Bioartificial Organ Growth — Scaffold Perfusion & Diffusion Limit

Bioreactor

Perfusion rate 0.7×

Scaffold radius 3.5 mm

Simulation speed 1.0×

Culture state

Avg. viability

–

Necrotic core

–

Core O₂

–

Surface O₂

–

Culture time

–

Live density

–

How it works

Each site on the scaffold grows a local cell population by logistic growth, dN/dt = r·N·(1−N/K), where the carrying capacity K is set by how much oxygen reaches that point. Oxygen enters only from the perfused surface and falls off toward the core over a characteristic penetration length set by the perfusion rate — the same diffusion-limit problem that caps how large a tissue-engineered construct can be before its center starves.

O2(r) = clamp(1 − (1−r)·R/L, 0, 1)
L = diffusion length ∝ perfusion rate
R = scaffold radius, r = 0(core)…1(surface)
dN/dt = r_growth·N·(1 − N/K(O2))

Perfusion rate — how fast the bioreactor pumps nutrient/oxygen-rich medium through the scaffold; higher perfusion pushes oxygen deeper before it's consumed.
Scaffold radius — a larger construct means a longer diffusion path from surface to core, so the same perfusion rate reaches proportionally less far in.
Necrotic core — sites where oxygen drops below the viability threshold stop growing and decay toward zero, shown as dark, shrunken cells instead of green ones.

high O₂

low O₂

Healthy cells Necrotic (hypoxic) Scaffold — oxygenated Scaffold — hypoxic

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