2. Characterization of biological cells

Characterization of biological entities like cells involves the utilization of various methods including but not limited to electrical, magnetic, acoustic, and optical characterization to explore cell properties. In this section, electrical method will be discussed (with focus on dielectrophoresis) since dielectrophoretic force is related, in part, to the electrical properties of the biological cell. In the utilization of electrical method for bioparticle characterization, it is not uncommon to use impedance cytometry, dielectrophoresis, and electrorotation. Impedance cytometry works on the principle that when a particle suspended in a conductive fluid passes through a small orifice (comparable to the size of the particle) created by two electrodes, the passage of the particle through the (usually AC) electric field between the electrodes results in the generation of electric signal, which can be processed to provide valuable information about the electrical properties of the particle. In electrorotation, four electrodes are each charged with AC voltage of different phases to generate a rotating electric field, thus setting up an electrical torque. When a (spherical) particle is placed within this rotating field, it becomes polarized inducing a dipole. The dipole moment induced within this particle rotates with the electric field at certain velocity. However, the multiphase nature of the four electrodes causes the particle to lag behind the field by a factor that depends on the

frequency of the rotating field. Since the particle velocity is determined by the torque in the rotating electric field, electrical properties of the particle can be extracted measuring the dependence of the torque on the field frequency. With dielectrophoresis, the case is different. When a charged or uncharged spherical particle is placed between an unequally dimensioned AC electrode-pair which is generating non-uniform electric field, (Figure 2A) the particle becomes polarized just as the medium in which the particle is suspended [3]. The particle could then move toward the region of high field (HF), low field (LF) or remain unperturbed by the field depending on the properties of the applied electric field, suspending medium and the particle itself. When the particle moves toward the HF region, the phenomenon is termed positive dielectrophoresis (pDEP) while it is called negative dielectrophoresis (nDEP) if the particle's translational motion is toward the LF region [4]. Usually, when a particle is experiencing nDEP, for instance, it does so over a range of frequency. As the frequency changes further, the particle can translate to the pDEP regime. Before this happens, however, at a specific point of inflection where the particle comes to a halt before changing regime must have been reached. The frequency at such point of inflection is termed crossover frequency. At the crossover frequency i.e. after the application of the AC electric field parameters, the particle is only seen vibrating at a spot without any appreciable translational motion. At this point, the particle experiences no DEP force (FDEP = 0).

$$F\_{\rm DEP} = 2\pi r^3 \varepsilon\_0 \varepsilon\_m \text{Re}\left[f\_{\rm CM}\right] \nabla E^2 = \mathbf{0} \tag{3}$$

Eq. (7) represents a simplified presentation of the first crossover frequency ( fcoÞ of a particle in relation to the permittivity and conductivity (electrical properties) of both the particle (εp, σpÞ and its suspending medium (εm, σmÞ respectively. To extract the electrical properties of the particle, it is common to obtain a data set comprising of varied medium conductivity and hence, varied crossover frequency. The conductivity-frequency data is then fitted with the appropriate model representing the biological materials of interest. Human red blood cells (RBCs), for instance, can be modeled as a bag of cytoplasm have an insulating plasma membrane. This type of model is popularly referred to as the single-shell model [5, 6]. Figure 3A shows the representative images of nDEP, pDEP, and crossover states for RBCs at a given AC amplitude and sweeping frequencies. Experiments resulting in these images are generally conducted by suspending the particles in an isotonic medium (5% dextrose and fed into a reservoir sealed onto a borosilicate glass with an interfacial 90°, low-separation electrode-pair connected to an arbitrary waveform generator. At a fixed amplitude output, the frequency of the AC field was varied until the crossover frequency was reached and surpassed. The conductivity of the suspending medium was then sequentially increased using phosphatebuffered saline (PBS) or other conductivity conditioners and at each increase, the corresponding crossover frequency was obtained. For other bioparticles such as the nucleated white blood cells and bacteria, the double-shell and three-shell models can be applied respectively. Detailed shell analysis for biological cells is available in

Images of the particle behavior under different field frequencies. (A) Particles well dispersed before field application. (B) Particles undergoing nDEP forming chains with increased particle-particle interaction. (C) Particles at cross over frequency; no response to the dielectrophoretic force. (D) Particles clinging to the

Applications of Electrokinetics and Dielectrophoresis on Designing Chip-Based Disease…

DOI: http://dx.doi.org/10.5772/intechopen.82637

The popularity of six sigma DMAIC (define, measure, analyze, improve, and control) approach has made more companies to embrace extensive modeling and

diverse literatures [7–10].

59

Figure 3.

high-field region depicting pDEP.

3. Modeling and simulation of microdevices

where <sup>f</sup> CM <sup>¼</sup> <sup>ε</sup> <sup>∗</sup> <sup>p</sup> �<sup>ε</sup> <sup>∗</sup> m ε ∗ <sup>p</sup> þ2ε <sup>∗</sup> m connecting both permittivity and conductivity (electrical properties) of both the particle (εp, σpÞ and its suspending medium (εm, σmÞ respectively.

This implies that the real part of the Clausius-Mossotti (CM) factor, Re f CM � � <sup>¼</sup> <sup>0</sup>:

$$\begin{aligned} \text{That is, } ℜ\left(\frac{\varepsilon\_p^\*-\varepsilon\_m^\*}{\varepsilon\_p^\*+2\varepsilon\_m^\*}\right) = \mathbf{0} \text{ where } \varepsilon\_i^\* = \varepsilon\_i - j\frac{\sigma\_i}{\alpha} \\ \text{Hence, } ℜ\left[\frac{\left(\varepsilon\_p - j\frac{\rho\_p}{\alpha}\right) - \left(\varepsilon\_m - j\frac{\alpha}{\alpha}\right)}{\left(\varepsilon\_p - j\frac{\rho\_p}{\alpha}\right) + 2\left(\varepsilon\_m - j\frac{\alpha\_m}{\alpha}\right)}\right] = \mathbf{0} \end{aligned}$$

$$\operatorname{Re}\left[\frac{\left(\mathbf{e}\_{\mathrm{p}}-\mathbf{j}\frac{\sigma\_{\mathrm{p}}}{\alpha}\right)-\left(\mathbf{e}\_{\mathrm{m}}-\mathbf{j}\frac{\mathbf{m}}{\alpha}\right)}{\left(\mathbf{e}\_{\mathrm{p}}-\mathbf{j}\frac{\sigma\_{\mathrm{p}}}{\alpha}\right)+2\left(\mathbf{e}\_{\mathrm{m}}-\mathbf{j}\frac{\sigma\_{\mathrm{m}}}{\alpha}\right)}\ge\frac{\left(\mathbf{e}\_{\mathrm{p}}-\mathbf{j}\frac{\sigma\_{\mathrm{p}}}{\alpha}\right)+2\left(\mathbf{e}\_{\mathrm{m}}-\mathbf{j}\frac{\sigma\_{\mathrm{m}}}{\alpha}\right)}{\left(\mathbf{e}\_{\mathrm{p}}-\mathbf{j}\frac{\sigma\_{\mathrm{p}}}{\alpha}\right)+2\left(\mathbf{e}\_{\mathrm{m}}-\mathbf{j}\frac{\sigma\_{\mathrm{m}}}{\alpha}\right)}\right]=\mathbf{0}\tag{4}$$

ω

$$\operatorname{Re}\left[\left(\varepsilon\_p - j\frac{\sigma\_p}{\alpha}\right) - \left(\varepsilon\_m - j\frac{m}{\alpha}\right)\right] \left[\left(\varepsilon\_p - j\frac{\sigma\_p}{\alpha}\right) + 2\left(\varepsilon\_m - j\frac{\sigma\_m}{\alpha}\right)\right] = 0\tag{5}$$

$$\begin{split} & \varepsilon\_{p}^{2} + \varepsilon\_{m}\varepsilon\_{p} - j\frac{\varepsilon\_{p}\sigma\_{p}}{\alpha} - 2j\frac{\varepsilon\_{p}\sigma\_{m}}{\alpha} - 2\varepsilon\_{m}^{2} + j\frac{\varepsilon\_{m}\sigma\_{p}}{\alpha} + 2j\frac{\varepsilon\_{m}\sigma\_{m}}{\alpha} + j\frac{\varepsilon\_{p}\left(\sigma\_{m} - \sigma\_{p}\right)}{\alpha} \\ & + 2j\frac{\varepsilon\_{m}\left(\sigma\_{m} - \sigma\_{p}\right)}{\alpha} - j^{2}\frac{\sigma\_{p}\left(\sigma\_{m} - \sigma\_{p}\right)}{\alpha^{2}} - 2j^{2}\frac{\sigma\_{m}\left(\sigma\_{m} - \sigma\_{p}\right)}{\alpha^{2}} = 0 \end{split} \tag{6}$$

Setting the real part to zero with j <sup>2</sup> ¼ �1 gives <sup>ε</sup><sup>2</sup> <sup>p</sup> <sup>þ</sup> <sup>ε</sup>mε<sup>p</sup> � <sup>2</sup>ε<sup>2</sup> <sup>m</sup> <sup>þ</sup> <sup>σ</sup>pð Þ <sup>σ</sup><sup>m</sup> � <sup>σ</sup><sup>p</sup> <sup>ω</sup><sup>2</sup> þ <sup>2</sup> <sup>σ</sup>mð Þ <sup>σ</sup><sup>m</sup> � <sup>σ</sup><sup>p</sup> <sup>ω</sup><sup>2</sup> ¼ 0, ∃ ω ¼ 2πf co with f co as the crossover frequency, then using the identity; a<sup>2</sup> <sup>þ</sup> ab � <sup>2</sup>b<sup>2</sup> <sup>¼</sup> ð Þ <sup>a</sup> � <sup>b</sup> ð Þ <sup>a</sup> <sup>þ</sup> <sup>2</sup><sup>b</sup> , we can rearrange to obtain <sup>f</sup> co as

$$f\_{co} = \frac{1}{2\pi} \sqrt{\frac{\left(\sigma\_p - \sigma\_m\right)\left(\sigma\_p + 2\sigma\_m\right)}{\left(\varepsilon\_p - \varepsilon\_m\right)\left(\varepsilon\_p + 2\varepsilon\_m\right)}}\tag{7}$$

Applications of Electrokinetics and Dielectrophoresis on Designing Chip-Based Disease… DOI: http://dx.doi.org/10.5772/intechopen.82637

### Figure 3.

frequency of the rotating field. Since the particle velocity is determined by the torque in the rotating electric field, electrical properties of the particle can be extracted measuring the dependence of the torque on the field frequency. With dielectrophoresis, the case is different. When a charged or uncharged spherical particle is placed between an unequally dimensioned AC electrode-pair which is generating non-uniform electric field, (Figure 2A) the particle becomes polarized just as the medium in which the particle is suspended [3]. The particle could then move toward the region of high field (HF), low field (LF) or remain unperturbed by the field depending on the properties of the applied electric field, suspending medium and the particle itself. When the particle moves toward the HF region, the phenomenon is termed positive dielectrophoresis (pDEP) while it is called negative dielectrophoresis (nDEP) if the particle's translational motion is toward the LF region [4]. Usually, when a particle is experiencing nDEP, for instance, it does so over a range of frequency. As the frequency changes further, the particle can translate to the pDEP regime. Before this happens, however, at a specific point of inflection where the particle comes to a halt before changing regime must have been reached. The frequency at such point of inflection is termed crossover frequency. At the crossover frequency i.e. after the application of the AC electric field parameters, the particle is only seen vibrating at a spot without any appreciable translational

motion. At this point, the particle experiences no DEP force (FDEP = 0).

3

This implies that the real part of the Clausius-Mossotti (CM) factor,

¼ 0

" #

ω � �

ω � � <sup>x</sup> <sup>ε</sup><sup>p</sup> � <sup>j</sup>

> m ω

<sup>2</sup> σ<sup>p</sup> σ<sup>m</sup> � σ<sup>p</sup> � �

<sup>i</sup> <sup>¼</sup> <sup>ε</sup><sup>i</sup> � <sup>j</sup> <sup>σ</sup><sup>i</sup>

ω

σp ω � � <sup>þ</sup> <sup>2</sup> <sup>ε</sup><sup>m</sup> � <sup>j</sup> <sup>σ</sup><sup>m</sup>

ε<sup>p</sup> � j σp ω � � <sup>þ</sup> <sup>2</sup> <sup>ε</sup><sup>m</sup> � <sup>j</sup> <sup>σ</sup><sup>m</sup>

ε<sup>p</sup> � j σp ω � �

> εmσ<sup>p</sup> <sup>ω</sup> <sup>þ</sup> <sup>2</sup><sup>j</sup>

<sup>2</sup> ¼ �1 gives <sup>ε</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �

� �

� � <sup>σ</sup><sup>p</sup> <sup>þ</sup> <sup>2</sup>σ<sup>m</sup>

� � <sup>ε</sup><sup>p</sup> <sup>þ</sup> <sup>2</sup>ε<sup>m</sup>

<sup>ω</sup><sup>2</sup> ¼ 0, ∃ ω ¼ 2πf co with f co as the crossover frequency, then using the

σ<sup>p</sup> � σ<sup>m</sup>

ε<sup>p</sup> � ε<sup>m</sup>

identity; a<sup>2</sup> <sup>þ</sup> ab � <sup>2</sup>b<sup>2</sup> <sup>¼</sup> ð Þ <sup>a</sup> � <sup>b</sup> ð Þ <sup>a</sup> <sup>þ</sup> <sup>2</sup><sup>b</sup> , we can rearrange to obtain <sup>f</sup> co as

s

<sup>m</sup> þ j

<sup>ω</sup><sup>2</sup> � <sup>2</sup><sup>j</sup>

properties) of both the particle (εp, σpÞ and its suspending medium

ε0εmRe f CM

connecting both permittivity and conductivity (electrical

� �∇E<sup>2</sup> <sup>¼</sup> <sup>0</sup> (3)

ω � �

¼ 0 (4)

¼ 0 (5)

(6)

(7)

ω � �

> σm ω

ε<sup>p</sup> σ<sup>m</sup> � σ<sup>p</sup> � � ω

<sup>m</sup> <sup>þ</sup> <sup>σ</sup>pð Þ <sup>σ</sup><sup>m</sup> � <sup>σ</sup><sup>p</sup>

<sup>ω</sup><sup>2</sup> þ

þ 2 ε<sup>m</sup> � j

εmσ<sup>m</sup> <sup>ω</sup> <sup>þ</sup> <sup>j</sup>

<sup>p</sup> <sup>þ</sup> <sup>ε</sup>mε<sup>p</sup> � <sup>2</sup>ε<sup>2</sup>

h i � �

<sup>2</sup> σ<sup>m</sup> σ<sup>m</sup> � σ<sup>p</sup> � � <sup>ω</sup><sup>2</sup> <sup>¼</sup> <sup>0</sup>

FDEP ¼ 2πr

<sup>¼</sup> 0 where <sup>ε</sup> <sup>∗</sup>

<sup>m</sup> ð Þ<sup>ω</sup>

<sup>σ</sup><sup>m</sup> ð Þ <sup>ω</sup>

� ε<sup>m</sup> � j

εpσ<sup>m</sup> <sup>ω</sup> � <sup>2</sup>ε<sup>2</sup>

<sup>f</sup> co <sup>¼</sup> <sup>1</sup> 2π

where <sup>f</sup> CM <sup>¼</sup> <sup>ε</sup> <sup>∗</sup>

Bio-Inspired Technology

(εm, σmÞ respectively.

Hence, Re <sup>ε</sup><sup>p</sup> � <sup>j</sup>

Re

ε2

<sup>2</sup> <sup>σ</sup>mð Þ <sup>σ</sup><sup>m</sup> � <sup>σ</sup><sup>p</sup>

58

Re f CM � � <sup>¼</sup> <sup>0</sup>: That is, Re <sup>ε</sup> <sup>∗</sup>

<sup>p</sup> �<sup>ε</sup> <sup>∗</sup> m ε ∗ <sup>p</sup> þ2ε <sup>∗</sup> m

<sup>p</sup> � <sup>ε</sup> <sup>∗</sup> m ε ∗ <sup>p</sup> þ2ε <sup>∗</sup> m � �

ε<sup>p</sup> � j <sup>σ</sup><sup>p</sup> ð Þ<sup>ω</sup> <sup>þ</sup><sup>2</sup> <sup>ε</sup><sup>m</sup> � <sup>j</sup>

ε<sup>p</sup> � j σp ω � � � <sup>ε</sup><sup>m</sup> � <sup>j</sup> <sup>m</sup>

σp ω � �

> εpσ<sup>p</sup> <sup>ω</sup> � <sup>2</sup><sup>j</sup>

ε<sup>m</sup> σ<sup>m</sup> � σ<sup>p</sup> � � <sup>ω</sup> � <sup>j</sup>

Setting the real part to zero with j

h i � �

ε<sup>p</sup> � j σp ω � � <sup>þ</sup> <sup>2</sup> <sup>ε</sup><sup>m</sup> � <sup>j</sup> <sup>σ</sup><sup>m</sup>

Re ε<sup>p</sup> � j

<sup>p</sup> þ εmε<sup>p</sup> � j

þ 2j

<sup>σ</sup><sup>p</sup> ð Þ<sup>ω</sup> � <sup>ε</sup><sup>m</sup> � <sup>j</sup>

� �

Images of the particle behavior under different field frequencies. (A) Particles well dispersed before field application. (B) Particles undergoing nDEP forming chains with increased particle-particle interaction. (C) Particles at cross over frequency; no response to the dielectrophoretic force. (D) Particles clinging to the high-field region depicting pDEP.

Eq. (7) represents a simplified presentation of the first crossover frequency ( fcoÞ of a particle in relation to the permittivity and conductivity (electrical properties) of both the particle (εp, σpÞ and its suspending medium (εm, σmÞ respectively. To extract the electrical properties of the particle, it is common to obtain a data set comprising of varied medium conductivity and hence, varied crossover frequency.

The conductivity-frequency data is then fitted with the appropriate model representing the biological materials of interest. Human red blood cells (RBCs), for instance, can be modeled as a bag of cytoplasm have an insulating plasma membrane. This type of model is popularly referred to as the single-shell model [5, 6]. Figure 3A shows the representative images of nDEP, pDEP, and crossover states for RBCs at a given AC amplitude and sweeping frequencies. Experiments resulting in these images are generally conducted by suspending the particles in an isotonic medium (5% dextrose and fed into a reservoir sealed onto a borosilicate glass with an interfacial 90°, low-separation electrode-pair connected to an arbitrary waveform generator. At a fixed amplitude output, the frequency of the AC field was varied until the crossover frequency was reached and surpassed. The conductivity of the suspending medium was then sequentially increased using phosphatebuffered saline (PBS) or other conductivity conditioners and at each increase, the corresponding crossover frequency was obtained. For other bioparticles such as the nucleated white blood cells and bacteria, the double-shell and three-shell models can be applied respectively. Detailed shell analysis for biological cells is available in diverse literatures [7–10].
