Show simple item record

Files in this item


Item metadata

dc.contributor.authorLorenzi, Tommaso
dc.contributor.authorMacfarlane, Fiona R.
dc.contributor.authorPainter, Kevin J.
dc.identifier.citationLorenzi , T , Macfarlane , F R & Painter , K J 2024 , ' Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion ' , European Journal of Mathematics , vol. FirstView .
dc.identifier.otherORCID: /0000-0003-2242-7745/work/154531464
dc.descriptionFunding: TL gratefully acknowledges support from the Italian Ministry of University and Research (MUR) through the grant PRIN 2020 project (No. 2020JLWP23) “Integrated Mathematical Approaches to Socio-Epidemiological Dynamics” (CUP: E15F21005420006) and the grant PRIN2022-PNRR project (No. P2022Z7ZAJ) “A Unitary Mathematical Framework for Modelling Muscular Dystrophies” (CUP: E53D23018070001), from the CNRS International Research Project “Modelisation de la biomecanique cellulaire et tissulaire” (MOCETIBI), and from the Istituto Nazionale di Alta Matematica (INdAM) and the Gruppo Nazionale per la Fisica Matematica (GNFM). KJP is a member of INdAM-GNFM and acknowledges “Miur-Dipartimento di Eccellenza” funding to the Dipartimento di Scienze, Progetto e Politiche del Territorio (DIST).en
dc.description.abstractWe formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger haptotaxis responses and have greater capacity to modify the extracellular matrix (ECM) through enhanced secretion of matrix-degrading enzymes (MDEs). However, as a trade-off, they have lower proliferative capacity than the more epithelial cells. The framework is multiscale in that we start with an individual- based model that tracks the dynamics of single cells, which is based on a branching random walk over a lattice representing both physical and phenotype space. We formally derive the corresponding continuum model, which takes the form of a coupled system comprising a partial integro-differential equation for the local cell population density function, a partial differential equation for the MDE concentration and an infinite-dimensional ordinary differential equation for the ECM density. Despite the intricacy of the model, we show, through formal asymptotic techniques, that for certain parameter regimes it is possible to carry out a detailed travelling wave analysis and obtain invading fronts with spatial structuring of phenotypes. Precisely, the most mesenchymal cells dominate the leading edge of the invasion wave and the most epithelial (and most proliferative) dominate the rear, representing a bulk tumour population. As such, the model recapitulates similar observations into a front to back structuring of invasion waves into leader-type and follower-type cells, witnessed in an increasing number of experimental studies over recent years.
dc.relation.ispartofEuropean Journal of Mathematicsen
dc.subjectIndividual-based modelsen
dc.subjectPartial integro-differential equationen
dc.subjectTravelling wave analysisen
dc.subjectPhenotypic diversityen
dc.subjectHaptotaxis models of cancer invasionen
dc.subjectQA Mathematicsen
dc.subjectSDG 3 - Good Health and Well-beingen
dc.titleDerivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasionen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

This item appears in the following Collection(s)

Show simple item record