Tumor containment as an anti-percolation process

Percolation theory from statistical physics has been applied to several aspects of tumor progression. Tumor growth on percolation clusters has been used to model spatial expansion, vascular percolation to describe nutrient supply and transport related percolation to investigate drug and gene delivery. At the molecular level, mutational percolation has been employed to account for the emergence of malignant phenotypes, while inverse percolation to represent treatment-induced structural disruption. We examined whether tumor containment can be interpreted as an anti percolation problem, in which spatial expansion depends on the formation of a connected malignant domain. We implemented a spatial simulation with biologically scaled parameters to represent tissue heterogeneity, local growth, cell movement and clearance. We measured both total malignant area and connectivity metrics, including the largest connected component and the probability of forming a spanning cluster. Our results indicate that tumor size and spatial connectivity are partially independent, with configurations of similar size showing different connectivity patterns. A transition from fragmented to connected structures emerged within a limited parameter range, consistent with a threshold like behavior. Incorporating spatial connectivity into quantitative analysis, our approach provides a complementary way to characterize tumor organization. Potential applications include integration of structural descriptors into computational models of tumor growth, design of experimental systems to probe spatial organization and interpretation of therapeutic approaches via connectivity-based metrics.