Related papers: On a nonlinear model for tumor growth in a cellula…
Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. These two classes of models can be related using a stiff pressure law. In the incompressible…
Tumors are defined by their intense proliferation, but sometimes cancer cells turn senescent and stop replicating. In the stochastic cancer model in which all cells are tumorigenic, senescence is seen as the result of random mutations,…
Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided…
We consider a (degenerate) cross-diffusion model of tumor growth structured by phenotypic trait. We prove the existence of weak solutions and the incompressible limit as the pressure becomes stiff extending methods recently introduced in…
We propose a new type of diffuse interface model describing the evolution of a tumor mass under the effects of a chemical substance (e.g., a nutrient or a drug). The process is described by utilizing the variables $\varphi$, an order…
In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…
We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by…
Cancers follow a clonal Darwinian evolution, with fitter subclones replacing more quiescent cells, ultimately giving rise to macroscopic disease. High-throughput genomics provides the opportunity to investigate these processes and determine…
We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms.…
In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…
Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell…
Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative…
Tumor growth is a complex process characterized by uncontrolled cell proliferation and invasion of neighboring tissues. The understanding of these phenomena is of vital importance to establish appropriate diagnosis and therapeutic strategy…
In this paper we study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a…
The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of…
This paper deals with the cellular biological network analysis of the tumor-growth model, consisting of multiple spaces and time scales. In this paper, we present a model in graph simulation using ABM for tumor growth. In particular, we…
Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…
The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we…