單層細胞片（monolayer cell sheet）相較於多層細胞片（multilayer cell sheet）在實驗上有著易於控制和觀測的優點。有別於多層細胞片，單層細胞片的細胞和基質間的後曳力（drag force）主宰了系統中的耗散機制，且系統中單位面積的細胞數可隨著擾動漲落。本論文建構了一理論模型以描述由不自行爬行且平行於邊界排列的紡錘狀細胞所組成的單層細胞片之動力學。我們的模型預測了在微小的擾動之下，細胞排列方向固定的單層細胞片總是穩定的。然而，當單層細胞片中之細胞排列方向隨著微擾擺動時，系統在長波長微擾下不穩定。增加細胞之活性收縮力或減少細胞片之寬度皆會使得系統回復至穩態的速率下降，並使得細胞排列方向不固定之系統更加不穩定。;In vitro, monolayer cell sheets are easy to be controlled and observed in comparison to multilayered cell sheets. Different from multilayered systems, cell-substrate drag in a monolayer cell sheet dominates and the number of cells per unit area fluctuates under perturbations. In this {\it thesis}, we construct a theoretical model to describe the dynamics of monolayer cell sheets with spindle-shaped non-motile cells aligned parallel to the boundaries. Our model predicts that monolayer cell sheets with fixed orientation are always stable under small perturbations, while those with fluctuating cell orientations are not stable in the long-wavelength limit. Increasing active contractility or decreasing sheet width decreases the relaxation rate of the system, and increases the range of the unstable region in the cases with fluctuating cell orientation.
