Tumor Growth — Gompertz Law & Vascular Nutrient Diffusion

Tumor growth follows the Gompertz law N(t) = N_∞ exp(-exp(-r(t-t₀))), reflecting the slowing caused by nutrient diffusion limits in avascular tumors. The spatial model shows a proliferating rim, necrotic core, and quiescent region determined by oxygen/nutrient concentration gradients from blood vessels.

Parameters

Growth rate r: 0.08 Max size K: 0.90 Diffusion D: 0.50 Necrosis threshold: 0.20 Vessel density: 0.30

Tumor State

Radius:—

Necrotic core r:—

Proliferating %:—

Doubling time:—

Time:0