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A short tutorial contribution to impedance and AC-electrokinetic characterization and manipulation of cells and media: Are electric methods more versatile than acoustic and laser methods? Cover

A short tutorial contribution to impedance and AC-electrokinetic characterization and manipulation of cells and media: Are electric methods more versatile than acoustic and laser methods?

Journal of Electrical Bioimpedance
Volume 5 (2014): Issue 1 (January 2014)
By: Jan Gimsa,  Marco Stubbe and  Ulrike Gimsa  
Open Access
|Nov 2014

Figures & Tables

Fig. 1

Two complementary models consisting of blocks of air and water representing the membranous and aqueous media in cellular systems. a) Air block confined by two water blocks. b) Water block confined by air blocks. The external electrode charges influence charges in water but not in air. Induced charges are drawn for DC or AC for the half-wave during which the left electrode is positively charged.
Two complementary models consisting of blocks of air and water representing the membranous and aqueous media in cellular systems. a) Air block confined by two water blocks. b) Water block confined by air blocks. The external electrode charges influence charges in water but not in air. Induced charges are drawn for DC or AC for the half-wave during which the left electrode is positively charged.

Fig. 2

Complementary polarization and force effects in air-water models. Induced charges are located in the medium with the higher polarizability. The interaction of these charges with the electrode charges, i.e. the external field, leads to a compression of the air bubble (a) and an elongation of the water droplet (b).
Complementary polarization and force effects in air-water models. Induced charges are located in the medium with the higher polarizability. The interaction of these charges with the electrode charges, i.e. the external field, leads to a compression of the air bubble (a) and an elongation of the water droplet (b).

Fig. 3

Single-shell cell model obtained by introducing the water droplet (Figure 2b) into a slightly larger air bubble (Figure 2a), leaving an air film (i.e. a "biological membrane") around the droplet’s surface. It was assumed that the external bulk medium has a lower conductivity than the internal bulk while both bulk media are isotonic.
Single-shell cell model obtained by introducing the water droplet (Figure 2b) into a slightly larger air bubble (Figure 2a), leaving an air film (i.e. a "biological membrane") around the droplet’s surface. It was assumed that the external bulk medium has a lower conductivity than the internal bulk while both bulk media are isotonic.

Fig. 4

The (horizontally oriented) external field (component) Ea induces the potentials Ψ0a=zEa  and  Ψca*$\Psi _{0}^{a}=z{{E}_{a}}\,\,and\,\,\Psi _{c}^{a*}$in the absence (subscript 0) and the presence (subscript c) of an ellipsoidal (cellular) object at the site of the pole of its semiaxis a. Ψca*$\Psi _{c}^{a*}$is highest for a vacuum object with a polarizability comparable to that of a membrane covered cell at low frequency. For example, a vacuum sphere attracts the equipotential plane that is located at the "influential radius" ainf distance of 3a/ 2 from the symmetry plane, which can be assumed to be at 0 V. While the maximum of Ψca*=ainfEa$\Psi _{c}^{a*}={{a}_{\inf }}{{E}_{a}}$is determined by the influential radius, i.e. the geometry of the object, its actual value is determined by the effective electric properties of object and suspension medium.
The (horizontally oriented) external field (component) Ea induces the potentials Ψ0a=zEa  and  Ψca*$\Psi _{0}^{a}=z{{E}_{a}}\,\,and\,\,\Psi _{c}^{a*}$in the absence (subscript 0) and the presence (subscript c) of an ellipsoidal (cellular) object at the site of the pole of its semiaxis a. Ψca*$\Psi _{c}^{a*}$is highest for a vacuum object with a polarizability comparable to that of a membrane covered cell at low frequency. For example, a vacuum sphere attracts the equipotential plane that is located at the "influential radius" ainf distance of 3a/ 2 from the symmetry plane, which can be assumed to be at 0 V. While the maximum of Ψca*=ainfEa$\Psi _{c}^{a*}={{a}_{\inf }}{{E}_{a}}$is determined by the influential radius, i.e. the geometry of the object, its actual value is determined by the effective electric properties of object and suspension medium.

Fig. 5

Equipotential plane distribution in and around a spherical single-shell model of radius r . The external distributions are identical for Maxwell's equivalent body (sketched for the left hemisphere) and the membrane-covered object (sketched for the right hemisphere). Important points in the model are marked by circles. The potentials at these points can be obtained from the RC-model at the bottom, which permits calculation of the induced dipole moment and transmembrane potential. From the existence of Maxwell's equivalent body, it follows that electric measurements (detecting the induced dipole moment) do not allow one to distinguish whether frequency-dependent object properties stem from internal structures or from the frequency-dependent properties of the media of which the object is composed.
Equipotential plane distribution in and around a spherical single-shell model of radius r . The external distributions are identical for Maxwell's equivalent body (sketched for the left hemisphere) and the membrane-covered object (sketched for the right hemisphere). Important points in the model are marked by circles. The potentials at these points can be obtained from the RC-model at the bottom, which permits calculation of the induced dipole moment and transmembrane potential. From the existence of Maxwell's equivalent body, it follows that electric measurements (detecting the induced dipole moment) do not allow one to distinguish whether frequency-dependent object properties stem from internal structures or from the frequency-dependent properties of the media of which the object is composed.

Fig. 6

(a) ED according to Figure 2. (b) For three-axial, ellipsoidal objects each axis may be oriented in parallel to the field. Orientation depends on field frequency, object and medium properties. The field electrodes as well as the possible (frequency-dependent) forces and torques are marked by bold dark lines and arrows, respectively.
(a) ED according to Figure 2. (b) For three-axial, ellipsoidal objects each axis may be oriented in parallel to the field. Orientation depends on field frequency, object and medium properties. The field electrodes as well as the possible (frequency-dependent) forces and torques are marked by bold dark lines and arrows, respectively.

Fig. 7

(a) Evenly polarizable objects always attract one another (compare to charges in Figure 2) leading to the formation of pairs or pearl-chains. (b) Elongation and compression according to Figure 2a and b translate into positive or negative DP, i.e. movement of the object towards high and low field, respectively. (c) Strongly inhomogeneous fields can be used for the collection of submicro-objects or field caging.
(a) Evenly polarizable objects always attract one another (compare to charges in Figure 2) leading to the formation of pairs or pearl-chains. (b) Elongation and compression according to Figure 2a and b translate into positive or negative DP, i.e. movement of the object towards high and low field, respectively. (c) Strongly inhomogeneous fields can be used for the collection of submicro-objects or field caging.

Fig. 8

(a) Rotating fields may induce a torque leading to object rotation in (increasing effective polarizability of object with frequency) or against (decreasing effective polarizability) the direction of field rotation. (b) This torque corresponds to the translational forces in TWDP. Lifting or attracting forces correspond to the DP forces in Figure 7b.
(a) Rotating fields may induce a torque leading to object rotation in (increasing effective polarizability of object with frequency) or against (decreasing effective polarizability) the direction of field rotation. (b) This torque corresponds to the translational forces in TWDP. Lifting or attracting forces correspond to the DP forces in Figure 7b.

Fig. 9

Real and imaginary parts of the Clausius-Mossotti factor (full lines, left ordinate) as well as the induced transmembrane potential (dashed line, right ordinate) at the pole of a spherical cell model (Table 1). Dotted lines: spectra are reduced to the membrane dispersion when the permittivities of the bulk media are neglected. Vertical dashed line: -3 dB frequency of the absolute value of the induced transmembrane potential.
Real and imaginary parts of the Clausius-Mossotti factor (full lines, left ordinate) as well as the induced transmembrane potential (dashed line, right ordinate) at the pole of a spherical cell model (Table 1). Dotted lines: spectra are reduced to the membrane dispersion when the permittivities of the bulk media are neglected. Vertical dashed line: -3 dB frequency of the absolute value of the induced transmembrane potential.

Fig. 10

Real and imaginary parts of the specific impedance (IMP=1/σS*)$\left( \text{IMP=}{1}/{\sigma _{S}^{*}}\; \right)$of a cell suspension over frequency (top), as well as in the complex plane (bottom) calculated for the parameters of Table 1 (full lines, equation (18)). The spectra are reduced to the membrane dispersion when the permittivities of the bulk media are neglected (dotted lines, equation (19)). The characteristic membrane-dispersion frequency of the suspension fc1IMP$f_{c1}^{IMP}$corresponds to the frequency of the peak in the imaginary part. In the complex plot, it is the frequency of the point obtained by dropping a perpendicular from the center of the semicircle.
Real and imaginary parts of the specific impedance (IMP=1/σS*)$\left( \text{IMP=}{1}/{\sigma _{S}^{*}}\; \right)$of a cell suspension over frequency (top), as well as in the complex plane (bottom) calculated for the parameters of Table 1 (full lines, equation (18)). The spectra are reduced to the membrane dispersion when the permittivities of the bulk media are neglected (dotted lines, equation (19)). The characteristic membrane-dispersion frequency of the suspension fc1IMP$f_{c1}^{IMP}$corresponds to the frequency of the peak in the imaginary part. In the complex plot, it is the frequency of the point obtained by dropping a perpendicular from the center of the semicircle.

Fig. 11

Volume fraction dependencies of fc1IMP$f_{c1}^{IMP}$obtained from four different models for σi>>σe,   σi=σe,${{\sigma }_{i}}>>{{\sigma }_{e}},\,\,\,{{\sigma }_{i}}={{\sigma }_{e}},$and σi=0.001σe.${{\sigma }_{i}}=0.001{{\sigma }_{\text{e}}}.$Equation (18) corresponds to the complete model of Foster and Schwan [1996] (dotted lines). While their simplified fc1IMP$f_{c1}^{IMP}$expression slightly increases with p (full lines), the new equation (20) predicts a moderate decrease (dashed lines), in accordance with the complete models. In all models, the points for p=0 are identical with fc1IMP=fc1$[f_{c1}^{IMP}={{f}_{c1}}$(equations 20-23).
Volume fraction dependencies of fc1IMP$f_{c1}^{IMP}$obtained from four different models for σi>>σe,   σi=σe,${{\sigma }_{i}}>>{{\sigma }_{e}},\,\,\,{{\sigma }_{i}}={{\sigma }_{e}},$and σi=0.001σe.${{\sigma }_{i}}=0.001{{\sigma }_{\text{e}}}.$Equation (18) corresponds to the complete model of Foster and Schwan [1996] (dotted lines). While their simplified fc1IMP$f_{c1}^{IMP}$expression slightly increases with p (full lines), the new equation (20) predicts a moderate decrease (dashed lines), in accordance with the complete models. In all models, the points for p=0 are identical with fc1IMP=fc1$[f_{c1}^{IMP}={{f}_{c1}}$(equations 20-23).

Fig. 12

Top- (a, b) and side-view (c) sketches of directly heated ETμP (a), T-channel ETμP (b), and ETTWμP (c) structures with temperature distributions in gray scaling (one gray step corresponds to approximately 1 K), fluid channel and metal-layer geometries. For the heat conductivities of the channel walls, bottom and cover see Stubbe et al. [2007]. Circumferences of field electrodes (E) and fluid channels are marked by thin and bold lines, respectively. G and H in (a) designate the common ground connector for field generation and the resistive heating meander. Straight arrows designate averaged medium velocities below the Maxwell-Wagner frequency (a and b) or in the β-dispersion range (c). Bent arrows in (c) sketch the effective AC and TW field distribution.
Top- (a, b) and side-view (c) sketches of directly heated ETμP (a), T-channel ETμP (b), and ETTWμP (c) structures with temperature distributions in gray scaling (one gray step corresponds to approximately 1 K), fluid channel and metal-layer geometries. For the heat conductivities of the channel walls, bottom and cover see Stubbe et al. [2007]. Circumferences of field electrodes (E) and fluid channels are marked by thin and bold lines, respectively. G and H in (a) designate the common ground connector for field generation and the resistive heating meander. Straight arrows designate averaged medium velocities below the Maxwell-Wagner frequency (a and b) or in the β-dispersion range (c). Bent arrows in (c) sketch the effective AC and TW field distribution.

Fig. 13

Idealized time-averaged volume forces FE$\left\langle {{F}_{E}} \right\rangle $of aqueous medium with a relative permittivity of 80 and a specific conductivity of 1.3 S/m over field frequency. The solid curve corresponds to finite-element simulations for the ETμP structures of Figures 11a and 13b obtained for an effective field-electrode voltage of 20 VPP over 390 μm field-electrode distance and a temperature difference across the electrode gap of approximately 5 K [Stubbe et al. 2013]. The dashed line presents the maximum force generated in a ETTWμP under the same conditions. The pump-peak frequency corresponds to the center frequency between the two ETμP plateaus.
Idealized time-averaged volume forces FE$\left\langle {{F}_{E}} \right\rangle $of aqueous medium with a relative permittivity of 80 and a specific conductivity of 1.3 S/m over field frequency. The solid curve corresponds to finite-element simulations for the ETμP structures of Figures 11a and 13b obtained for an effective field-electrode voltage of 20 VPP over 390 μm field-electrode distance and a temperature difference across the electrode gap of approximately 5 K [Stubbe et al. 2013]. The dashed line presents the maximum force generated in a ETTWμP under the same conditions. The pump-peak frequency corresponds to the center frequency between the two ETμP plateaus.

Fig. 14

DP collection of baker's yeast at the electrode pads of a glass neurochip with a 52 microelectrode MEA. The on-chip conducting paths of the MEA were 5 μm wide, insulated by >1μm silicon-nitride and terminated by circular pad openings with a diameter of 25 μm. The rectangular MEA-pad distances were 100 μm. All conducting structures were made from Pt. (a) Sedimented cells after cell seeding; (b) after 2 min of cell collection.
DP collection of baker's yeast at the electrode pads of a glass neurochip with a 52 microelectrode MEA. The on-chip conducting paths of the MEA were 5 μm wide, insulated by >1μm silicon-nitride and terminated by circular pad openings with a diameter of 25 μm. The rectangular MEA-pad distances were 100 μm. All conducting structures were made from Pt. (a) Sedimented cells after cell seeding; (b) after 2 min of cell collection.

Fig. 15

Microscopic images of ETμP structures on thin glass according to Figures 12b and 12a (dark: 100 nm thick platinum structures; light gray: 60 μm thick polymer-wall structures; light areas: fluid channels). The central pump channels were 250 μm wide.
Microscopic images of ETμP structures on thin glass according to Figures 12b and 12a (dark: 100 nm thick platinum structures; light gray: 60 μm thick polymer-wall structures; light areas: fluid channels). The central pump channels were 250 μm wide.

Fig. 16

(a) Glass cell-culture chip (size: half a microscopic slide) with two ETμPs according to Figure 12a (diagonally oriented structures at the lower left and upper right corners), eight IDES for impedance detection of cell adhesion (light rectangular structures), one oxygen sensor (fine structure with two connectors at the lower right) and two pH sensors (dark rectangles at the lower center and in the top row). (b) ETμP-flow simulation in the closed microfluidic poly-dimethyl-siloxane structure. The highest velocity is reached in the back-flow path. (c) All sensors and pump structures were located in the fluid channels. From the left: oxygen sensor, ETμP, two 1.4 x 0.5 mm2 IDES with 30 μm and 50 μm pitches.
(a) Glass cell-culture chip (size: half a microscopic slide) with two ETμPs according to Figure 12a (diagonally oriented structures at the lower left and upper right corners), eight IDES for impedance detection of cell adhesion (light rectangular structures), one oxygen sensor (fine structure with two connectors at the lower right) and two pH sensors (dark rectangles at the lower center and in the top row). (b) ETμP-flow simulation in the closed microfluidic poly-dimethyl-siloxane structure. The highest velocity is reached in the back-flow path. (c) All sensors and pump structures were located in the fluid channels. From the left: oxygen sensor, ETμP, two 1.4 x 0.5 mm2 IDES with 30 μm and 50 μm pitches.

Standard parameters of the spherical cell model_

ParameterValue
Cell radius (r)5 μm
Membrane thickness (d)8 nm
Conductivities
external (σe)0.1 S/m
membrane (σm)10-6 S/m corresponding to 125 S/m2
internal (σi)0.01σe to σi>>σe
Relative permittivities ε
external ( e)80
membrane (ε) mε9.04 corresponding to 0.01 F/m2
internal ( i)50
Volume fraction (p)≤10% (not for single cell calculations)
External field strength for calculation of transmembrane potential133.33 kV/m
DOI: https://doi.org/10.5617/jeb.557 | Journal eISSN: 1891-5469
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Language: English
Page range: 74 - 91
Submitted on: Feb 7, 2013
Published on: Nov 2, 2014
Published by: University of Oslo
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Mixing equation,
single-shell model,
travelling wave,
electro-osmosis,
micropump,
induced transmembrane potential,
RC model,
influential radius,
Maxwell's equivalent body
Related subjects:
Engineering,
Bioengineering and biomedical engineering,
Biomedical electronics,
Physics,
Spectroscopy and metrology,
Life sciences,
Biophysics,
Medicine,
Biomedical engineering

© 2014 Jan Gimsa, Marco Stubbe, Ulrike Gimsa, published by University of Oslo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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