Biomedical Engineering Reference
In-Depth Information
F
w
0
2
a
R
Figure 10-5. Schematic of an AFM indentation of a thin-walled microcapsule.
however, taken into account for the deviation of force-displacement
relation from a non-adhesive surface indented by an AFM-tip.
3.1.2.
Shell model
Contrasting the balloon model, Boulbitch
et al
.
19
derived a shell model
that ignores membrane stretching but accounts for the out-of-plane
bending stresses only. The indented profile
w
is found to be
w
=
w
t
K
0
(
ξ
)/
K
0
(
ζ
)
(10-4)
and a linear spring constant
k
as
k
=
π
Rp
ζ [
K
1
(
ζ
)/
K
0
(
ζ
)]
(10-5)
=
c/a
, and
K
i
is the
i
th
order of second kind modified
Bessel function. For the model to be valid, the indentation depth must be
negligibly small compared to the cell membrane thickness.
where
ξ
=
r/a
,
ζ
3.1.3.
Model including both bending and stretching
To circumvent the shortcomings of the two aforementioned modeling
approaches, Wan
et al
.
20
developed a model which takes account of both
bending and stretching stresses. Here a spherical capsule with wall
thickness,
b
, elastic modulus,
E
, Poisson's ratio,
ν
, and original
membrane pressure,
σ
0
=
pR
/2
b
, is indented via an AFM tip. The loading
process breaks down into 2 consecutive steps: (i) the capsule is
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