Related papers: Multifocality and recurrence risk: a quantitative …
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
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…
Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of…
In this work we explore the temporal dynamics of spatial heterogeneity during the process of tumorigenesis from healthy tissue. We utilize a spatial stochastic process model of mutation accumulation and clonal expansion in a structured…
The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cancer. In this paper, we investigate how phenotypic switching at…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
Two models of circulating tumor cell (CTC) dynamics have been proposed to explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the primary tumor and accelerate growth: Primary Seeding, where cells from a primary tumor…
Over 80% of human cancers originate from the epithelium, which covers the outer and inner surfaces of organs and blood vessels. In stratified epithelium, the bottom layers are occupied by stem and stem-like cells that continually divide and…
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…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
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…
Recent progress in microdissection and in DNA sequencing has enabled subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led…
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…
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer…
Cancer results from a sequence of genetic and epigenetic changes which lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells, and thus, to a selective advantage of pre-cancerous cells. The…
Tumor recurrence, driven by the evolution of drug resistance is a major barrier to therapeutic success in cancer. Resistance is often caused by genetic alterations such as point mutation, which refers to the modification of a single genomic…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
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.…
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…
The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This…