The 3D version narrates the MACI clinical pipeline stage by stage. This 2D companion isolates one quantitative sub-problem from that pipeline — the diffusion limit that governs whether a scaffold's core survives at all — and actually solves it, live, as you change scaffold thickness and cell density:
∂C/∂t = D·∂²C/∂x² − Vmax·C/(Km+C) (O2 reaction-diffusion, explicit FD)
dGAG/dt = k·Sload(load)·C/(C+Ks) (strain- & O2-gated matrix synthesis)
A 1D grid runs from the media-facing surface (Dirichlet boundary fixed at the O2-tension slider) to the construct's mid-plane (no-flux/symmetry boundary — this model treats the construct as fed equally from both faces, so only the near-surface-to-center half needs solving). Oxygen is consumed by chondrocytes via Michaelis-Menten kinetics scaled by the seeding-density slider; the diffusion coefficient used is representative of O2 in a collagen/hydrogel scaffold (~1.5×10⁻⁹ m²/s), so thicker constructs genuinely develop a hypoxic — and past a critical thickness, necrotic — core, matching the well-documented ~150–200 µm avascular diffusion limit in cartilage tissue engineering.
- O2 field — the colour gradient across the cross-section is the live finite-difference solution, not a canned animation; drag the thickness slider and watch the profile re-equilibrate.
- Loading intensity — follows the same anabolic/catabolic bell curve as real dynamic-compression bioreactor protocols: synthesis peaks near moderate strain (~40–50%) and falls off — even below baseline — at high strain, mirroring catabolic MMP-driven matrix breakdown under overload.
- GAG & stiffness — GAG content integrates the local synthesis rate over simulated culture days across the whole depth profile; construct stiffness is derived from accumulated GAG via a simplified power-law fit to published biphasic-compression data.