微血管是人體內物質交換場所，透過微血管運輸血液、氧氣及養份供給身體器官與組織，代謝出體內有害物質，若可以在了解微血管的形成，對於疾病治療與防止人造器官與組織壞死有很大的幫助。 本文建立數學模型分析體外培養內皮細胞，細胞自發性移動而形成微血管的網狀結構，將影響微血管網狀分佈的因素加入模型中，此數學模型考慮阿米巴型細胞密度、間質型細胞密度、旁泌性血管內皮生長因子濃度、基質密度及基質位移。模型假設阿米巴型細胞與間質型細胞在基質上的因貼附力的不同，所以有不同的遷徙行為，血管內皮生長因子為旁泌性包含在生物膠內，並會釋出與細胞外基質結合，細胞移動受到基質趨觸性及血管內皮生長因子趨化性的的影響與基質受到細胞牽引力的位移等作用，使得細胞逐漸移動而構成網狀微血管。為了分辨及解析微血管網狀結構的形成因素，本文分別建立僅有趨化性影響細胞移動的化學模型，基質趨觸性影響細胞移動的力學模型，與趨化性、趨觸性皆影響細胞移動的化學力學模型。再藉由線性穩定性分析方式探討不同模型及參數對於網狀形態產生的影響，並將參數分類為穩定和不穩定參數，調控參數探討細胞聚落分佈型態的力學機制。 ;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.
