Related papers: A Spatial Mutation Model with Increasing Mutation …
We consider a free boundary tumor model under the presence of angiogenesis and time delays in the process of proliferation, in which the cell location is incorporated. It is assumed that the tumor attracts blood vessels at a rate…
We propose a one mutation model for cancer with a mutation rate that increases with time. Under rather general hypotheses the number of mutations is necessarily a (non homogeneous) Poisson process with the prescribed mutation rate. We show…
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…
The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps…
Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with…
We consider the population genetics problem: how long does it take before some member of the population has $m$ specified mutations? The case $m=2$ is relevant to onset of cancer due to the inactivation of both copies of a tumor suppressor…
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. The model features two moving…
In this paper we consider a free boundary tumor growth model with a time delay in cell proliferation and study how time delay affects the stability and the size of the tumor. The model is a coupled system of an elliptic equation, a…
We study a free boundary problem modeling multi-layer tumor growth with a small time delay $\tau$, representing the time needed for the cell to complete the replication process. The model consists of two elliptic equations which describe…
Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced in McFarland et al. as a mathematical model for…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
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…
Mathematical and computational modelling in oncology has played an increasingly important role in not only understanding the impact of various approaches to treatment on tumour growth, but in optimizing dosing regimens and aiding the…
A spatiotemporal noise is assumed to reflect the environmental fluctuation in a spatially extended tumor system. We introduce firstly the structure factor to reveal the invasive tumor growth quantitatively. The homogenous environment can…
Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…
Mutations can arise from the chance misincorporation of nucleotides during DNA replication or from DNA lesions that are not repaired correctly. We introduce a model that relates the source of mutations to their accumulation with cell…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…