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Study on the tumor-induced angiogenesis using mathematical models

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Chaplain_2017_CS_Angiogenesis_CC.pdf (930.1Kb)
Date
01/2018
Author
Suzuki, Takashi
Minerva, Dhisa
Nishiyama, Koichi
Koshikawa, Naohiko
Chaplain, Mark Andrew Joseph
Keywords
Angiogenesis
Extracellular matrix degradation
Hybrid simulation
Mathematical model
Tumor microenvironment
RC0254 Neoplasms. Tumors. Oncology (including Cancer)
QA Mathematics
NDAS
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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.
Citation
Suzuki , T , Minerva , D , Nishiyama , K , Koshikawa , N & Chaplain , M A J 2018 , ' Study on the tumor-induced angiogenesis using mathematical models ' , Cancer Science , vol. 109 , no. 1 , pp. 15-23 . https://doi.org/10.1111/cas.13395
Publication
Cancer Science
Status
Peer reviewed
DOI
https://doi.org/10.1111/cas.13395
ISSN
1349-7006
Type
Journal article
Rights
© 2017 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description
This work was supported by JSPS KAKENHI 16H06576 and JSPS Core-to-Core Project International Research Network.
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/12256

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