Kaiserslautern - Fachbereich Mathematik
Refine
Language
- English (18)
Has Fulltext
- yes (18)
Keywords
- haptotaxis (4)
- multiscale model (4)
- asymptotic behavior (2)
- cancer cell invasion (2)
- degenerate diffusion (2)
- delay (2)
- global existence (2)
- pH-taxis (2)
- parabolic system (2)
- weak solution (2)
- Acid-mediated tumor invasion (1)
- Multiscale model (1)
- Random differential equations (1)
- Reaction-diffusion equations (1)
- acid-mediated tumor invasion (1)
- chemotaxis (1)
- chemotherapy (1)
- go-or-grow (1)
- go-or-grow dichotomy (1)
- intra- and extracellular proton dynamics (1)
- multiscale models (1)
- nonlocal sample dependence (1)
- partial differential equations (1)
- radiotherapy (1)
- reaction-diffusion-taxis equations (1)
- reaction-diffusion-transport equations (1)
- stochastic differential equations (1)
- time-delayed carrying capacities (1)
- tumor acidity (1)
- tumor cell invasion (1)
- tumor cell migration (1)
Faculty / Organisational entity
In this paper we propose a phenomenological model for the formation of an interstitial gap between the tumor and the stroma. The gap
is mainly filled with acid produced by the progressing edge of the tumor front. Our setting extends existing models for acid-induced tumor invasion models to incorporate
several features of local invasion like formation of gaps, spikes, buds, islands, and cavities. These behaviors are obtained mainly due to the random dynamics at the intracellular
level, the go-or-grow-or-recede dynamics on the population scale, together with the nonlinear coupling between the microscopic (intracellular) and macroscopic (population)
levels. The wellposedness of the model is proved using the semigroup technique and 1D and 2D numerical simulations are performed to illustrate model predictions and draw
conclusions based on the observed behavior.
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.
Glioma is a common type of primary brain tumor, with a strongly invasive potential, often exhibiting nonuniform, highly irregular growth. This makes it difficult to assess
the degree of extent of the tumor, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the
migratory behavior of glioma in greater detail.
In this paper we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the
surrounding tissue) with a kinetic transport equation for the cell density on the mesoscopic level of individual cells. On the latter scale we also include the
proliferation of tumor cells via effects of interaction with the tissue. An adequate parabolic scaling yields a convection-diffusion-reaction equation, for which the coefficients
can be explicitly determined from the information about the tissue obtained by diffusion tensor imaging. Numerical simulations relying on DTI measurements confirm the biological
findings that glioma spreads
along white matter tracts.
We propose a multiscale model for tumor cell migration in a tissue network. The system of equations involves a structured population model for the tumor cell density, which besides time and
position depends on a further variable characterizing the cellular state with respect to the amount
of receptors bound to soluble and insoluble ligands. Moreover, this equation features pH-taxis and
adhesion, along with an integral term describing proliferation conditioned by receptor binding. The
interaction of tumor cells with their surroundings calls for two more equations for the evolution of
tissue fibers and acidity (expressed via concentration of extracellular protons), respectively. The
resulting ODE-PDE system is highly nonlinear. We prove the global existence of a solution and
perform numerical simulations to illustrate its behavior, paying particular attention to the influence
of the supplementary structure and of the adhesion.
Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the
consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy
(e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells
preserve this aerobic glycolytic phenotype for its use in invasion and metastasis. We follow this hypothesis and propose a new model
for cancer invasion, depending on the dynamics of extra- and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account
for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.
We consider the multiscale model for glioma growth introduced in a previous work and extend it to account
for therapy effects. Thereby, three treatment strategies involving surgical resection, radio-, and
chemotherapy are compared for their efficiency. The chemotherapy relies on inhibiting the binding
of cell surface receptors to the surrounding tissue, which impairs both migration and proliferation.
A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed.
The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion
equation for the extracellular proton concentration on the macroscale. In a more general context
the existence and uniqueness of solutions for local and nonlocal
SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both,
in its local version and the case with nonlocal path dependence.
Numerical simulations are performed
to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.
SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness
(2018)
We deduce cell population models describing the evolution of a tumor (possibly interacting with its
environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations
of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer
stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher
sensitivity towards chemo- and radiotherapy. Our approach relies on stochastic differential equations
in order to account for randomness in the system, arising e.g., by the therapy-induced decreasing
number of clonogens, which renders a pure deterministic model arguable. The equations are deduced
relying on transition probabilities characterizing innovations of the two cancer cell subpopulations,
and similarly extended to also account for the evolution of normal tissue. Several therapy approaches
are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor
control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal
tissue with respect to time and to cell population densities which can vary continuously in a given set
of states. Analytical approximations of solutions to the obtained PDE system are provided as well.
Gliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .
We propose a model for glioma patterns in a microlocal tumor environment under
the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction
eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell
population densities, of which the former infers flux limitation both in the self-diffusion and taxis
terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of
glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor
vascularization on the establishment and maintenance of these histological patterns which are typical
for high-grade brain cancer. Numerical simulations of the population level dynamics are performed
to investigate several model scenarios containing this and further effects.