Page 239 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

238 CHAPTER 9 Application of microfluidics in cancer treatment

diagnostic or prognostic marker for tumor. The chip can carefully count CTCs in
blood and become a trusty tool for clinical settings for rapid CTC capture as well
as subsequent counting. The blood cell size distribution, especially WBCs and lym-
phocytes, in different patients can vary from 8 to 20 µm [74,75]. The differences in
deformability between cancer cells and blood cells can be applied in order to WBCs
or lymphocytes separation. A new generation of chips is imaginable in which chan-
nels with different sizes for constriction regions and the trapping chambers can be
fabricated and it may lead to creating a second degree of separation within the same
chip. Also, if a more number of CTC exist in the bloodstream, another channels can
be added to each row to make it suitable for clinical samples. CTC-HTECH chips can
be used in a series mode in identical or different channel dimensions. CTC-HTECH
can be connected in a series as multistage multicycle CTC enrichment [62]. CTCs
and cfDNA technologies are used parallel in prospective clinical trials, which might
be able to explain the current resistance by solid tumors to targeted therapies [48].

9.4 Governing equations

In the following sections, in order to consider the SAW problem, the three general
equations of continuity, momentum (Navier-Stokes), and energy in the presence of
the SAW are described below. First, considering the fully developed microchannel
profiles, the viscose and thermal boundary layer thicknesses are discussed.
The nonlinear relationship of the first-order of velocity, pressure, and temperature
fields occurs at a thin thermocouple boundary near the surface. One of the numerical
challenges is the dissolving of the thermo viscous boundary layers [76]. The thick-
δth ness of the thermal boundary layers δ and the hydrodynamic(viscos) boundary layer
th
δ in a fluid due to the application of an ultrasound wave are as follows:
δ = 2 D (9.1)
δth=2Dw th ω

2ϑ
δ = (9.2)
δ=2ϑw ω
where w is the angular frequency of the SAW in radians per second and is calculated
from the frequency f as follows:
w=2πf ω = 2π f (9.3)
Dth ϑ where ϑ is a kinematic viscosity and equivalent (µ/ρ), µ and D are dynamic viscos-
th
ity and thermal diffusivity of the thermal boundary layer, calculated as follows:
k
D = (9.4)
th
Dth=kρ cp ρ 0 c p
0
3
cp ρ 0 where c , ρ , and k are heat capacity at constant pressure (j/m k), equilibrium density
p
0
3
(kg/m ) and thermal conductivity (w/mk).