Biomedical Engineering Reference
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Fig. 3.5 Average force per
post F avg exertedbyasquare
cell in steady state vs. post
stiffness k for cells of edge
lengths L
the center of the cell, and a high degree of alignment around the cell perimeter. This
reflects the larger gradient of stress and stress fiber concentration near the cell edge
in this case.
We find that increasing the post stiffness further to k
500 nN / µm does not
cause appreciable changes in the focal adhesion and stress fiber distributions, as
shown in Figs. 3.3 (d) and 3.4 (d), respectively. Thus, the cellular response reaches
an asymptote at a post stiffness of approximately k
=
100 nN / µm. Further increases
in the post stiffness above this level do not affect the cell response.
=
3.4.2.2 Average Force Versus Post Stiffness
We calculate the average force per post F avg as the sum of the magnitude of the force
exerted by the cell on each post in contact with the cell divided by the number of
posts. In Fig. 3.5 we plot F avg versus post stiffness k for square cells having various
edge lengths. To vary cell size, we utilize square cells of edge length L
=
10 , 30 and
50 µm laid on 3
×
3, 8
×
8 and 14
×
14 post arrays, respectively. For each case, we
vary the post stiffness from k
500 nN / µm and plot the resulting
F avg values in Fig. 3.5 . In all cell sizes, we find a common trend between average
force and post stiffness; namely, the average force per post F avg increases with post
stiffness, but reaches an asymptote. We also find that this trend prevails even if
the post-bed parameters, such as post diameter and post density, are varied, but
do not present these results here. The relationship between average force and post
stiffness observed in our simulations agrees qualitatively as well as quantitatively
with the experimental results of Saez et al. ( 2005 ), presented as a superimposed
line in Fig. 3.5 . It is this quantitative agreement that is used to justify the parameter
calibration used throughout the simulations presented in this paper.
=
2nN / µm to k
=
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