Vascularizing a Tissue Scaffold

Sprouting Angiogenesis

Chemotactic bias (VEGF gradient) 0.55

Branching rate 0.35

Tip migration speed 1.00

Scaffold tortuosity 0.30

Perfusion Status

Vessel network length0.0 mm

Oxygenated tissue0%

Anastomoses (loops)0

Active sprout tips0

Active tip cell

Capillary sprout

Oxygenated tissue voxel

Hypoxic tissue voxel

How it works

A hypoxic core at the scaffold's centre secretes VEGF (vascular endothelial growth factor), which diffuses outward and forms a concentration gradient. Endothelial tip cells at the parent vessel sense this gradient and migrate up it — a biased random walk (the Anderson–Chaplain "snail-trail" model used to study tumour and tissue-engineering angiogenesis):

dir(t+dt) = normalize( (1-χ)·dir(t) + χ·∇VEGF + tortuosity·ξ(t) )
pos(t+dt) = pos(t) + v·dir(t+dt)·dt

where χ is the chemotactic bias, ξ(t) a random unit vector representing collagen-fibre steering inside the scaffold, and v the migration speed. Each step a tip may branch — spinning off a daughter sprout at a randomised angle — with probability proportional to the branching-rate slider. When two independently-grown sprouts pass within a capillary diameter of each other they undergo anastomosis: they fuse into a single connected loop, which is how a real sprouting network becomes a perfusable circuit rather than a set of dead ends.

Tissue oxygenation is recomputed from Krogh's cylinder model — each voxel's oxygen level falls off with distance to the nearest vessel segment, O₂(d) = exp(−d / L), with L the diffusion length (~150–200 μm in real tissue, the reason engineered constructs thicker than a few hundred microns need a vascular network before cells at the core survive).

Chemotactic bias — how strongly tips follow the VEGF gradient vs. wander randomly.
Branching rate — probability per second that an active tip spins off a new sprout.
Tip migration speed — how fast endothelial tip cells advance.
Scaffold tortuosity — how much the scaffold's fibre architecture deflects a sprout's path; higher values make longer, winding capillaries and slow effective vascularization.

Tip cells Oxygenated

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