組織工程是利用細胞、支架以及訊息因子等三大要素進行組織修補，達到組織修復的目的。組織工程體外培養細胞，研究細胞新陳代謝，進而影響細胞在支架內生長情況，探討細胞增殖、隨機漫步、碰撞、接觸抑制等微觀行為。
本研究以數學模型模擬軟骨細胞在支架培養情況，探討葡萄糖、氧氣與乳酸濃度，以及酸鹼值對細胞代謝速率的影響。結果顯示在高葡萄糖濃度下，細胞代謝葡萄糖而生成乳酸，致使培養環境酸度增加，減緩細胞代謝速率，減低細胞對葡萄糖及氧氣的攝取。由於氧氣可獲得補充，使得在高酸的環境中，支架內氧氣濃度產生不減反增的情況。在低葡萄糖濃度條件，氧氣濃度不減反增情況則不明顯。以上結果可提供軟骨細胞體外培養代謝資訊，了解細胞培養對於養分消耗、乳酸分泌以及環境酸鹼值變化等作用的交互影響。
本論文亦結合連續體養分擴散方程式及離散體格狀自動機模型，建立靜態培養細胞生長模型，模擬細胞增殖、隨機漫步、碰撞、接觸抑制等微觀行為，以探討細胞移動與種殖模式對細胞生長的影響。細胞在支架內的移動速度會影響到整體細胞生長，在細胞培養初期，不移動細胞增殖速率較緩慢，增高細胞移動速率，會得到較高細胞體積分率。到培養後期，不移動細胞形成群落，養分擴散到支架內部，使細胞得到較高的體積分率，但是，高移動速度細胞因養分傳輸的阻礙，細胞增殖受到限制。在不同持續移動時間，細胞持續移動時間愈長，細胞碰撞與接觸抑制機率較高，細胞體積分率會降低。在不同初始種殖模式下，以中間種殖模式，因支架周圍較少細胞，使養分得以擴散至內部，最終可得到最高的細胞體積分率。本研究期望能將單一細胞在微觀上的行為詳實描述，提供組織工程體外培養上有用的模擬數據，並應用在實際細胞培養系統上，來改進細胞培養技術。

Tissue engineering integrates biomedicine and engineering by introducing engineering analysis into biomedical research in order to develop artificial tissue substitutes with complete biological functions. These tissue substitutes can be used to repair, maintain, or improve human tissues and organs. This study presents a mathematical model for simulating cartilaginous culture of chondrocytes seeded in scaffolds and investigating the effects of cell density, glucose, oxygen, lactate concentration, and pH value on cell metabolic rates. Results show that under high glucose concentration (HG) condition, cells are able to metabolize effectively and form large amounts of lactate, increasing acidity in the environment. This increased acidity reversely causes cell metabolic rate to decrease and consequently lower oxygen and glucose uptake. Since oxygen can be replenished through the free surface of the culture medium, oxygen concentration within the scaffold increases rather than decreases over time in acidic environment. In low glucose concentration (LG) conditions, however, oxygen concentration monotonically decreases with culture time. From the simulation results, additional information regarding in vitro culture of chondrocytes can be obtained. The correlations between nutrient consumption, lactate secretion and pH changes during cell culture are also understood. The nutrient metabolic model is then incorporates into a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell-construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by nutrients concentration are studied. Using this model, this study investigates the influence of cell migration speed on the overall cell growth within the cellular scaffolds. It is found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, increasing cell motility may lead to reduced cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Under different cell persistence time conditions, increasing the persistence time, cell collision and contact inhibition are increased, but the cell amount is decreased. This paper also compares cell growth in scaffolds with various seeding modes, and proposes a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount for tissue engineering construct developments. Mathematical models help interpret experimental results and may serve as a reference for in vitro cell culture research of tissue engineering.

Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD2. 1989. Molecular biology of the cell. Garland Publishing, New York.
Baek CH, Ko YJ. 2006. Characteristics of tissue-engineered cartilage on macroporous biodegradable PLGA scaffold. The Laryngoscope 116: 1829-1834.
Bailey JE, Ollis DF. 1986. Biochemical engineering fundamentals 2nd ed. McGraw-Hill, New York.
Bell E, Ivarsson B, Merrill C. 1979. Production of a tissue-like structure by contraction of collagen lattices by human fibroblasts of different proliferative potential in vitro. Proceeding of the National Academy of Sciences of the USA 76: 1274-1278.
Bibby SRS, Jones DA, Ripley RM, Urban JPG. 2005. Metabolism of the intervertebral disc: Effects of low levels of oxygen, glucose, and pH on rates of energy metabolism of bovine nucleus pulposus cells. Spine 30: 487-496.
Bird GA. 1994. Appendix C: Sampling from a prescribed distribution. In: Molecular dynamics and the direct simulation of gas flows. Pergamon, Oxford, pp. 423-428.
Boyce ST. 2004. Fabrication, quality assurance, and assessment of cultured skin substitutes for treatment of skin wounds. Biochemical Engineering Journal 20: 107-112.
Burstein D, Gray ML, Hartman, AL, Gipe R, Foy BD. 1993. Diffusion of small solutes in cartilage as measured by nuclear magnetic resonance spectroscopy and imaging. Journal of Orthopaedic Research 11: 465-478.
Chang C, Lauffenburger DA, Morales TI. 2003. Motile chondrocytes from newborn calf: migration properties and synthesis of collagen II. Osteoarthritis and Cartilage 11: 603-612.
Cheng G, Youssef BB, Markenscoff P, Zygourakis K. 2006. Cell population dynamics modulate the rates of tissue growth processes. Biophysical Journal 90: 713-724.
Cheng G, Markenscoff P, Zygourakis K. 2009. A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics. Biophysical Journal 97: 401-414.
Chung CA, Yang CW, Chen CW. 2006. Analysis of Cell Growth and Diffusion in a Scaffold for Cartilage Tissue Engineering. Biotechnology and Bioengineering 94: 1138-1146.
Chung CA, Chen CW, Chen CP, Tseng CS. 2007. Enhancement of Cell Growth in Tissue-Engineering Constructs Under Direct Perfusion: Modeling and Simulation. Biotechnology and Bioengineering 97: 1603-1616.
Chung CA, Chen CP, Lin TH, Tseng CS. 2008. A compact computational model for cell construct development in perfusion culture. Biotechnology and Bioengineering 99: 1535-1541.
Chung CA, Ho SY. 2010. Analysis of collagen and glucose modulated cell growth within tissue engineered scaffolds. Annals of biomedical engineering 38: 1655-1663.
Dover R, Potten CS. 1988. Heterogeneity and cell cycle analysis from time-lapse studies of human keratinocytes in vitro. Journal of Cell Science 89: 359-364.
Fuchs E and Segre JA. 2000. Stem cells: a new lease on life. Cell 100: 143-155.
Freed LE, Marquis JC, Vunjak-Novakovic G, Emmanual J, Langer R. 1994a. Composition of cell-polymer cartilage implants. Biotechnology and Bioengineering 43: 605-614.
Freed LE, Vunjak-Novakovic G, Marquis JC, Langer R. 1994b. Kinetics of chondrocyte growth in cell-polymer implants. Biotechnology and Bioengineering 43: 597-604.
Galban CJ, Locke BR. 1999a. Analysis of cell growth kinetic and substrate diffusion in a polymer scaffold. Biotechnology and Bioengineering 65: 121-132.
Galban CJ, Locke BR. 1999b. 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: 633-643.
Griffith LG, Naughton G. 2002. Tissue engineering: Current challenges and expanding opportunities. Science 295: 1009-1014.
Gu W, Yao H, Vega A, Flagler D. 2004. Diffusivity of Ions in agarose gels and intervertebral disc: Effect of porosity. Annals of biomedical engineering 32: 1710-1717.
Haselgrove JC, Shapiro IM, Silverton SF. 1993. Computer modeling of the oxygen supply and demand of cells of the avian growth cartilage. American Journal of Physiology. Cell Physiology 256: C497-C506.
Holm S, Maroudas A, Urban JPG, Selstam G, Nachemson A. 1981. Nutrition of the intervertebral disc: Solute transport and metabolism. Connective Tissue Research 8: 101-119.
Horner HA, Urban JPG. 2001. Effect of nutrient supply on the viability of cells from the nucleus pulposus of the intervertebral disc. Spine 26: 2543-2549.
Hunziker EB. 2001. Articular cartilage repair: Basic science and clinical progress. A review of the current status and prospects. Osteoarthritis and Cartilage 10: 432-463.
Ishaug-Riley SL, Okun LE, Prado G, Applegate MA, Ratcliffec A. 1999. Human articular chondrocyte adhesion and proliferation on synthetic biodegradable polymer films. Biomaterials 20: 2245-2256.
Ishihara H, Urban JPG. 1999. Effects of low oxygen concentrations and metabolic inhibitors on proteoglycan and protein synthesis rates in the intervertebral disc. Journal of Orthopaedic Research 17: 829-835.
Jain RA. 2000. The manufacturing techniques of various drug loaded biodegradable poly(lactide-co-glycolide) (PLGA) devices. Biomaterials 21: 2475-2490.
Karp JM, Shoichet MS, Davies JE. 2003. Bone formation on two-dimensional poly (DL-lactide-co-glycolide) (PLGA) films and three-dimensional PLGA tissue engineering scaffolds in vitro. Journal of Biomedical Materials Research Part A 64A: 388-396.
Kino-oka M, Maeda Y, Yamamoto T, Sugawra K, Taya M. 2005. A kinetic modeling of chondrocyte culture for manufacture of tissue-engineered cartilage. Journal of Bioscience and Bioengineering 99: 197-207.
Kleis SJ, Schreck S, Nerem RM. 1990. A viscous pump bioreactor. Biotechnology and Bioengineering 36: 771-777.
Koch RJ, Gorti GK. 2002. Tissue engineering with chondrocytes. Facial Plastic Surgery 18: 59-68.
Kremer M, Lanf E, Berger AC. 2000. Evaluation of dermal-epidermal skin equivalents (‘composite-skin’) of human keratinocytes in a collagen-glycosaminoglycan matrix (IntegraTM Artificial Skin). British journal of plastic surgery 53: 459-465.
Lackie JM. 1986. Cell movement and cell behaviour. Allen and Unwin, London, UK.
Langer R, Vacanti JP. 1993. Tissue engineering. Science 260: 920-926.
Lanza R, Langer R, Vacanti J. 2007. Principles of tissue engineering 3rd ed. Academic Press.
Lerou PH, Daley GQ. 2005. Therapeutic potential of embryonic stem cells. Blood Reviews 19: 321-331.
Lee RB, Urban JPG. 1997. Evidence for a negative Pasteur effect in articular cartilage. Biochemical Journal 321: 95-102.
Lee RB, Urban JPG. 2002. Functional replacement of oxygen by other oxidants in articular cartilage. Arthritis & Rheumatism 46: 3190-3200.
Lee Y, Mclntire LV, Zygourakis K. 1994. Analysis of endothelial cell locomotiom: Differential effects of motility and contact inhibition. Biotechnology and Bioengineering. 43: 622-634.
Lee Y, S. Kouvroukoglou, Mclntire LV, Zygourakis K. 1995. A cellular automaton model for the proliferation of migrating contact-inhibited cells. Biophysical Journal 69: 1284-1298.
Luu YK, Capilla E, Rosen CJ, Gilsanz V, Pessin JE, Judex S, Rubin CT. 2009. Mechanical stimulation of mesenchymal stem cell proliferation and differentiation promotes osteogenesis while preventing dietary-induced obesity. Journal of Bone and Mineral Research 24: 50-61.
Lysaght MJ, Hazlehurst AL. 2004. Tissue engineering: the end of beginning. Tissue Engineering 10: 309-317.
Mader SS, Galliart PL. 2000. Understanding human anatomy & physiology 4th ed. McGraw-Hill, New York.
Mahmoudifar N, Doran PM. 2005. Tissue engineering of human cartilage in bioreactors using single and composite cell-seeded scaffolds. Biotechnology and Bioengineering 91: 338-355.
Malda J, Rouwkema J, Martens DE, Le Comte EP, Kooy FK, Tramper J, van Blitterswijk CA, Riesle J. 2004. Oxygen gradients in tissue-engineered PEGT/PBT cartilaginous constructs: Measurement and modeling. Biotechnology and Bioengineering 86: 9-18.
Malda J, Woodfield TBF, van der Vloodt F, Wilson C, Martens DE, Tramper J, van Blitterswijk CA, Riesle J. 2005. The effect of PEGT/PBT scaffold architecture on the composition of tissue engineered cartilage. Biomaterials 26: 63-72.
Marcus RE. 1973. The effect of low oxygen concentration on growth, glycolysis, and sulfate incorporation by articular chondrocytes in monolayer culture. Arthritis & Rheumatism 16: 646-656.
Martin I, Obradovic B, Freed LE, Vunjak-Novakovic G. 1999. Method for quantitative analysis of glycosaminoglycan distribution in cultured natural and engineered cartilage. Annals of Biomedical Engineering 27: 656-662.
Martin I, Wendt D, Heberer M. 2004. The role of bioreactors in tissue engineering. Trends in Biotechnology 22: 80-86.
Metcalfe DA, Ferguson MWJ. 2007. Tissue engineering of replacement skin: the crossroads of biomaterials, wound healing, embryonic development, stem cells and regeneration. Journal of the Royal Society Interface 4: 413-437.
Moutos FT, Freed LE, Guilak F. 2007. A biomimetic three-dimensional woven composite scaffold for functional tissue engineering of cartilage. Nature Materials 6: 162-167.
Nesic D, Whiteside R, Brittberg M, Wendt D, Martin I, Mainil-Varlet P. 2006. Cartilage tissue engineering for degenerative joint disease. Advanced Drug Delivery Reviews 58: 300-322.
Nimer E, Schneiderman R, Maroudas A. 2003. Diffusion and partition of solutes in cartilage under static load. Biophysical Chemistry 106: 125-146.
Obradovic B, Freed LE, Langer R, Vunjak-Novakovic G. 1997. Bioreactor studies of natural and engineered cartilage metabolism. Proceedings of the Topical Conference on Biomaterials, Carriers for Drug Delivery, and Scaffolds for Tissue Engineering. New York: AIChE, pp. 335-337.
Obradovic B, Carrier RL, Vunjak-Novakovic G, Freed LE. 1999. Gas exchange is essential for bioreactor cultivation of tissue engineered cartilage. Biotechnology and Bioengineering 63: 197-205.
Obradovic B, Meldon JH, Freed LE, Vunjak-Novakovic G. 2000. Glycosaminoglycan deposition in engineered cartilage: Experiments and mathematical model. AIChE Journal 46:1860-1871.
Pamela KL, Cynthia CN. 2001. Joint structure and function: A comprehensive analysis 3rd ed. FA Davis Company, Philadelphia.
Pazzano D, Mercier KA, Moran JM, Fong SS, DiBiasio DD, Rulfs JX, Kohles SS, Bonassar LJ. 2000. Comparison of chondrogensis in static and perfused bioreactor culture. Biotechnology Progress 16: 893-896, 2000.
Pittenger MF, Mackay AM, Beck SC, Jaiswal RK, Douglas R, Mosca JD, Moorman MA, Simonetti DW, Craig S, Marshak DR. 1999. Multilineage potential of adult human mesenchymal stem cells. Science 284: 143-147.
Ratna D, Karger-Kocsis J. 2008. Recent advances in shape memory polymers and composites: a review. Journal of Materials Science 43: 254-269.
Razaq S, Wilkins RJ, Urban JPG. 2003. The effect of extracellular pH on matrix turnover by cells of the bovine nucleus pulposus. European Spine Journal 12: 341-349.
Reggia JA, Chou HH, Lohn JD. 1998. Cellular automata models of self-replicating systems. Advances in Computers 47: 141-183.
Richardson RS. 2003. Oxygen transport and utilization: An integration of the muscle system. Advances in Physiology Education 27: 183-191.
Schwartz ER, Kirkpatrick PR, Thompson RC. 1976. The effect of environmental pH on glycosaminoglycan metabolism by normal human chondrocytes. The Journal of Laboratory and Clinical Medicine 87: 198-205.
Schulz RM, Bader A. 2007. Cartilage tissue engineering and bioreactor systems for the cultivation and stimulation of chondrocytes. European Biophysics Journal 36: 539-568.
Seitz H, Rieder W, Irsen S, Leukers B, Tille C. 2005. Three-dimensional printing of porous ceramic scaffolds for bone tissue engineering. Journal of Biomedical Materials Research Part B: Applied Biomaterials 74: 782-788.
Sengers BG, Heywood HK, Lee DA, Oomens CWJ, Bader DL. 2005. Nutrient utilization by bovine articular chondrocytes: A combined experimental and theoretical approach. Journal of Biomechanical Engineering 127: 758-766.
Singh H, Hutmacher DW. 2009. Bioreactor studies and computational fluid dynamics. Bioreactor Systems for Tissue Engineering 112: 231-249.
Soukane DM, Shirazi-Adl A, Urban JPG. 2007. Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc. Journal of Biomechanics 40: 2645-2654.
Tannehill JC, Anderson DA, Pletcher RH. 1997. Computational fluid mechanics and heat transfer 2nd ed. Taylor & Francis, Philadelphia.
Tharakan JP, Chau PC. 1986. A radial flow hollow fiber bioreactor for the large-scale culture of mammalian cells. Biotechnology and Bioengineering 28: 329-342.
Torzilli PA, Askari E, Jenkins JT. 1990. Water content and solute diffusion properties in articular cartilage. In: Biomechanics of Diarthrodial Joints. Springer, New York, pp. 363-390.
Vacanti CA, Langer R, Schloo B, Vacanti JP. 1991. Synthetic polymers seeded with chondrocytes provide a template for new cartilage formation. Plastic & Reconstructive Surgery 88: 753-759.
Vacanti JP, Morse MA, Saltzman WM, Domb AJ, Perez-Atayde A, Langer R. 1988. Selective cell transplantation using bioabsorbable artificial polymers as matrices. Journal of Pediatric Surgery 23: 3-9.
Venkatasubramanian R, Henson MA, Forbes NS. 2006. Incorporating energy metabolism into a growth model of multicellular tumor spheroids. Journal of Theoretical Biology 242: 449-453.
Wang D, Park JS, Chu JSF, Krakowski A, Luo K, Chen DJ, Li S. 2004. Proteomic profiling of bone marrow mesenchymal stem cells upon transforming growth factor β1 stimulation. The Journal of Biological Chemistry 279: 43725-43734.
Windhaber RAJ, Wilkins RJ. 2003. Functional characterisation of glucose transport in bovine articular chondrocytes. Pflügers Archiv European Journal of Physiology 446: 572-577.
Wu L, Jing D, Ding J. 2006. A “room-temperature” injection molding/particulate leaching approach for fabrication of biodegradable three-dimensional porous scaffolds. Biomaterials 27: 185-191.
Wu MH, Urban JPG, Cui ZF, Cui Z, Xu X. 2007. Effect of Extracellular pH on Matrix Synthesis by Chondrocytes in 3D Agarose Gel. Biotechnology Progress 23: 430-434.
Yashiki S, Hara Y, Kino-oka M, Taya M. 2004. A three-dimensional growth model for chondrocytes embedded in collagen gel. Kagaku Kogaku Ronbunshu 30: 515-521.
Zhang WJ, Liu W, Cao Y. 2007. Tissue engineering of blood vessel. Journal of Cellular and Molecular Medicine 11: 945-957.
Zhou S, Cui Z, Urban JPG. 2004. Factors influencing the oxygen concentration gradient from the synovial surface of articular cartilage to the cartilage-bone interface: A modeling study. Arthritis & Rheumatism 50: 3915-3924.
Zhou S, Cui Z, Urban JPG. 2008. Nutrient gradients in engineered cartilage: Metabolic kinetics measurement and mass transfer modeling. Biotechnology and bioengineering 101: 408-421.
Zygourakis K, Bizios R, 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, Markenscoff P, Bizios R. 1991b. Proliferation of anchorage-dependent contact-inhibited cells. II: Experimental results and validation of the theoretical models. Biotechnology and Bioengineering 38: 471-479.
鄭佩綺，2010，全球再生醫學市場解析，工業技術研究產業經濟與趨勢研究中心。