Abstract
In this chapter, two of the most widely used tumor growth models (TGM) are studied: the logistic and Gompertz models. The chapter begins with a study of the logistic model and the generalized logistic model. A study of the immune system (IS) and the angiogenesis process is also presented, since both subsystems can influence tumor growth. The IS is responsible for the human organism’s defense against infections and diseases and may help to suppress tumors. However, it can also be affected by the tumor, leading to a balance between the tumor volume and the evolution of immunocompetent cell densities. The angiogenesis process corresponds to the formation of new blood vessels from preexisting ones, which can supply the tumor with oxygen and nutrients, thus allowing the tumor to grow. The overall model used for simulations is described, and typical intervals for the model parameters are presented. The overall model comprises the PK and PD models, as well as the models that represent the tumor growth and the subsystems that affect it (immune system and angiogenesis).
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References
Barbolosi D, Ciccolini J, Lacarelle B, Barlési F, Andrée N (2016) Computational oncology mathematical modelling of drug regimens for precision medicine. Nat Rev Clin Oncol 13(4):242–254
Benzekry S, Lamont C, Beheshti A, Tracz A, Ebos JML, Hlatky L, Hahnfeldt P (2014) Classical mathematica models for description and prediction of experimental tumor growth. PLOS Comput Biol 10(8):e1003800
de Pillis LG, Gu W, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 238(4):841–862
Eftimie R, Bramson JL, Earn DJ (2011) Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull Math Biol 73(1):2–32
Eladdadi A, Kim P, Mallet D (eds) (2014) Mathematical models of tumor- immune system dynamics. Springer, Berlin
Garber K (2014) Promising early results for immunotherapy-antiangiogenesis combination. J Natl Cancer Inst 106(11)
Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L (1999) Tumor development under angiogenic signalling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res 59:4770–4775
Janeway CA, Travers P, Walport M, Shlomchik MJ (2001) Immunobiology, 5th edn. Garland Science, New York. ISBN:100-8153-3642-X
Kumar V, Abbas AK, Aster JC (2013) The future of modern genomics, 9th edn. Saunders, Philadelphia
Oden JT, Prudencio EE, Hawkins-Daarud A (2013) Selection and assessment of phenomenological models of tumor growth. Math Models Methods Appl Sci 23(07):1309–1338
Schattler H, Ledzewicz U (2010) Optimal control for mathematical models of cancer therapies. Springer, Berlin
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Belfo, J.P., Lemos, J.M. (2021). Tumor Growth Models. In: Optimal Impulsive Control for Cancer Therapy. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-50488-5_3
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DOI: https://doi.org/10.1007/978-3-030-50488-5_3
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