組織工程的目的是能製造出具有完整功能性的組織，並且成功修復病患的受損組織。目前常見的治療方式是先在體外將細胞種殖在具有生物相容性的支架上，培養出一定數量的細胞之後再將支架殖入體內。組織工程是結合多種領域的綜合學門，而量化的數學模型可較充分的解釋實驗結果，並且歸納出影響系統的重要因子，預測出的模擬結果更有助於改善培養環境的設計。 本文針對靜態培養環境下，細胞在支架內的生長與活動進行研究，使用格狀自動機模擬細胞的活動行為，包括細胞增殖、隨機漫步、細胞聚合、接觸限制以及細胞活性抑制等現象，並且以有限差分法對養分的擴散-消耗方程式進行數值計算，將計算所得的養分濃度場導入細胞增殖的機制內，以產生對應於養分濃度的非同步細胞增殖行為。本研究發現在靜態培養且細胞均勻種殖的條件下會存在一個最佳的細胞移動速度，細胞移動的速度過快反而不利於細胞生長。並且在均勻種殖條件下的細胞生長已經趨緩之後，集中種植條件下的細胞還可繼續增殖。 本模型所使用的格狀自動機提供了非常具有彈性的方法來描述細胞生長的問題，可繼續擴展模型中的規則以探討更深入的細胞活動機制。而在集中種殖條件下配合極緩慢的細胞移動速度可得到更緊密的細胞分佈的概念也可用以改進細胞的種植及培養技術。 To manufacture functional tissues and repair damaged tissues in patients are the aims of the tissues engineering. The popular therapeutic strategy is implantation of generated tissues from in vitro cell-scaffold construction, and then implanted the scaffold into the patients. Tissues engineering is a discipline composed of many subjects, quantification by means of mathematical model can interpret experimental results and identify the dominating factors of the system. Furthermore, predictive modeling offers huge potential in the optimization of culture conditions. The literature studied the dynamic process of cells growth in the scaffold under static culture, used cellular automata to simulate cell proliferation, random walk, cell aggregation, contact inhibition, and inhibition of cell viability. Also using the finite difference method to solve diffusion-reaction equation of the nutrients can find the concentration field of nutrients in the scaffold, and then integrate it into cells dynamic process to form asynchronous cell proliferation. The research found there was the optimal cell migration speed with initial uniform seeding in static culture, and over-high migration speed was disadvantageous to cells growth, and cells in non-uniform seeding could proliferate for a long time as cells proliferation in uniform seeding slowed down. The model offered an alternative method to describe the cells growth process using cellular automata, and expanding the rules in the model to study other process of cells growth was possible. The concept of using slow migration speed in non-uniform seeding to form compact cell distribution may improve the design of cell seeding and culture.
