注流式生物反應器系統的發展是為了改善體外培養時質量傳輸到三維組織工程支架的問題。除了促進養分和代謝產物的交換外，此系統同時提供了種植在支架內的細胞流體剪應力的作用。本文建立注流式系統的數學模型來說明並預測軟骨細胞在多孔性聚合物支架的增生和移動，以及養分消耗和新陳代謝產物生成的行為。包含了改良的Contois細胞生長模型，其中養分的飽和、代謝產物抑制描述了細胞在支架上的增生。並利用靜態培養時支架四周養分充足的極端例子，來瞭解養分和代謝產物的質量傳輸對系統的影響。結果顯示靜態培養模擬和實驗比較可以證實養分和代謝產物僅依靠擴散作用來傳輸的話，細胞必然會集中增生於支架外圍處。而在有注流影響下所得到的細胞平均總量會比靜態培養來的多，在空間的分布也較為均勻，且隨著對流速度的增加而更明顯，但最後會趨向一漸進值。在流量0.0024 cm^3/s的條件下，支架處的平均流體剪應力約為0.06 mPa (6e-4 dyne/cm^2)，和文獻的結果相比是類似的。細胞具有的隨機漫步行為會影響細胞在培養時的數量上的多寡，且隨著隨機漫步速度增加則細胞分布的更加均勻，而其他物理參數的定性分析，以及細胞初始不均勻種植和改變管徑大小對於注流系統的影響也會在文中加以討論。

Perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional tissue-engineered scaffolds cultured in vitro. In addition to enhancing the exchange of nutrients depletion and product accumulation, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. In this work, a computational model explaining, as well as predicting, cell proliferation and random walk within the porous scaffold, nutrients consumption and product accumulation, is developed. It incorporates a modified Contois cell-growth model that includes the effects of nutrient saturation, competitive product inhibition to describe the scaffold–cell system. To assess the extent to which mass transfer can be influenced theoretically, extreme cases were distinguished in which the culture medium was assumed fully sufficient in static culture. A comparison between predictions and experimental evidence found in the literature shows that cell-scaffold constructs that rely solely on diffusion for supply of nutrients will inevitably produce proliferation-dominated regions near the outer edge of the scaffold. When the cells are cultured in a scaffold subjected to a perfused velocity field, they penetrate to a greater extent into the scaffold core and give uniform spatial distribution. The amount of cells in the perfusion culture is more than in static culture, and increases with the velocity of perfusion, and it will tend to a constant as the perfusion is intensified. Relating the simulation results to perfusion experiments, an average surface shear stress of 0.06 mPa (6e-4 dyne/cm^2) was found at a flow rate of 0.0024 cm^3/s, and which is similar with other studies. We find the properties of random walks will influence the growth of cells, and it may let cell distribute uniformly when the random walk velocity increases. A parametric analysis is performed and the result is compared qualitatively with previous findings in the literature. Additional cases, where cell nonuniform-seeding and the change of tube diameter can be influential for a perfusion bioreactor system, are also studied.

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