Scaffold-Guided Organ Regeneration

Scaffold Parameters

Cell proliferation rate r 0.60

Angiogenesis rate 0.18

Oxygen diffusion rate 0.35

Hypoxia tolerance 0.18

Regeneration Status

Tissue coverage

0.0%

Vascularized

0.0%

Average oxygenation

0.0%

How it works

The scaffold is a lattice of pore sites forming a small spherical organ construct. Tissue starts only at the base, where the construct meets host vasculature; everything above must be reached by both proliferating cells and ingrowing blood vessels before it can survive.

Tissue density D at each site:
 dD/dt = r·D·(1-D)·f(O)  -  k·D·max(0, H-O)
   f(O) = clamp(O/0.3, 0, 1)   (growth needs oxygen)
   necrosis fires when local O2 falls below H

Oxygen O (vascularized sites are clamped to O=1):
 dO/dt = Ddiff·(mean neighbor O - O) - c·D

Vessel front: an existing vessel converts an adjacent
non-vascularized site to vascularized with probability
 p = angioRate·dt·(1-O_neighbor)·(0.2+0.8·D_neighbor)
so new vessels are drawn toward oxygen-starved tissue —
a simplified stand-in for VEGF-driven chemotaxis.

Proliferation rate — how fast seeded cells divide and spread to neighboring pores once they have enough oxygen.
Angiogenesis rate — how quickly new vessels sprout from the perfused base toward hypoxic tissue.
Oxygen diffusion rate — how far oxygen reaches from a vessel before it is consumed by nearby cells.
Hypoxia tolerance — the oxygen level below which tissue starts to die back (necrotic core, shown dark).

Real-world relevance: this diffusion-vascularization race is the central engineering limit on bioartificial organs today — without host or engineered blood supply keeping pace, a scaffold's interior starves before it can regenerate, which is why constructs are grown thin, pre-vascularized, or perfused externally.

Unseeded scaffold pore Growing tissue Necrotic tissue Vessel front

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