Mathematical modelling of cancer invasion: a review

Nikolaos Sfakianakis; Mark Chaplain

doi:10.1007/978-981-16-4866-3_10

Mathematical modelling of cancer invasion: a review

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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 language	English
Title of host publication	Methods of Mathematical Oncology
Subtitle of host publication	Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020
Editors	Takashi Suzuki, Clair Poignard, Mark Chaplain, Vito Quaranta
Place of Publication	Singapore
Publisher	Springer
Pages	153-172
Number of pages	20
ISBN (Electronic)	9789811648663
ISBN (Print)	9789811648656
DOIs	https://doi.org/10.1007/978-981-16-4866-3_10
Publication status	Published - 2021
Event	International Conference by Center for Mathematical Modeling and Data Science - Osaka University, Japan Duration: 26 Oct 2020 → 28 Oct 2020 http://www-mmds.sigmath.es.osaka-u.ac.jp/faculty/personal/suzuki/jsps/index.html

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer Nature Switzerland
Volume	370
ISSN (Print)	2194-1017
ISSN (Electronic)	2194-1009

Conference

Conference	International Conference by Center for Mathematical Modeling and Data Science
Abbreviated title	MMDS 2020
Country/Territory	Japan
Period	26/10/20 → 28/10/20
Internet address	http://www-mmds.sigmath.es.osaka-u.ac.jp/faculty/personal/suzuki/jsps/index.html

UN SDGs

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

Access to Document

10.1007/978-981-16-4866-3_10

Sfakianakis-2021-Mathematical-model-cancer-invasion-MoMO-AAM
Copyright © 2021 Springer Nature Singapore Pte Ltd. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/978-981-16-4866-3_10.
Accepted author manuscript, 232 KB

SofTMech with MIT and POLIMI: SofTMech with MIT and POLIMI (SofTMechMP)
Chaplain, M. A. J. (PI)
EPSRC
1/01/20 → 31/12/23
Project: Standard

Cite this

Sfakianakis, N., & Chaplain, M. (2021). Mathematical modelling of cancer invasion: a review. In T. Suzuki, C. Poignard, M. Chaplain, & V. Quaranta (Eds.), Methods of Mathematical Oncology: Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020 (pp. 153-172). (Springer Proceedings in Mathematics & Statistics; Vol. 370). Springer. https://doi.org/10.1007/978-981-16-4866-3_10

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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.",

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note = "Funding: MAJC gratefully acknowledges the support of EPSRC Grant No. EP/S030875/1 (EPSRC SofTMech∧MP Centre-to-Centre Award).; International Conference by Center for Mathematical Modeling and Data Science, MMDS 2020 ; Conference date: 26-10-2020 Through 28-10-2020",

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Sfakianakis, N & Chaplain, M 2021, Mathematical modelling of cancer invasion: a review. in T Suzuki, C Poignard, M Chaplain & V Quaranta (eds), Methods of Mathematical Oncology: Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020. Springer Proceedings in Mathematics & Statistics, vol. 370, Springer, Singapore, pp. 153-172, International Conference by Center for Mathematical Modeling and Data Science, Japan, 26/10/20. https://doi.org/10.1007/978-981-16-4866-3_10

Mathematical modelling of cancer invasion: a review. / Sfakianakis, Nikolaos ; Chaplain, Mark.
Methods of Mathematical Oncology: Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020. ed. / Takashi Suzuki; Clair Poignard; Mark Chaplain; Vito Quaranta. Singapore: Springer, 2021. p. 153-172 (Springer Proceedings in Mathematics & Statistics; Vol. 370).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Mathematical modelling of cancer invasion

T2 - International Conference by Center for Mathematical Modeling and Data Science

AU - Sfakianakis, Nikolaos

AU - Chaplain, Mark

N1 - Funding: MAJC gratefully acknowledges the support of EPSRC Grant No. EP/S030875/1 (EPSRC SofTMech∧MP Centre-to-Centre Award).

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N2 - 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.

AB - 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.

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Sfakianakis N , Chaplain M. Mathematical modelling of cancer invasion: a review. In Suzuki T, Poignard C, Chaplain M, Quaranta V, editors, Methods of Mathematical Oncology: Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020. Singapore: Springer. 2021. p. 153-172. (Springer Proceedings in Mathematics & Statistics). Epub 2021 Aug 22. doi: 10.1007/978-981-16-4866-3_10

Mathematical modelling of cancer invasion: a review

Abstract

Publication series

Conference

UN SDGs

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Projects

SofTMech with MIT and POLIMI: SofTMech with MIT and POLIMI (SofTMechMP)

Cite this