**1. Introduction**

Thanks to the accurate description of changes in material mechanics, finite element method has been widely used in the field of bioengineering to study cellular tissue related problems such as neurulation and epithelial mechanics [1, 2]. However, majority of current finite element models are only restricted on tissues undergoing changes of shapes and displacements at small scale. In addition, during the simulation, the cellular tissue is required to be remained as one integrity. These limitations restrict the traditional finite element method to be applied to study the essential physiological processes such as morphogenesis, tissue regeneration, tumor metastasis, and cancer invasion, where cells often migrate collectively as large coherent strands or tubes. Such large scale of collective cell movement is recognized as the hallmark of tissue-remodeling events. During the past decade, to overcome the limitation of traditional finite element method, dynamic finite element method such as PFEM has been developed to extend the traditional FEM to study mechanics of materials with more flexibility or undergoing larger scale of motility. The object domain (either fluid or solid) is represented as nodes tessellated by triangular mesh. The mathematical equations governing the physical rules of the mechanical property of the discretized domain defined by the mesh connecting nodes are subsequentially solved in the standard FEM. Under the analysis using dynamic finite element method, the motion of sub-domain of the object can freely move and even separate from the main domain [3]. The advancement of dynamic finite element in achieving both accurate description of material mechanics and large scale of geometric and topological changes makes it suitable to simulate the physiological processes such as wound healing and cancer invasion. During these physiological processes, cells move in collective fashion and respond with chemical and mechanical signals through cell–cell junctions and interactions between cells and their micro-environment.

In this chapter, we introduced our newly developed dynamic finite element cellular model and its application to study the influence of cell-substrate mechanics and intercellular adhesions on collective cell migration. Our model represents each cell as a mesh of triangular elements at sub-cellular level [4]. Each triangular element exhibits viscoelastic characteristic using a Maxwellian model [5]. The effects of line tension forces along the cell boundary according to the local curvature is incorporated [6]. The intercellular adhesions are modeled as elastic springs at sub-cellular scale [7]. In addition, a mechano-chemical feedback pathway including focal adhesion, proteins of Paxillin, Rac, PAK, and Merlin, which are all responsible for cell protrusion [8] is embedded in individual cell. This pathway is collaborated with another mechano-chemical pathway, which is responsible for transmitting mechanical cue through intercellular adhesions [9]. Our model is used to study collective cell migration using a simplified wound tissue. We then compare our simulation results to an *in vitro* study [10]. Finally, we discussed and made the conclusion that the mechanics between cell-substrate play a crucial role in guiding highly efficient collective cell migration. This guidance cue is well maintained and transmitted between cells through the intercellular adhesions.
