本文多孔性介質的概念並加入細胞化學趨向與隨機漫步的特性來建立一數學模型，包含了連續方程式、動量守恆方程式、細胞質量守恆方程式以及養份濃度守恆方程式來描述細胞在多孔性支架中的培養情況，並分為靜置式培養模擬與注流式培養模擬。其中靜置式培養是模擬傳統培養皿的培養環境，並與之前學者的實驗數據做比對來驗證數學模型的正確性。注流式培養是模擬支架置於注流式生物反應器中，以注流的方式將培養細胞時所需的養分利用對流的特性帶入支架中，彌補傳統養分擴散的缺點，並以其為模擬系統使得模擬的結果可以定性的描述整個物理現象、建立預測並提供實際培養時的參考。在模擬中顯示，細胞在有注流影響下所得到的平均總量會比靜置式培養來的多，且隨著對流速度的增加而更明顯但最後會趨向一漸進值。細胞所具有的化學趨向移動行為與隨機漫步運動均會影響細胞在培養時的數量上的多寡，且隨著流場注流效果的增加而產生不同的物理現象。 This article uses a porous-medium approach, combining chemotaxis and random walk of the cells, to develop a mathematical model, which comprises the continuity equation, momentum equation, cell conservation equation and nutrient conservation equation to describe the growth of chondrocytes in porous scaffolds. Two cases of simulation are performed: static culture and perfusion culture. We use the results of the simulation of the static culture to compare with the experimental studies reported previously. In the perfusion flow case, we simulate the cell growth in a perfusion bioreactor. The results can qualitatively describe the physical phenomena, set up the prediction and offer the actual cultivated reference. The amount of cells in the perfusion culture is more than in static culture and increase with the velocity of perfusion, and it will tend to a constant as the perfusion is intensified. We find the properties of chemotaxis and random walk will influence the growth of cells, and they may reveal different effects when the perfusing is getting stronger.
