細胞是組成生命的最基本單位，細胞的運動對生物現象具有廣泛的影響，例如：組織的生長，傷口治癒，發炎反應，或是癌細胞的散佈和轉移等行為都受細胞運動的影響。而細胞的運動與外界環境的刺激有關，必須由受體與刺激物質結合，藉由激活多種傳遞訊息路徑，細胞才會有所反應。
本文建立一個包含細胞、化學趨向因子與細胞表面受體三者的完整數學模型，並採用有限差分法來離散方程式，以模擬軟骨細胞於博登量測器中的沉積、隨機漫步和對第二型膠原蛋白的化學趨向性等現象。藉由擬合實驗結果而求得各項影響軟骨細胞的運動係數，包含受體與膠原蛋白間的結合與解離速率、隨機漫步和化學趨向性係數，並做無因次參數分析，以了解各參數的物理意義及影響。從模擬結果發現，細胞的沉積過程大約需要三個小時，一些學者忽略了此現象，因此只考慮薄膜中的細胞行為是不合理的。本文建立的模型可完整描述博登量測器中，細胞沉積對量測細胞運動的影響，增加量測結果與測定細胞運動係數的準確性。

Cell is the most fundamental unit of life. Cell locomotion has extensive influences, including tissue development, wound healing, and inflammation, as well as tumor cell dissemination and metastasis. Cellular interactions with the extracellular stimuli are regulated by cell surface receptors which mediate a range of different signal paths.
This work develops a full mathematical model including cell, chemoattractant, and receptors on the cell surface, simulating the phenomenon incorporating cell sedimentation, random walks, and chemotaxis of chondrocytes to type II collage in the Boyden chamber assay, which is calculated using the finite difference method. By fitting the experimental data, we determine the cell random motility, chemotactic coefficient, and the rates for the processes of association and dissociation of the receptor-chemical complex. In order to understand the physical meaning and influence of each parameter, we use the dimensionless parameters analysis. Simulation results show the cell sedimentation lasts about three hours, so it is not reasonable to ignore this event. The current model can describe the full processes of cell transport in a Boyden chamber assay, and therefore increases the measuring accuracy for quantifying cell locomotion coefficients.

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