A computational framework for the personalized clinical treatment of glioblastoma multiforme

Agosti, Abramo; Cattaneo, Clara; Giverso, Chiara; Ambrosi, Davide Carlo; Ciarletta, Pasquale

doi:10.1002/zamm.201700294

Cited by 45 publications

(73 citation statements)

References 78 publications

(136 reference statements)

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“…|Ω| Ω µ dx. To handle the boundary integral, we will derive an estimate for the L ρ (∂Ω)−norm for ϕ, where ρ ∈ [2,6] is an exponent connected to the growth rate of the potential ψ(·). Furthermore, we comment on the assumption σ ∞ ∈ L 4 (L 2 (∂Ω)), which is not needed to prove existence of weak solutions, but crucial to establish well-posedness of the system.…”

Section: B)mentioning

confidence: 99%

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On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits

Ebenbeck¹,

Garcke²

2019

SIAM J. Math. Anal.

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In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient density and a Brinkmantype equation for the velocity. We equip the system with Neumann boundary for the tumour cell variable and the chemical potential, Robin-type boundary conditions for the nutrient and a "nofriction" boundary condition for the velocity, which allows us to consider solution dependent source terms. Well-posedness of the model as well as existence of strong solutions will be established for a broad class of potentials. We will show that in the singular limit of vanishing viscosities we recover a Darcy-type system related to Cahn-Hilliard-Darcy type models for tumour growth which have been studied earlier. An asymptotic limit will show that the results are also valid in the case of Dirichlet boundary conditions for the nutrient.

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Section: B)mentioning

confidence: 99%

“…where the viscous stress tensor is defined by 2) and the symmetric velocity gradient is given by Dv := 1 2 (∇v + ∇v T ).…”

Section: Introductionmentioning

confidence: 99%

On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits

Ebenbeck¹,

Garcke²

2019

SIAM J. Math. Anal.

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“…A1 TCs proliferate when oxygen is available. As soon as the latter decreases below a critical threshold, they stop proliferating and start necrosis (Chaplain et al, 2006; Gerlee and Anderson, 2007; Agosti et al, 2018).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…As we do not focus on a specific cell line we use the generic estimate for TC motility and proliferation rate reported in (Chaplain et al, 2006). For the critical oxygen concentration, below which cells experience hypoxic conditions, we take a value similar to the one in (Gerlee and Anderson, 2007; Agosti et al, 2018). Also, we select the TC death rate in accordance to the estimate in (Kolokotroni et al, 2011; Martínez-González et al, 2012).…”

Section: Mathematical Modelmentioning

confidence: 99%

Investigating the physical effects in bacterial therapies for avascular tumors

Mascheroni

Meyer‐Hermann

Hatzikirou

2019

Preprint

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Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. As the mechanisms of action of bacterial therapies are still to be completely elucidated, mathematical modeling could aid the understanding of the dynamical interactions between tumor cells and bacteria in different cancers. Here we propose a mathematical model for the anti-tumor activity of bacteria in tumor spheroids. We consider constant infusion and time-dependent administration of bacteria in the culture medium, and analyze the effects of bacterial chemotaxis and killing rate. We show that active bacterial migration towards tumor hypoxic regions is necessary for successful spheroid infiltration and that intermediate chemotaxis coefficients provide the smallest spheroid radii at the end of the treatment. We report on the impact of the killing rate on final spheroid composition, and highlight the emergence of spheroid size oscillations due to competing interactions between bacteria and tumor cells.

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“…This has been incorporated by extending the diffusion models to include linear momentum balance, adding the presence of an external body force describing the displacement of brain tissue by tumor cells 28,29 . Another modeling approach makes use of the theory of mixtures to account for mechanical effects in a sound mathematical framework [30][31][32] . Within this description, a tumor is modeled as a saturated medium comprising solid (e.g.…”

Section: Introductionmentioning

confidence: 99%

On the impact of chemo-mechanically induced phenotypic transitions in gliomas

Mascheroni

Alfonso

Kalli

et al. 2018

Preprint

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Tumor microenvironment is a critical player in glioma progression and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work, we perform experiments to analyze the effects of mechanical compression on migration and proliferation of two glioma cell lines. From these experiments, we derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. The model reveals a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these findings can improve the current understanding of glioma/microenvironment interactions, and suggest strategies to improve therapeutic outcomes. 4/2513/25 14/25

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A computational framework for the personalized clinical treatment of glioblastoma multiforme

Cited by 45 publications

References 78 publications

On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits

On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits

Investigating the physical effects in bacterial therapies for avascular tumors

On the impact of chemo-mechanically induced phenotypic transitions in gliomas

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