Biomedical Engineering Reference
In-Depth Information
Fig. 2.8
Correlations between PD
6,max
, defined by (
2.3
), and the normalized channel length
L
/
L
m
.
The figure contains all experimental data under
the conditions of
Re
p
¼
0.16-0.62 and
L
¼
0.5-2.0 cm.
Error bars
indicate standard deviations [
22
]
Consequently, Ca becomes greater than unity only when the shear rate
g
exceeds
10
5
s
1
. In the present study, the average
g
at the highest flow rate (
Re
p
¼
0.62) was
10
4
s
1
. Therefore, the effect of cell deformability can be neglected. This
was confirmed by the overlapping results of PD
6,max
obtained for different values of
Re
p
, which are plotted on a single curve in Fig.
2.8
.
The other factor that might have affected the migration length of cancer cells
compared with rigid spheres is the size variation of the cancer cells. The migration
length
L
m
, given by (
2.1
), is proportional to
a
3
,where
a
is the particle radius.
Consequently, a small variation in cancer cell size results in a large difference in
migration length. For example, the migration length of a cancer cell with radius
a
0
is
double that of a cancer cell with radius 1.26
a
0
. The diameter distribution of cancer
cells, measured using a cell counter (Vi-CELL XR cell viability analyzer; Beckman
Coulter, Brea, CA), showed that the average cell diameter was about 15
about 1.2
m
m, with a
standard deviation of ~4.3
m. In general, the size distribution of cancer cells can be
expressed by the Gaussian profile of the probability density function (PDF) as
m
!
2
1
2
p
ð
d
d
0
Þ
PDF
ð
d
Þ¼
p
exp
;
(2.4)
2
s
2
s
where
d
is the diameter,
d
0
is the average diameter, and
s
is the standard deviation.
The cumulative distribution function (CDF) in this case is
1
2
d
d
0
2
s
p
CDF
ð
d
Þ¼
1
þ
erf
(2.5)
2
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