Bioprinted Filament Cross-Section: 2D Oxygen Diffusion Map & Necrotic Core

Extrusion-based bioprinting builds tissue one filament at a time, and every filament has no blood supply until vascularization catches up — every cell inside survives purely on oxygen diffusing in from the surrounding medium. This simulator solves the steady-state cylindrical diffusion–reaction equation directly on a 2D grid (successive over-relaxation), rendering the solved concentration field as a cross-section heatmap alongside its radially-averaged profile. Push the radius up, the consumption rate up, or the medium oxygen down, and watch a dark necrotic core appear at the centre exactly where the numbers predict it — and notice it appears sooner than an equivalent-radius sphere would, because a cylinder's geometry gives cells less of a diffusion "cushion" than a sphere's.