Stem Cell Wound Regeneration

Growth-Factor Signalling

Secretion rate S 1.00×

Diffusion coefficient D 1.00×

Cell Behaviour

Proliferation rate k_p 1.00×

Differentiation threshold θ 1.00×

Tissue State

Live cells

Differentiated

Wound closure

Mean [GF] in wound

0.00

Stem cell (proliferating)

Differentiated tissue

Open wound bed

How it works

Growth factor (GF) released at the wound margin spreads through the tissue by diffusion and decays as it is taken up by cells — a standard reaction-diffusion field:

∂C/∂t = D∇²C − k_decay·C + S(x,t)

Each mesenchymal stem cell samples the local concentration C and divides stochastically with a saturating, Michaelis–Menten-style probability per step (more receptors occupied → diminishing extra benefit from more ligand):

P(divide) = dt · k_p · C / (C + K_m)

A daughter cell is placed near its parent inside the wound bed while capacity remains. Each cell also integrates its exposure over time; once the cumulative signal crosses the differentiation threshold θ it exits the cell cycle and commits to mature tissue (green), permanently closing that patch of the wound:

exposure += C·dt;  differentiate when exposure ≥ θ

Secretion rate — strength of the continuous GF source at the wound margin.
Diffusion coefficient — how fast GF spreads across the tissue plane (surface tint shows the live field).
Proliferation rate — scales how readily stem cells divide once exposed to GF.
Differentiation threshold — how much cumulative GF signal a stem cell needs before committing to mature tissue; lower it and cells mature (and stop dividing) sooner.
Inject GF Pulse — a one-off burst of growth factor across the whole wound bed, the way a hydrogel/scaffold bolus delivery works in real regenerative-medicine protocols.

This mirrors real regenerative-medicine strategies — MSC delivery scaffolds loaded with growth factors (e.g. PDGF, TGF-β) that drive proliferation and lineage commitment to close a tissue defect.

t = 0.0 s

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