Table 1.
Oxygen diffusion and consumption parameters.
Fig 1.
Schematic of the simulation environment including microchannel distribution.
A 2D tissued grid with randomly positioned cancer stem cell (CSC) and oxygen microchannels shown as white dots. The model simulates CSC behavior under spatial and oxygen constraints.
Table 2.
Sensitivity analysis of a00.
Table 3.
Sensitivity analysis of a01.
Table 4.
Sensitivity analysis of migration.
Fig 2.
Simulated tumor growth initiated by a single cancer stem cell after 20 days.
Blue represents CSCs; red indicates two phenotypic types of non-stem cells. The tumor exhibits hierarchical expansion and local heterogeneity.
Fig 3.
Time course of CSC and non-CSC population expansion.
The number of CSCs and non-stem cancer cells over simulation time, reflecting asymmetric and symmetric division dynamics with emergence of hierarchical tumor structure.
Fig 4.
Histogram of cell migration frequency during tumor development.
Most cells exhibit minimal migration, with a few undergoing multiple migrations- matching a power law distribution pattern.
Fig 5.
Reference power-law distribution for comparison.
A generic power-law function is used as a conceptual benchmark for interpreting cell migration distribution in the simulation.
Fig 6.
Spatial distribution of cell location by migration frequency.
Cells with higher migration counts tend to spread further from the origin. CSCs are shown as circles, non-CSCs as triangles.
Fig 7.
Cross-sectional oxygen concentration map in simulated tissue.
Oxygen gradients reflect diffusion from microchannels and local consumption. Hypoxic zones emerge where tumor density increases.
Fig 8.
Oxygen concentration fluctuates in cancerous vs. non-cancerous regions.
Pixel-wise oxygen levels plotted to demonstrate depletion caused by tumor metabolic activity and spatial constraints.
Fig 9.
Experimental tumor growth data from Norton er al.
[10]. Shows CSC-driven tumor progression in vivo used for model validation.
Table 5.
Non-divergence and stability analysis of model.
Table 6.
Key similarities and differences.
Fig 10.
Comparison between experimental and simulated tumor area growth.
Model prediction closely matches biological data in both shape and saturation behavior.
Table 7.
Numerical validation between experimental and simulation data.
Table 8.
Quantitative results of Q-learning therapy.
Table 9.
Comparison with previous Models.