組織工程的目的為培養生物替代物來修復與改善人體組織與器官的缺陷。關節軟骨為結締組織的一種，由於軟骨缺乏血管與神經，因此受傷後，難以修補受傷的組織；另外細胞外基質包覆著軟骨細胞，所以健康的軟骨也不太能夠遷移至受損的區域進行修護。為了解決軟骨自我修復能力有限的缺點，因此組織工程希望能在體外培養出軟骨替代物。 本文模擬在靜態培養環境下，將軟骨細胞種植在不同厚度的支架上，培養30天，並且每3天更換一次培養液。考慮養分的擴散與消耗、細胞的隨機漫步特性、養份促進細胞的生長和膠原蛋白調控細胞的增殖，以及膠原蛋白的分泌與降解的現象，將這些現象以數學模型來表現，以探討養份對細胞生長的影響，以及膠原蛋白如何調控細胞的生長。模擬得到細胞密度與膠原蛋白含量與文獻的實驗結果一致。模擬結果發現，細胞分佈在第10天相當均勻，因為此時養份在支架的分佈也相當均勻，在第20天和第30天時，細胞在支架表面有較高的細胞密度，支架內部的細胞分佈主要受到氧氣的濃度的影響，而在支架的徑向表面，因為葡萄糖在此處的濃度較高，促使細胞在支架的徑向表面生長較佳。膠原蛋白隨著培養時間增加，其含量逐漸增加，膠原蛋白分佈與細胞分佈相似，因為膠原蛋白的分泌是受到細胞的影響。本研究也發現支架相對於培養液的厚度也影響靜態培養下細胞的生長對於養分的敏感度，種植在支架厚度較薄的細胞，細胞生長主要受到氧氣濃度的影響；而支架厚度較厚則是受到葡萄糖濃度的影響。 Tissue engineering is aimed to culture biological substitutes to repair and improve the damaged human tissue and organ. Articular cartilage is a connective tissue, which is difficult to repair after injury because the tissue lacks blood vessels and nerves. Even worse is that chondrocytes are embeded within the extracellular matrix, therefore healthy chondrocytes cannot migrate to the injury site for repair. In order to solve the limited capability of cartilage repair, tissue engineering hopes to develop cartilage substitutes in vitro. To help engineer cartilage implants, we simulate chondrocyte growth considering cells are seeded on the scaffolds of different thicknesses under static culture for 30 days, in which the medium is replaced every 3 days. We consider the phenomena of diffusion and consumption of nutrients, random walks of cells, nutrient-promoted cell growth, collagen-regulated cell proliferation, and collagen synthesis and degradation. We probe nutrient effects to cell growth, and how the collagen regulates cell growth. Results show the cell distribution is quite uniform at 10 days since the nutrient is still quite uniform in the scaffold at the moment. At 20 and 30 days, cells have higher density on the surface of the scaffold. Cell distribution within the scaffold is mainly influenced by oxygen concentration. Glucose is virtually relatively depleted but has higher concentration on the radial surface of the scaffold so that cell density is higher on the radial than on the horizontal surface. The synthesized collagen increases in amount with cultivation time. Collagen distributes similarly to cells because it is secreted by cells. Results also show that cell growth is more sensitive to oxygen variation for thinner scaffolds; on the contrary, to glucose for thicker scaffolds.