Steady-State Drug Accumulation Simulator (2D)

Dosing Regimen

Dose per administration 400 mg

Dosing interval τ 8 h

Elimination half-life 6 h

Volume of distribution 40 L

Simulation speed 3 h/s

Live Readouts

Elapsed time / doses given

0.0 h · 1 dose

Plasma concentration (ODE)

0.00 mg/L

Gut depot remaining

— mg

Accumulation ratio R

1.00×

Steady-state peak / trough

— / — mg/L

How it works (2D model)

The 3D version of this sim evaluates the closed-form Bateman equation directly. This 2D companion computes the same real one-compartment-with-absorption pharmacokinetics a genuinely different way: it numerically integrates the underlying mass-balance ODEs step by step with 4th-order Runge‑Kutta (RK4), the way a real PK simulation engine actually works, and shows the two physical compartments — the gut depot and the plasma pool — as flowing tanks instead of a single particle cloud.

dA_gut/dt   = −ka·A_gut                     (first-order absorption)
dA_plasma/dt =  ka·A_gut − ke·A_plasma        (input − elimination)
C(t) = A_plasma(t) / Vd
ke = ln(2)/t½,  ka = 1.5 h⁻¹ (fixed, oral)

Each oral dose is injected as an instantaneous bolus into the gut depot at its administration time; RK4 then advances both compartments forward in fixed sub-steps between events. Run against the closed-form Bateman superposition used by the 3D sim for the same parameters, this independent integrator matches it to within about 10⁻⁶% at every sampled time (see the verification notes below the sliders), confirming both computational routes describe the same physics.

Dose / τ — how much drug enters the depot and how often; a shorter interval relative to the half-life accumulates more before the previous dose clears.
Half-life — sets ke; longer half-lives drain the plasma tank more slowly, so more of each new dose lands on top of leftover drug.
Volume of distribution (Vd) — a bookkeeping constant that converts the plasma tank's absolute drug mass into a concentration; the mass balance itself never depends on it.
Loading dose — doubles only the first bolus into the gut depot, pushing the plasma tank close to its steady-state fill level immediately.

The flow arrows carry moving dots whose speed and density track the instantaneous flux ka·A_gut (absorption, into the plasma tank) and ke·A_plasma (elimination, out of it) — so you can watch input and output visibly balance once the system reaches steady state.

💊 Dose administered

Gut depot (absorbing) Plasma compartment Concentration-time trace