Effect-Compartment PK/PD Hysteresis Simulator

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 — effect rising toward plasma

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))

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, plotting effect against plasma concentration traces a counterclockwise hysteresis loop instead of a single curve: for the same plasma level, effect is lower on the way up (still equilibrating) than on the way down (effect site draining slower than plasma). The 3D view plots C_p (x), effect (y) and time (z) as one continuous trajectory; its shadow on the floor is exactly that clinical hysteresis loop, the reason a drug's peak effect always arrives after its peak plasma level. This is 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.

Trajectory (Cp, Effect, time) Hysteresis loop (floor projection)

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