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Tumor growth model of ductal carcinoma: from in situ phase to stroma invasion

hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorGALLINATO, Olivier
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOLIN, Thierry
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorSAUT, Olivier
hal.structure.identifierModélisation Mathématique pour l'Oncologie [MONC]
dc.contributor.authorPOIGNARD, Clair
dc.date.accessioned2024-04-04T03:08:34Z
dc.date.available2024-04-04T03:08:34Z
dc.date.issued2017-09
dc.identifier.issn0022-5193
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193537
dc.description.abstractEnThis paper aims at modeling breast cancer transition from the in situ stage –when the tumor is confined to the duct– to the invasive phase. Such a transition occurs thanks to the degradation of the duct membrane under the action of specific enzymes so-called matrix metallo-proteinases (MMPs). The model consists of advection–reaction equations that hold in the duct and in the surrounding tissue, in order to describe the proliferation and the necrosis of the cancer cells in each subdomain. The divergence of the velocity is given by the increase of the cell densities. Darcy law is imposed in order to close the system. The key-point of the modeling lies in the description of the transmission conditions across the duct. Nonlinear Kedem-Katchalsky transmission conditions across the membrane describe the discontinuity of the pressure as a linear function of the flux. These transmission conditions make it possible to describe the transition from the in situ stage to the invasive phase at the macroscopic level. More precisely, the membrane permeability increases with respect to the local concentration of MMPs. The cancer cells are no more confined to the duct and the tumor invades the surrounding tissue. The model is enriched by the description of nutrients concentration, tumor necrosis factors, and MMPs production. The mathematical model is implemented in a 3D C ++-code, which is based on well-adapted finite difference schemes on Cartesian grid. The membrane interface is described by a level-set, and the transmission conditions are precisely approached at the second order thanks to well-suited sharp stencils. Our continuous approach provides new significant insights in the macroscopic modeling of the breast cancer phase transition, due to the membrane degradation by MMP enzymes.
dc.language.isoen
dc.publisherElsevier
dc.title.enTumor growth model of ductal carcinoma: from in situ phase to stroma invasion
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jtbi.2017.06.022
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal of Theoretical Biology
bordeaux.page253 - 266
bordeaux.volume429
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01598837
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01598837v1
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