Biomedical Engineering Reference
In-Depth Information
Fig. 2.7 Probability density of the width position of cancer cells at the downstream of the test
section: ( a ) effect of particle Reynolds number Re p ( L ¼ 1.0 cm); and ( b ) effect of the channel
length L ( Re p ¼ 0.31). Error bars indicate standard deviations [ 22 ]
For Re p ¼
0.16, cancer cell migration was not clearly observed, as for rigid spheres
( cf . Fig. 2.5a ). For L
1.5 and 2.0 cm (Fig. 2.7b ), obvious migration of cancer cells
was seen. These basic tendencies were the same for the rigid spheres and
cancer cells.
To quantify the differences in migration properties between the rigid spheres and
cancer cells, we normalized the experimental results using the migration length L m
( 2.2 ). To quantify the migration strength, the maximum probability densities of six
sections, PD 6, max , were calculated using the following equation:
¼
"
#
max ;
X
5
PD 6 ; max ¼
P i
ð
i
¼
1
45
Þ
(2.3)
i
where max indicates the maximum value. A large value of PD 6, max indicates that
large numbers of rigid spheres or cancer cells were focused in a narrow band in the
width direction.
Figure 2.8 shows the correlation between L / L m and PD 6, max . All of the results
are plotted in the figure, covering the experimental conditions Re p ¼
0.16-0.62 and
L
0.5-2.0 cm. The results differed markedly between the rigid spheres and
cancer cells; the cancer cells required a greater channel length than the rigid spheres
to reach the equilibrium state.
Two possible factors might have affected the migration length of cancer cells as
compared with rigid spheres: their deformability and their variation in size.
Firstly, to estimate the effect of cell deformability, we introduced the capillary
number, defined as Ca
¼
,where E is Young's modulus. At a large capillary
number, cells undergo marked deformation owing to high shear stress, whereas when
Ca is small, cells maintain their original shape. Young's modulus for typical breast
cancer cells is about 10 2 Pa [ 13 , 20 ], and the fluid viscosity is of the order of 10 3 Pa s.
¼ mg E
=
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