Venom deposited in tissue spreads by molecular diffusion and is simultaneously removed by the lymphatic and circulatory systems — a real pharmacokinetic picture, not a decorative animation. Because a single bite is (to a good approximation) a point source in locally uniform tissue, the concentration field is radially symmetric around the bite, so this engine solves the exact 3D diffusion-clearance PDE reduced to one spatial variable, the radius r:
∂C/∂t = D·[∂²C/∂r² + (2/r)·∂C/∂r] − k·C
This is Fick's second law (diffusion term) plus a first-order clearance term. It is solved on a 90-point radial grid with explicit finite differences every frame, sub-stepped for numerical stability as D changes.
- Diffusion coefficient D — how fast venom molecules spread through tissue; larger D flattens the concentration bump outward faster.
- Clearance rate k — first-order removal by lymph/blood flow; larger k shrinks total venom load faster without needing it to spread first.
- Tissue density — denser tissue (e.g. more collagen/fat) impedes molecular motion, scaling the effective diffusivity Deff = D / density.
- Antivenom — neutralises a fraction of circulating venom immediately and boosts the clearance rate afterward, mirroring how antivenom antibodies bind toxin and accelerate its removal.
The green cloud renders 3000 point samples drawn from the current concentration profile weighted by shell volume (∝ C(r)·r²), so particle density visualises C(r,t) directly; the translucent shells are iso-concentration surfaces. Click the limb to move the bite site (cosmetic — the physics is translation-invariant in uniform tissue).