This is a mean-field reduction of the same receptor-binding tropism problem, not a flattened view of a 3D scene. Instead of tracking individual particles through a random walk, the whole dose is treated as a continuous mass that flows through a compartmental network and is numerically integrated (RK4) as a system of ODEs:
dC/dt = −r·C·Σ pᵢ·(κᵢ + (1−κᵢ)·c)
dcapᵢ/dt = r·C·pᵢ·κᵢ
dclear/dt = r·C·Σ pᵢ·(1−κᵢ)·c
pᵢ = flowᵢ / Σflow (cardiac-output routing share)
- C — mass still freely circulating; κᵢ is the serotype's per-pass capture probability at organ i; c is the per-pass renal/immune clearance applied to whatever a pass through organ i did not capture.
- Serotype and target tissue set κᵢ and which node the "on-target" readout tracks — AAV8's high liver κ means most systemic dose is consumed by dcap₀/dt long before dC/dt empties.
- Injection route — local delivery is modelled as one boosted instantaneous pass straight into the target compartment (κ_target·1.35, capped at 1) before the remainder re-enters the same systemic ODE — exactly mirroring why real local routes (intrathecal, subretinal) front-load capture at the target before the liver ever gets a chance.
- Circulation rate and clearance are exposed directly as ODE rate constants here — turn circulation rate up to watch the whole system reach its steady-state split in seconds; turn clearance up and less of every dose survives to reach any organ.
- As t→∞, the analytic steady-state fraction captured at organ i is exactly pᵢ·κᵢ / Σⱼ pⱼ·(κⱼ + (1−κⱼ)·c) — the flow diagram's edge glow and the stacked chart both converge to that limit.
Real-world relevance: this is the deterministic large-dose limit of the same hepatic-sequestration problem that dose-limits systemic AAV gene therapy — the stochastic single-particle picture and this continuous mass-balance picture must agree in the limit of many particles, which is exactly what the verification for this page checks.