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Tumor metastasis is one of the main factors responsible for the high fatality rate of cancer. Metastasis can occur after malignant cells transition from the epithelial phenotype to the mesenchymal phenotype. This transformation allows cells…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
Cancer evolves continuously over time through a complex interplay of genetic, epigenetic, microenvironmental, and phenotypic changes. This dynamic behavior drives uncontrolled cell growth, metastasis, immune evasion, and therapy resistance,…
A mathematical model of genome degradation is proposed that takes into account a variable rate of mutation and increasing number of cells in a developing human organism. The model explains known properties of cancer development, in…
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…
Purpose of review: The epithelial-Mesenchymal Transition (EMT) and the generation of Cancer Stem Cells (CSC) are two fundamental aspects contributing to tumor growth, acquisition of resistance to therapy, formation of metastases, and tumor…
We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radioteraphy or chemoteraphy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion…
Biological living systems in general exhibit complex and diverse dynamics. The latter, in particular, is essential, since diversification increases the odds of survival of an organism while reducing the risk of extinction of the population.…
In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes involved in tumor growth, such as oxygen diffusion, carcinogen penetration, and…
Much progress has been made, and continues to be made, towards identifying candidate mutated driver pathways in cancer. However, no systematic approach to understanding how candidate pathways relate to each other for a given cancer (such as…
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…
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
Cancer cells exhibit increased motility and proliferation, which are instrumental in the formation of tumours and metastases. These pathological changes can be traced back to malfunctions of cellular signalling pathways, and calcium…
Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…
Abnormal metabolism is an emerging hallmark of cancer. Cancer cells utilize both aerobic glycolysis and oxidative phosphorylation (OXPHOS) for energy production and biomass synthesis. Understanding the metabolic reprogramming in cancer can…
Interstitial fluid flow is a feature of many solid tumours. In vitro Experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis…
Despite recent advances in the field of Oncoimmunology, the success potential of immunomodulatory therapies against cancer remains to be elucidated. One of the reasons is the lack of understanding on the complex interplay between tumor…
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in…
Death ligand mediated apoptotic activation is a mode of programmed cell death that is widely used in cellular and physiological situations. Interest in studying death ligand induced apoptosis has increased due to the promising role of…