Blood vessel tortuosity selects against evolution of aggressive tumor cells in confined tissue environments: A modeling approach
Fig 4
Stages of development in simulations with mutating cells and stable vasculature.
Mutation rate = 10%. (a) Number of cells and nutrient levels as in Fig 3f, using a logarithmic time-scale with the three stages indicated with numbers. (b) Cell configurations of each stage with oxygen concentrations color coded. (c) Population size (pink) and averages of all 10 evolving parameters scaled with their respective step sizes σp and shifted to their initial values. Intracellular growth signal: N0. (d) Normalized parameter values at the end of the simulation runs (t = 105 MCS). (e-f) Stage 1: expansion. Configuration of cells from a simulation showing the instantaneous growth rate (e) defined as the increase in target volume in the current MCS, and generation age (f) at t = 2200 MCS. Patches of high growth appearing independently from the localization of sources. (g-i) Stage 2: hypoxia. Configuration of cells from a simulation showing the intracellular growth signal N0 (g), level of hypoxia (h), and glucose uptake (i) at t = 6000 MCS. (j-k) Stage 3: starvation. Configurations of cells from a simulation showing growth rates (j) and intracellular pressure (k) at late stages of development. (l-m) Evolution of cellular metabolism showing intracellular hypoxia and ROS (l) and nutrient uptake (m). Line graphs show average of 10 independent simulations with standard deviation, box plots show median with interquartile range and minimum / maximum values from 10 independent simulations.