Chemotherapy Log-Kill: Tumor Shrinkage Simulator

Dosing Regimen

Dose per cycle 600 mg

Cycle interval 21 d

Drug half-life 12 h

Kill potency k 0.0060

Live Readouts

Tumor volume

50.0 cm³

Of baseline

100%

Plasma conc.

0.0 mg/L

Cycle #

Time elapsed

Day 0

How it works

Two coupled models run every frame. A one-compartment pharmacokinetic model gives the plasma drug concentration C(t): each cycle injects a bolus that instantly raises C by Dose/V_d, then first-order elimination decays it exponentially between doses.

dC/dt = −k_e·C          (between doses)
C → C + Dose/V_d        (at each dose, V_d = 30 L)
k_e = ln(2) / t½

Tumor volume V follows Gompertzian growth — the standard model for solid tumors, whose growth rate slows as V approaches a carrying capacity V_max because the hypoxic, nutrient-starved core stops dividing — opposed by a log-kill term from Skipper's Laws: each unit of drug exposure kills a constant fraction of the surviving cell population, not a constant number.

dV/dt = a·V·ln(V_max/V) − k·C(t)·V
          ↑ Gompertz regrowth      ↑ log-kill (Norton–Simon)

Dose / interval — set the chemotherapy schedule; a shorter interval keeps C(t) higher for longer, deepening each kill before regrowth resumes.
Half-life — how fast the drug clears; a short half-life means each dose's kill window closes quickly.
Kill potency k — the drug's intrinsic cytotoxicity per unit concentration.

The rim of bright cells is the actively proliferating tumor surface; the dim core is the diffusion-limited, oxygen-starved region that drives Gompertzian slowdown even before treatment starts. This is why chemotherapy is dosed in pulsed cycles rather than one continuous infusion: it lets the log-kill exposure act repeatedly while giving healthy tissue recovery time between doses.

Proliferating rim Hypoxic core Plasma drug

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