A structural stiffness matrix-based computational mechanics method of epithelial monolayers

Abstract

Epithelial monolayers are the simplest tissues in multicellular organisms, yet they play a vital role in many physiological processes, including development, growth, and wound healing. During these processes, the epithelia are usually subjected to mechanical cues, and involve multiple scales acting at molecular, cellular, and tissue levels. Computational techniques provide a useful and convenient means to investigate biological and mechanical behaviors of cell monolayers. Here, we propose a structural stiffness matrix-based computational method that can accurately and rapidly evaluate the mechanical properties of cell monolayers. By harmoniously calculating spatial movements of cellular positions and changes in cellular shapes over time, the present method holds higher computational efficiency than orthodox vertex model, especially the time ratio of these two methods exceeds an order of magnitude for large-scale cell monolayers. Furthermore, the structural features of cells, neglected in other methods, can be naturally integrated in the present approach. Then, this method is employed to examine the effects of cell division direction and molecular and cellular level changes on mechanical behaviors of cell monolayers. Our predictions are in good agreement with a broad range of experiments. The proposed method with high accuracy and efficacy holds great promise for application in simulating large-scale biological tissues.