Page 292 - Advances in Biomechanics and Tissue Regeneration

290 15. COMPUTATIONAL SIMULATION OF CELL BEHAVIOR FOR TISSUE REGENERATION

of these models, the actual forces acting on the cell body are not considered [79, 81–83]. However, the main limitation in
many of them is that they have ignored the cell mechanosensing process that is an essential feature in cell-ECM inter-
action [36, 79, 82]. In addition, the above-mentioned 2D models, which simulate cell shape change, do not study cell
configuration in a free mode. Instead, they restrict the cell shape to a rigid ellipse by which the cell shape change is
represented by an alteration of the aspect ratio of the ellipse (the ratio of the major axis to the minor axis). A typical rigid
mode of cell configuration is also assumed in some 3D models [84] in which a 3D epithelial cell interacts with a plane
ECM. The main limitation of this model is that the cell can have different rigid shapes such as a hexagonal prism,
columnar, cuboidal, and/or squamous. Vermolen et al. [37] presented a 3D phenomenological numerical model to
investigate the effect of chemotactic cues on cell morphology. Although in their model the cell can take irregular
shapes, their model is formulated in such a way that the cell velocity fundamentally depends on the chemical gradient,
which is not sufficiently precise according to many experimental works [24, 31, 85]. They also assumed that the cell
volume changes when the cell sends out pseudopods. This is an unrealistic assumption since recent experimental
investigations [86–88] have demonstrated that the overall cellular volume remains constant as the cell shape changes.
Han et al. [89] investigated the spatiotemporal dynamics of cell migration using a biochemical-mechanical contractility
model that incorporates the traction forces developed by the cell during cell migration in 2D ECMs. Unfortunately,
their model does not include cell shape changes during cell migration. In their model, the formation of a new adhesion
regulates a reactivation of stress fiber assembly within the cell and predicts the spatial distribution of traction forces.
Besides the concerns discussed earlier, signaling mechanisms by which the microenvironment stiffness controls cell
differentiation and proliferation are not computationally considered at the cell level. Several mechanobiological
macrolevel models have been established to describe cell lineage specification during bone fracture healing [76, 77,
90–95]. All these numerical models are able to predict the general patterns of cellular differentiation due to external
mechanical stimuli in the macrolevel. A 2D model presented by Stops et al. [77] considers cell differentiation and pro-
liferation in a collagen-glycosaminoglycan scaffold subjected to mechanical strain and perfusive fluid flow. Their find-
ings indicate that specific combinations of scaffold strains and inlet fluid flows define the specific cell fate. Besides, the
2D model developed by Kang et al. [76] to simulate bone fracture healing is formulated based on the density of each cell
phenotype. It is assumed that the cell differentiation and proliferation can be modulated according to the magnitude
and frequency of mechanical stimuli. According to their numerical results, the bone healing process can be improved
when the magnitude and the frequency of the mechanical stimuli are employed as control factors of cell proliferation.
To our knowledge, there is no numerical models to consider cell differentiation and/or proliferation based on the
mechanosensing process during cell migration.
In addition to the experimental research, theoretical studies and numerical models also deliver deep insights into
cell behavior. Experimental investigations of cell behavior are relatively time consuming and expensive. Nevertheless,
the numerical models can save experimental resources and time. These models not only associate the experimental
results to the first principles but also describe the behavior and sensitivity of the systems as a function of each param-
eter. Furthermore, mathematical models are helpful in identifying the key parameters that play a main role in defining
the overall behavior of the system. Hence, they can lead to new and more effective in vitro experiments.
Consequently, the main aim of the present chapter is to cover different aspects of cell behavior such as cell migra-
tion, differentiation, proliferation, shape changes, and cell-cell interactions in a 3D multisignaling ECM. For this pur-
pose, we first modeled the mechanosensing process of a single cell. Next, the model will be extended to include
individual cell migration, cell-cell interaction, and collective cell migration due to pure mechanotaxis. Afterward,
the effect of different signals will be added to consider the behavior of individual cells and populations of cells in
a 3D multisignaling matrix. To consider these processes, for the sake of simplification, initially a constant spherical
cell morphology is assumed. Subsequently, the model will be extended to study the cell morphological changes
due to mechanotaxis, thermotaxis, chemotaxis, and electrotaxis. Finally, the basic model of cell migration will be
employed to include cell differentiation and proliferation because of the mechanosensing process.

15.2 METHODOLOGY

Cell migration is similar to many other physical events. It depends on the equilibrium of effective forces acting on
the cell body. Traction force, which is generated due to cell internal deformation, is transmitted through the integrins at
the focal adhesions to the ECM [13, 24]. This force is the only directional force, in the absence of other external cues, that
guides the cell movement together with a random protrusion force. In the presence of thermotactic and chemotactic
signals, the direction of this force is modified according to the pointed direction by those stimuli. In the presence of
electrotaxis, the cell is exposed to an independent electrostatic force. Therefore, in a multisignaling environment, all

II. MECHANOBIOLOGY AND TISSUE REGENERATION