The 3D companion sim renders one capillary as a cylinder with a spatially-uniform leak probability (its own source code notes this is left uniform "for future spatial-gradient extensions"). This 2D version is that extension: it solves the same Starling–Landis filtration law as a reaction-diffusion field over a tissue cross-section containing four parallel capillaries at different depths —
J_v(x,y) = K_f · [ (P_c − P_i(x,y)) − σ·(π_c − π_i(x,y)) ]
∂edema/∂t = source(J_v) + D∇²edema − v_g·∂edema/∂y − k_lymph·edema
∂alb/∂t = source((1−σ)K_f) + D_alb∇²alb − v_g·∂alb/∂y
Kf, σ and the blood-side πc still come from one systemic cytokine-exposure state (real IL-6/TNF-α are blood-borne, so junction leakiness itself has no spatial pattern here either) — but the fluid that leaks out no longer vanishes into a generic scalar. It diffuses through the interstitium and drifts slowly downward under a gravity term vg, exactly like real "third-spacing" edema pools in dependent tissue (ankles, sacrum) rather than distributing evenly. A finite-difference solver advances the field with as many stability-limited sub-steps as the diffusion/advection Courant numbers demand, so the field never goes unstable even at high permeability.
- Storm intensity and anti-cytokine therapy drive the same systemic permeability state as the 3D view.
- IV fluid resuscitation raises capillary hydrostatic pressure Pc uniformly, so it refills every capillary in the field at once — and, at high permeability, filters straight back out through all of them, the same clinical dilemma the 3D view illustrates.
- Dependent pooling ratio — mean edema in the lowest capillary's row divided by the topmost's — is a number the spatially-uniform 3D model cannot produce at all; it only emerges once leaked fluid is allowed to move through space.
- A slow lymphatic drainage term is added here (real interstitial fluid is not permanently trapped); the 3D scalar model has no reabsorption pathway, so its edema counter can only ever grow.