Biomedical Engineering Reference
In-Depth Information
17.2.2.2 Particles with Heterogeneous Structure
The. DEP. derivations. mentioned. earlier. are. done. on. a. homogeneous. particle.. This.
assumption. is. generally. suficient. for. dielectric. particles. like. latex. beads.. But. when.
applying. it. to. particles. with. complicated,. inhomogeneous. structures,. such. as. bacteria.
and.mammalian.cells,.the.uniform.spherical.model.becomes.too.simpliied..To.deal.with.
these.heterogeneous.particle.structures,.multishell.models.are.often.used.in.which.the.
particle.structure.is.simpliied.into.two.or.more.coherent.layers.(Jones.1995)..For.exam-
ple,.erythrocytes.are.usually.simpliied.to.a.two-shell.model:.a.thin.spherical.membrane.
layer. as. the. outer. shell. and. a. homogenous. spherical. cytoplasm. as. the. core.. For. leuko-
cytes. with. a. nucleus,. a. three-shell. model,. the. plasma. membrane,. the. cytoplasm,. and.
the.nucleus.membrane.envelop,.is.widely.used..The.multishell.models.for.cells.are.sche-
matically. shown. in. Figure. 17.3a. and. b.. To. apply. the. same. DEP. formula. shown. earlier,.
an.effective.complex.permittivity.of.the.nonuniform.particle. ε
( )
.is.used.to.calculate.the.
Clausius-Mossotti.factor.(
K
*
).in.Equation.17.7..For.example,.in.the.two-shell.model,.the.
Membrane:
c
mem
,
g
mem
R
2
R
3
R
1
R
ε*
p
, σ*
p
ε
1
, σ
1
Cytoplasm:
ε
cyt
, σ
cyt
ε
3
, σ
3
ε
2
, σ
2
External medium:
ε
1
, σ
1
(a)
(b)
1
Membrane integrity and morphology
Cell size and shape, cytoskeleton
RBC
T-lymphocytes
0.5
f
xo
0
100 Hz
10 kHz
1 MHz
1 GHz
E. coli
0
Yeast
Nucleus-cytoplasm volume ratio
endoplasmic reticulum
Membrane
surface charge
membrane
conductivity
-0.5
10
4
10
5
10
6
Frequency (Hz)
10
7
10
8
10
9
(c)
(d)
Figure 17.3
(See companion CD for color igure.)
.Multishell.models.for.DEP.simulation.on.heterogeneous.particles..(a).A.
two-.and.three-shell.cell.models..(b).The.simpliication.of.a.two-shell.model.of.a.cell.to.a.particle.with.an.effec-
tive.complex.permittivity.
ε
( )
..(c).A.typical.frequency.spectrum.of.the.DEP.force.on.a.cell..(Reproduced.with.
kind.permission.from.Springer.Science+Business.Media:.
BioMEMS Biomed. Nanotechnol
.,.Cell.physiometry.tools.
based.on.dielectrophoresis,.2,.2007,.103-126,.Pethig,.R.,.Springer,.E.D.,.Ferrari,.M.S.,.Bashir,.R.,.and.Wereley,.S.,.
Copyright.2007.).(d).The.simulated.frequency.spectrum.of.Re[
K
*].for.several.common.cell.types..(Reprinted.with.
permission.from.Huang,.Y.,.Ewalt,.K.L.,.Tirado,.M.,.Haigis,.R.,.Forster,.A.,.Ackley,.D.,.Heller,.M.J.,.O'Connell,.J.P.,.
and.Krihak,.M.,.Electric.manipulation.of.bioparticles.and.macromolecules.on.microfabricated.electrodes,.
Anal.
Chem.,
.73,.1549-1559..Copyright.2001.American.Chemical.Society.)
