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|Issue Date: ||2014-10-15 17:20:40 (UTC+8)|
;Capillary vessels function as an exchange network, which bring in oxygen and nutrients and take away the metabolites for the organs and tissues in the human body. Understanding the formation of capillary networks is helpful to the treatment of cancer and developing engineered tissues of large size.
This study developed a mathematical model for describing the plexus formation by endothelial cells cultivated in vitro. The model variables include the cell densities of the amoeboid-type angioblasts and the mesenchymal-type endothelial cells, the concentration of vascular endothelial growth factor (VEGF) embedded in and released from the substrate, and the substrate density and displacement. The amoeboid cells seeded onto the substrate gradually differentiate into the mesenchymal cells. These two cell types have different attachment behaviors to the substrate and migrate with different speeds. Due to the traction by the mesenchymal cells, the substrate is displaced and in turn drags the cells with it. The motion of the amoeboid cells is affected by the directed migration to the chemotaxis of VEGF. The mesenchymal cells migrate not only to the chemotaxis but also to the haptotaxis induced by the variation of the substrate density. The interactions of these factors ultimately determine the distribution of the cells. In order to carefully distinguish the effects of the possible factors, this study set up three models: the first called the chemical model considered only the chemotaxis and assumed a uniform substrate; the second termed the mechanical model consider only the interaction between the cells and the substarte displacement and assumed there was no VEGF being released from the substrate; and the final one referred to as the mechano-chemical model included both VEGF chemotaxis and heptotaxis between the cells and substrate. The model parameters were investigated by linear stability analysis. The mechanisms that underlie the plexus formation of the endothelial cells were explained via the parameter analysis.
|Appears in Collections:||[機械工程研究所] 博碩士論文|
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