Mathematical Biosciences and Engineering, 2013, 10(1): 221-234. doi: 10.3934/mbe.2013.10.221.

Primary: 92B05; Secondary: 37N25.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response

1. Universidade de São Paulo, Depto de Matemática Aplicada e Estatística, ICMC, USP, 13560-970, São Carlos
2. Universidade Estadual Paulista, Depto de Bioestatística, IBB, UNESP, 18618-970, Botucatu

Dosage and frequency of treatment schedulesare important for successful chemotherapy.However, in this work we argue that cell-kill response and tumoralgrowth should not be seen as separate and therefore are essential in a mathematical cancer model.This paper presents a mathematical model for sequencing of cancer chemotherapy andsurgery. Our purpose is to investigate treatments for large human tumoursconsidering a suitable cell-kill dynamics. Weuse some biological and pharmacological data in a numerical approach,where drug administration occurs in cycles (periodic infusion)and surgery is performed instantaneously. Moreover, we alsopresent an analysis of stabilityfor a chemotherapeutic model with continuous drug administration.According to Norton & Simon [22], our results indicate that chemotherapy is lessefficient in treating tumours that have reached a plateau level of growingand that a combination with surgical treatment can provide better outcomes.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Norton-Simon hypothesis; chemotherapy; mathematicalmodelling.; Tumour

Citation: Diego Samuel Rodrigues, Paulo Fernando de Arruda Mancera. Mathematical analysis and simulations involving chemotherapy and surgeryon large human tumours under a suitable cell-kill functional response. Mathematical Biosciences and Engineering, 2013, 10(1): 221-234. doi: 10.3934/mbe.2013.10.221

References

  • 1. World Scientific Publishing Co. Inc., River Edge, 1983.
  • 2. Cancer Res., 60 (2000), 1878-1886.
  • 3. in "Cancer Chemotherapy Handbook'' (Ed. R. T. Dorr and D. D. V. Hoff), Appleton & Lange, (1994), p.9.
  • 4. J. Theor. Med., 3 (2001), 79-100.
  • 5. Math. Biosc., 209 (2007), 292-315.
  • 6. Math. Biosc., 222 (2009), 13-26.
  • 7. McGraw-Hill, 1994.
  • 8. available from http://www.avon.nhs.uk/aswcs-chemo/STCP/index.htm.
  • 9. Acta Haematol., 106 (2001), 148-156.
  • 10. SIAM J. Appl. Math., 63 (2003), 1954-1971.
  • 11. Eur. J. Cancer, 32A (1996), 722-726.
  • 12. Carcinogenesis, 21 (2000), 505-515.
  • 13. J. Theor. Biol., 242 (2006), 62-68.
  • 14. J. Theor. Biol., 297 (2012), 41-47.
  • 15. Math. Biosc., 110 (1992), 221-252.
  • 16. World Scientific, 1994.
  • 17. Automatica 28 (1992), 113-1123.
  • 18. accessed 29/02/2012.
  • 19. N. Engl. J. Med., (1987), 1098.
  • 20. Scribner, 2010.
  • 21. Math. Biosc., 163 (2000), 159-199.
  • 22. Cancer Treat. Rep., 70 (1986), 163-169.
  • 23. Math. Comp. Model., 36 (2002), 773-803.
  • 24. Nonlin. Anal.: Real World Appl., 14 (2013), 815-828.
  • 25. TEMA, 13 (2012), 1-12 (in portuguese).
  • 26. 2012, preprint.
  • 27. Cancer, 35 (1975), 15-24.
  • 28. Cancer Chemother. Rep., 35 (1964), 1-111.
  • 29. J. Surg. Oncol., 61 (1996), 68-73.
  • 30. J. Theor. Biol., 266 (2010), 124-139.
  • 31. Int. J. Biom. Comput., 13 (1982), 19-35.
  • 32. accessed 02/03/2012.
  • 33. Garland Science, 2008.

 

This article has been cited by

  • 1. Rafael T. Guiraldello, Marcelo L. Martins, Paulo F.A. Mancera, Evaluating the efficacies of Maximum Tolerated Dose and metronomic chemotherapies: A mathematical approach, Physica A: Statistical Mechanics and its Applications, 2016, 456, 145, 10.1016/j.physa.2016.03.019
  • 2. D. J. Argyle, E. Pecceu, Canine and feline lymphoma: challenges and opportunities for creating a paradigm shift, Veterinary and Comparative Oncology, 2016, 14, 1, 10.1111/vco.12253
  • 3. Tatiana R. Souza, Paulo F. A. Mancera, Rodney C. Bassanezi, Dynamics of tumor growth: chemotherapy and integrative oncology, Computational and Applied Mathematics, 2020, 39, 1, 10.1007/s40314-019-0988-0

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved