Related papers: Tumor containment as an anti-percolation process
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Disease maps are an important tool in cancer epidemiology used for the analysis of geographical variations in disease rates and the investigation of environmental risk factors underlying spatial patterns. Cancer maps help epidemiologists…
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…
We developed a mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing)…
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…
We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also…
A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
Tumors are extremely heterogeneous and comprise of a number of intratumor microenvironments or sub-regions. These tumor microenvironments may interact with eac based on complex high-level relationships, which could provide important insight…
The brain is a complex organ controlling cognitive process and physical functions. Tumors in the brain are accelerated cell growths affecting the normal function and processes in the brain. MRI scans provides detailed images of the body…
We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the…
In this work, we develop a kinetic model of tumour growth taking into account the effects of clinical uncertainties characterising the tumours' progression. The action of therapeutic protocols trying to steer the tumours' volume towards a…
A U-Net based deep learning architecture is designed to segment brain tumors as they appear on various MRI modalities. Special emphasis is lent to the non-enhancing tumor compartment. The latter has not been considered anymore in recent…
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…
We introduce here a new diffuse interface thermodynamically consistent non-isothermal model for tumor growth in presence of a nutrient in a domain $\Omega \subset \mathbb{R}^3$. In particular our system describes the growth of a tumor…
Cancer cells utilize large amounts of ATP to sustain growth, relying primarily on non-oxidative, fermentative pathways for its production. In many types of cancers this leads, even in the presence of oxygen, to the secretion of carbon…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
With the long-term rapid increase in incidences of colorectal cancer (CRC), there is an urgent clinical need to improve risk stratification. The conventional pathology report is usually limited to only a few histopathological features.…