Biomedical Engineering Reference
In-Depth Information
The value of
Γ
varies from 0 to 1, corresponding to perfectly uniform and totally
aligned distributions, respectively.
3.3 Modeling Cell Behavior on Flat Substrates of Variegated
Stiffness
We first investigate the cell-substrate interaction where a single cell is adhered to a
flat surface. In our simulations, we utilize isotropic material properties for the flat
substrate on which the cell attaches and forms focal adhesions. The stiffness of the
substrate is prescribed by its Young's modulus.
3.3.1 Finite Element Implementation
The cell behavior is investigated in a finite strain setting (i.e. the effects of geometry
changes on the momentum balance and constitutive behavior through material rota-
tions are taken into account). We implement a 3D model of the gel using 8-noded
linear brick elements, and a cell composed of membrane elements of unit thickness.
We choose a circular cross-section for both the gel and the cell to obviate any geo-
metrical irregularities in the simulations. The diameter of the cell is 34 µm. The gel
diameter and thickness are taken to be approximately 350 µm to emulate the exper-
iments where a cell is laid on a relatively thick gel substrate. Simulations based on
the chosen geometry show that the reaction forces in the gel substrate are negligible
away from the cell; thus, the chosen setup behaves like a cell lying on an infinitely
thick gel substrate.
In each simulation, we start with a quiescent, stress free cell, having no stress
fibers and a negligible quantity of adhesions (there exist a few that keep the cell
located in place on the gel, consistent with Eqs. (
3.12
) and (
3.13
)). To commence
the simulation, we turn on the signal in Eq. (
3.2
) at time
t
0, which has the effect
of causing the formation of stress fibers and focal adhesions. Progressive polymer-
ization and depolymerization of stress fibers, the growth of focal adhesions, and the
generation of contractile stress take place within the cell. This process is continued
in the simulation until a steady state is reached, with a stable configuration of stress
fibers, mature focal adhesions, and a constant stress at any given location in the cell.
=
3.3.2 Simulation Results
We vary the stiffness of the gel, characterized by its Young's modulus
E
from 2 to
200 kPa and record the cell behavior. We calculate the focal adhesion distribution as
the normalized concentration
ξ
H
/ξ
o
of the high affinity integrins at each node, i.e. a
