Including blood vasculature into a game-theoretic model of cancer dynamics

• Published in: Games 2019-03, Vol.10 (1), p.1-22
• Main Authors: You, Li, von Knobloch, Maximilian, Lopez, Teresa, Peschen, Vanessa, Radcliffe, Sidney, Sam, Praveen Koshy, Thuijsman, Frank, Staénková, Kateérina, Brown, Joel S
• Format: Article
• Language: English
• Subjects: Acids; Androgens; Angiogenesis; Applied mathematics; Blood vessels; Cancer therapies; Cells; Estrogens; Evolution; Game theory; Games; Influence; Mathematical models; Medical prognosis; Metastasis; metastatic castrate-resistant prostate cancer; Nutrients; Prostate cancer; Radiation therapy; Residential density; spatial game theory; Testosterone; Toxins; tumorigenesis; Tumors; Vascular endothelial growth factor
• ISSN: 2073-4336; 2073-4336
• DOI: 10.3390/g10010013

For cancer, we develop a 2-D agent-based continuous-space game-theoretical model that considers cancer cells' proximity to a blood vessel. Based on castrate resistant metastatic prostate cancer (mCRPC), the model considers the density and frequency (eco-evolutionary) dynamics of three cancer cell types: those that require exogenous testosterone ( T + ), those producing testosterone ( T P ), and those independent of testosterone ( T - ). We model proximity to a blood vessel by imagining four zones around the vessel. Zone 0 is the blood vessel. As rings, zones 1-3 are successively farther from the blood vessel and have successively lower carrying capacities. Zone 4 represents the space too far from the blood vessel and too poor in nutrients for cancer cell proliferation. Within the other three zones that are closer to the blood vessel, the cells' proliferation probabilities are determined by zone-specific payoff matrices. We analyzed how zone width, dispersal, interactions across zone boundaries, and blood vessel dynamics influence the eco-evolutionary dynamics of cell types within zones and across the entire cancer cell population. At equilibrium, zone 3's composition deviates from its evolutionary stable strategy (ESS) towards that of zone 2. Zone 2 sees deviations from its ESS because of dispersal from zones 1 and 3; however, its composition begins to resemble zone 1's more so than zone 3's. Frequency-dependent interactions between cells across zone boundaries have little effect on zone 2's and zone 3's composition but have decisive effects on zone 1. The composition of zone 1 diverges dramatically from both its own ESS, but also that of zone 2. That is because T + cells (highest frequency in zone 1) benefit from interacting with T P cells (highest frequency in zone 2). Zone 1 T + cells interacting with cells in zone 2 experience a higher likelihood of encountering a T P cell than when restricted to their own zone. As expected, increasing the width of zones decreases these impacts of cross-boundary dispersal and interactions. Increasing zone widths increases the persistence likelihood of the cancer subpopulation in the face of blood vessel dynamics, where the vessel may die or become occluded resulting in the 'birth' of another blood vessel elsewhere in the space. With small zone widths, the cancer cell subpopulations cannot persist. With large zone widths, blood vessel dynamics create cancer cell subpopulations that resemble the ESS of zone 3 as the larg