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Use mathematical models to describe the growth of cancerous tumors

Uso de modelos matemáticos para la descripción del crecimiento de tumores cancerosos




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Artículo Original

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Zapata Peña, J., & Ortiz, A. C. (2010). Use mathematical models to describe the growth of cancerous tumors. NOVA, 8(14). https://doi.org/10.22490/24629448.446

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NOVA by http://www.unicolmayor.edu.co/publicaciones/index.php/nova is distributed under a license creative commons non comertial-atribution-withoutderive 4.0 international.

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Jair Zapata Peña
    Alba Cristina Ortiz

      The production of cancerous tumors or tumorigenesis has been studied from principles of the twentieth century by mathematicians and physicists interested in biological applications. In this paper we discuss various models using ordinary differential equations, partial differential equations, discrete stochastic models, statistical-cal and numerical analysis to describe the growth of cancerous tumors. Shows a comparison between these mathematical models, setting characteristics and limitations due to the specific cancer populations. It extends a model study competition for nutrients using a computer simulation, which shows graphical results of simulations for populations of cancer cells and dead.

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      1. Kolev M, Zubik-Kowal B. Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells. Comput Math Methods Med. 2011;2011:452320.
      2. Solé RV, Deisboeck TS. An error catastrophe in cancer?. J Theor Biol. 2004;228:47-54.
      3. Menchón S.A. Modelado de diversas etapas del crecimiento del cáncer y de algunas terapias antitumorales. Córdoba. Tesis Doctoral
      4. (Doctorado en física), Universidad Nacional de Córdoba, Argentina, Departamento de física. 2007.
      5. Wodarz D, Komarova NL. Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling. Ed. World Scientific, Singapore. 2005. p.13-26.
      6. Sotolongo-Costa O, Morales L, Rodríguez D, Antoranz JC, Chacon M. Behavior of tumor under nonostationary therapy. Physical D.
      7. ;178:242-253.
      8. Kim Y, Friedman A. Interaction of tumor with its micro-environment: A mathematical model. Math Biol. 2010;72:1029-1068.
      9. Doumic-Jauffret M, Kim PS, Perthame B. Stability analysis of a simplified yet complete model for chronic myelogenous leukemia.
      10. Bull Math Biol. 2010;72:1732-1759.
      11. Anderson AR, Chaplain MA. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol. 1998;60:857-899.
      12. Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck TS. Simulated brain tumor growth dynamics using a three-dimensional
      13. cellular automaton. J Theo Biol. 2000;203:367-382.
      14. Azuaje F. Computational discrete models of tissue growth and regeneration. Brief Bioinform. 2011;12:64-77.
      15. Komarova NL, Sengupta A, Nowak MA. Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability. J Theor Biol. 2003;223:433-450.
      16. Knudson AG. Hereditary cancer: two hits revisited. J Cancer Res Clin Oncol. 1996;122:135-140.
      17. Knudson AG. Mutation and cancer: statistical study of retinoblastoma. En: Proc Natl Acad Sci USA. 1971;68:820-823.
      18. Frank SA. Age-specific acceleration of cancer. Curr Biol. 2004;14:242-246.
      19. Krewski D, Zielinski JM, Hazelton WD, Garner MJ, Moolgavkar SH. The use of biologically based cancer risk models in radiation
      20. epidemiology. Radiat Prot Dosimetry. 2003;104:367-376.
      21. Pescarmona GP, Scalerandi M, Delsanto PP, Condat CA. Nutrient competition as a determinant for cancer growth. Med Hypotheses.
      22. ;53:497-503.
      23. Zapata J.Jair M. Simulaciones por computadora de un modelo espaciotemporal para la interacción del sistema inmunológico y los tumores
      24. cancerosos. Dissertations & Theses. 2009;1:76-80.
      25. Menchón SA, Ramos RA, Condat CA. . Modeling subspecies and tumor-immune system interaction: Step towards understanding therapy.
      26. Physica A. 2007;386:713-719.
      27. Brú A, Pastor JM, Brú I, Melle S, Berenguer C. Super rough dynamics on tumor growth. Phys Rev Lett. 1998;18:4008- 4011.
      28. Brú A, Albertos S, López García-Asenjo JA, Brú I. Pinning of tumoral growth by enhancement of the immune response. Phys Rev Lett.
      29. ;92:238101-238104.
      30. Kolobov AV, Gubernov VV, Polezhaev AA. Autowaves in a model of growth of an invasive tumor. Biofizika. 2009;54:334-342.
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      32. DOI: http://dx.doi.org/10.22490/24629448.446
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