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Anti-angiogenic Therapy Models

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Mathematical Models of Cancer and Different Therapies

Part of the book series: Series in BioEngineering ((SERBIOENG))

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Abstract

Anti-angiogenic therapy is used to interrupt the development of blood vessels towards and into the tumors from the existing blood vessels that surround the tumor micro-environment [1]. Anti-angiogenic therapy models primarily involves the dynamics of tumor cells, endothelial cells, angiogenesis inhibitory agents, and angiogenesis stimulatory agents. In this chapter, two mathematical models are discussed that depict different aspects of cancer dynamics under anti-angiogenic therapy.

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References

  1. J. Folkman, Role of angiogenesis in tumor growth and metastasis. Semin. Oncol. 29(6), Sup16, 15–18 (2002)

    Google Scholar 

  2. G. Mangialardi, A. Cordaro, P. Madeddu, The bone marrow pericyte: an orchestrator of vascular niche. Regen. Med. 11(8), 883–895 (2016)

    Article  Google Scholar 

  3. W. Liang, N. Ferrara, The complex role of neutrophils in tumor angiogenesis and metastasis. Cancer Immunol. Res. 4(2), 83–91 (2016)

    Article  Google Scholar 

  4. H. Rieger, M. Welter, Integrative models of vascular remodeling during tumor growth. Wiley Interdiscip. Rev. Syst. Biol. Med. 7(3), 113–129 (2015)

    Article  Google Scholar 

  5. B. Al Husein, M. Abdalla, M. Trepte, D.L. DeRemer, P.R. Somanath, Antiangiogenic therapy for cancer: an update. Pharmacother.: J. Hum. Pharmacol. Drug Ther. 32(12), 1095–1111 (2012)

    Google Scholar 

  6. J. Folkman, Tumor angiogenesis: therapeutic implications. N. Engl. J. Med. 285(21), 1182–1186 (1971)

    Article  Google Scholar 

  7. R.S. Kerbel, A cancer therapy resistant to resistance. Nature 390(6658), 335 (1997)

    Google Scholar 

  8. A. Ergun, K. Camphausen, L.M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors. Bull. Math. Biol. 65(3), 407–424 (2003)

    Article  Google Scholar 

  9. A. Anderson, M. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60(5), 857–899 (1998)

    Article  Google Scholar 

  10. P. Hahnfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59(19), 4770–4775 (1999)

    Google Scholar 

  11. C.J.W. Breward, H.M. Byrne, C.E. Lewis, A multiphase model describing vascular tumour growth. Bull. Math. Biol. 65, 609–640 (2003)

    Article  Google Scholar 

  12. A. d’Onofrio, U. Ledzewicz, H. Maurer, H. Schättler, On optimal delivery of combination therapy for tumors. Math. Biosci. 222(1), 13–26 (2009)

    Google Scholar 

  13. J. Sápi, D.A. Drexler, I. Harmati, Z. Sápi, L. Kovács, Linear state-feedback control synthesis of tumor growth control in antiangiogenic therapy, in 10th International Symposium on Applied Machine Intelligence and Informatics (SAMI) (2012), pp. 143–148

    Google Scholar 

  14. U. Ledzewicz, H. Schättler, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, in Proceedings of the 44th IEEE Conference on Decision and Control (2005), pp. 934–939

    Google Scholar 

  15. D.A. Drexler, L. Kovács, J. Sápi, I. Harmati, Z. Benyó, Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study. IFAC Proc. Vol. 44(1), 3753–3758 (2011)

    Article  Google Scholar 

  16. P. Yazdjerdi, N. Meskin, M. Al Naemi, A.E. Al Moustafa, L. Kovács, Reinforcement learning-based control of tumor growth under anti-angiogenic therapy. Comput. Methods Programs Biomed. 173, 15–26 (2019)

    Google Scholar 

  17. J. Sápi, D.A. Drexler, L. Kovács, Comparison of mathematical tumor growth models, in 2015 IEEE 13th International Symposium on Intelligent Systems and Informatics (SISY) (2015), pp. 323–328

    Google Scholar 

  18. D.A. Drexler, L. Kovács, J. Sápi, I. Harmati, Z. Benyó, Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study. IFAC Proc. 44(1), 3753–3758 (2011). 18th IFAC World Congress

    Google Scholar 

  19. D. Csercsik, J. Sápi, T. Gönczy, L. Kovács, Bi-compartmental modelling of tumor and supporting vasculature growth dynamics for cancer treatment optimization purpose, in 2017 IEEE 56th Annual Conference on Decision and Control (CDC) (2017), pp. 4698–4702

    Google Scholar 

  20. J. Sápi, L. Kovács, D.A. Drexler, P. Kocsis, D. Gajári, Z. Sápi, Tumor volume estimation and quasi-continuous administration for most effective bevacizumab therapy. PLoS One 10(11), e0142190 (2015)

    Google Scholar 

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Padmanabhan, R., Meskin, N., Moustafa, AE.A. (2021). Anti-angiogenic Therapy Models. In: Mathematical Models of Cancer and Different Therapies. Series in BioEngineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-8640-8_5

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  • DOI: https://doi.org/10.1007/978-981-15-8640-8_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-8639-2

  • Online ISBN: 978-981-15-8640-8

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