Effect-Compartment PK/PD Hysteresis Simulator (2D)

Dose & Kinetics

Peak plasma conc. C_p0 8.0 mg/L

Elimination half-life 3.0 h

Effect-site equilibration t½ (k_e0) 8 min

EC₅₀ (effect-site) 2.0 mg/L

Live Readouts

Onset — molecules flowing into effect site

Time

0.0 min

Plasma C_p

8.00 mg/L

Effect-site C_e

0.00 mg/L

Clinical effect

0.0%

How it works

Plasma concentration and clinical effect do not rise and fall in lock-step — the drug must first cross into the "biophase" (the effect site: brain, synapse, receptor-rich tissue). This delay is modelled with a hypothetical, unmeasurable effect compartment linked to plasma by a first-order rate constant k_e0 (Sheiner–Hull link model):

Plasma (1-compartment IV bolus):  Cp(t) = Cp0 · e^(−ke·t),  ke = ln2 / t½,elim

Effect-site equilibration:        dCe/dt = ke0 · (Cp(t) − Ce(t)),  ke0 = ln2 / t½,ke0

Pharmacodynamic response (Emax):  E(t) = 100 · Ce(t) / (EC50 + Ce(t))

This 2D view renders the same equations as a physical two-tank diffusion analogy: the plasma tank's liquid level is C_p(t), the effect-site tank's level is C_e(t), and molecules physically stream through the connecting channel at a rate proportional to the instantaneous flux k_e0·(C_p−C_e) — exactly the same first-order equilibration, just rendered as diffusing particles rather than a 3D trajectory. The strip chart traces C_p and C_e against time; the loop panel plots effect against C_p directly, tracing the same counterclockwise hysteresis loop as the 3D version's floor shadow.

C_p0 — peak plasma concentration right after the bolus (sets dose/volume-of-distribution).
Elimination half-life — how fast the plasma level itself decays.
k_e0 half-life — how sluggishly the effect site follows plasma; a fast drug (short t½,ke0) tracks plasma almost immediately, a slow one lags for tens of minutes.
EC₅₀ — the effect-site concentration producing 50% of maximal effect.

Because C_e lags C_p, effect is lower for a given plasma level on the way up (still equilibrating) than on the way down (effect site draining slower than plasma) — the same mechanism anesthesiologists use to explain why a propofol or opioid bolus "kicks in" minutes after infusion, and why trough-only plasma monitoring can under- or over-estimate real-time effect.

Plasma → effect-site flow Hysteresis loop (effect vs Cp)