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A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…
Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. We propose a classification scheme of growth laws which includes human aging,…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms.…
In this paper we analyse a differential system related to a Glioblastoma growth. Using numerical simulations, we prove that model captures different kind of growth changing adequately the parameters of the model. Firstly, we make an…
Asymmetric partition of fate determinants during cell division is a hallmark of cell differentiation. Recent work suggested that such a mechanism is hijacked by cancer cells to increase both their phenotypic heterogeneity and plasticity and…
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…
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…
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and…
Williams and Bjerknes proposed a simple stochastic growth model to describe the tumor growth in the basal layer of an epithelium. In this work we generalize this model by including the possibility of saturation in the tumor growth as it is…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
A tumor often consists of multiple cell subpopulations (clones). Current chemo-treatments often target one clone of a tumor. Although the drug kills that clone, other clones overtake it and the tumor reoccurs. Genome sequencing and…
The ability to estimate how a tumor might evolve in the future could have tremendous clinical benefits, from improved treatment decisions to better dose distribution in radiation therapy. Recent work has approached the glioma growth…
Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative…
Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…
The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the…
In this paper, we study an optimal control problem for a nonlinear system of reaction-diffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally…
Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often…
Background and Objective: In an in-vivo situation, the tissue near the blood vessels is rich in oxygen supply compared to the one far from blood vessels. Hence, non-uniform oxygen distribution is observed in biological tissues. Our…