This is a lumped physiologically-based compartmental model. Injected mass is tracked as fractions across five compartments (blood, liver, spleen, kidney/cleared, target tissue) that always sum to the injected dose:
dC_blood/dt = −(k_liver + k_spleen + k_renal + k_target) · C_blood
dC_organ/dt = k_organ · C_blood (organ = liver, spleen, target)
dC_renal/dt = k_renal · C_blood (irreversibly cleared)
Each rate constant depends on the three sliders, following the well-established nanomedicine size/charge rules used to reason about nanoparticle safety:
- Renal filtration k_renal — the kidney's glomerular pores pass only particles below roughly an 8 nm hydrodynamic diameter; k_renal is a steep sigmoid that collapses to ~0 above that cutoff. Small particles clear fast and safely; larger ones cannot leave the body this way at all.
- RES (liver + spleen) uptake k_liver, k_spleen — the reticuloendothelial system's macrophages opsonize and engulf nanoparticles; uptake rises with particle size and with positive/very negative charge (both promote protein adsorption), and falls as PEG stealth coating increases (PEGylation sterically blocks opsonin binding — the mechanism behind "stealth" nanomedicines like Doxil).
- Target accumulation k_target — a small, roughly size-independent leak rate standing in for EPR-effect/receptor-mediated accumulation in the tissue the particle was designed to reach.
Why this is a nanoethics simulator, not just a nanotech one: the same three physical dials — size, charge, coating — that a bioengineer tunes for efficacy are exactly what regulators cannot pin down when they assess nanomedicine safety. A particle that clears the kidneys quickly is usually considered lower-risk; one trapped for weeks in the liver or spleen raises long-term toxicity and informed-consent questions that classical pharmacology's clearance models were never built for. Drag the sliders toward "large + charged + no coating" and watch the RES-uptake readout climb — that is the biodistribution uncertainty at the center of real nanomedicine risk-benefit and regulatory-approval debates.