Study on the tumor-induced angiogenesis using mathematical models

Takashi Suzuki, Dhisa Minerva, Koichi Nishiyama, Naohiko Koshikawa, Mark Andrew Joseph Chaplain

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.
Original languageEnglish
Pages (from-to)15-23
Number of pages9
JournalCancer Science
Volume109
Issue number1
Early online date4 Dec 2017
DOIs
Publication statusPublished - Jan 2018

Keywords

  • Angiogenesis
  • Extracellular matrix degradation
  • Hybrid simulation
  • Mathematical model
  • Tumor microenvironment

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