Biomedical Engineering Reference
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Fig. 8 Example of cell migration in a substrate with two different stiffness and boundary
conditions
The main relevant components of the cell, the traction forces exerted and the major
phases in cell migration are taken into account. The model includes important
parameters such ECM stiffness and viscosity and the boundary conditions. With all
these, it is able to predict some features such as cell movement tendencies, traction
forces and cell speeds in several substrates with different stiffness and under
different constraints. The influence of the stiffness and topography of the (ECM)
has been recently investigated both computationally and experimentally [
70
,
85
,
99
,
107
]. Some important experimental findings are that cells prefer to migrate to
the stiffer part of a substrate [
70
,
109
]. Furthermore focal adhesions are more
stable and traction forces increase on stiffer substrates [
70
,
109
]. The model
presented here reproduces these findings (see Fig.
8
). For example, a case of an
elastic substrate with two different rigidities (E
2
[ E
1
) is simulated. Note that both
the stiffer and the softer side, are constrained. Depending on the initial position of
the cell, it migrates in different directions according to the mechano-sensing
process described above. In general the cell tends to move toward the stiffer side
(E
2
) and never goes from the stiffer to the softer one. However, if the cell is
initially placed close enough to the softer side constraint, the cell senses it and
moves in that direction. If the cell reaches the constraint, it begins to move ran-
domly but does not deviate far from the boundary. This model appears to agree
with experimental data, and its parameters can be adjusted for several types of
cells and substrates, nevertheless, additional factors such as matrix-remodeling,
mechano-chemistry, cell-cell interactions or a complete focal adhesion model
must be introduced to improve the results and get closer to a more realistic
approach.
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