Tumor-targeted drug delivery combines two independent mechanisms modeled here:
1. Passive targeting — the EPR effect. Tumor blood vessels grow fast and abnormally, leaving gaps (fenestrations) of ~100–780 nm between endothelial cells, versus ~6–12 nm tight junctions in most healthy vasculature. A particle can only cross a gap smaller than itself, so extravasation follows size-exclusion sieving:
P(cross) ∝ (1 − d/d_pore) · k · dt, d < d_pore
P(cross) = 0, d ≥ d_pore
This "Enhanced Permeability and Retention" effect (Matsumura & Maeda, 1986) is why nanoparticles 10–200 nm accumulate preferentially in tumors while sparing most normal tissue — the physical basis of nanomedicines like liposomal doxorubicin.
2. Active targeting — ligand-receptor binding. Once inside tumor tissue, a particle decorated with targeting ligands (antibodies, peptides, folate, etc.) can bind overexpressed tumor-cell receptors. Binding probability follows a Langmuir isotherm on the product of ligand and receptor surface density:
P(bind) = (L · R) / (L · R + Kd) · k · dt
where L = ligand density, R = receptor density and Kd is the effective dissociation constant. Multivalent display (many ligands per particle meeting many receptors per cell) increases avidity beyond single-molecule affinity — this is why raising either slider alone still improves binding.
- Particle diameter — larger particles are excluded by both vessel walls sooner (EPR window closes above ~400 nm) but too small a particle is filtered by the kidneys before it can act (not modeled here).
- Ligand / receptor density — set both to zero to see pure passive EPR accumulation with no active retention.
- Off-target tissue — particles that leak into healthy tissue represent the systemic toxicity that ligand size, PEGylation and dosing schedules are designed to minimize in real therapeutics.