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Selected Topics in Cancer ModelingMultiphase Models of Tumour Growth

Selected Topics in Cancer Modeling: Multiphase Models of Tumour Growth Sergey Astanin and Luigi Preziosi Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy {sergey.astanin, luigi.preziosi}@polito.it 9.1 Introduction Mixture theory has been applied to describe the mechanics of biological tissues since the 1960s. Most of the work was focused on the behaviour of articular car- tilages [HHLM89, KLM90, LHM90, MHL84, MKLA80, ML79, MRS90], but applications can be found to many soft tissues, e.g., brain [Nic85, SCZM06], heart mechanics [SS86, TIZB84, YTC94], subcutaneous layer [OVCG87], and flow through arteries [Jay83, Ken79, KT87]. In the last few years mixture theory has also been applied with success to tumour growth. Examples of applications can be found in [BBL02, BBL03, + + BKMP03, BP04, CGP06, FBK 03, FBM 03, FK03] while [AP02, AM05, GP07] are review papers on this approach and on the mechanical aspects re- lated to tumour growth. Here, we shall deduce a general multiphase modelling framework for a few essential constituents (cells, extracellular matrix, and ex- tracellular liquid with the solutes dissolved in it). We shall also show how to take into account several subpopulations of the cells, and several components of the extracellular matrix (ECM). There are three basic hypotheses that allow us to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Selected Topics in Cancer ModelingMultiphase Models of Tumour Growth

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2008
ISBN
978-0-8176-4712-4
Pages
1 –31
DOI
10.1007/978-0-8176-4713-1_9
Publisher site
See Chapter on Publisher Site

Abstract

Sergey Astanin and Luigi Preziosi Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy {sergey.astanin, luigi.preziosi}@polito.it 9.1 Introduction Mixture theory has been applied to describe the mechanics of biological tissues since the 1960s. Most of the work was focused on the behaviour of articular car- tilages [HHLM89, KLM90, LHM90, MHL84, MKLA80, ML79, MRS90], but applications can be found to many soft tissues, e.g., brain [Nic85, SCZM06], heart mechanics [SS86, TIZB84, YTC94], subcutaneous layer [OVCG87], and flow through arteries [Jay83, Ken79, KT87]. In the last few years mixture theory has also been applied with success to tumour growth. Examples of applications can be found in [BBL02, BBL03, + + BKMP03, BP04, CGP06, FBK 03, FBM 03, FK03] while [AP02, AM05, GP07] are review papers on this approach and on the mechanical aspects re- lated to tumour growth. Here, we shall deduce a general multiphase modelling framework for a few essential constituents (cells, extracellular matrix, and ex- tracellular liquid with the solutes dissolved in it). We shall also show how to take into account several subpopulations of the cells, and several components of the extracellular matrix (ECM). There are three basic hypotheses that allow us to

Published: Aug 21, 2008

Keywords: Constitutive Equation; Interaction Force; Mass Balance Equation; Mixture Theory; Growth Term

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