Cell density detection based on a microfluidic chip with two electrode pairs

Cell density detection is usually the counting of cells in certain volume of liquid, which is an important process in biological and medical fields. The Coulter counting method is an important method for biological cell detection and counting. In this paper, a microfluidic chip based on two electrode pairs is designed, which uses the Coulter principle to detect the flow rate of liquid and count the cells, and then calculate the cell density. When the cell passes through the sensor channel formed by the electrode pair on the chip, the impedance will change between the electrodes. This phenomenon has been proved by experiments. The designed chip has the advantages of simple structure, small size and low manufacturing cost. The cell density detection method proposed in this article is of great significance to the research in the field of biological cell detection and development of related medical devices.


Introduction
In recent years, the medical field has developed rapidly. In the process of disease detection, it is particularly important to measure the density of cells in the blood (Hejazian et al. 2015). Traditionally, the cell density is obtained manually under a microscope (Jimbo et al. 2017;Minghao et al. 2020; Van de Geijn et al. 2016;Zeng et al. 2018;Zhang et al. 2020). The commonly used method of cell density is to calculate the number of cells in certain volume of liquid (Noor et al. 2018;Freitas et al. 2014;Pui et al. 2013;Smadi et al. 2019). This method of cell density detection requires cells to be uniformly distributed in the liquid, and then to count the cells in certain volume of sample (Alahmari et al. 2019;Drieschner et al. 2020;Falk et al. 2019;Tian et al. 2018). Commonly used methods for detecting cells are laser induced fluorescence method (Priesnitz et al. 2016;Gamarra et al. 2019;Qi et al. 2018;Riccio et al. 2019;Tamminga et al. 2016), image processing method (Imashiro et al. 2020;He et al. 2021;Yang et al. 2018;Safuan et al. 2018;Coakley et al. 2020;Ahn et al. 2018;Tran et al. 2019) and impedance method (Caselli et al. 2021; toolbox which can automatically count these cells. Due to the influence of cell aggregation and overlap, the number of cells detected by this method will be relatively low. Kim et al. designed an rWBC (residual white blood cell) counter based on optical devices (optical imaging sensors) to achieve high-throughput cell counting. The device has a complex structure resulting in the expensive cost to manufacture, and requires complex blood processing before detection (Kim et al. 2019). When the biological particles pass through the micropores, the resistance of the pores will increase because the insulating particles replace the conductive solution in the pores. This directly leads to a significant drop in the current passing through the hole, which is commonly referred to as the Coulter principle (Mansoorifar et al. 2019).
The early impedance flow cytometry (IFC) chips were based on the principle of Coulter counter using a DC supply. In 2002, Satake developed a silicon-based Coulter counter to detect polystyrene beads and red blood cells (RBCs) (Satake et al. 2002). Later, a fourchannel parallel micro-Coulter counter was designed to simultaneously detect particles flowing through four sensing channels, and the device was capable of rapidly differentiating and counting micro-polymethacrylate particles and Juniper pollen (Jagtiani and Zhe 2011). To avoid the polarization of metal electrodes, polyelectrolyte salt bridge-based electrodes (PSBEs) have successfully been fabricated by photopolymerization to distinguish RBCs and white blood cells (WBCs) in human blood (Kim et al. 2005). Afterwards, impedance micro-cytometry based on AC supply was established, with microelectrodes integrated into the walls of the microchannel instead of fabricating sensing electrodes at both sides of the aperture. In 2001, Morgan et al. (2007) fabricated two pairs of microelectrodes on the bottom of a microchannel and energized them with a voltage at one or more discrete frequencies. One pair is used for sensing the electric current fluctuation caused by a cell, whereas the other acts as a reference. This design can clearly detect the differentiation of beads, erythrocytes, and cells. Following that, a pair of parallel facing electrodes was proposed for impedance sensing and this electrodes design theoretically has a better performance because the electric field distribution is least divergent (Morgan et al. 2007). Then, a chip with this parallel facing electrodes is fabricated to measure the di-electric properties of RBCs (Chun et al. 2005). With these two types of electrodes: coplanar and parallel facing electrodes, microfluidic impedance cytometers have been used to analyze a wide variety of particles, human cell lines, phytoplankton, erythrocytes, and bead-labeled CD4 T lymphocytes.
Impedance measurement of live biological cells is widely accepted as a label free, non-invasive and quantitative analytical method to assess cell status. This method is easy-to-use and flexible for device design and fabrication. The Coulter counter based on impedance measurement is a powerful tool for characterizing biological particles suspended in a liquid electrolyte environment (Guo et al. 2013), and has been widely used in the analysis of particles (Jagtiani et al. 2006), human cells (Wu et al. 2013), bacteria (Zheng et al. 2007), viruses (Zwicker 2010), DNA and other biological molecules (Bayley and Martin 2000;Steinbock et al. 2010).
In this paper, a microfluidic chip with two electrode pairs structure is designed based on Coulter principle, which can realize the absolute count of cells in the sample liquid. The single-electrode pair of the chip realizes cell counting, and the two electrode pairs realize the measurement of cells flow rate. Finally, we calculate the cell density in the detected liquid according to the structure parameters of the chip. The structure of this microfluidic chip is novel, and it is also innovative to detect the density of insulating particles.

Theory and methods
When we apply an AC voltage to the electrode pair, the impedance between the electrodes will change because the cell replaces the liquid medium between the electrodes. Since the cell is a kind of insulating particle, when it passes through the electrodes, the impedance change will be significant. By capturing change of the impedance, it is possible to confirm the timing of the cell passing the detection electrode and the number of cells passing the detection electrodes in a period of time. As a non-invasive, label-free electrochemical method, impedance measurements can automatically provide sensitive and quantitative results. These advantages make impedance measurements widely used methods to study cells, especially for live cell analysis and long-time live cell monitoring.
The microfluidic chip in this paper is composed of two electrode pairs and a microfluidic channel, and there is a micro-sensing channel in the middle of each pair of electrodes. When a cell passes through the micro-sensing channel, the impedance between the electrodes will change significantly. By continuously detecting the impedance signal of the electrode pair, the change of the impedance signal can be detected when certain quantity cells (n) pass, so as to realize the cell count. The distance (s) between the two electrode pairs is fixed. The average flow rate of the cell from one electrode pair to the other one is calculated by detecting the time difference (∆t) of the same cell flowing through the two electrode pairs. The average flow rate of the cell represents the average flow velocity of the liquid in this period of time (v). The width (d) and height (h) of the microchannel are known. The total time from the first cell passing through the first electrode pair to the last cell passing through the second electrode pair is denoted as t. According to the above principle, the cell density can be calculated. The formula for density (ρ) is as follows: v represents the average flow velocity of n cells, and as follows: represents the average flow velocity of each cell between the two electrode pairs, and as follows: Δt i represents the time difference between successive cells passing through two electrode pairs.

Design and fabrication of the chip
The diagram of the designed chip is shown as Fig. 1.
The chip utilizes ultraviolet lithography technology to form metal patterns and microchannel patterns on the substrate. The metal pattern is formed on the glass substrate using AZ-5214 (Micro-Chemicals, Ulm, Germany) photoresist. The technological process is shown in Fig. 2a. (1) After preheating the glass substrate on the heating plate at 110 °C for 120 s, remove the glass substrate and cool it to room temperature and fix it on the turntable of the spin coater; (2) Take 3 ml of AZ-5214 photoresist and pour it onto the glass surface. First, spin at 500 rpm for 30 s with acceleration of 100 rpm/s, and then spin at 1000 rpm for 10 s with acceleration of 200 rpm/s. Let it stand for 5 min; (3) Remove the glass substrate, place it on the heating plate and bake it at 110 °C for 90 s; (4) Expose the glass substrate with the photomask for electrodes via a photoetching machine at the exposure energy of 16.7 mJ/s cm 2 for 8 s; (5) Immerse the exposed glass substrate in the AZ developer (Micro-Chemicals, Ulm, Germany) for 40 s; (6) After cleaning the glass substrate with deionized water for 30 s, blow it dry with filtered, pressurized nitrogen (do not leave water marks); (7) Post-baking the patterned glass substrate with a 70 ℃ heating plate for 120 s; (8) A layer of Cr (adhesion layer) is first plated on the patterned glass surface with a sputtering apparatus, and then a layer of Au is plated; (9) Soak the metal-plated glass substrate in acetone, and use lowpower ultrasonic to wash away the metal on the photoresist other than the metal patterning. Through this process, a metal electrode can be obtained, as shown in Fig. 3a. We adopt SU-8 2015 photoresist (Micro-Chem Corp, MA, USA) to obtain the convex microchannel pattern on the silicon wafer. According to the SU-8 2015 user manual, the exposure energy required for lithography of 50 mm thick pattern is 160 mJ/ cm 2 , the exposure energy of the lithography machine is 16.7 mJ/s cm 2 , and the exposure time is calculated as 9.6 s. We place the photomask for microchannels directly over the wafer before exposure. The elastoplastic material polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning, USA) mixture, with an adequate mix in the ratio of cross-linker/curing agent A:prepolymer B = 1:10, was degassed and poured onto the SU-8 molds. Then heat it with a 115 °C hot plate for 30 min to completely cure the PDMS. After separating the PDMS from the silicon wafer, a microchannel structure is formed, which is shown in Fig. 3b. Place the glass substrate with electrodes in for surface treatment for 1 min, and then fix the glass substrate on the stage of the inverted microscope (Nikon Corp. TI2-U, Japan), so that the microchannel structure on the PDMS can be accurately bonded to the glass sheet with metal electrodes. The complete chip is shown in Fig. 3c, the actual chip produced is shown in Fig. 3d, and the chip structure under the microscope is shown in Fig. 3e. The structure parameters of the chip are as follows: the distance between the inlet of the chip and the outlet of the chip is 24 mm, the width (d) of the main channel is 200 mm, and the height (h) of the micro-channel is 50 mm according to the manufacturing process; Micro-sensing channel 1 and microsensing channel 2 have the same structural parameters. Their width is 30 mm, length is 15 mm, and the center distance (s) between the two electrode pairs is 6 mm; The structural parameters of the electrode pair 1 and the electrode pair 2 are the same, the distance between the positive and negative electrodes of the electrode is 1.1 mm, and the center distance between the electrode pair 1 and the electrode pair 2 is 6 mm.

Experiment setup
The experimental setup mainly includes an impedance analyzer (Made in Switzerland, HF2-DEV1285), an impedance analysis software (ziControl) on the PC and a microfluidic chip. The schematic diagram of the device configuration is shown in Fig. 4. This type of testing equipment can collect the impedance signals of two channels at the same time. Through the impedance analysis software, we can obtain the impedance signals of the two electrode pairs (electrode pair 1 and electrode pair 2) on the chip. The software can also store the impedance data of the two channels and time data corresponding to each impedance signal. In order to inject liquid into the microfluidic chip at a steady flow rate, we use a syringe pump (LongerPump, LSP01-2A) to inject the liquid mixed with cells into the chip.

Cell culture
The experiment used HL60 cells (human promyelocytic leukemia cells), which were cultured in suspension in cell culture medium (RPMI 1640 + 10% FBS). We place the medium for culturing cells in a constant temperature (37 °C) incubator while maintaining the pH value of the incubator at 7.2-7.4 and the concentration of CO 2 at 5%.We dilute the HL60 cells solution after centrifuging and removing the cell suspension according to the requirements of the cell concentration in the experiment.

Cells count and flow velocity measurement
Experiments were performed with 20 mm fluorescent microbeads (Tianjin Base Line Chrom Tech Research Centre) to verify the cell counting efficiency of the chip and the liquid flow rate measurement efficiency. After connecting the experimental device as shown in Fig. 4, set the injection speed of the syringe pump to 5 ml/min, set the impedance analyzer applying to the two electrode pairs to 1 Vpp and the frequency to 500 kHz. When the microbeads continuously pass through the two micro-sensing channels, electrode pair 1 and electrode pair 2 generate obvious impedance change signals, as shown in Fig. 5.
When 20 mm microbeads pass through the microsensing channel, they will cause impedance change. The width of the sensing channel will affect the detection results. For this, we make micro-sensing channels with different widths (25 mm, 30 mm, 35 mm, 40 mm) to optimize the parameter. Set the injection speed of the syringe pump to 5 ml/min, set the impedance analyzer applying to the two electrode pairs to 1 Vpp and the frequency to 500 kHz. The chip parameters are optimized according to the impedance change of the microbeads passing through the micro-sensing channels of different widths. As shown in Fig. 6, the change of impedance decreases as the width of the micro-sensing channel increases. However, when the width of the micro-sensing channel is 25 mm, the microbeads will block the micro-sensing channel with high probability. Therefore, the microsensing channel width of 30um is the best parameter for chip design.
Save the data collected by electrode pair 1 and electrode pair 2, and perform data processing to obtain the impedance value of the two electrode pairs and the time difference (∆t) between the microbeads passing through the two electrodes in turn. By detecting the peak value in the impedance data and the time data corresponding to the peak value, the liquid flow rate ( v i ) is obtained according to formula (3).
HL60 cell experiments prove that the cell counting efficiency of the chip and the measurement efficiency  of the liquid flow rate are important. Impedance analyzer parameters remain unchanged and the injection pump speed is set to 5 ml/min. When the cell continuously passes through the two micro-sensing channels on the chip, the impedance was plotted vs. time in seconds shown in Fig. 7.
When the cell passes through the micro-sensing channel, the impedance change of the electrode is 70% of the 20 mm microbead but the signal can be detected. Because the diameter of HL60cells ranges from 5 to 12 mm, it is generally smaller than the diameter of microbeads.

Algorithm
For the impedance data of the two channels mentioned above, the peak value of the impedance data and the time corresponding to the peak value are extracted through the multi-peak extraction algorithm, where the number of effective peak values is the number of detected microbeads/cells. The effective peaks are the obvious peaks we can see in the impedance diagram. We hope the computer can find them. Due to the drift of the impedance data, the peak value cannot be extracted directly by setting the threshold of the impedance peak value. Using the well-known zero-derivate method. Due to the noise, which is always there in real-life signals, accidental zero-crossings of the first derivative occur, yielding false detections. The typical solution is to smooth the curve with some low-pass filter, usually killing the original signal at the same time. The result is usually that the algorithm goes horribly wrong where it's so obvious to the eye. But we realize that a peak is the highest point betweem "valleys". What makes a peak is the fact that there are lower points around it. Besides, we require a difference of at least X (a value) between a peak and its surrounding in order to declare it as a peak . Same goes with valleys. This paper uses this strategy to find the highest point: there are points below it on both sides around the highest point. At the same time, the detection time corresponding to the effective peak point is obtained.
As shown in Fig. 8, part of the peak data is extracted from a set of impedance data. Calculate the slope of each point on the curve. According to the change of slope (the slope of peak and valley points is zero), three peak points (P 1 , P 2 , P 3 ) and four valley points (V 1 , V 2 , V 3 , V 4 ) can be identified from the curve. The difference between the effective peak point P 2 and the valley points V 2 and V 3 is much larger than the difference between the noise peak points P 1 and P 3 and the corresponding valley. Therefore, the effective peak point P 2 is extracted as the target peak point, and It can be determined that P 2 is the only peak point in the current data.

Microbeads experiment results
Through the microfluidic chip, as shown in the results of Fig. 9, the number of microbeads can be detected as 10, the detected flow velocity is in the range of 0.006 m/s to 0.011 m/s, and the average flow velocity ( v ) is 0.0093 m/s. The total time (t) for all microbeads to flow through the detection chip is 8.47 s. From this, it can be calculated that the average density of microbeads in the liquid is 1.270 × 10 4 beads/ml. The experiment was repeated three times, and the average density was calculated to be 1.492 × 10 4 beads/ml. The original density of the microbeads is 1.62 × 10 4 Fig. 8 The multi-peak extraction algorithm beads/ml. The relative error of the detection results is 7.9%.

Cell experiment results
Through the designed microfluidic chip, as shown in the results in Fig. 10, the number of cells detected is 11, the flow velocity detected at the same time is in the range of 0.0006 m/s to 0.0012 m/s, and the average flow velocity ( v ) is 0.001 m/s. The total time (t) for all microbeads to flow through the detection chip is 40.65 s. From this, it can be calculated that the average cell density in the liquid is 2.710 × 10 4 cells/ ml. The experiment was repeated three times, and the average density was calculated to be 2.477 × 10 4 cells/ ml. The density of HL60 cells was obtained by artificial dilution and sampling and counting under the microscope. The detected cell density was 2.89 × 10 4 cells/ml. The relative error of the detected results was 14.3%.
The remaining HL60 cell solution after passage was taken as sample 1, the cell solution diluted by one time was taken as sample 2, and the solution diluted three times was taken as sample 3. The dilution process is as follows: 6 ml of cell solution is divided into three equal parts and placed in three test tubes, test tube 1 is left untreated, 2 ml of culture medium is added to test tube 2, and 4 ml of culture medium is added to test tube 3. Three samples were taken and counted under the microscope to obtain the original density of cells. The average value obtained by detecting the density of the cell solution three times in succession with the chip was used as the detection result. The obtained results and relative errors are shown in Fig. 11.

Result analysis
The detection of flow rate through this chip has certain limitations, which is requiring cells to pass through two electrodes in sequence. Once the cells overlap as getting through the electrodes, it will likely lead to missed detection, resulting in lower cell count and flow rate measurement results. However, by comparing the detection signals of microbeads and HL60 cells, it can be seen that when cells of different sizes Fig. 9 Experimental results of microbeads: a impedance peak extraction of electrode 1; b impedance peak extraction of electrode 2; c flow velocity of microbeads; d repeated experimental results

Fig. 10
Experimental results of microbeads: a impedance peak extraction of electrode 1; b impedance peak extraction of electrode 2; c flow velocity of cells; d repeated experimental results pass through the electrodes, the impedance peak signals are different. On the premise of ensuring that the particles can pass through the micro-sensing channel, the larger the diameter of the particles, the larger the impedance change. If the impedance change caused by the same kind of particles passing through the micro sensing channel is large, it can be considered that the particles are stuck together. Based on this conclusion, the algorithm can be improved later to solve the problem of missed detection caused by overlapping cells.
The detected cell density and microbead density are lower than the actual density because during the experiment, due to the slow injection speed of the syringe pump, microbeads and cells are easily deposited on the inner wall of the syringe and injection pipe, resulting in the detection result being lower than the actual density.

Conclusion
This paper designs a microfluidic chip based on Coulter principle that uses two electrode pairs to detect cell density. The chip adopts two electrode pairs and a micro-sensing channel structure to realize cell counting and liquid flow rate detection, hence obtain the cell density of the liquid to be measured. The microbead experiment and the HL60 cell experiment verified that the method can achieve cell density detection and the relative error of the detection results is within 15%.
The designed microfluidic chip can be used to assist biological cell experiments, helping researchers detect the current density of cultured cells. In addition, it can also be applied to cell counting in blood, and cell density detection. This technology will advance the development of the biomedical field.
Author contributions YW and XG: contributed to the study conception and design. Material preparation, data collection and analysis were performed by YW and DC. The first draft of the manuscript was written by YW and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of interest
The authors have no relevant financial interests in the manuscript and no other potential conflicts of interest to disclose.