Biomedical Engineering Reference
In-Depth Information
or the projected area at the pre-indented plane. Complications such as the
hysteretic mechanical response during loading-unloading cycle, elastic
recovery at the indent based upon unloading, piling-up or sinking-in at
the contact edge, interplay of elastic and plastic deformation, and
viscoelastic behaviour upon cyclic loading are accounted for by a
number of standard models in the literature. The complex stress fields at
the indent can be derived as variant forms of the classical Hertz contact
model that is based on deformation of an elastic half-space by a spherical
indenter.
Unlike the typical hard surfaces of metals or ceramics, soft biological
tissues do not leave a permanent dent on the sample surface upon
external load removal in most situations because of elastic recovery of
the shallow indentation depth. Nevertheless, there are voluminous studies
in the literature reporting indentation using a conical tip on
biomembranes laying flat on a rigid substrate. Ignoring the
aforementioned complications, the most straightforward mechanical
response is given by
F
π
−
1
ν
2
h
=
+
F
(10-1)
k
2
tan
α
E
c
t
with
F
the applied load,
h
the penetration at the tip, α the half-angle of
the conical indenter,
E
t
the elastic modulus in the traverse direction (
i.e.
across the film thickness), and
k
c
the stiffness of the measuring device. It
is obvious that the measurement only yields
E
t
, rather than the more
relevant two-dimensional planar film area. As noted earlier, it is the
“large area” of cell membrane of individual cells that makes adhesive
contact at the cell-cell and cell-substrate interfaces. Indentation confined
to volumes small compared to the sample thickness is therefore quite
irrelevant to the overall deformation of cells, especially the cell
membrane that encloses the internal cytoplasmic fluid. In fact, the
classical Hertz contact assumption of an elastic half space breaks
down completely in the case of indentation of a single cell with an
encapsulating membrane. The external point load acting locally causes
the membrane to deform, the internal pressure to rise, and ultimately the
entire cell to swell globally.
Search WWH ::
Custom Search