Inertial Migration of Cancer Cells in a Microfluidic Device - Bioanalysis Advanced Materials Methods and Devices - page 17

force effect to isolate platelets from other blood cells in a dilute suspension,
enriching the relative number of platelets by 100-fold. These examples illustrate
the potential of applying inertial migration to the development of a microfluidic
device for the CTC test.
If cancer cells could be separated from blood cells using the inertial migration
effect, this would facilitate the development of a microfluidic device for the CTC
test. To this end, we have recently studied the inertial migration of cancer cells in a
straight microchannel [ 22 ], which is introduced in this chapter. In Sect. 2.2, we
briefly explain the basic mechanism of inertial migration. Section 2.3 describes the
fabrication of a polydimethylsiloxane (PDMS) microchannel, for the sake of
readers who are not familiar with microfluidics. We explain the preparation of
cancer cells in Sect. 2.4, particularly for readers who have no experience of cell
culturing. Section 2.5 gives the results of initial experiments using rigid spheres:
these enable the efficiency of inertial migration to be demonstrated. Section 2.6
presents experimental results using cancer cells, thus showing how inertial migra-
tion may be applied to them. The results given in Sects. 2.5 and 2.6 are mainly from
Tanaka et al. [ 22 ], and further details such as the effects of red blood cells on the
migration of cancer cells can be found in that paper. This chapter focuses on the
fundamental principles of the inertial migration of cancer cells in a microchannel.

2.2 Mechanism of Inertial Migration

Figure 2.1a shows the principles governing the inertial migration of particles
flowing in a tube. The particles are subject to drag and inertial lift forces. The
drag force ( F D ) drives particles along their streamlines, while the shear-induced
inertial lift force ( F IL ) drives them away from the channel center and toward the
sidewalls. The particle Reynolds number ( Re p ) is a key factor in inertial migration,
being defined asRe p ¼ rd 2 , where d is the diameter of a particle, g the shear rate,

and r and m the density and viscosity respectively. It represents the ratio of the
inertial force to the viscous force acting on the particles. When Re p 1, inertial
migration does not occur, and the particles follow the streamlines. When Re p is not
negligibly small, inertial force acts on the particles, and they tend to drift from the
streamlines. When particles come close to the wall, the wall-induced inertial lift
force ( F WL ) appears in addition to F IL . These two forces act in opposite directions,
and the particles tend to migrate towards equilibrium positions, where the
magnitudes of the two inertial forces are balanced.
These equilibrium positions depend mainly on the channel geometry and Re p
(Fig. 2.1b ). In a cylindrical channel with moderate Re p , particles align in an annulus
at a radius of about 0.6 R , where R is the channel wall radius [ 17 ]. The radius of the
equilibrium annulus increases with increasing Re p because of the increase in F IL
[ 14 , 15 ]. For a channel with a square cross-section, particles tend to align near the
wall, and the equilibrium positions form the sides of a small square (cf. Fig. 2.1b ).
For a channel with a rectangular cross-section, the equilibrium positions are near

_ g=