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Found 5 papers, 1 papers with code
Evolutionary dynamics of glucose-deprived cancer cells: insights from experimentally-informed mathematical modelling
Glucose is a primary energy source for cancer cells.
A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis
Neovascularisation is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development.
Mechanical models of pattern and form in biological tissues: the role of stress-strain constitutive equations
Mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems and describe the physical interactions between cells and their local surroundings.
Evolutionary dynamics in vascularised tumours under chemotherapy
In order to disentangle the impact of different evolutionary parameters on the emergence of intra-tumour phenotypic heterogeneity and the development of resistance to chemotherapy, we construct explicit solutions to the equation for the phenotypic distribution of tumour cells and provide a detailed quantitative characterisation of the long-time asymptotic behaviour of such solutions.
Modelling 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 phenotypic evolution of tumour cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoural vascular network.
