Biomedical Engineering Reference
In-Depth Information
Exercise A.4.5.
Calculate and compare the resonance frequency of the following two can-
tilevers A and B. Cantilever A has dimensions of 3.4 mm × 1.6 mm × 1 mm (length × width ×
thickness) and cantilever B has dimensions of 112 μm × 2.94 μm × 650 nm (length × width ×
thickness). Which cantilever would be better suited for making sensitive measurements and
why?
Exercise A.4.6.
Cantilevers are great tools for analyzing biomolecular binding forces. he
force can be calculated easily by knowing the parameters of the cantilever material and the
tip displacement. A silicon cantilever is used to detect the binding force between one type of
biomolecule and a speciic substrate with known parameters (width, 5 μm; thickness, 0.5 μm;
length, 50 μm). If the displacement of the tip is 0.25 µm, the integrated binding force of all the
biomolecules on the tip is _________.
Exercise A.4.7.
Given a cantilever of spring constant
k
, resonance frequency ω
0
, and dimen-
sions width
w
, length
L
and thickness
t
, determine how
k
and
ω
0
would change if dimensions
w
and
L
were both doubled, keeping
t
constant.
A.5 Suggested Exercises for Chapter 5
Exercise A.5.1.
Describe at least three designs of microluidic low cytometers. Rank their rela-
tive performance qualitatively, in terms of their ability to focus low, the throughput that can be
achieved with them, and the ease of fabrication.
Exercise A.5.2.
Describe the main advantages that microluidic cell cultures confer over
conventional cell cultures (e.g., in a petri dish). What are the main limitations of microluidic
cultures over conventional ones?
Exercise A.5.3.
State the advantages and limitations of extracellular recordings (obtained
with multielectrode arrays, MEAs) and compare to advantages and limitations of intracellular
recordings (obtainable with current patch clamp chips). It is important that you demonstrate
a knowledge of the microfabrication procedures (in particular, the dimensions and materials
involved) and a critical discussion on the cell-electrode interface.
Exercise A.5.4.
Describe at least three designs of microluidic patch clamp chips. Explain
their advantages and disadvantages in terms of ease of fabrication (i.e., aperture resolution, inte-
gration of microluidics, etc.), fabrication throughput, and expected quality of giga-seal.
Exercise A.5.5.
Hydrodynamic focusing has been widely used for cell sorting and focal stim-
ulation of cells in microluidic chips. Suppose a hydrodynamic focusing chip with a center low
of BSA and sheath lows of water lowing along the
y
direction under a constant low rate. At the
convergence point, the center low is 100 μm wide. How much wider is the center low due to dif-
fusive broadening of BSA approximately 1 second ater the convergence of the center and sheath
lows? (Assume that the butterly efect due to Taylor dispersion is negligible.)
Exercise A.5.6.
Using a ive-loop spiral microchannel
W
= 100 μm wide and
H
= 50 μm
high, Ian Papautsky's group separated 7.3 μm beads from 1.9 μm beads at Dean number,
De
=
(ρ
VD
h
/μ)(
D
h
/2
R
)
1/2
= Re (
D
h
/2
R
)
1/2
= 0.47, where ρ is the density of the luid medium,
V
is the
average luid velocity,
D
h
is the microchannel's hydraulic diameter (
D
h
≡ 2
HW
/(
H+W
)), μ is the
luid viscosity, and
R
is the radius of curvature of the path of the channel.
What would the Dean number be if
D
h
were doubled and the radius of curvature,
R
, were
halved?
A.6 Suggested Exercises for Chapter 6
Exercise A.6.1.
Describe how cell biology research beneits from microfabrication technology.
Bring up at least three advantages.
