Oxygenated
Hypoxic
Necrotic
Vascular channel
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This simulation narrows tissue engineering down to the single problem that limits how thick a lab-grown construct can get: oxygen only diffuses so far through living tissue before cells consume it faster than it arrives. Cells are seeded through a spherical construct and oxygen enters from the surface, following a Fick's-law reaction–diffusion balance with Michaelis–Menten cell uptake, solved on a live radial grid every frame. Grow the construct past roughly 150–200 microns without a blood supply and a hypoxic, then necrotic, core opens up at the centre — visibly, as the innermost shell of cells fades from green to amber to dark red. Tune construct radius, cell density and the external oxygen level to see the diffusion-limited shell shrink or expand, or add an internal vascular channel — the real strategy tissue engineers use to defeat this limit — and watch the core reoxygenate around it.