Biomedical Engineering Reference
In-Depth Information
displacement in several commercial indenters. If the probe material is
made from a comparably rigid material such as diamond, glass, or a
glassy polymer such as polystyrene, the elastic properties of the probe
can be reasonably neglected, such that the elastic modulus of the
indenter-material contact (
Eq. 2-9
) equals the indentation (plane strain)
elastic modulus of the material. The maximum load
P
max
corresponding
to this desired maximum indentation depth can be calculated as
P
max
=
4/3
E
r
R
1/2
h
3/2
(see
Chapter 5
) and is only 420 nN. This
P
max
competes
with the actual load resolution of most commercial instrumented
indenters. In contrast, the maximum load required to deform an
idealized, 60% mineralized bone of
E
= 10 GPa
1
for the same
h
max
and
indenter probe geometry would be 420 mN, well within the normal
operating range of the same instrumented indenters.
From this simple example, several points regarding resolution and
range are apparent. First, the load resolution required of the most
compliant biological samples is not a common feature of commercial
instrumented indenters; this requirement differs from the electronic noise
floor of the force transducers that may be quoted by manufacturers, and
is most easily verified through direct experimental testing on well-
characterized samples. This calculation demonstrates the increasingly
reported use of structurally compliant, cantilevered scanning probe or
atomic force microscope probes to infer mechanical properties of tissues
and cells; the associated challenges and advantages of that approach are
detailed in Section 3. Second, the depth range required to deform
materials to loads within the calibrated range of instrumented indenters
can easily exceed the range defined by the displacement transducer
devices, which is typically on the micrometer scale. Third, the depth
resolution and the load range available on commercial instrumented
indenters are sufficient for mechanical characterization of biological
materials, owing to the comparably lower stiffness but greater toughness
of such natural composites. Thus, the challenges in designing
informative experiments are in the judicious choice of (1) probe
geometry and maximum loads or depths required to infer mechanical
response that are attributable to individual phases, interphases, or
macroscale volumes as desired by the user; and (2) loading times
and physicochemical environments that reflect the extent of
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