Figure 3.

Analysis of overall model behavior and parameter sensitivity. (A) Effect of proliferation and diffusion input values on proliferation ratio (p_app/p₀) in the three models. Colors indicate the input value for diffusion coefficient (D) in μm² h⁻¹. The plots display a negative trend in the models that account for cell–cell interactions (middle and right columns). (B) Effect of proliferation and diffusion input values on diffusion coefficient ratio (D_app/D₀) in the three models. The overlapping models (left and middle columns) show dependence on D₀ and p₀, particularly at low diffusion coefficient and high proliferation rate. This is due to the growth and division of cells at early time points, rather than diffusive movement, which generates an artifactual apparent movement, which appears as a significant boost in motility when the nominal diffusion coefficient is small. The non-overlapping model shows little dependence of apparent diffusion on proliferation, but does have a true boost in apparent diffusion due to jamming effects, particularly at low D₀. (C) Tumor velocity as a function of both input parameters. In most cases, the overlapping + cc model progresses much slower than the non-overlapping model, reflecting the abrupt rise in velocity due to jamming in the non-overlapping case only. Thus, the analysis reveals synergy between proliferation and migration in the non-overlapping model to strongly enhance tumor growth rate, particularly at the lower diffusion coefficients consistent with single cell experimental measurements.