1 Introduction

In the completion the sequencing of the human genome (Consortium 2001; Venter 2001), scientists need to develop new research tools to analyze a vast array of biological information. The growing availability of the genome sequence data is opening up the possibility of developing a comprehensive understanding of complex cellular processes. In traditional approaches, cellular parameters are represented by populations. They are averages and cannot exactly represent individual cells. Additionally, heterogeneity cannot be evaluated in bulk cultures. Multiple parameters must be measured in real time in single living cells to correlate cellular events with genomic information and thus understand complex cellular processes.

For single cell analysis, cell impedance analysis (Gilchrist et al. 2001; Schmukler et al. 1988; Bao et al. 1993) has developed rapidly and has become an effective method of biological measurement. The temperature, electric conductivity and mobility of a cell can influence its impedance characteristics directly or indirectly so the cell impedance characteristic can be used to understand biological characteristic behavior. Measurements on single cells also provide more accurate and in-depth information about electrical properties than do those of pathological tissues. Single-cell impedance also can be applied to study the effect of pharmaceutical compounds (Ye et al. 2003), the effect of viral and bacterial infections (Niikura et al. 2004; Yang et al. 2003; Verma and Singh 2003; Gau et al. 2001), and environmental parameters (Gilchrist et al. 2005), toxicity (Giaever and Keese 1992) and other factors.

Microsensors are one of the preferred technologies that are adopted to characterize cells according to their electrical properties in the frequency domain for single cell sensing. Recent developments in miniaturized impedance measurement systems enabled the impedance of cells to be measured (Gomez et al. 2001; Gawad et al. 2004; Ayliffe et al. 1999). Impedance studies of cells have demonstrated that the measurement of dielectric properties can reveal the pathological status of the cell. Bio-impedance analysis detects the effects of multiple physiological parameters on gene behavior. In the production of microscale sensors and actuators, micro-electro-mechanical-systems (MEMS) is an enabling technology that is used in semiconductor fabrication (Liao et al. 2005; Jang et al. 2007), and involves the integration of mechanical elements, sensors, actuators, and electronics on a common silicon substrate using microfabrication technology. Such microsystems have the potential to lower the cost, increase the accuracy, and reduce the labor involved in performing assays, as compared to macroscale systems. Therefore, the development of MEMS modules for characterizing single cells is essential to measuring multiple parameters in small colonies of living cells in real time.

Stable environments must be maintained for cells of interest to probe cellular functions at the single cell level. Simultaneously, the environment must also be designed to enable effective determination of multiple parameters of cells in real time as functions of environmental changes. In recent years, the general methods used to capture cells have been mechanical trapping, electric trapping and optical tweezers. Mechanical trapping employs MEMS technology and pressure driving to cause fluids to flow through the microchannel. It separates cells of various cell exteriority and sizes (Carlson et al. 1997; Bakajin et al. 1998) or utilizes silicon pillars to catch biological particles (Andersson et al. 2000). Electric trapping uses dielectric characterization of cells to separate them. Xu et al. (2001) demonstrated that the electrodes attracted leukocyte and repelled erythrocyte at frequencies of between 2 and 10 MHz. Fiedler et al. (1998) and Huang et al. (2001) adopted similar approaches to divide various biological particles. Optical tweezers are scientific instruments that use a laser beam to provide an attractive or repulsive force to hold or move dielectric objects. Rusu et al. (2001) and Liang et al. (1994) employed optical tweezers successfully to move and control cells. However, electric trapping may alter the characteristics of a cell because of the high electric field (Weaver and Chizmadzhev 1996) and optical tweezers may damage cells because of the heat generated by the laser beam. Hence, a method that employs simple three-pillar microstructures as a passive means of capturing single cells physically is developed in this study.

This work presents a microfluidic device for physical capture and measuring impedance by impedance spectroscopy at the single cell level. The device has a PDMS channel and a glass substrate with electrodes. Additionally, an equivalent circuit model is established and fits well with the experimental results of single HeLa cells. Furthermore, the commercial software CFD–ACE+ is used to study the flow around the microstructures in the channel.

2 Materials and methods

2.1 Fabrication of devices

The microfluidic device was composed of a PDMS channel with micro pillars and a glass substrate with electrodes. The PDMS channel was defined using an SU-8 (MicroChem SU-8) mold. The SU-8 was placed on a 4 in. silicon wafer and developed to define structures with a height of 25 μm. The commercially available SYLGARD 184A (pre-polymer) and SYLGARD 184B (a curing agent) were mixed with a 10:1 weight ratio and placed on an SU-8 mold. The width and depth of the microchannel were 100 and 25 μm, respectively. The size of the micro pillars was 10 × 10 × 25 μm. The electrodes, including a layer of 15 nm-thick Cr and 65-nm thick Au, were deposited using an E-beam evaporator on glass substrate, patterned by standard photolithographic techniques, and etched using Au and Cr etchant. Finally, the PDMS channel and the glass substrate with electrodes were treated by O2 plasma (800 W, 12 s) to increase bonding strength. The alignment of the PDMS channel with electrodes was completed in few minutes to prevent loss of O2 plasma effectiveness. Figure 1 schematically depicts the device and the complete process of cell-trapping.

Fig. 1
figure 1

(a) 3D schematic of the device and complete cell trapping process (b) 2D schematic of the device

Full size image

2.2 Cell culture

In this study, the impedance of HeLa cells (human cervical epithelioid carcinoma) was measured. The HeLa cells were cultured in a humidified incubator at 37°C with 5% CO2. The culture medium consisted of 90% minimum essential medium (Eagle) with Eagle’s BSS, 2 mM l-glutamine, 1.5 g/l sodium bicarbonate, 0.1 mM non-essential amino acids, and 1.0 mM sodium pyruvate + 10% fetal bovine serum.

3 Theory

An equivalent circuit model, including the cell, dielectric capacitance and electrodes is established. The system can be modeled electrically as cell impedance Z cell in parallel with a dielectric capacitance C di and both in series with a pair of electrodes resistor R e, as presented in Fig. 2. The model is operated at low frequency between 1 and 100 kHz. Z cell comprises both cell membrane C c and cytoplasm R c. C di represents a capacitance that has contributions from all of the materials that are between two electrodes, including the solution. The impedance Z cell is R c+1/jωC c, where ω is the angular frequency of the electrical single. The overall impedance of the system can be written as

$$ Z = 2R_{{\text{e}}} + \frac{1} {{j\omega C_{{{\text{di}}}} + \frac{1} {{R_{{\text{c}}} + \raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {j\omega C_{{\text{c}}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${j\omega C_{{\text{c}}} }$}}}}} $$
(1)

Z R and Z I are real and imaginary part of Z, respectively, and given by Eqs. 2 and 3.

$$ Z_{{\text{R}}} = 2R_{{\text{e}}} + \frac{{C^{2}_{{\text{c}}} R_{{\text{c}}} }} {{{\left( {C_{{\text{c}}} + C_{{{\text{di}}}} } \right)}^{2} + {\left( {\omega C_{{\text{c}}} C_{{{\text{di}}}} R_{{\text{c}}} } \right)}^{2} }} $$
(2)
$$ Z_{{\text{I}}} = - \frac{1} {\omega }\frac{{C_{{\text{c}}} + C_{{{\text{di}}}} + \omega ^{2} C^{2}_{{\text{c}}} C_{{{\text{di}}}} R^{2}_{{\text{c}}} }} {{{\left( {C_{{\text{c}}} + C_{{{\text{di}}}} } \right)}^{2} + {\left( {\omega C_{{\text{c}}} C_{{{\text{di}}}} R_{{\text{c}}} } \right)}^{2} }} $$
(3)
Fig. 2
figure 2

The equivalent circuit model of the system

Full size image

4 Simulation

A commercial software package, CFD–ACE+ (CFD Research Corporation), was used to produce a model to study the flow of the channel. The code has unique capabilities for multiphysics, multiscale and coupled simulations of fluid, thermal, chemical, biological, electrical and mechanical phenomena for real-world applications. The program provided an integrated geometry and grid generation module, a graphical user interface for preparing the model, a computational solver for performing the simulation, and an interactive visualization program. These were used to analyze the simulation results.

Figure 3 presents the velocity field around the micro pillars at a pressure difference of 100 Pa between the inlet and the outlet of the channel. This numerical model was two-dimensional and incorporated a fluid module. The width and length of the model were 200 and 100 μm, respectively, and the size of three micro pillars was 10 × 10 μm. The maximum velocity of the fluid near the region of the three micro pillars was about 0.26 m/s. The probability of cell capture was calculated from the percentage of the channel width where the velocity vectors flow into the trap. According to the velocity field, the probability of cell capture by three micro pillars was around 10%.

Fig. 3
figure 3

Velocity field around micro pillars at pressure difference of 100 Pa between and outlet of the channel

Full size image

5 Results and discussion

The micro pillars easily trapped cell debris when the cell solution flowed through the channel, causing the experiment to fail. Accordingly, a protocol with a centrifuge was developed and applied to eliminate the cell debris in the solution. The solution of HeLa cells with a concentration of 2.25 × 105 cells/c.c was injected into the microfluidic channel using an infusion pump (KD Scientific Inc., KDS100) at a flow rate of 5 ml/h. The chips were visually inspected using an optical microscope (Nikon 50i) during the experimental process. Figure 4(a) shows the cell-trapped structures before injection and a single cell of HeLa was trapped successfully among pillars as shown in Fig. 4(b).

Fig. 4
figure 4

(a) The cell-trapped structure before injection of cell solution (b) the cell-trapped structure with a single cell of HeLa after injection

Full size image

When the cell was captured, the infusion pump was switched off to enable the impedance measurement using Precision Impedance Analyzers (Kayne Kerr Inc., 6440B). The 6440B impedance analyzer was self-calibrated, using short and open standard calibration, before the cells were measured. The measurement system was set to the probe station chuck. The Faraday cage was applied to shield electromagnetically the chuck zone. Since the measurement system was capacitive before the samples were injected, the impedance phase angle of the system was −90° at the overall excitation frequency after calibration.

Figures 5 and 6 plot the magnitude and phase of impedance, respectively, as functions of frequency for two different samples (isotonic solution and a single HeLa cell) at operating voltages of 0.1 and 1.5 V. At 0.1 V, the curves of the magnitude and phase were much rougher than those at 1.5 V because the noise was significant when the sample was measured at low voltage. The impedance of isotonic solution at 0.1 V was similar to those at 1.5 V because the electrical resistivity and dielectric of isotonic solution did not vary with the operating voltage. The magnitude of the HeLa cell impedance was smaller than magnitude of isotonic solution about 1∼2 orders in both cases, because these cells were more conductive than isotonic solution. At 1.5 V, the cell phase rose from −74.5 to −27.8° between 1 and 100 kHz, in a manner similar to the phase of the series circuit.

Fig. 5
figure 5

Impedance magnitude of isotonic solution and the single HeLa cell

Full size image
Fig. 6
figure 6

Impedance phase of isotonic solution and the single HeLa cell at operating voltages of (a) 0.1 V (b) 1.5 V

Full size image

Figure 7 plots the impedance of a single HeLa cell at various operating voltages from 0.1 to 1.5 V and frequencies from 1 to 100 kHz. In the frequency range from 1 to 100 kHz, the magnitude of the HeLa cell decreased at all operating voltages: for example, from 2.6 × 107 to 3.3 × 105 Ω at 0.1 V. Increasing the frequency reduced the magnitude of the HeLa cell impedance because the HeLa cell was capacitive. Additionally, increasing the operating voltage decreased the magnitude of the HeLa cell impedance. The impedance of the HeLa cell fell from 1.1 × 106 to 8.5 × 104 Ω between 0.1 and 1.5 V at a frequency of 30 kHz. A strong electric filed may open the ionic channels of the cell membrane, increasing ion exchange between the cytoplasm and the isotonic solution (Weaver and Chizmadzhev 1996). Therefore, the electrical resistivity of the cells declines and the dielectric constant of the cells increases. Figure 7(b) plots the phase of the HeLa cell impedance. At an operating voltage of 0.8 V, the phase decreased from −66.9 to −72.2° below 30 kHz because the system impedance response was characteristic of a parallel circuit. In contrast, the phase increased from −72.2 to −67.5° at 0.8 V between 30 and 100 kHz because the system impedance response was characteristic of a series circuit. The phase of the HeLa cell impedance was characteristics of a series circuit when the operating voltage exceeded 0.8 V because Z cell became significant.

Fig. 7
figure 7

a Impedance magnitude and b phase of single HeLa at various operating voltages from 0.1 to 1.5 V

Full size image

The equivalent circuit model of the system including C c and R c, C di and R e shown in Fig. 2 was fitted to the experimental results. The values R e = 3 × 104 Ω and C di = 5 × 10−12 F were extracted by curve fitting for the HeLa cell and held fixed when the model was fitted to all other samples. Figure 8 plots simulated (solid line) and measured (circles) system impedance magnitude and phase response at 0.1 V, with parameters R c = 6 × 107 Ω, C c = 2.5 × 10−12 F, R e = 3 × 104 kΩ and C di = 5 × 10−12 F. Table 1 presents the values of C c and R c obtained from the fits to all the samples. Since increasing the operating voltage may open ionic channels, R c declines and C c increases. Yao et al. (2004) demonstrate that the approximate capacitance of malignant tumor cell membrane is 6.95 × 10−9 F. It is higher than that obtained in this study because they use higher operation voltage (100 V). According to the developed model, it can be seen that the higher operation voltage results in higher cell capacitance.

Fig. 8
figure 8

Plot of simulated (solid line) and measured (circles) system impedance magnitude and phase response at 0.1 V, with parameter R c = 6 × 107 Ω, C c = 2.5 × 10−12 F, R e = 3 × 104 Ω and C di = 5 × 10−12 F

Full size image
Table 1 Parameters obtained from fitting circuit model to impedance data
Full size table

6 Conclusions

This study presents a microfluidic device that can perform physical capture and measure impedance by impedance spectroscopy at the single cell level. This microfluidic device comprises a PDMS channel with micro pillars and a glass substrate with electrodes. The experiments reveal that the single HeLa cell is successfully captured by the micro pillars. Its impedance is measured by impedance spectroscopy at frequencies of between 1 and 100 kHz. The commercial software CFD–ACE+ is adopted to study the flow of the microstructures in the channel; the probability of cell capture by three micro pillars is about 10%. Additionally, an equivalent circuit model, incorporating the cell, dielectric capacitance and electrodes, is established. The circuit can be modeled electrically as Z cell in parallel with C di and both in series with a pair of R e. The equivalent circuit model fits the experimental results closely at various operating voltages. The system parameters can be obtained from the curving fitting of all samples. According to the experimental results for HeLa cell and isotonic solution, the magnitude of the HeLa cell is smaller than magnitude of isotonic solution about 1∼2 orders at 0.1 and 0.5 V because this cell is more conductive than isotonic solution. The results of the HeLa cell experiments show that the magnitude of the HeLa cell declines as the frequency increases at all operation voltages because the HeLa cell is capacitive. Furthermore, increasing the operating voltage reduces the magnitude of the HeLa cell impedance because a strong electric filed may increase the exchange of ions between cytoplasm and isotonic solution. Below the operating voltage of 0.9 V, the system impedance responds like a parallel circuit below 30 kHz and like a series circuit between 30 and 100 kHz. The phase of the HeLa cell impedance is characteristic of a series circuit when the operating voltage exceeds 0.8 V because Z cell is then significant.