2019
DOI: 10.1002/cnm.3253
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An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

Abstract: The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex… Show more

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Cited by 41 publications
(83 citation statements)
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References 89 publications
(347 reference statements)
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“…with the lymphatic filtration coefficient L p S V � � ly . This is similar to the mass transfer term for drainage of fluid from the IF as presented in Kremheller et al [13,14]. In the following, we assume p ly � 0.…”
Section: Nanoparticle Transportmentioning
confidence: 73%
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“…with the lymphatic filtration coefficient L p S V � � ly . This is similar to the mass transfer term for drainage of fluid from the IF as presented in Kremheller et al [13,14]. In the following, we assume p ly � 0.…”
Section: Nanoparticle Transportmentioning
confidence: 73%
“…Our multiphase tumour growth model is based on Sciumè et al [17] with the extension to a five-phase model including the vasculature as presented in Kremheller et al [13,14]. The model is based on the Thermodynamically Constrained Averaging Theory (TCAT) [27], which has several benefits.…”
Section: The Vascular Multiphase Tumour Growth Modelmentioning
confidence: 99%
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“…where ω iα identifies the mass fraction of the species i dispersed with the phase α, ε α r iα is a reaction term that allows to take into account the reactions between the species i and the other chemical species dispersed in the phase α, and u iα is the diffusive velocity of the species i. iα→iκ M are mass exchange terms accounting for mass transport of species i at the κα interface from phase α to phase κ. Applying the product rule and introducing eqn (8), the previous equation can be also written in this alternative form (commonly called distribution form)…”
Section: General Form Of Governing Equations From Tcatmentioning
confidence: 99%