2017
DOI: 10.1016/j.jtbi.2017.06.022
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Tumor growth model of ductal carcinoma: from in situ phase to stroma invasion

Abstract: This 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 metalloproteinases (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 v… Show more

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Cited by 15 publications
(11 citation statements)
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“…Using a modelling strategy similar to that proposed by Gallinato et al [35] and Giverso et al [37], we define the effective mobility coefficient µ 23 as whereμ 23 > 0 is the maximum mobility of ovarian cancer cells through the interface that models the peritoneal lining, the function A(t, x) > 0 represents the average cross-section of the pores of the membrane at position x ∈ Σ 23 and time t ≥ 0, and the parameter A 0 > 0 is the critical value of the average pores' cross-section below which, according to "the physical limit of cell migration" [83], the membrane is completely impermeable to cancer cells. The evolution of the function A(t, x) is governed by the following differential equation In Eq.…”
Section: S2 Formal Derivation Of the Continuity Condition (46) Forφmentioning
confidence: 99%
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“…Using a modelling strategy similar to that proposed by Gallinato et al [35] and Giverso et al [37], we define the effective mobility coefficient µ 23 as whereμ 23 > 0 is the maximum mobility of ovarian cancer cells through the interface that models the peritoneal lining, the function A(t, x) > 0 represents the average cross-section of the pores of the membrane at position x ∈ Σ 23 and time t ≥ 0, and the parameter A 0 > 0 is the critical value of the average pores' cross-section below which, according to "the physical limit of cell migration" [83], the membrane is completely impermeable to cancer cells. The evolution of the function A(t, x) is governed by the following differential equation In Eq.…”
Section: S2 Formal Derivation Of the Continuity Condition (46) Forφmentioning
confidence: 99%
“…Moreover, Gallinato et al [35] have proposed a mixture model of breast cancer cell invasion whereby the presence of the basement membrane of the milk ducts is taken into account by imposing nonlinear Kedem-Katchalsky interface conditions [19,28,29,51,55,70] at the interface between the tumour and the host region. In the setting of Gallinato et al [35], such transmission conditions lead the normal velocity of the cells and the cell volume fraction to be continuous across the basement membrane, which is not necessarily the case. Finally, Arduino & Preziosi [11] and Giverso et al [37] have presented a number of multiphase models of cancer cell migration and invasion through the ECM.…”
Section: Introductionmentioning
confidence: 99%
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“…In the last twenty years, biological applications of membrane problems have increased. Furthermore, they can describe phenomena on several dierent scales: from the nucleus membrane [4,8,26] to thin interfaces traversed by cancer cells [5,11] and to exchanges in bloody vessels, numerically studied in [23]. Also semi-discretization of mass diusion problems requires numerical treatment in adjoint domains coupled at the interface (see [3]).…”
Section: Introductionmentioning
confidence: 99%
“…In the last twenty years, biological applications of membrane problems have increased. Furthermore, they can describe phenomena on several different scales: from the nucleus membrane [4,8,26] to thin interfaces traversed by cancer cells [5,11] and to exchanges in bloody vessels, numerically studied in [23]. Also semi-discretization of mass diffusion problems requires numerical treatment in adjoint domains coupled at the interface (see [3]).…”
Section: Introductionmentioning
confidence: 99%