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.

Anderson TB, Jackson R. 1967. A fluid mechanical description of fluidized beds. Industrial & Engineering Chemistry Fundamentals , 6: 527–538.
Contois, D.E., 1959. Kinetics of bacterial growth: Relationship between population density and specific growth rate of continuous cultures. The Journal of General Microbiology , 21: 40-50.
Freed, L.E., Vunjak-Novakovic, G., Marquis, J.C., and Langer R. 1994. Kinetics of chondrocyte growth in cell-polymer implants. Biotechnology and Bioengineering, 43: 597-604
Galban, C.J., and Locke, B.R., 1997. Analysis of cell growth in a polymer scaffold using a moving boundary approach. Biotechnology and Bioengineering, 56(4): 422-432.
Galban, C.J., and Locke, B.R., 1999a. Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold. Biotechnology and Bioengineering, 64(6): 633-643.
Galban, C.J., and Locke, B.R., 1999b. Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold. Biotechnology and Bioengineering, 65(2): 121-132.
Goldstein, A.S., Juarez, T.M., Helmke, C.D., Gustin, M.C., and Mikos, A.G., 2001. Effect of convection on osteoblastic cell growth and function in biodegradable polymer foam scaffolds. Biomaterials, 22: 1279-1288
Hillesdon, A.J., Pedley, T.J., and Kessler, J.O., 1995. The development of concentration gradients in a suspension of chemotactic bacteria. Bulletin of Mathematical Biology, 57: 299–344.
Langer R.and Vacanti J. P., 1993, Tissue engineering, Science, 260: 920-926
Lind, M., Deleuran, B., Yssel, H., Eriksen, E.F., and Pedersen, K.T., 1995. IL-4 and IL-13, but Not IL-10, are chemotactic factors for human osteoblasts. Cytokine, 7(1): 78-82.
Lind, M., Eriksen, E.F., and Bunger, C., 1996. Bone morphogenetic protein-2 but not bone morphogenetic protein-4 and -6 stimulates chemotactic migration of human osteoblasts, human marrow osteoblasts, and U2-OS cells. Bone, 18(1): 53-57.
Martin I., Suetterlin R., Baschong W., Heberer M., Vunjak-Novakovic G., and Freed L. E. 2001. Enhanced cartilage tissue engineering by sequential exposure of chondrocytes to FGF-2 during 2D expansionand BMP-2 during 3D cultivation. Journal of Cellular Biochemistry, 83:121-128
Obradovic, B., Carrier, R.L., Vunjak-Novakovic, G., and Freed, L.E., 1999. Gas exchange is essential for bioreactor cultivation of tissue engineered cartilage. Biotechnology and Bioengineering, 63(2): 197-205.
Shina, H., Zygourakisb, K., Farach-Carsonc, M.C., Yaszemskid, M. J., Mikos, A. G., 2004. Attachment, proliferation, and migration of marrow stromal osteoblasts cultured on biomimetic hydrogels modified with an osteopontin-derived peptide. Biomaterial, 25: 895-906.
Shreiber, D.I., Barocas, V.H., and Tranquillo, R.T. 2003. Temporal variations in cell migration and traction during fibroblast-mediated gel compaction. Biophysical Journal, 84: 4102–4114.
Singhvi, R., Stephanopoulos, G., Wang, D. 1994. Review: Effects of substratum morphology on cell physiology. Biotechnology and Bioengineering, 43: 764–771.
Slattery JC. 1967. Flow of viscoelastic fluids through porous media.　 AICHE Journal, 13: 1066–1071.
Whitaker S. 1967. Diffusion and dispersion in porous media. AICHE Journal, 13: 420–427.
Zygourakis, K.,Bizios, R., and Markenscoff, P., 1991a. Proliferation of anchorage-dependent contact-inhibited cells: I. Development of theoretical models based on cellular automata. Biotechnology and Bioengineering, 38: 459-470.
Zygourakis, K.,Bizios, R., and Markenscoff, P., 1991b. Proliferation of anchorage-dependent contact-inhibited Cells: II. Experimental results and validation of the theoretical models. Biotechnology and Bioengineering, 38: 471-479.
楊婷琪，2002. 組織工程醫療應用與產品之發展. 工研院經資中心
張根源，2002. 組織工程技術與應用. 化工科技與商情，33: 27-31