Modeling of Tumor Occurrence and Growth - I

УДК 517:612.6

  • S.N. Antontsev Lavrentyev Institute of hydrodynamics SB RAS (Novosibirsk, Russia); Center for Mathematics, Fundamental Applications and Operations Research (CMAF-CIO), University of Lisbon (Lisbon, Portugal) Email: antontsevsn@mail.ru
  • A.A. Papin Altai State University (Barnaul, Russia) Email: papin@math.asu.ru
  • M.A. Tokareva Altai State University (Barnaul, Russia) Email: tma25@mail.ru
  • E.I. Leonova Altai State University (Barnaul, Russia) Email: leonova.eve@gmail.com
  • E.A. Gridushko Altai State University (Barnaul, Russia) Email: katya19992012@gmail.com
Keywords: mathematical modeling, tumor modeling, free boundary problems, Stokes equation, multiscale models, hybrid models, multiphase systems

Abstract

Cancer has recently overtaken heart disease as the world’s biggest killer. Cancer is initiated by gene mutations that result in local proliferation of abnormal cells and their migration to other parts of the human body, a process called metastasis. The metastasized cancer cells then interfere with the normal functions of the body, eventually leading to death. There are 200 types of cancer, classified by their point of origin. Most of them share some common features, but they also have their specific character. In this paper, we consider mathematical models of non-specific solid tumors in a tissue. The models incorporate the constitutive nature of the tissue, and the need for growing tumors to attract blood vessels. We also describe a general multiscale approach that involves cell cycle and incorporates non-specific genes mutation. Also, the trends and general features of modeling tumor growth are discussed. The main goal is set at revealing some trends and challenges on cancer modeling, especially related to the development of multiphase and multiscale models.

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Author Biographies

A.A. Papin , Altai State University (Barnaul, Russia)

заведующий кафедрой дифференциальных уравнений

M.A. Tokareva, Altai State University (Barnaul, Russia)

кандидат физико-математических наук, доцент кафедры дифференциальных уравнений

E.I. Leonova, Altai State University (Barnaul, Russia)

студентка Института математики и информационных технологий

E.A. Gridushko , Altai State University (Barnaul, Russia)

студентка Института математики и информационных технологий

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Published
2020-09-09
How to Cite
Antontsev S., Papin A., Tokareva M., Leonova E., Gridushko E. Modeling of Tumor Occurrence and Growth - I // Izvestiya of Altai State University, 2020, № 4(114). P. 70-80 DOI: 10.14258/izvasu(2020)4-11. URL: https://izvestiya.asu.ru/article/view/%282020%294-11.
Section
Математика и механика