人體內的各個器官以及組織都佈滿著許多的毛細血管，其為血液與周圍組織進行物質交換的場所，主要由一層內皮細胞所組成。人體必須透過毛細血管才有辦法對器官及組織供給氧氣以及營養物質，同時代謝對人體有害的產物，以維持器官及組織的功能。因此，為防止人造組織及器官壞死，必須培養出分佈完整的毛細血管網路。本文透過建立包含細胞密度、基質密度以及基質位移量的數學模型，模擬培養內皮細胞在纖維基質上形成毛細血管結構前期之分佈形態變化，描述細胞的遷徙特性以及基質受到細胞遷徙之牽引力而產生的位移。藉由線性穩定性分析的方式，本文討論系統參數的改變能夠促進或抑制細胞產生不均勻分佈的形態，據此將參數歸納為不穩定參數以及穩定參數，以作為執行非線性數值模擬前的初步分析。非線性計算結果顯示由於細胞與基質力交互作用的關係使細胞與基質分佈產生網狀結構，細胞分佈呈現數量較低的空隙，隨著時間的變化其空隙部分將擴大並與相鄰空隙進行合併。透過改變細胞種植的密度以及定義網狀結構指標，模擬結果顯示必須在適當的細胞數量下，細胞才能帶動基質產生網狀結構，符合文獻的實驗結果。Various organs and tissues of the human body are covered with capillaries, mainly composed of a layer of endothelial cells. The capillaries are where blood and surrounding tissues exchange materials. The human body relies on the capillaries to provide the organs and tissues with oxygen and nutrients; at the same time capillaries help remove the metabolic waste to maintain the tissue function. In order to prevent necrosis of tissues and organs, the whole network of the capillaries is essential to engineered tissues.By developing a mathematical model that includes cell density, gel density, and gel displacement, this study simulates the early stage behavior of vasculogenesis generated by the endothelial cells cultured on the fibrin gel. The model describes the cell migration characteristics and the gel displacement by the traction of the cells. A linear analysis is performed to check whether the system parameters will enhance or inhibit the cells to form a non-uniform distribution. By classifying the parameter as being stabiling and destabilizing, nonlinear stimulations are also carried out.Results from simulation show that due to the cell-gel interaction, the lacunae will appear over the cell population. As time goes by, the lacunae will expand and combine with other lacunaes in the surrounding. By testing the cell number density and defining the structure of network index, simulations show the gel’s network structure forms only for a adequate amount of cells.
