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In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E, Phys. Biol. 2 (2005) 8-22). Here we describe a…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
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.…
Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the…
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the…
We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of…
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…
Cancer forms a robust system and progresses as stages over time typically with increasing aggressiveness and worsening prognosis. Characterizing these stages and identifying the genes driving transitions between them is critical to…
Background. A large number of algorithms is being developed to reconstruct evolutionary models of individual tumours from genome sequencing data. Most methods can analyze multiple samples collected either through bulk multi-region…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…
The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…
Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that…
We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Cancer is a complex disease driven by dynamic regulatory shifts that cannot be fully captured by individual molecular profiling. We employ a data-driven approach to construct a coarse-grained dynamic network model based on hallmark…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
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…
A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial…
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…
One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical…