This is the 2D companion to the 3D reperfusion-injury sim. The reaction kinetics are identical — ATP hydrolysis during cold storage builds up hypoxanthine, and reperfusion drives the xanthine-oxidase (XO) burst:
ATP(hours) = exp(−hours/τ), hypoxanthine = 1 − ATP (per tissue patch, τ heterogeneous)
Reperfusion: d(hyp)/dt = −k_XO·hyp·O2_local·sensitivity
d(ROS)/dt = k_XO·hyp·O2_local·sensitivity − decay·ROS (+ paracrine diffusion)
Damage rate ∝ ROS × (1−ATP) × sensitivity; ATP resumes ∝ (1−damage)·(1−ATP) once local O2 > 0
The 3D sim treats every cell as independently reperfused the instant you click the button — full oxygen everywhere, all at once. This 2D version instead resolves a genuine 2D reaction-diffusion field on a tissue cross-section: the vertical axis is depth from the vascular surface (bottom, where capillaries sit) down into the avascular core (top); the horizontal axis is position along the graft. Oxygen only enters at the vascular surface and has to diffuse inward before the XO reaction can run at each patch (production rate is scaled by the local O2 fraction), so you can watch a genuine reoxygenation front sweep from the surface into the core — a diffusion-limited effect real grafts show and the 3D sim cannot, since it applies the same instantaneous full-body reperfusion everywhere. Free radicals also diffuse a short distance between neighboring patches (paracrine bystander spread), so injury can propagate slightly beyond the cells that produced it, another effect the independent-particle 3D model omits entirely.
With the O2 front set to arrive everywhere at once and paracrine diffusion switched off, this field reduces exactly to the 3D sim's per-cell ODE — the two are the same reaction, verified by direct numerical comparison; the spatial spread is the genuinely 2D addition.
- Cold ischemia time — longer cold storage depletes more ATP and builds up more hypoxanthine substrate before you reperfuse, patch by patch.
- Antioxidant defense — models superoxide dismutase / glutathione capacity; scavenges ROS faster everywhere, blunting the burst.
- Xanthine oxidase inhibitor — models allopurinol, blocking the enzyme at its source across the whole field.
- O2 front depth — how far the reoxygenation front has diffused from the vascular surface into the tissue core.
Real-world relevance: watershed zones far from the microvasculature reoxygenate last and are known to suffer the worst reperfusion injury — this is exactly the diffusion-limited front this field visualizes, and why machine perfusion protocols aim to restore flow gradually and uniformly rather than all at once.