Related papers: Modeling tumor growth: a simple individual-based m…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…
As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
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…
Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…
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…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…
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…
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 conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division…
This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as…
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…
In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…
In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation…
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,…