Angiogenesis Model — Blood Vessel Regrowth After Burn

01

Why Angiogenesis Matters After Burns

Angiogenesis — the growth of new blood vessels from existing vasculature — is essential to supply oxygen and nutrients to the wound for all subsequent healing phases. After a severe burn, most vessels supplying the wound area are destroyed or occluded by thermal damage.

The death of cells in the wound signals the critical need for angiogenesis to begin. Without new vessel formation, the healing cascade stalls entirely.

The key cell type in vascular regrowth is the Endothelial Cell — which proliferates, migrates along cytokine gradients, and forms new capillary networks. This model focuses on how varying the initial endothelial cell count changes inflammatory dynamics across the wound space.

02

The Simulation

The videos below show how varying the initial endothelial cell count changes cytokine concentrations and inflammation across the wound patch over the first 4 days (~100 hours) post-injury.

What to Look For

Watch the cytokine field first. Cytokines are signalling proteins that attract cells to where they are needed — different cytokines serve different roles in wound resolution. The table below summarises key cytokines modeled in this simulation.

Cytokine function table — Cytokine roles in inflammation and wound response. Adapted from Chen and Deng et al., 2017.

03

Model Parameters and Assumptions

The simulation varies a single parameter across runs — the initial endothelial cell count (denoted E_x in the videos, or S_x in the paper). All other parameters — Lambda and the Saturation coefficient — remain constant across simulations.

Lambda controls how strongly a cell is attracted toward a cytokine gradient. The Saturation coefficient sets the cytokine concentration threshold required to trigger a given cellular behaviour.

Model Variables and Interactions

MAP4b model variable table — Variable definitions and relationships in the MAP4b angiogenesis model. Adapted from Korkmaz et al., 2024.

Key Assumptions

The wound patch is divided into an outer ring of 9 cm² (surrounding the wound) containing cells and cytokines from the systemic circulation via remaining blood vessels, and an inner square of 16 cm² representing the burn wound itself.
The simulation starts immediately after burn injury and runs to day 4 post-injury (approximately 100 hours).
Cells and cytokines follow the biological interaction rules described in the MAP4b diagram. View Figure C (interaction diagram) →

Spatio-temporal PDE Agent-based 16 cm² patch 100-hour window