# Finite Element Modeling of Cells Adhering to a Substrate: An Overview
## 2 Physical Modeling of Cells in Adhesion Phenomena  
The development of physical models schematizing cellular architecture and cell interaction with the surrounding environment underlies the realization of computational frameworks able to simulate cellular behavior by reproducing experimental findings. The definition of the most suitable physical model to analyze the adhesion phenomenon between cell and substrate is strongly influenced by the nature of the cell and by the type and conditions of the interacting environment. Based on these distinguishing phenomenological factors, and by adopting simplifications, it is possible to select the appropriate cellular physical model that will be used to build up the computational framework in the chosen simulation software platform. The numerical framework originating from the physical model relies on the definition of environment and cell morphology, constitutive equations with related material properties, and boundary conditions, as stated by the physical model. In order to maximize the reliability of numerical models in predicting the cell's response, frameworks should be enriched by reducing the level of simplification and by adding characteristic phenomenological aspects. In the study of cellular adhesion mechanisms, physical models of cell structure generally rely on the principles of continuum mechanics and fluid mechanics. The physical models address cell structure as a multi-region domain constituted of an inner portion surrounded by an elastic membrane or an actin-enriched envelope (elastic cortex) [66; 67; 68]. The inner part of the cell consists of the nuclear region, cytoskeletal region, and cytoplasm. Differences in the nature of cells imply variations in functional and structural aspects of cellular regions. Therefore, depending on cell typology and functionality, a specific constitutive behavior can be associated with each cellular domain region. Viscous fluid mechanics can be suitable for modeling the cytoskeleton conformation of cells (e.g., white and red blood cells) lacking a defined supporting cytoskeletal architecture and whose mechanical behavior is mainly influenced by an elastic cortex enveloping the internal fluid region. Conversely, for endothelial and epithelial cells that have a well-developed cytoskeletal architecture playing a relevant role in cell mechanical response, it is more appropriate to model cell inner regions as continuum domains following elastic and viscoelastic constitutive laws [69]. Furthermore, schematizing load-carrying cytoskeletal components through an architecture consisting of prestressed cables and struts, to which continuum mechanics constitutive properties can be assigned, results in a better physical model than assuming the cytoskeleton as a whole continuum region. However, the increasing complexity of the cell's physical model makes it more difficult to characterize material parameters. Therefore, a satisfactory balance between model accuracy and complexity must be achieved by adopting an appropriate level of simplification. In the study by [PERSON] et al. [70] on the behavior of chick fibroblasts spreading on glass microplates, a cellular physical model commonly used for leukocytes was extended to fibroblasts on the basis of a similarity in the adhesion mechanism of the two cell types. The authors highlighted that fibroblasts, just like leukocytes, may unfold packed sectors of the cellular membrane to increase cell surface area during spreading. In particular, experimental evidence in [70] showed that the surface area of spreading fibroblasts may increase up to almost 50%. The proposed fibroblast physical model schematizes the cell as a highly viscous fluid region encased in a cortical envelope behaving like an isotropic elastic membrane that undergoes a biaxial tension \(\tau\).