies C(t) = (D/Vd)·e−ke·t; for oral dosing it uses the Bateman equation, C(t) = F·D·ka / (Vd·(ka−ke))·(e−ke·t − e−ka·t). It then reports half-life, Cmax, tmax, AUC and clearance.
You pick a route, then adjust dose (10–2000 mg), volume of distribution Vd, elimination rate ke, and, for oral, absorption rate ka and bioavailability F. Five drug presets (aspirin, penicillin, warfarin, morphine, metformin) load realistic values, and a log-scale toggle linearises the elimination phase. PK like this underpins dose selection and dosing intervals in clinical medicine and drug development.
What is a one-compartment pharmacokinetic model?
It treats the whole body as a single, well-mixed compartment of volume Vd into which a drug distributes instantly and from which it is eliminated by a first-order process. It is a simplification, but it captures the headline behaviour of many drugs and gives clean closed-form concentration curves.
What does this simulation actually show?
It plots plasma drug concentration against time after a single dose, on either a linear or logarithmic y-axis. The shaded area beneath the curve represents exposure (AUC), while dashed markers highlight the half-life and the peak concentration Cmax at time tmax.
How is half-life calculated here?
The elimination half-life is t½ = 0.693 / ke, where 0.693 is the natural logarithm of 2. It is the time for the plasma concentration to fall by half during the elimination phase, and it depends only on ke, not on the dose given.
Vd (1–200 L) sets the apparent volume the drug spreads into and so scales the concentration down. ke (0.01–2 h⁻¹) governs how fast the drug is removed. For oral dosing, ka (0.1–5 h⁻¹) controls absorption speed and F (5–100%) the fraction of the dose reaching the bloodstream.
An oral dose must first be absorbed before it can be eliminated. The Bateman equation combines two competing exponentials: absorption (ka) lifts the concentration early on, while elimination (ke) pulls it down. The curve peaks at tmax when the two rates balance, then declines.
Cmax is the highest plasma concentration reached, and tmax is the time at which it occurs. AUC, the area under the concentration–time curve, measures total drug exposure. The simulator finds Cmax and tmax by sampling the curve and computes AUC numerically with the trapezoidal rule.
Clearance is the volume of plasma cleared of drug per unit time. In a one-compartment model it equals Vd·ke, which the simulator reports in litres per hour. Higher clearance means the drug is removed faster and steady-state concentrations on repeat dosing are lower.
An intravenous bolus places the entire dose directly into the bloodstream, so absorption is complete and instantaneous. Its concentration starts at a maximum of D/Vd and decays mono-exponentially, which is why on a log scale the IV curve is a straight line while the oral curve still rises first.
It is a faithful textbook one-compartment model with first-order absorption and elimination, and the preset parameters are broadly realistic. It deliberately ignores complications such as multi-compartment distribution, non-linear (saturable) kinetics, protein binding and tissue-specific effects, so it is a teaching tool rather than a clinical dosing calculator.
On a log y-axis, first-order elimination appears as a straight line because the concentration falls by a constant fraction per unit time. This makes the terminal elimination slope easy to read and the half-life easy to estimate, which is why pharmacokineticists routinely plot concentration data this way.
PK guides how much drug to give and how often. Half-life sets a sensible dosing interval, Vd and clearance inform loading and maintenance doses, and AUC and Cmax relate to both efficacy and toxicity. Adjusting these is central to dosing in renal impairment, paediatrics and therapeutic drug monitoring.