Buckling
Deformation
l 2
l 1
h 2a
(a)
h 1a
Cell
Substrats
F
(b)
δ 2
Deformation
h 1b
h 2b
F
173
Nanorobotic Manipulation for a Single Biological Cell
and Brotzen (2002) have shown that Equations (9.8)–(9.10) are also valid for a
nonrevolute indenter as well such as pyramidal tip.
9.3.3 Stiffness Measurement Using Nanoprobes
We designed two approaches for determining the stiffness of a single cell as
shown in Figure 9.6.
The first approach is based on the buckling phenomenon of a nanoprobe.
A schematic of this approach is shown in Figure 9.6a. It is, to the best of our
knowledge, a novel technique in determining the stiffness of a cell (Ahmed
et al., 2008a). In this technique, the nanoprobe and the cell can be modeled
as two springs in series. In order to model the nanoprobe as a spring, firstly,
the nanoprobe should be able to buckle linearly, and secondly, it should have
a lower or equivalent spring constant as the cell. This technique prevents
damage to the cell because the indentation is minimized from the buckling
FIGURE 9.6
Schematic diagrams of nanoprobe indentation experiments indicate local single-cell stiffness
measurement using (a) a soft nanoprobe and (b) a hard nanoprobe.