2018
DOI: 10.1016/j.cma.2018.06.009
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A monolithic multiphase porous medium framework for (a-)vascular tumor growth

Abstract: We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovascula… Show more

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Cited by 22 publications
(82 citation statements)
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“…These equations are equivalent to the ones derived in Kremheller et al . Herein, ψ α denotes the generic primary variable of phase α , which can be either its saturation S α , its pressure p α , or a pressure difference p αβ to another phase β .…”
Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning
confidence: 99%
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“…These equations are equivalent to the ones derived in Kremheller et al . Herein, ψ α denotes the generic primary variable of phase α , which can be either its saturation S α , its pressure p α , or a pressure difference p αβ to another phase β .…”
Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning
confidence: 99%
“…We model the solid phase, ie, the ECM as the skeleton of the porous medium, where Terzaghi's principle of effective stress bold-italicσeffs=bold-italicσtots+psbold-italicI can be applied. Herein, the solid pressure ps=εε+εv.25emα=t,h,l.25emSαpα+εvε+εv.25empv is defined as a weighted average of the involved phases . This formulation recovers the definition of the solid pressure as a weighted sum of TC, HC, and IF pressures with their saturations if no NV is present.…”
Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning
confidence: 99%
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