# Finite Element Modeling of Cells Adhering to a Substrate: An Overview
## 1 Introduction
### Finite Element Modeling (FEM)  
Computational models became increasingly valuable in supplementing experimental observations to better understand the mechanisms underlying collective cell migration. Cell models were developed in order to investigate mechanical interactions between cells and the ECM. Among computational approaches, finite element modeling (FEM) [54; 55; 56; 57; 58] represents a very effective tool for mimicking cell behavior in adhesion. FEM provides researchers with useful techniques, instruments, and modeling options that allow them to address crucial issues, such as stiffness differentiation within cellular components, prestressed auto-supporting architecture, and rearranging the cytoskeletal load-bearing structure [59]. FEM-based approaches including lattice spring modeling were adopted to simulate cells adhering to a substrate and subjected to nanoindentation measurements [60]. High-fidelity computational models can be developed by embedding in the FEM framework strategies that (i) divide cells into regions with assigned specific constitutive behaviors, (ii) subdivide numerical analysis into consecutive steps where material properties and loading conditions are updated as analysis proceeds, thus accounting for intrinsic changes in adhering cell behavior, and (iii) adopt predefined fields by assigning pre-existing tensional and deformation states to cell domain. The strong multidisciplinary character of FEM is the pivotal aspect characterizing the development of these techniques over the years. The broad range of applications has led finite element software to be equipped with numerous algorithms and simulation techniques suited for the various fields (i.e., structural, thermal, fluid dynamic, electromagnetic, chemical, and diffusive aspects). This peculiarity is very useful in the investigation of complex systems, like cells, as it provides analysts with several routines derived from many scientific fields for simulating cellular behavior. Indeed, the study of cellular adhesion phenomena encompasses several aspects ranging from materials science and mechanics to fluid mechanics, passing through signal transmission via cellular pathways. General-purpose finite element codes (i.e., ABAQUS, ANSYS, ADINA, COMSOL) include user-friendly interfaces to integrate modules with analysis procedures and routines for modeling the cell and its environment. This multidisciplinary approach to modeling may result in a fruitful interaction among research profiles with different backgrounds. In this sense, researchers with expertise in physics and engineering may share information with biochemists, biotechnology, and physicians to obtain a comprehensive perspective of the cell-substrate system. Therefore, the integrated approach offered by finite element software may result in an enhanced predictive ability of the cell model. Moreover, FE numerical solutions allow us to overcome difficulties in defining a closed-form analytical formulation that takes into account the complex multi-physical character of cellular behavior. The finite element method is also able to handle geometrical and material nonlinearity, which inherently characterize cell-substrate interaction, by resorting to the implicit and explicit formulation to limit convergence problems due to the nonlinear behavior of the analyzed system. Furthermore, large deformation FE analysis allows researchers to investigate cell behavior at a larger time scale than that commonly analyzed with linear elastic theory, thus providing a more complete perspective on the cell-environment interaction mechanisms. Another advantage of FEM is the possibility of implementing user-defined routines either written in some programming language (i.e., Python and Fortran) or coded in commercial software, such as MATLAB. This allows us to customize the modeling strategy by integrating innovative algorithms able to face complex cellular physics.