Two-Compartment Pharmacokinetics Simulator

Dose & Administration

IV Bolus Dose 200 mg

Rate Constants (h⁻¹)

k₁₂ central → peripheral 0.55

k₂₁ peripheral → central 0.30

k₁₀ elimination 0.25

Plasma / Tissue Concentration

C_central (mg/L)C_peripheral (mg/L)

C central

0.0 mg/L

C peripheral

0.0 mg/L

Elapsed time

0.0 h

β-phase t½

—

How it works

Many drugs (e.g. lidocaine, thiopental, digoxin, vancomycin) don't equilibrate with the whole body instantly. A two-compartment model splits the body into a well-perfused central compartment (blood + fast organs, volume V_c) and a peripheral compartment (muscle/fat, volume V_p) that fills more slowly:

dX_c/dt = -(k10 + k12)·X_c + k21·X_p
dX_p/dt =  k12·X_c - k21·X_p
C_c = X_c / V_c,   C_p = X_p / V_p

This simulator runs a Monte‑Carlo version of the same process: every drug molecule (particle) in the central compartment independently faces two competing exponential hazards each instant — transfer to the periphery (rate k₁₂) or elimination by the liver/kidneys (rate k₁₀) — while molecules in the periphery redistribute back at rate k₂₁. Averaged over many particles this Monte‑Carlo simulation converges to the same solution as the differential equations above.

Solving the linear system analytically gives a biexponential plasma curve, C_c(t) = A·e^-αt + B·e^-βt, with two rate constants derived from k₁₀, k₁₂, k₂₁:

s = k10 + k12 + k21
α,β = ( s ± √(s² - 4·k10·k21) ) / 2      (α > β)
t½(β) = ln(2) / β   ← terminal half-life

The fast α-phase (steep initial drop) is mostly redistribution of drug out of the blood into tissue — not elimination.
The slow β-phase (shallow tail) is the true elimination phase, once distribution has equilibrated.
Raising k₁₂ relative to k₂₁ pulls more drug into tissue (bigger apparent volume of distribution); raising k₁₀ shortens the terminal half-life.

Clinical relevance: mistaking the fast distribution phase for elimination is a classic dosing error — e.g. a repeat IV bolus given too early (during the α-phase) can cause toxic accumulation once redistribution catches up.

Central (blood) compartment Peripheral (tissue) compartment

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.