Displaying similar documents to “An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development”

Global Existence and Boundedness of Solutions to a Model of Chemotaxis

J. Dyson, R. Villella-Bressan, G. F. Webb (2008)

Mathematical Modelling of Natural Phenomena

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A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in -dimensional space. We prove the existence of solutions, which exist globally, and are -bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant. ...

Vasculogenesis Models Revisited - Measurement of VEGF Diffusion in Matrigel

T. Miura, R. Tanaka (2009)

Mathematical Modelling of Natural Phenomena

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The circulatory system is one of the first to function during development. The earliest event in the system's development is , whereby vascular progeniter cells form clusters called blood islands, which later fuse to form capillary networks. There exists a very good system that mimics this process. When HUVECs (Human Umbilical Vein Endothelial Cells) are cultured on Matrigel, they spontaneously form a capillary network structure. Two theoretical models have been proposed to explain...