Instead of tracking individual sprout tips, this version solves two coupled fields on a 2D grid over the wound: a diffusing VEGF concentration secreted by hypoxic tissue, and an endothelial-cell density that spreads from the capillary margin by random motility, proliferates locally, and is advected up the VEGF gradient by volume-limited chemotaxis (it slows as a cell already crowds a patch, so density can't run away past 1).
HIF-1α stabilization: S = H · (1 − k·Gn), k = 0.85 (0.20 on therapy)
Glucose term: Gn = clamp((glucose − 90) / 310, 0, 1)
VEGF field: ∂V/∂t = D_v·∇²V + α·S·[in wound] − β·V
Endothelial field: ∂E/∂t = D_e·∇²E − χ(S)·∇·(E(1−E)∇V) + r(S)·E(1−E)
with χ(S) = χ₀·(0.25+0.75S), r(S) = r₀·S (same HIF gating as the 3D speed/branch terms)
In normoxic tissue, prolyl-hydroxylase (PHD) enzymes use O₂ to mark HIF-1α for degradation; under hypoxia, PHD activity falls and HIF-1α accumulates, driving VEGF transcription. Chronic hyperglycemia keeps PHD activity abnormally high even when the tissue is hypoxic, so HIF-1α is degraded almost as if oxygen were still plentiful (Botusan et al., PNAS 2008; Catrina & Zheng, Diabetologia 2016). The same glucose term throttles the VEGF source strength and the chemotactic/proliferative gain of the endothelial field here, so the vascular front spreads thinner and stalls before covering the wound.
- Glucose slider — sets the glycemic suppression of HIF-1α stabilization.
- Hypoxia signal — the strength of the VEGF source inside the wound bed.
- PHD-inhibitor therapy — mimics drugs like roxadustat/DMOG that block PHD directly, bypassing the glucose effect and rescuing the field's spread.
- Orange glow is the VEGF field; red-to-green density is the endothelial field, greening where it has perfused the wound bed.