體外培養內皮細胞形成微血管網絡結構，是組織工程領域中一項日趨重要的議題。經由先前學者的相關研究發現，已知促使內皮細胞聚集形成微血管之機制可能有二：其ㄧ為細胞與細胞外基質之間的受力平衡關係，其二則為在培養環境中血管內皮生長因子的濃度變化。本研究建立了同時包含此兩種機制之數學模型，在模型中以離散之細胞帕茲模型描述內皮細胞的個體遷移行為，而對於細胞外基質的變形以及血管內皮生長因子的濃度分布則以連續體模型進行定量分析。以此模型計算後得到之內皮細胞分布形態與實驗數據相符，證明內皮細胞形成微血管網絡結構之過程，確實為力學與化學機制共同作用下所產生的結果，並且藉由調整模型中之各項參數值進行數值模擬分析，推論得知此兩種機制於細胞、基質、以及血管內皮生長因子三者之間的交互作用關係為：內皮細胞之牽引力使基質材料產生密度變化後，將間接造成血管內皮生長因子在空間中的不均勻分布，其後內皮細胞將因趨觸性影響而於血管內皮生長因子之濃度較高處聚集，最終發展為穩定之微血管網絡結構。

How the endothelial cells forming capillary networks is an important issue that has not been completely addressed in tissue engineering. Studies have showed that there might be two mechanisms underlying the network patterning: the mechanical force balance between cells and extracellular matrix, and the chemical attraction by VEGF in the surroundings. This study proposes a mathematical model that considers both the mechanical and chemical mechanisms. The stochastic behavior of cell migration is described using the cellular Potts model, and the biogel and chemical attractant VEGF are treated as continua in modeling the biogel displacement and VEGF distribution. Results from the simulation agree well with previous experimental data, showing that endothelial cells can form capillary-like structures only when both the mechanical and chemical mechanisms work together. The interaction between cells, biogel and VEGF could also be inferenced from the parametric analysis. That is, once the cells impair the uniform distribution of biogel, the VEGF gradients form as well since VEGF is binding with biogel molecules, thus the endothelial cells migrate and gather via haptotaxis. Finally, the cells, biogel and bound VEGF will accumulate at some local locations and form the stable in vitro plexus.

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吳思穎，2012，體外培養內皮細胞形成毛細血管結構前期之穩定性分析及模擬，國立中央大學碩士論文。