A two-compartment first-order toxicokinetic model tracks a xenobiotic entering the body, distributing into blood and fatty tissue, and leaving through hepatic/renal clearance:
dC_b/dt = k_a·D − (k_e + k_p)·C_b + k_r·C_f
dC_f/dt = k_p·C_b − k_r·C_f
C_b, C_f = blood / fat concentrations (equal reference volumes); D = dose rate; k_a = route-dependent absorbed fraction; k_e = hepatic/renal elimination from blood (now a slider — real clearance varies a lot between substances and species); k_p, k_r = partition (blood→fat) and release (fat→blood) rates, whose ratio is set by the lipophilicity slider. A more lipophilic toxicant partitions harder into fat and releases more slowly — the mechanism behind bioaccumulation of persistent organic pollutants.
- Exposure route — inhalation and ingestion absorb quickly (high k_a); dermal absorption is slower and route-limited (low k_a).
- Dose rate — continuous daily intake, shown as particles streaming in from the environment node on the left panel (drag it to pan).
- Lipophilicity — controls how strongly the toxicant sequesters in fat instead of being cleared.
- Clearance k_e — how fast the liver/kidneys remove the compound from blood; higher clearance suppresses both blood and fat burden.
A correction versus the naive estimate: a common shortcut reports the elimination half-life as t½ = ln(2)/k_r — treating the fat compartment as if it decayed in isolation. Solving the coupled 2×2 linear system's eigenvalues shows the true dominant (slowest) mode is set by both compartments together, not k_r alone. Checked numerically across the whole lipophilicity range at the default clearance, the naive formula under-estimates the true half-life by a consistent factor of roughly 2.3× (e.g. at log K_ow = 4: naive ≈ 3.6 d vs true ≈ 8.1 d) — because it ignores that the blood compartment's own slow leakage back from fat also delays overall elimination. This simulator reports both numbers side by side so the discrepancy is visible, and uses the eigenvalue-based figure as the physically correct "True system t½".
Real-world relevance: this is the same compartmental logic environmental toxicologists use to model PCBs, dioxins, PFAS and other persistent lipophilic pollutants accumulating in human and wildlife tissue over chronic exposure.