92C17 Cell movement (chemotaxis, etc.)
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- haptotaxis (5)
- multiscale model (3)
- asymptotic behavior (2)
- cancer cell invasion (2)
- degenerate diffusion (2)
- delay (2)
- global existence (2)
- pH-taxis (2)
- parabolic system (2)
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We study a multi-scale model for growth of malignant gliomas in the human brain.
Interactions of individual glioma cells with their environment determine the gross tumor shape.
We connect models on different time and length scales to derive a practical description of tumor growth that takes these microscopic interactions into account.
From a simple subcellular model for haptotactic interactions of glioma cells with the white matter we derive a microscopic particle system, which leads to a meso-scale model for the distribution of particles, and finally to a macroscopic description of the cell density.
The main body of this work is dedicated to the development and study of numerical methods adequate for the meso-scale transport model and its transition to the macroscopic limit.
We propose and analyze a multiscale model for acid-mediated tumor invasion
accounting for stochastic effects on the subcellular level.
The setting involves a PDE of reaction-diffusion-taxis type describing the evolution of the tumor cell density,
the movement being directed towards pH gradients in the local microenvironment,
which is coupled to a PDE-SDE system characterizing the
dynamics of extracellular and intracellular proton concentrations, respectively.
The global well-posedness of the model is shown and
numerical simulations are performed in order to illustrate the solution behavior.
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network
under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features
two interacting cell populations with their mutual transitions and involves tissue-dependent degenerate diffusion and
haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs
for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by
numerical simulations in a two-dimensional setting.
We investigate a PDE-ODE system describing cancer cell invasion in a tissue network. The model is an extension of the multiscale setting in [28,40], by considering two subpopulations of tumor cells interacting mutually and with the surrounding tissue. According to the go-or-grow hypothesis, these subpopulations consist of moving and proliferating cells, respectively. The mathematical setting also accommodates the effects of some therapy approaches. We prove the global existence of weak solutions to this model and perform numerical simulations to illustrate its behavior for different therapy strategies.
We propose and study a strongly coupled PDE-ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the
extracellular matrix. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations for a two-dimensional setting.
Starting from the two-scale model for pH-taxis of cancer cells introduced in [1], we consider here an extension accounting for tumor heterogeneity w.r.t. treatment sensitivity and a treatment approach including chemo- and radiotherapy. The effect of peritumoral region alkalinization on such therapeutic combination is investigated with the aid of numerical simulations.
We propose a model for acid-mediated tumor invasion involving two different scales: the microscopic one, for the dynamics of intracellular protons and their exchange with their extracellular counterparts, and the macroscopic scale of interactions between tumor cell and normal cell populations, along with the evolution of extracellular protons. We also account for the tactic behavior of cancer cells, the latter being assumed to biase their motion according to a gradient of extracellular protons (following [2,31] we call this pH taxis). A time dependent (and also time delayed) carrying capacity for the tumor cells in response to the effects of acidity is considered as well. The global well posedness of the resulting multiscale model is proved with a regularization and fixed point argument. Numerical simulations are performed in order to illustrate the behavior of the model.
We prove the global existence, along with some basic boundedness properties, of weak solutions to a PDE-ODE system modeling the multiscale invasion of tumor cells through the surrounding tissue matrix. The model has been proposed in [22] and accounts on the macroscopic level for the evolution of cell and tissue densities, along with the concentration of a chemoattractant, while on the subcellular level it involves the binding of integrins to soluble and insoluble components of the peritumoral region. The connection between the two scales is realized with the aid of a contractivity function characterizing the ability of the tumor cells to adapt their motility behavior
to their subcellular dynamics.
The resulting system, consisting of three partial and three ordinary differential equations including a temporal delay, in particular involves chemotactic and haptotactic cross-diffusion. In order to overcome technical obstacles stemming from the corresponding highest-order interaction terms, we base our analysis on a certain functional, inter alia involving the cell and tissue densities in the diffusion and haptotaxis terms respectively, which is shown to enjoy a quasi-dissipative property. This will be used as a starting point for the derivation of a series of integral estimates finally allowing for the construction of a generalized solution as the limit of solutions to suitably regularized problems.
Cancer cell migration is an essential feature in the process of tumor spread and establishing of metastasis. It characterizes the invasion observed on the level of the cell population, but it is also tightly connected to the events taking place on the subcellular level. These are conditioning the motile and proliferative behavior of the cells, but are also influenced by it. In this work we propose a multiscale model linking these two levels and aiming to assess their interdependence. On the subcellular, microscopic scale it accounts for integrin binding to soluble and insoluble components present in the peritumoral environment, which is seen as the onset of biochemical events leading to changes in the cell's ability to contract and modify its shape. On the macroscale of the cell population this leads to modifications in the diffusion and haptotaxis performed by the tumor cells and implicitly to changes in the tumor environment. We prove the (local) well posedness of our model and perform numerical simulations in order to illustrate the model predictions.