Christina Surulescu

Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion

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 [G. Meral, C. Stinner, and C. Surulescu, On a Multiscale Model Involving Cell Contractivity and its Effects on Tumor Invasion, preprint, TU Kaiserslautern, Kaiserslautern, Germany, 2013] 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 particul...

Glioma follow white matter tracts: a multiscale DTI-based model

Gliomas are a class of rarely curable tumors arising from abnormal glia cells in the human brain. The understanding of glioma spreading patterns is essential for both radiological therapy as well as surgical treatment. Diffusion tensor imaging (DTI) allows to infer the white matter fibre structure of the brain in a noninvasive way. Painter and Hillen (J Theor Biol 323:25–39, 2013) used a kinetic partial differential equation to include DTI data into a class of anisotropic diffusion models for glioma spread. Here we extend this model to explicitly include adhesion mechanisms between glioma cells and the extracellular matrix components which are associated to white matter tracts. The mathematical modelling follows the multiscale approach proposed by Kelkel and Surulescu (Math Models Methods Appl Sci 23(3), 2012). We use scaling arguments to deduce a macroscopic advection-diffusion model for this process. The tumor diffusion tensor and the tumor drift velocity depend on both, the directions of the white matter tracts as well as the binding dynamics of the adhesion molecules. The advanced computational platform DUNE enables us to accurately solve our macroscopic model. It turns out that the inclusion of cell binding dynamics on the microlevel is an important factor to explain finger-like spread of glioma.

A MULTISCALE APPROACH TO CELL MIGRATION IN TISSUE NETWORKS

We derive a multiscale model for tumor cell migration allowing to account for the receptor-mediated movement of the cells, the degradation of tissue fibers and the subsequent production of a soluble ligand whose concentration gradient then acts together with the distribution of tissue fibers as a directional cue for the cells. For this model we present a result on the local existence and uniqueness of a solution in all biologically relevant space dimensions.

On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces

The system of functional differential equations considered here is motivated by a concrete class of multiscale models for tumor cell migration involving chemotaxis, haptotaxis, and subcellular dynamics proposed in [J. Kelkel and C. Surulescu, A multiscale approach to cell migration in tissue networks, Math. Models Methods Appl. Sci. 22 (2012) 1150017]. Tissue fibers, cell densities and concentrations of chemotactic signals are assumed to be just square Lebesgue integrable in space, but not necessarily essentially bounded (as in [J. Kelkel and C. Surulescu, A multiscale approach to cell migration in tissue networks, Math. Models Methods Appl. Sci. 22 (2012) 1150017] and related previous settings). The focus of interest is on sufficient conditions for the well-posedness of the underlying larger problem class.

Global existence for a go-or-grow multiscale model for tumor invasion with therapy

We investigate a PDE–ODE system describing cancer cell invasion in a tissue network. The model is an extension of the multiscale setting in [G. Meral, C. Stinner and C. Surulescu, On a multiscale model involving cell contractivity and its effects on tumor invasion, Discrete Contin. Dynam. Syst. Ser. B 20 (2015) 189–213] and [C. Stinner, C. Surulescu and M. Winkler, Global weak solutions in a PDE–ODE system modeling multiscale cancer cell invasion, SIAM J. Math. Anal. 46 (2014) 1969–2007], 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.

Global existence for a degenerate haptotaxis model of cancer invasion

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 behavior by numerical simulations for a two-dimensional setting.

A multiscale model for glioma spread including cell-tissue interactions and proliferation.

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. They are highly invasive and lead to irregular tumor margins which are not precisely identifiable by medical imaging, thus rendering a precise enough resection very difficult. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. In this paper we propose a multiscale model for glioma growth including interactions of the cells with the underlying tissue network, along with proliferative effects. Our current accounting for two subpopulations of cells to accomodate proliferation according to the go-or-grow dichtomoty is an extension of the setting in [16]. As in that paper, we assume that cancer cells use neuronal fiber tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we perform a parabolic scaling to obtain an approximating reaction-diffusion-transport equation on the macroscale of the tumor cell population. Numerical simulations based on DTI data are carried out in order to assess the performance of our modeling approach.

Mathematical Analysis and Numerical Simulations for a System Modeling Acid-Mediated Tumor Cell Invasion

This work is concerned with the mathematical analysis of a model proposed by Gatenby and Gawlinski (1996) in order to support the hypothesis that tumor-induced alteration of microenvironmental pH may provide a simple but comprehensive mechanism to explain cancer invasion. We give an intuitive proof for the existence of a solution under general initial conditions upon using an iterative approach. Numerical simulations are also performed, which endorse the predictions of the model when compared with experimentally observed qualitative facts.

On some models for cancer cell migration through tissue networks.

We propose some models allowing to account for relevant processes at the various scales of cancer cell migration through tissue, ranging from the receptor dynamics on the cell surface over degradation of tissue fibers by protease and soluble ligand production towards the behavior of the entire cell population. For a genuinely mesoscopic version of these models we also provide a result on the local existence and uniqueness of a solution for all biologically relevant space dimensions.

MODELING AND SIMULATION OF SOME CELL DISPERSION PROBLEMS BY A NONPARAMETRIC METHOD

Starting from the classical descriptions of cell motion we propose some ways to enhance the realism of modeling and to account for interesting features like allowing for a random switching between biased and unbiased motion or avoiding a set of obstacles. For this complex behavior of the cell population we propose new models and also provide a way to numerically assess the macroscopic densities of interest upon using a nonparametric estimation technique. Up to our knowledge, this is the only method able to numerically handle the entire complexity of such settings.