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Cancer Models Based on Reaction-Diffusion Equations

Khanzad, Zahra | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52423 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fotouhi, Morteza
  7. Abstract:
  8. The role of a mathematical model is to explain a set of experiments, and to make predictions. In setting up a mathematical model of a biological process, by a set of differential equations, it is very important to determine the numerical value of the parameters. For biological processes are typically valid only within a limited range of parameters. In the last decades, various cancer models have been developed in which the evolution of the densities of cells (abnormal, normal, or dead) and the concentrations of biochemical species are described in terms of differential equations. Some of these models use only ordinary differential equations (ODEs), ignoring the spatial effects of tumor growth. The models which take spatial effects into consideration are expressed in terms of partial differential equations (PDEs), and they also need to take into account the fact that the tumor region is changing in time.in this thesis, we discuss about different types of cancer models and their analyses. We use partial differential equation for modeling different types of cancer tumors. The growth of cancer tumors is considered as a free boundary problem. If some initial and boundary conditions are met, we review the existence of solutions and their uniqueness for mentioned equations. According to what kind of cells exist in the tumor region, we classify them in four groups:
    1. The tumor consists of quiescent, proliferating, and dead cells.
    2. The tumor consists of quiescent and dead cells.
    3. The tumor consists of only proliferating cells.
    4. The tumor consists of a necrotic core and Proliferating Shell-like Region.The results which we obtain will be useful for estimating the tumor growth; chemical substances and nutrient concentrations in tumor region; and additionally for treatments
  9. Keywords:
  10. Tumors ; Tumor Region ; Boundary Conditions ; Chemical Substances ; Drug Concentration

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