Oxygen Diffusion Limit in Engineered Tissue

Grown outside the body, engineered tissue has no blood vessels until the body (or a bioreactor) builds them — so every oxygen molecule a cell uses must diffuse in from a free surface while neighboring cells along the way consume their share first. This simulator renders a 3D block of tissue as a grid of instanced cells and solves the real steady-state reaction–diffusion balance, D·d²C/dx² = Q, to color each cell by its local oxygen level. Push the construct's thickness past the classic ~150–200 µm Krogh diffusion limit and a necrotic core appears at the center; raise the cells' metabolic demand or lower the scaffold's diffusivity and the same thing happens even in a thin slab. Adding a vascular channel through the middle inserts a second oxygen source and halves the unsupported diffusion distance, rescuing the core exactly as vascularization does in real regenerative-medicine constructs — cartilage grafts, tumor spheroids, and thick organoids all live or die by this one number.