Multiphase modelling of vascular tumour growth in two spatial dimensions

Handle URI:
http://hdl.handle.net/10754/598907
Title:
Multiphase modelling of vascular tumour growth in two spatial dimensions
Authors:
Hubbard, M.E.; Byrne, H.M.
Abstract:
In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model.Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters is investigated. © 2012 Elsevier Ltd.
Citation:
Hubbard ME, Byrne HM (2013) Multiphase modelling of vascular tumour growth in two spatial dimensions. Journal of Theoretical Biology 316: 70–89. Available: http://dx.doi.org/10.1016/j.jtbi.2012.09.031.
Publisher:
Elsevier BV
Journal:
Journal of Theoretical Biology
KAUST Grant Number:
KUK-013-04
Issue Date:
Jan-2013
DOI:
10.1016/j.jtbi.2012.09.031
PubMed ID:
23032218
Type:
Article
ISSN:
0022-5193
Sponsors:
This publication was based on work supported in part by Award no. KUK-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHubbard, M.E.en
dc.contributor.authorByrne, H.M.en
dc.date.accessioned2016-02-25T13:43:29Zen
dc.date.available2016-02-25T13:43:29Zen
dc.date.issued2013-01en
dc.identifier.citationHubbard ME, Byrne HM (2013) Multiphase modelling of vascular tumour growth in two spatial dimensions. Journal of Theoretical Biology 316: 70–89. Available: http://dx.doi.org/10.1016/j.jtbi.2012.09.031.en
dc.identifier.issn0022-5193en
dc.identifier.pmid23032218en
dc.identifier.doi10.1016/j.jtbi.2012.09.031en
dc.identifier.urihttp://hdl.handle.net/10754/598907en
dc.description.abstractIn this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model.Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters is investigated. © 2012 Elsevier Ltd.en
dc.description.sponsorshipThis publication was based on work supported in part by Award no. KUK-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectCancer modellingen
dc.subjectContinuum mechanicsen
dc.subjectNonlinear couplingen
dc.subjectNumerical simulationsen
dc.subjectPartial differential equationsen
dc.titleMultiphase modelling of vascular tumour growth in two spatial dimensionsen
dc.typeArticleen
dc.identifier.journalJournal of Theoretical Biologyen
dc.contributor.institutionUniversity of Leeds, Leeds, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institution, ,en
kaust.grant.numberKUK-013-04en

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