Mathematical modelling of cancer invasion: a review

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Abstract

A defining feature of cancer is the capability to spread locally into the surrounding tissue, with cancer cells spreading beyond any normal boundaries. Cancer invasion is a complex phenomenon involving many inter-connected processes at different spatial and temporal scales. A key component of invasion is the ability of cancer cells to alter and degrade the extracellular matrix through the secretion of matrix-degrading enzymes. Combined with excessive cell proliferation and cell migration (individual and collective), this facilitates the spread of cancer cells into the local tissue. Along with tumour-induced angiogenesis, invasion is a critical component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we present an overview of the various mathematical models and different modelling techniques and approaches that have been developed over the past 25 years or so and which focus on various aspects of the invasive process.
Original languageEnglish
Title of host publicationMethods of Mathematical Oncology
Subtitle of host publicationFusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020
EditorsTakashi Suzuki, Clair Poignard, Mark Chaplain, Vito Quaranta
Place of PublicationSingapore
PublisherSpringer
Pages153-172
Number of pages20
ISBN (Electronic)9789811648663
ISBN (Print)9789811648656
DOIs
Publication statusPublished - 2021
EventInternational Conference by Center for Mathematical Modeling and Data Science - Osaka University, Japan
Duration: 26 Oct 202028 Oct 2020
http://www-mmds.sigmath.es.osaka-u.ac.jp/faculty/personal/suzuki/jsps/index.html

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer Nature Switzerland
Volume370
ISSN (Print)2194-1017
ISSN (Electronic)2194-1009

Conference

ConferenceInternational Conference by Center for Mathematical Modeling and Data Science
Abbreviated titleMMDS 2020
Country/TerritoryJapan
Period26/10/2028/10/20
Internet address

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