Biophysical Feasibility Constraints Govern Phase Transitions in Tumor Control Dynamics

Tumor behavior is strongly influenced by microenvironmental acidity, molecular transport, and metabolic resource limitations, yet quantitative principles governing their coupled effects remain incompletely understood. Here we present a biophysical modeling framework showing that sustained tumor control is governed by feasibility constraints rather than by individual parameter magnitudes. Three dimensionless control parameters (Ξ, Λ, Ψ) capture independent dynamical, spatial, and energetic limitations arising from nonlinear tumor–immune interactions, reaction–diffusion transport of acidity, and metabolic costs of alkalinization. Analytical feasibility boundaries defined by these parameters predict distinct outcome regimes, including tumor persistence, partial control, and clearance. Numerical parameter sweeps reveal sharp transitions across feasibility thresholds, and sensitivity analysis demonstrates that regime structure depends primarily on the dimensionless constraint geometry rather than on specific kinetic coefficients. These results introduce a constraint-based interpretation of tumor regulation and clarify how transport and energetic limitations can fundamentally restrict therapeutic outcomes. The framework provides a generalizable approach for analyzing environmentally coupled biological systems subject to physical constraints.