Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective
Background: Immunotherapy is a recently developed method of cancer therapy, aiming to strengthen a patient’s immune system in different ways to fight cancer. One of these ways is to add stem cells into the patient’s body.
Methods: The study was conducted in Kermanshah, western Iran, 2016-2017. We first modeled the interaction between cancerous and healthy cells using the concept of evolutionary game theory. System dynamics were analyzed employing replicator equations and control theory notions. We categorized the system into separate cases based on the value of the parameters. For cases in which the system converged to undesired equilibrium points, “stem-cell injection” was employed as a therapeutic suggestion. The effect of stem cells on the model was considered by reforming the replicator equations as well as adding some new parameters to the system.
Results: By adjusting stem cell-related parameters, the system converged to desired equilibrium points, i.e., points with no or a scanty level of cancerous cells. In addition to the theoretical analysis, our simulation results suggested solutions were effective in eliminating cancerous cells.
Conclusion: This model could be applicable to different types of cancer, so we did not restrict it to a specific type of cancer. In fact, we were seeking a flexible mathematical framework that could cover different types of cancer by adjusting the system parameters.
2. Hanahan D, Weinberg RA (2011). Hallmarks of Cancer: The Next Generation Douglas. Cell, 144(5): 646–74.
3. Magi S, Iwamoto K, Okada-Hatakeyama M (2017). Current Status of Mathematical Modeling of Cancer–From the Viewpoint of Cancer Hallmarks. Curr Opin Syst Biol, 2: 39–48.
4. Cairns J (1975). Mutation selection and the natural history of cancer. Nature, 255: 197–200.
5. Dingli D, Chalub FACC, Santos FC et al (2009). Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells. Br J Cancer,101(7): 1130–6.
6. Malekian N, Habibi J, Zangooei MH, Aghakhani H (2016). Integrating evolutionary game theory into an agent-based model of ductal carcinoma in situ: Role of gap junctions in cancer progression. Comput Methods Programs Biomed,136: 107–17.
7. Khadem H, Kebriaei H, Veisi Z (2017). Inactivation of tumor suppressor genes and cancer therapy: An evolutionary game theory approach. Math Biosci, 288: 84–93.
8. Chen DS, Mellman I (2013). Oncology meets immunology: The cancer-immunity cycle. Immunity, 39(1):1–10.
9. Konstorum A, Vella AT, Adler AJ, Laubenbacher RC (2017). Addressing current challenges in cancer immunotherapy with mathematical and computational modelling. J R Soc Interface, 14(131): 20170150.
10. Doban AI, Lazar M (2017). A switching control law approach for cancer immunotherapy of an evolutionary tumor growth model. Math Biosci, 284: 40–50.
11. Jeanbart L, Swartz MA (2015). Engineering opportunities in cancer immunotherapy. Proc Natl Acad Sci, 112(47): 14467–72.
12. Hu X, Zhang Z (2016). Understanding the Genetic Mechanisms of Cancer Drug Resistance Using Genomic Approaches. Trends Genet, 32(2): 127–37.
13. Weekes SL, Barker B, Bober S, et al (2014). A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics. Bull Math Biol, 76(7): 1762–82.
14. Serre R, Benzekry S, Padovani L, et al (2016). Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy. Cancer Res, 76(17): 4931–40.
15. Deng L, Liang H, Burnette B, et al (2014). Irradiation and anti – PD-L1 treatment synergistically promote antitumor immunity in mice. J Clin Inves, 124(2): 687–95.
16. Golden EB, Chhabra A, Chachoua A, et al (2015). Local radiotherapy and granulocyte-macrophage colony-stimulating factor to generate abscopal responses in patients with metastatic solid tumours: A proof-of-principle trial. Lancet Oncol,16(7): 795–803.
17. Nowak MA, Michor F, Komarova NL, Iwasa Y (2004). Evolutionary dynamics of tumor suppressor gene inactivation. Proc Natl Acad Sci U S A, 101(29): 10635–8.
18. Kazanets A, Shorstova T, Hilmi K et al (2016). Epigenetic silencing of tumor suppressor genes: Paradigms, puzzles, and potential. Biochim Biophys Acta, 1865(2): 275–88.
19. Bozic I, Allen B, Nowak MA (2012). Dynamics of targeted cancer therapy. Trends Mol Med, 18: 311–6.
20. Hatzikirou H, Alfonso JCL, Leschner S et al (2017). Therapeutic potential of bacteria against solid tumors. Cancer Res, 77(7): 1553–63.
21. Alfonso JCL, Schaadt NS, Schönmeyer R, et al (2016). In-silico insights on the prognostic potential of immune cell infiltration patterns in the breast lobular epithelium. Sci Rep, 6: 33322.
22. Reppas AI, Alfonso JCL, Hatzikirou H (2016). In silico tumor control induced via alternating immunostimulating and immunosuppressive phases. Virulence, 7(2): 174–86.
23. Hahnfeldt P, Panigrahy D, Folkman J, et al (1999). Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res, 59:4470–5.
24. d'Onofrio A, Gandolfi A (2004). Tumour eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999). Math Biosci,191(2):159–84.
25. Araujo A, Cook LM, Lynch CC, Basanta D (2014). An integrated computational model of the bone microenvironment in bone-metastatic prostate cancer. Cancer Res, 74(9): 2391–401.
26. Haeno H, Gonen M, Davis MB et al (2012). Computational modeling of pancreatic cancer reveals kinetics of metastasis suggesting optimum treatment strategies. Cell, 148(1–2): 362–75.
27. Werner B, Dingli D, Traulsen A (2013). A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues. J R Soc Interface, 10(85): 20130349.
28. Eftimie R, Gillard JJ, Cantrell DA (2016). Mathematical Models for Immunology: Current State of the Art and Future Research Directions. Bull Math Biol, 78(10):2091–2134.
29. Banerjee J, Ranjan T, Layek RK (2015). Dynamics of cancer progression and suppression: A novel evolutionary game theory based approach. Conf Proc IEEE Eng Med Biol Soc, 2015:5367-71.
30. Greenhalgh S, Galvani AP, Medlock J (2015). Disease elimination and re-emergence in differential-equation models. J Theor Biol, 387:174–80.
31. Liao D, Tlsty TD (2014). Evolutionary game theory for physical and biological scientists.II. Population dynamics equations can be associated with interpretations. Interface Focus, 4(4): 20140038.
32. De Pillis LG, Gu W, Radunskaya AE (2006). Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations. J Theor Biol, 238(4): 841–62.
33. de Pillis L, Renee Fister K, Gu W, et al (2009). Mathematical model creation for cancer chemo-immunotherapy. Comput Math Methods Med, 10(3): 165–84.
34. Tomlinson IP (1997). Game-theory models of interactions between tumour cells. Eur J Cancer, 33(9): 1495–500.
35. Tomlinson IPM, Bodmer WF (1997). Modelling the consequences of interactions between tumour cells. Br J Cancer, 75(2): 157–60.
36. Ardeshir K, Veltri R, Pienta KJ (2014). Critical transitions in a game theoretic model of tumour metabolism. Interface Focus, 4(4): 20140014.
37. Archetti M (2013). Evolutionary game theory of growth factor production: Implications for tumour heterogeneity and resistance to therapies. Br J Cancer, 109(4):1056–62.
38. Gerstung M, Nakhoul H, Beerenwinkel N (2011). Evolutionary Games with Affine Fitness Functions: Applications to Cancer. Dyn Games Appl, 1(3): 370–85.
39. Khadem H, Kebriaei H (2015). A study of inactivation of TSG and cancer therapy: An evolutionary game theory approach. 22nd Iranian Conference on Biomedical Engineering (ICBME), 325–30.
40. Pacheco JM, Santos FC, Dingli D (2014). The ecology of cancer from an evolutionary game theory perspective. Interface Focus, 4(4): 20140019.