Related papers: Mass concentration in a nonlocal model of clonal s…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation…
Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental…
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study…
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,…
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…
We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are transported by actin which they help to polymerize. This leads to…
For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called "resting cells" was studied from numerical…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single…
This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia (CML) through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy…
We present a phase-space analysis of a mathematical model of tumor growth with an immune responses. We consider mathematical analysis of the model equations with multipoint initial condition regarding to dissipativity, boundedness of…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
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…