Study on the tumor-induced angiogenesis using mathematical models

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

doi:10.1111/cas.13395

Study on the tumor-induced angiogenesis using mathematical models

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

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	15-23
Number of pages	9
Journal	Cancer Science
Volume	109
Issue number	1
Early online date	4 Dec 2017
DOIs	https://doi.org/10.1111/cas.13395
Publication status	Published - Jan 2018

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Angiogenesis
Extracellular matrix degradation
Hybrid simulation
Mathematical model
Tumor microenvironment

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10.1111/cas.13395Licence: CC BY-NC-ND

Chaplain_2017_CS_Angiogenesis_CC
© 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.
Final published version, 930 KBLicence: CC BY-NC-ND

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title = "Study on the tumor-induced angiogenesis using mathematical models",

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.",

keywords = "Angiogenesis, Extracellular matrix degradation, Hybrid simulation, Mathematical model, Tumor microenvironment",

author = "Takashi Suzuki and Dhisa Minerva and Koichi Nishiyama and Naohiko Koshikawa and Chaplain, \{Mark Andrew Joseph\}",

note = "This work was supported by JSPS KAKENHI 16H06576 and JSPS Core-to-Core Project International Research Network.",

year = "2018",

month = jan,

doi = "10.1111/cas.13395",

language = "English",

volume = "109",

pages = "15--23",

journal = "Cancer Science",

issn = "1349-7006",

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TY - JOUR

T1 - Study on the tumor-induced angiogenesis using mathematical models

AU - Suzuki, Takashi

AU - Minerva, Dhisa

AU - Nishiyama, Koichi

AU - Koshikawa, Naohiko

AU - Chaplain, Mark Andrew Joseph

N1 - This work was supported by JSPS KAKENHI 16H06576 and JSPS Core-to-Core Project International Research Network.

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

KW - Angiogenesis

KW - Extracellular matrix degradation

KW - Hybrid simulation

KW - Mathematical model

KW - Tumor microenvironment

U2 - 10.1111/cas.13395

DO - 10.1111/cas.13395

M3 - Article

SN - 1349-7006

VL - 109

SP - 15

EP - 23

JO - Cancer Science

JF - Cancer Science

IS - 1

ER -

Study on the tumor-induced angiogenesis using mathematical models

Abstract

UN SDGs

Keywords

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