本文建立軟骨細胞在多孔性聚合物支架的增殖與遷移以及養份消耗的數學模型。為了驗證所建立的數學模型的可靠度，我們先與之前學者的實驗數據做比對。然後對於四個種植位置探討，因為細胞的遷移影響，細胞體積分率及養分濃度的改變。模擬培養40天後結果發現，四個種植位置的細胞體積分率的相對大小，會隨著時間增加而改變。軟骨細胞會受到化學趨向性的遷移和隨機漫步的移動的增加會讓細胞的生長速率增加，但細胞對養份的消耗量增加，則會降低細胞的生長速率，物理參數的執行分析和結果定性的比較討論都在論文中說明。 A mathematical model describing chondrocyte proliferation and migration, and nutrient consumption is developed to analyze the behavior of cell growth in a polymer scaffold. In order to check the validity of the mathematical model, the result of simulation is compared to the previous experiment in the literature. Then we probe for four different seeding positions the influence of the migration of cells on the volume fractional variation of cells and nutrient concentration. During the 40 days of simulated cultivation, the relative magnitudes of volume fraction of cells change with time. The proliferous rate of cells increases with increasing the chemotactic and random walk intensity, but decreases with the consumption rate of nutrient. A parametric analysis is performed and the result is compared qualitatively with previous findings in the literature.
