Biomedical Engineering Reference
In-Depth Information
receptors (AChRs) get clustered, as “pretzels” in mature and diferentiated myotubes (
Figure
6.13c
). Let us assume that an average AChR pretzel can be approximated by an ellipse with a
major axis of 20 μm and a minor axis of 10 μm. We would like to design a three-input channel
(as in
Figure 6.13a
) to focally stimulate these AChR pretzels with agrin (molecular weight =
90 kDa). Ideally, we would like the width of the middle stream to be less than or equal to the
size of the average pretzel. Let us assume that the height and width of the main microchannel is
200 μm and 2 mm, respectively.
(a) Assuming the length of the three-input channels and the pressure at the inlets to be
the same, design the ratio of the resistances of the input channels (the two lanking
channels and the central channel), so that the width of the central stream in the main
channel is 60 μm. In reality, will the width of the central stream be exactly the same
as the calculated value? Please reason your answer.
(b) Now that we have found out the ratio of the resistances, what would be the heights
and widths of the inlet channels (assuming the height of the lanking channels is
200 μm)?
(c) Assuming a parabolic low proile and a low rate of 20 μL/s, calculate the approxi-
mate width of the central stream of agrin (which you designed to be 60 μm wide)
(i) 1 mm downstream, (ii) 1 cm downstream, and (iii) 5 cm downstream. Assume
only difusive broadening. Are there other efects that contribute to broadening of the
agrin stream?
(d) Let's assume that you can allow the agrin stream to broaden by 20 μm on either side.
How many myotube tracks can you focally stimulate, if the low rate is 20 μL/s?
(e) Let's assume that you have two syringe pumps, so that you can control the low of the
central channels and the side channels separately. What low rates will you use so that
the width of the central stream remains between 20 and 100 μm for the entire length
of the channel (5 cm)?
(f) Can you estimate an approximate value of luidic shear stress at the bottom of the
channel, where the myotubes are patterned (assuming parabolic low) for the low
rates you used in the earlier parts? Are these values acceptable for cell culture?
Exercise A.6.7.
Calculate the maximum shear stress experienced by endothelial cells inside
a closed microluidic cell-culture chamber of dimensions 21 mm × 150 μm × 14 μm (length ×
width × height). Endothelial cells are attached to the ibronectin-coated loor of this chamber,
and cell culture medium is lowed through the chamber at 0.10 mL/min. Assume laminar low
conditions inside the chamber. For convenience, also assume that the velocity changes only as a
function of the chamber height, and the cells are of a uniform height. Justify the selected height
of cells and any additional assumptions made. he density and viscosity values of the culture
medium can be assumed to be same as water.
Hint:
Use equations describing pressure-driven low through a narrow rectangular
channel.
A.7 Suggested Exercises for Chapter 7
Exercise A.7.1.
Elaborate (in four to ive sentences/lines) on the importance of micropatterned
cocultures of hepatocytes+ibroblasts. Why do people use them? What applications/subields are
they important for?
