Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation

Fritz, Marvin; Lima, Ernesto A. B. F.; Nikolić, Vanja; Oden, J. T.; Wohlmuth, Barbara

doi:10.1142/s0218202519500519

Cited by 30 publications

(23 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We believe that, on account of the results obtained in this paper, we could go beyond the mere existence of a weak solution. It is worth observing that nonlocal models for tumor growth have been recently considered in [26,27]…”

Section: Discussionmentioning

confidence: 99%

Nonlocal Cahn–Hilliard–Hele–Shaw Systems with Singular Potential and Degenerate Mobility

Cavaterra

Frigeri

Grasselli

2021

J. Math. Fluid Mech.

View full text Add to dashboard Cite

We study a Cahn-Hilliard-Hele-Shaw (or Cahn-Hilliard-Darcy) system for an incompressible mixture of two fluids. The relative concentration difference ϕ is governed by a convective nonlocal Cahn-Hilliard equation with degenerate mobility and logarithmic potential. The volume averaged fluid velocity u obeys a Darcy's law depending on the so-called Korteweg force μ∇ϕ, where μ is the nonlocal chemical potential. In addition, the kinematic viscosity η may depend on ϕ. We establish first the existence of a global weak solution which satisfies the energy identity. Then we prove the existence of a strong solution. Further regularity results on the pressure and on u are also obtained. Weak-strong uniqueness is demonstrated in the two-dimensional case. In the three-dimensional case, uniqueness of weak solutions holds if η is constant. Otherwise, weak-strong uniqueness is shown by assuming that the pressure of the strong solution is α-Hölder continuous in space for α ∈ (1/5, 1).

show abstract

Section: Discussionmentioning

confidence: 99%

Nonlocal Cahn–Hilliard–Hele–Shaw Systems with Singular Potential and Degenerate Mobility

Cavaterra

Frigeri

Grasselli

2021

J. Math. Fluid Mech.

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Nonlocal Cahn-Hilliard-Hele-Shaw systems with singular potential and degenerate mobility

Cavaterra,

Frigeri,

Grasselli

2021

Preprint

View full text Add to dashboard Cite

We study a Cahn-Hilliard-Hele-Shaw (or Cahn-Hilliard-Darcy) system for an incompressible mixture of two fluids. The relative concentration difference ϕ is governed by a convective nonlocal Cahn-Hilliard equation with degenerate mobility and logarithmic potential. The volume averaged fluid velocity u obeys a Darcy's law depending on the so-called Korteweg force µ∇ϕ, where µ is the nonlocal chemical potential. In addition, the kinematic viscosity η may depend on ϕ. We establish first the existence of a global weak solution which satisfies the energy identity. Then we prove the existence of a strong solution. Further regularity results on the pressure and on u are also obtained. Weak-strong uniqueness is demonstrated in the two dimensional case. In the three-dimensional case, uniqueness of weak solutions holds if η is constant. Otherwise, weak-strong uniqueness is shown by assuming that the pressure of the strong solution is α-Hölder continuous in space for α ∈ (1/5, 1).

show abstract

“…One can then consider the two-phase porous medium as cancerous and healthy cells with the surrounding extracellular matrix, and the fluid as the interstitial fluid. Similar models involving Cahn-Hilliard-type evolution of tumor growth can be seen in [7,8,9,10,11,12,13,14,15,16,17]. Additional applications of poroelastic media with solid phase changes range from biogrout to wood growth, where sapwood transforms to heartwood.…”

Section: Introductionmentioning

confidence: 94%

A Cahn-Hilliard-Biot system and its generalized gradient flow structure

Storvik¹,

Both²,

Nordbotten³

et al. 2021

Preprint

View full text Add to dashboard Cite

In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material follow a Cahn-Hilliard type evolution, with additional impact from both elastic and fluid effects, and the coupling between flow and deformation is governed by Biot's theory. This results in a three-way coupled system which can be seen as an extension of the Cahn-Larché equations with the inclusion of a fluid flowing through the medium. The model covers essential coupling terms for several relevant applications, including solid tumor growth, biogrout, and wood growth simulation. Moreover, we show that this coupled set of equations follow a generalized gradient flow framework. This opens a toolbox of analysis and solvers which can be used for further study of the model. Additionally, we provide a numerical example showing the impact of the flow on the solid phase evolution in comparison to the Cahn-Larché system.

show abstract

Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation

Cited by 30 publications

References 60 publications

Nonlocal Cahn–Hilliard–Hele–Shaw Systems with Singular Potential and Degenerate Mobility

Nonlocal Cahn–Hilliard–Hele–Shaw Systems with Singular Potential and Degenerate Mobility

Nonlocal Cahn-Hilliard-Hele-Shaw systems with singular potential and degenerate mobility

A Cahn-Hilliard-Biot system and its generalized gradient flow structure

Contact Info

Product

Resources

About