Displaying similar documents to “Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model”

A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes

J. Dyson, R. Villella-Bressan, G. Webb (2010)

Mathematical Modelling of Natural Phenomena

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A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments...

Individual Cell-Based Model for In-Vitro Mesothelial Invasion of Ovarian Cancer

C. Giverso, M. Scianna, L. Preziosi, N. Lo Buono, A. Funaro (2010)

Mathematical Modelling of Natural Phenomena

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In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular...

Application of Hybrid Models to Blood Cell Production in the Bone Marrow

N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

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A hybrid model of red blood cell production, where cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models, is proposed. Spatial organization and regulation of red blood cell production (erythropoiesis) are investigated. Normal erythropoiesis is simulated in two dimensions, and the influence on the output of the model of some parameters involved...