Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012 Dec;9(6):065007.
doi: 10.1088/1478-3975/9/6/065007. Epub 2012 Nov 29.

Cancer Treatment as a Game: Integrating Evolutionary Game Theory Into the Optimal Control of Chemotherapy

Affiliations
Free PMC article

Cancer Treatment as a Game: Integrating Evolutionary Game Theory Into the Optimal Control of Chemotherapy

Paul A Orlando et al. Phys Biol. .
Free PMC article

Abstract

Chemotherapy for metastatic cancer commonly fails due to evolution of drug resistance in tumor cells. Here, we view cancer treatment as a game in which the oncologists choose a therapy and tumors 'choose' an adaptive strategy. We propose the oncologist can gain an upper hand in the game by choosing treatment strategies that anticipate the adaptations of the tumor. In particular, we examine the potential benefit of exploiting evolutionary tradeoffs in tumor adaptations to therapy. We analyze a math model where cancer cells face tradeoffs in allocation of resistance to two drugs. The tumor 'chooses' its strategy by natural selection and the oncologist chooses her strategy by solving a control problem. We find that when tumor cells perform best by investing resources to maximize response to one drug the optimal therapy is a time-invariant delivery of both drugs simultaneously. However, if cancer cells perform better using a generalist strategy allowing resistance to both drugs simultaneously, then the optimal protocol is a time varying solution in which the two drug concentrations negatively covary. However, drug interactions can significantly alter these results. We conclude that knowledge of both evolutionary tradeoffs and drug interactions is crucial in planning optimal chemotherapy schedules for individual patients.

Figures

Figure 1
Figure 1
Three different tradeoffs in allocation of resistance between the two drugs.
Figure 2
Figure 2
The effects of two drugs on cancer cell fitness in two different scenarios. In A the cancer cells are using their best evolutionary strategy against the combination of drugs. In B the cancer cells have a fixed level of resistance and are using their worst evolutionary strategy in terms of allocation to either drug. The linear, concave, and convex tradeoffs are represented by solid, dashed, and dotted lines, respectively. Note that the total concentration of drug 1 and drug 2 is fixed at 10, consistent with the optimization problem. Parameters in common for both panels: r = 1, Kmax = 10, σk = 30, k1 = k2 = 10, β = 0. For panel B u1=3.
Figure 3
Figure 3
Optimal state profiles for the three different tradeoff types without drug interactions. The left panels show tumor cell densities (solid line) and the concentrations of drug 1 (dashed line) and drug 2 (dotted line). The right panel shows the tumor cells resistance to drug 1 (solid line) and drug 2 (dashed line). The top, middle, and bottom panels show the solutions for the linear, concave, and convex tradeoffs, respectively. Parameters in common to all panels: r = 1, Kmax = 10, σk = 30, k1 = k2 = 10, β = 0, z1 = z2 = 0.9.
Figure 4
Figure 4
Optimal state profiles for the three different tradeoff types with drug interactions. The left panels show tumor cell densities (solid line) and the concentrations of drug 1 (dashed line) and drug 2 (dotted line). The right panel shows the tumor cells resistance to drug 1 (solid line) and drug 2 (dashed line). The top, middle, and bottom panels show the solutions for the linear tradeoff with antagonistic drugs (β = −0.01), concave tradeoff with synergistic drugs (β = 0.01), and convex tradeoff with antagonistic drugs (β = −0.01), respectively. Parameters in common to all panels: r = 1, Kmax = 10, σk = 30, k1 = k2 = 10, z1 = z2 = 0.9.

Similar articles

See all similar articles

Cited by 14 articles

See all "Cited by" articles

Publication types

Substances

LinkOut - more resources

Feedback