Related papers: Cancer and nonextensive statistics
We consider a model describing the evolution of a tumor inside a host tissue in terms of the parameters $\varphi_p$, $\varphi_d$ (proliferating and dead cells, respectively), $u$ (cell velocity) and $n$ (nutrient concentration). The…
We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a…
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor…
Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain $\Omega(t)$, and the coincidence set $\Lambda(t)$ captures…
In this work, we develop a structure-preserving numerical scheme for a Cahn-Hilliard-Darcy model that describes tumor growth in a fluid-saturated porous medium. First, we derive a physically consistent model from the general framework…
We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…
We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
The topology of gene expression space for a set of 12 cancer types is studied by means of an entropy-like magnitude, which allows the characterization of the regions occupied by tumor and normal samples. The comparison indicates that the…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population…
A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
This paper is devoted to exploring the effects of non-Gaussian fluctuations on dynamical evolution of a tumor growth model with immunization, subject to non-Gaussian {\alpha}-stable type L\'evy noise. The corresponding deterministic model…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…