A Mic oelec ode-Cell Senso Model o Real Time Moni o ing
Albe o Yú e a, Daniel Cañe e
Se ille Mic oelec onics Ins i u e (IMSE)
Mic oelec onic Na ional Cen e (CNM), Se ille Uni
A . Ame ico Vespucio, sn, 41092, Se ille, Spain
yu e [email protected]
Paula Daza
Dp . Cell Biology
Biology Facul y, Se ille Uni e si y
A . Reina Me cedes sn, 41012, Se ille, Spain
[email protected]
Abs ac -- In his pape he applica ion o a cell-
mic oelec ode model o cell biome y expe imen s is p oposed,
using he cell-elec ode a ea o e lap as main pa ame e . The
model can be applied o cell size iden i ica ion, cell coun , and
hei ex ension o cell g ow h and dosime y p o ocols.
Expe imen al esul s using AA8 cell line a e p esen ed,
ob aining p omising esul s.
Keywo ds- Mic oelec ode; ECIS; bio-impedance; impedance
senso ; cell cul u e; dosime y.
I. INTRODUCTION
Many biological pa ame e s and p ocesses can be sensed
and moni o ed using i s impedance as ma ke [1-5], wi h he
ad an age o being a non-in asi e and ela i ely cheap
echnique. Cell g ow h and ac i i y, changes in cell
composi ion and shape, o in cell loca ion a e examples o how
p ocesses can be de ec ed wi h mic oelec ode-cell impedance
senso s [6-9]. Among Impedance Spec oscopy (IS) echniques,
Elec ical Cell-subs a e Impedance Spec oscopy (ECIS)
[7,8], based on wo-elec ode se ups, allows he measu e o
cell-cul u e impedances and he de ini ion o he biological
na u e (ma e ial, in e nal ac i i y, mo ili y and size) o a kind o
cell and i s ela ionship wi h he en i onmen [11]. One o he
d awbacks o ECIS echnique is he need o e icien models o
decode he ull sys em elec ical pe o mance composed by he
elec odes, medium and cells. Se e al wo ks ha e been
de elopped in his ield. In [8], magni ude and phase
impedance a e deduced om elec ic ield equa ion solu ion a
he cell-elec ode in e ace, gi ing a h ee pa ame e based
model. h, he cell-elec ode dis ance, Rb, cell- o-cell ba ie
esis ance and cell, cell adius. In [9,10], ini e elemen
simula ion (FEM) a e execu ed o sol e elec ical ield
conside ing he whole s uc u e. This me hod gi es one
pa ame e model (Rgap) o desc ibe he gap o cell-elec ode
egion esis ance. In bo h, he model conside s cells a e in
con luen phase [7] o a ixed a ea o e he elec ode [9]. The
la es was ex ended in [10] o se e al cell sizes, allowing o
de ine he cell-elec ode co e ed a ea as he main model
pa ame e . In his wo k is conside ed a model ex ension o Rgap
based model, o inco po a e he a iable cell-mic oelec ode
a ea o e lap [10]. Impedance senso sensi i i y cu es based on
he cell size and densi y will be p esen ed and applied o
measu e he g ow h- ax in cell-cul u es and o desc ibe cell
oxici y expe imen s.
In his pape , sec ion II esumes he elec ode solu ion
model o cell-elec ode cha ac e iza ion. The p ocess o ex ac
p ac ical models is included a sec ion III, illus a ing he
simula ions on a simpli ied sys em leading o cell size
de ec ion. Sec ion IV elies on eal ime cell cul u e moni o ing
and i s applica ion o dosime y expe imen s. Conclusions will
be highligh ed a sec ion V.
II. ELECTRODE-ELECTROLYTE MODEL
The impedance o elec odes in ionic liquids has been a he
ex ensi ely in es iga ed. An excellen e iew can be ound a
[6]. The main compone s desc ibing he elec ical pe o mance
o an elec ode me al inside a solu ion a e ou : he double laye
capaci ance, CI, he cu en lowing h ough he elec i ied
in e ace will encoun e a esis ance Rc caused by he elec on
ans e a he elec ode su ace and Wa bu g impedance ZW
due o limi ed mass di usion om he elec ode su ace o he
solu ion. The elec on ans e esis ance Rc is in se ies wi h
he mass di usion limi ed impedance ZW. As he cu en
sp eads ou o he bulk solu ion, he elec ode has a solu ion
conduc i i y de e mined by se ies esis ance, ep esen ed as
sp eading esis ance RS in he equi alen ci cui . These ou
pa ame e s depends on echnology, medium and geome y.
Figu e 1. Equi alen ci cui o elec ode-solu ion in e ace. CI is he
double laye capaci ance. Fa adic impedance includes Zw, he Wa bu g
impedance and Rc , he cha ge- ans e esis ance. Rs is he sp eading
esis ance.
III. CELL-ELECTRODE MODEL
The Fig. 2 illus a es a wo-elec ode impedance senso
use ul o ECIS echnique: e1 is he sensing elec ode and e2 he
e e ence one. Elec odes can be manu ac u ed in CMOS
p ocess wi h me al laye s [9] o using pos -p ocessing s eps
[13]. The cell loca ion and size on e1 op mus be de ec ed.
The model in Fig. 3 conside s he sensing su ace o e1
could be o al o pa ially illed by cells. Fo he wo-elec ode
senso in Fig. 2, e1 is he sensing a ea A, Z( ) is he impedance
by uni a ea o he emp y elec ode (wi hou cells on op).
When e1 is pa ially co e ed by cells in a su ace Ac, Z( )/(A-
Ac) is he elec ode impedance associa ed o non-co e ed a ea
by cells, and Z( )/Ac he impedance o he co e ed a ea. Rgap
models he cu en lowing la e ally in he elec ode-cell
in e ace, which depends on he elec ode-cell dis ance a he
in e ace (in he ange o 15-150nm). Rs is he sp eading
esis ance h ough he conduc i e solu ion. Fo an emp y
elec ode, he impedance model Z( ) is ep esen ed by he
ci cui in Fig. 1. I has been conside ed o e2 he model in Fig
3a, no co e ed by cells. The e2 elec ode is commonly la ge
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and g ound connec ed, being i s esis ance small enough o be
ejec ed. Figu e 4 ep esen s he impedance magni ude, Zc, o
he senso sys em in Fig. 2, conside ing ha e1 could be ei he
emp y, pa ially o o ally co e ed by cells. The pa ame e ,
called ill ac o , can be ze o o Ac=0 (e1 elec ode emp y), and
1 o Ac=A (e1 elec ode ull). I is de ined Zc ( =0)=Znc as he
impedance magni ude o he senso wi hou cells.
Figu e 2. Two elec odes o ECIS: e1 (sensing) and e2 ( e e ence). AC
cu en ix is injec ed be ween e1-e2, and ol age esponse Vx is measu ed.
Figu e 3. P oposed model o he an elec ode-solu ion-cell model wi h
a ea A, unco e ed wi h cells (a) and co e ed and a ea Ac (b).
The ela i e changes a impedance magni ude, de ined as,
c nc
nc
ZZ
Z
(1)
in o m mo e accu a e om hese a ia ions, being he change
o impedance magni ude o he wo-elec ode wi h cells (Zc)
wi h espec o he sys em wi hou hem (Znc). The g aphics o
e sus equency is plo ed in Fig. 5, o a cell- o-elec ode
co e age om 0.1 o 0.9 in s eps o 0.1, using a Rgap=90 k .
The size o he elec ode is 32x32 m2 [9,10]. I can be
iden i ied again he equency ange whe e he sensi i i y o
cells is high a 100kHz, ep esen ed by inc emen s. Fo a
gi en equency, each no malized impedance alue o can be
linked wi h i s , being possible he cell de ec ion and
es ima ion o he co e ed a ea Ac. E en mo e, a ea co e ed can
be in ep e ed as consequence han wo o mo e cells, allowing
cell coun o a gi en cell size.
F om Fig. 5, i can be deduced ha models o elec ode-cell
elec ical pe o mance can be used o de i e he o e lapping
a ea in cell-elec ode sys ems, use ul o biological s udies. I
can be obse ed how he cu e i s well wi h he equency
ange, placing he maximum alue a ound 100 kHz, as
p edic s he FEM simula ions [9, 10]. A alue o Rgap= 90k
was selec ed o his cu e, ep esen ing a maximum alue o
he cu e wi h =0.69, which ep esen s he a io (Ac/A), o
a cell size o 30 m diame e ep esen ed a igu e ob ained
using FEM simula ions [10]. Impedance senso cu es a
igu es 4 and 5 we e ob ained using Spec eHDL [15] mixed-
mode simula o , wi h Analog Ha dwa e Desc ip ion Language
(AHDL) o ci cui s in Fig. 3. An ad an age o using AHDL
models is he possibili y o including non-linea pe o mance o
ci cui elemen s, in ou case, he equency squa ed- oo
unc ion a he Wa bu g impedance.
Figu e 4. Impedance e olu ion when ill ac o inc eases 32 x 32 m2.
Figu e 5. No malized impedance e sus equency de i ed om Fig. 4.
Cu es co espond o in he ange o 0.1 (nea emp y) o 0.9 (nea ull).
IV. CELL CULTURE APPLICATIONS
A: Elec ode Model
The p oposed model based in Fig 3 has h ee main
pa ame e s: he elec ode a ea (A), he ill- ac o ( ), and he
esis ance o he gap egion (Rgap). Technology da a we e
included and simula ion esul s ob ained o model a
comme cial elec ode: 8W10E, om Applied Biophysics [12].
I is composed by eigh wells; each one con ains en ci cula
gold mic oelec odes, wi h 250 m diame e . Ten sensing
elec odes, in pa alell, we e used o e1 and only one common
e e ence elec ode, much la ge han sensing ones. Figu e 6
ep esen s he no malized impedance expec ed o hese
elec odes, o Rgap=22k , i ill ac o changes om elec odes
wi hou cell on op ( =0.1) o nea hose ully co e ed ( =0.9).
Values o Rgap can be used o ma ch he models o obse ed
pe o mance. In Fig. 7, Rgap alues we e changed o =0.9,
obse ing la ge changes. Finally, i was also modi yed he
elec ode a ea o Rgap=22k and =0.9, showing he esul s a
Fig. 8. I can be obse ed ha op imal wo king equency is
nea he p oposed by he elec ode ac o y (a ound 4 kHz), and
ha elec ode a ea co e ed by cells can be app oxima ed by
using he ill ac o pa ame e s. The pe o mance cu es
ob ained be o e can be used o i expe imen al esul s o
p oposed model and ind ele an biome ic cha ac e is ics.
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Figu e 6. Ob ained cu es o s equency, o [0.1,0.9] and Rgap =
22k , using 8W10E elec odes.
Figu e 7. Ob ained cu es o s equency, o Rgap [10k ,100k ] in
s eps o 10k , o =0.9, using 8W10E elec odes.
Figu e 8. Ob ained cu es o he s equency, o Rgap=22k and
=0.9, o di e en s elec ode a eas (1n o 100n). 49n (49.10-9m2)
co esponds o a ci cula elec ode wi h a 250 m diame e .
B: Cell g ow h
In Fig. 9a i is shown he g ow h cu e ob ained by us
du ing se en days using 8W10E senso s wi h a simila se up in
[8]. AA8 cells o chinese hams e we e seeded ini ially, in an
app oxima ed numbe o 5000. The impedance ange is a ound
1220 (380 1600 . Conside ing an ini ial cell numbe o
5000 e y low, we ake he ini ial impedance as due o no-cell
impedance alue (Znc). A =6000 min, he medium was
changed, and he con luen phase was achie ed a = 8500 min
app oxima ely. The maximum expe imen al alue gi en om
eq. (1) is a ound = 3.1, as illus a es Fig. 9b. We conside in
ou model ha he elec odes a e ap oxima elly ully co e ed
by cells o =0.9, he alue o Rgap ha be e i s is 22k .
Sys em esponse co esponds o - alues illus a ed in Fig. 6.
F om hese cu es, i can be ob ained he ill ac o a di e en
imes. Table I summa ized he ela i e no malized impedance
alues a se e al imes. Using Fig. 6 o he senso esponse,
ill ac o is calcula ed a e e y ins an . Fo a well a ea o 0.8
cm2, he maximum cell numbe goes om 0.8x106 o 1.6x106.
Numbe o cells, ncell, in Table I, is ob ained om 0.8x106
expec ed inal cell numbe . A alue o Znc=380 o calculus
in eq. (1) was conside ed.
Figu e 9. (a) Impedance e olu ion o he cell g ow h expe imen . (b) The
no malised impedance e olu ion ob ained.
TABLE ME: CELL NUMBER (ncell) OBTAINED FROM IMPEDANCE ZC MEASURE
IN Fig. 9, AND USING THE CURVES PROPOSED FOR 8W10E SENSORS.
(min)
ncell
0
0
-
5000
500
0.024
0.020
18000
1000
0.050
0.050
44000
1500
0.072
0.070
63000
2000
n.a.
n.a.
n.a.
2500
n.a.
n.a.
n.a.
3000
0.374
0.362
322000
3500
0.437
0.395
351000
4000
0.615
0.475
422000
4500
0.777
0.530
471000
5000
0.903
0.581
516000
5500
1.033
0.602
535000
6000
1.074
0.620
551000
6500
1.507
0.710
631000
7000
1,970
0.775
689000
7500
2,353
0.810
720000
8000
2,837
0.860
764000
8500
3.113
0.890
791000
9000
3.134
0.900
800000
9500
3.010
0.875
778000
10000
2,857
0.864
768000
C: Dosime y
Expe imen s o cha ac e ize he in luence o some d ugs in
cell g ow h we e done. The objec i e is o p oo ha p oposed
model allows coun ing cell numbe a di e en dosis. I was
conside ed he AA8 cell line and as d ug, six di e en doses o
MG132 o g ow h inhibi ion ( om 0.2 M o 50 M). A e 72
hou s no mal cell g ow h, he medium was changed and he
d ug added a di e en doses: 0.2, 0.5, 1, 5, 10 and 50 M o
wells 3 o 8 espec i ely. Well 2 is he con ol.
Measu ed impedances o he 8 wells a e a Fig. 10, o
4kHz wo king equency. A he end o he expe imen can be
obse ed ha impedance dec eases as d ug dosis inc eases.
Con ol (W2) is ull o cells wi h he maximum impedance,
while maximum dosis (W8) has he lowes esis ance, a he
bo on. The black line (W1) ep esen s he elec ode-solu ion
impedance. A e he medium change ( =4000min), i is
obse ed a dec easing impedance below he ini ial baseline
le el (400 ) ha we canno explain. Final impedance alues a
8000min, Zc, we e conside ed, a Table II. F om Znc and Zc,
alues a e calcula ed in hi d colunm. Using cu es o e sus
equency in Fig. 6, es ima ed alues om p oposed model
a e ob ained. The cell numbe a he end o he expe imen was
also coun and shown a he las column o each well.
Conside ing max=0.9 o a measu ed cell numbe o 8.06x105,
he expec ed alues o a e calcula ed.
The same da a a e summa ized a Table III o 2, 4 and
10kHz equencies espec i ely. The be e ag eemen i is
ob ained a 4kHz in ill ac o ( ). I is obse ed ha he
impedance baseline, Znc, o calculus dec eases wi h
equency due p obably o elec ode impedance dependence.
(a)
(b)
(b)
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Fo medium esis ance (W1) and high d ug concen a ions
wells (W6-W8), he esis ance measu ed is below o Znc, so eq.
(1) can no be applied o calcula ion.
Figu e 10. Impedance measu e in dosime y a 8 wells o 4kHz equency.
W1: Medium. W2: Con ol. W3: 0.2 M. W4: 0.5 M. W5: 1 M. W6: 5
M. W7: 10 M and W8: 50 M.
TABLE II: EXPERIMENTAL VALUES FOR RELATIVE IMPEDANCE ( ) AND
FILL-FACTOR ( ) FOR Znc = 400 . FREQUENCY = 4 KHZ.
Well
Zc
=8000min
Zc ,Znc
es ima ed
expec ed
ncell
measu ed
1
259.2
-
-
-
Medium
2
1631.7
3.1
0.90
0.900
8.06x105
3
1454.7
2.6
0.85
0.690
6.13x105
4
1030.6
1.5
0.72
0.610
5.41x105
5
625.8
0.5
0.44
0.410
3.60x105
6
417.4
0.05
0.037
0.036
3.20x104
7
406.8
0.015
0.016
0.024
2.10x104
8
99.6
< 0
-
0.005
4.00x103
TABLE III: EXPERIMENTAL VALUES FOR RELATIVE IMPEDANCE ( ) AND
FILL FACTOR ( ) AT VARIOUS FREQUENCIES. ZNC = 480 , 400 , AND
315 FOR 2, 4 AND 10 kHz WORKING FREQUENCY RESPECTIVELY.
( om Zc and Znc)
( om model)
Well
2kHz
4kHz
10kHz
2kHz
4kHz
10kHz
expec .
1
-
-
-
-
-
-
Medium
2
2.43
3.1
3.76
0.98
0.90
0.90
0.900
3
2.18
2.6
3.24
0.94
0.85
0.88
0.690
4
1.17
1.5
2.21
0.82
0.72
0.82
0.610
5
0.21
0.5
0.84
0.32
0.44
0.44
0.410
6
-
0.05
-
-
0.037
-
0.036
7
-
0.015
-
-
0.016
-
0.024
8
-
-
-
-
-
-
0.005
V. DISCUSSION AND CONCLUSIONS
This wo k desc ibes an a ea dependen model o cell-
elec ode sys ems and i s applica ion o measu e and iden i y
cells du ing cell cul u e p o ocols. A p ac ical ci cui o
elec ode-solu ion-cell simula ion was employed, using an
AHDL desc ip ion o comme cial elec odes, ob aining a good
ma ching. Op imal measu emen equency was iden i ied nea
4 kHz. I was p oposed he cell g ow h e olu ion s udy based
on 8W10E elec ode models. Cu es ob ained expe imen ally,
allows he eal ime g ow h moni o ing by i ing he Rgap
pa ame e . An es ima ion o he numbe o cells was ob ained
by using senso cu es calcula ed om elec ical model
p oposed. Dosime y expe imen s ep oduce simila condi ions
han cell g ow h, bu in his case, i is added a g ow h inhibi o
a di e en dosis. The e is obse ed a dec easing impedance,
below he baseline expec ed (Znc) ha we can no explain.
Howe e , o he con ol and small d ug dosis, impedance
cu es a e pe ec ly aligned. I was i ed a p oposed model
wi h Rgap=22k o explain expe iemen al da a. De ia ions om
da a a e o e 10-20% in ill ac o , mo e accu a e o 4 kHz.
The de ia ions in ill ac o s measu ed a e no small, being
equi ed o analize he in luence o e o sou ces o inc ease he
sys em pe o mance. Fi s , Signal- o-Noise Ra io (SNR) should
be inc eased a he se up. Second, p oposed model has he
ad an age ha need only one pa ame e (Rgap), e sus o he
epo ed model using h ee pa ame e s [8]. One pa ame e
model makes easy o i expe imen al da a, bu can in oduce
inaccu acy. The possibili y o add mo e pa ame e s o he
model should be conside ed in he u u e.
ACKNOWLEDGEMENTS
Pa o his wo k was done hanks he inancial help om
he p ojec : Au o-calib ación y au o- es en ci cui os
analógicos, mix os y de adio ecuencia: Andalusian
Go e nmen p ojec P0-TIC-5386, co- inanced wi h FEDER
p og am. Also, we hanks o Ci oquimica
Ul aes uc u al G oup (BIO132) o Cell Biology Depa men ,
Biology Facul y, Se ille Uni e si y, o i s help a he lab o
de elop he cell cul u e expe imen s.
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