Mathematical analysis of models for tumour angiogenesis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We deal with well known two mathematical models of tumour angiogenesis. We first review the solvability and the asymptotic profile of the solution to a parabolic ODE system proposed by Othmer and Stevens. 'Next we consider the model of tumour induced angiogenesis by Anderson and Chaplain in the same line. We modify Anderson and Chaplain model to the same type system of Othmer and Stevens model. This implies a similarity between these models and we can show the existence of global solutions and numerical simulations of Anderson and Chaplain model by using such similarity.

Original languageEnglish
Title of host publicationBioMedical Engineering and Informatics
Subtitle of host publicationNew Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008
Pages700-705
Number of pages6
DOIs
Publication statusPublished - 17-09-2008
EventBioMedical Engineering and Informatics: New Development and the Future - 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008 - Sanya, Hainan, China
Duration: 27-05-200830-05-2008

Publication series

NameBioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008
Volume1

Other

OtherBioMedical Engineering and Informatics: New Development and the Future - 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008
CountryChina
CitySanya, Hainan
Period27-05-0830-05-08

Fingerprint

Tumors
Mathematical models
Computer simulation

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Signal Processing
  • Biomedical Engineering

Cite this

Kubo, A. (2008). Mathematical analysis of models for tumour angiogenesis. In BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008 (pp. 700-705). [4548760] (BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008; Vol. 1). https://doi.org/10.1109/BMEI.2008.92
Kubo, Akisato. / Mathematical analysis of models for tumour angiogenesis. BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008. 2008. pp. 700-705 (BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008).
@inproceedings{fc555ca9be0c4c67ad299de62b9d6d08,
title = "Mathematical analysis of models for tumour angiogenesis",
abstract = "We deal with well known two mathematical models of tumour angiogenesis. We first review the solvability and the asymptotic profile of the solution to a parabolic ODE system proposed by Othmer and Stevens. 'Next we consider the model of tumour induced angiogenesis by Anderson and Chaplain in the same line. We modify Anderson and Chaplain model to the same type system of Othmer and Stevens model. This implies a similarity between these models and we can show the existence of global solutions and numerical simulations of Anderson and Chaplain model by using such similarity.",
author = "Akisato Kubo",
year = "2008",
month = "9",
day = "17",
doi = "10.1109/BMEI.2008.92",
language = "English",
isbn = "9780769531182",
series = "BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008",
pages = "700--705",
booktitle = "BioMedical Engineering and Informatics",

}

Kubo, A 2008, Mathematical analysis of models for tumour angiogenesis. in BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008., 4548760, BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008, vol. 1, pp. 700-705, BioMedical Engineering and Informatics: New Development and the Future - 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008, Sanya, Hainan, China, 27-05-08. https://doi.org/10.1109/BMEI.2008.92

Mathematical analysis of models for tumour angiogenesis. / Kubo, Akisato.

BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008. 2008. p. 700-705 4548760 (BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008; Vol. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Mathematical analysis of models for tumour angiogenesis

AU - Kubo, Akisato

PY - 2008/9/17

Y1 - 2008/9/17

N2 - We deal with well known two mathematical models of tumour angiogenesis. We first review the solvability and the asymptotic profile of the solution to a parabolic ODE system proposed by Othmer and Stevens. 'Next we consider the model of tumour induced angiogenesis by Anderson and Chaplain in the same line. We modify Anderson and Chaplain model to the same type system of Othmer and Stevens model. This implies a similarity between these models and we can show the existence of global solutions and numerical simulations of Anderson and Chaplain model by using such similarity.

AB - We deal with well known two mathematical models of tumour angiogenesis. We first review the solvability and the asymptotic profile of the solution to a parabolic ODE system proposed by Othmer and Stevens. 'Next we consider the model of tumour induced angiogenesis by Anderson and Chaplain in the same line. We modify Anderson and Chaplain model to the same type system of Othmer and Stevens model. This implies a similarity between these models and we can show the existence of global solutions and numerical simulations of Anderson and Chaplain model by using such similarity.

UR - http://www.scopus.com/inward/record.url?scp=51549092711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51549092711&partnerID=8YFLogxK

U2 - 10.1109/BMEI.2008.92

DO - 10.1109/BMEI.2008.92

M3 - Conference contribution

AN - SCOPUS:51549092711

SN - 9780769531182

T3 - BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008

SP - 700

EP - 705

BT - BioMedical Engineering and Informatics

ER -

Kubo A. Mathematical analysis of models for tumour angiogenesis. In BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008. 2008. p. 700-705. 4548760. (BioMedical Engineering and Informatics: New Development and the Future - Proceedings of the 1st International Conference on BioMedical Engineering and Informatics, BMEI 2008). https://doi.org/10.1109/BMEI.2008.92