Electrical non-destructive real-time cell monitoring device and method therefor

The device allows for simultaneous measurement of cell impedance and local field potential by processing digital signals to remove noise, overcoming interference issues and enhancing cellular analysis capabilities.

WO2025211563A1PCT designated stage Publication Date: 2025-10-09CELLAMES INC
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Patent Information

Application Number
PCT/KR2025/001927
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2024-04-03
Filing Date
2025-02-10
Publication Date
2025-10-09

AI Technical Summary

Technical Problem

Existing technologies face challenges in simultaneously measuring cell impedance and local field potential due to interference between reference voltages and AC signals, making simultaneous measurement impossible.

Method used

An electrical non-destructive real-time cell monitoring device that includes a first electrode, a second electrode spaced apart, an impedance measuring unit, an LFP measuring unit, and a collection signal processing unit, which processes digital signals to remove noise and convert between domains, enabling simultaneous measurement of impedance and local field potential.

Benefits of technology

Enables accurate, simultaneous monitoring of cell impedance and local field potential, allowing for a more comprehensive understanding of cellular electrical activity and characteristics.

✦ Generated by Eureka AI based on patent content.

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Abstract

An electrical non-destructive real-time cell monitoring device according to an exemplary embodiment of the present invention comprises: a first electrode in contact with a cell; a second electrode provided at a position spaced apart from the first electrode; an impedance measurement unit connected to the first electrode and the second electrode; an LFP measurement unit connected to the first electrode and the second electrode; and a collected signal processing unit connected to the impedance measurement unit and the LFP measurement unit so as to receive and process measurement results, wherein the impedance measurement unit applies an alternating current to the second electrode so as to measure the impedance between the first electrode and the second electrode, the LFP measurement unit measures a local field potential between the first electrode and the second electrode and outputs a first digital signal, the impedance measurement unit and the LFP measurement unit operate simultaneously, and the collected signal processing unit processes a first digital signal so as to obtain a second digital signal.
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Description

Electrical non-destructive real-time cell monitoring device and method

[0001] One embodiment of the present invention relates to an electrical non-destructive real-time cell monitoring device.

[0002] The inventor of the present invention has conducted research and development to exclusively use an ITO electrode as a cell-substrate impedance measurement sensor (ECIS, Electric Cell-Substrate Impedance Sensing), and has designed an ECIS system that can measure the impedance of cells in conjunction with an ECIS sensor, and can be implemented at a lower manufacturing cost and with more accurate cell response characteristics by applying a DAQ board. The related technology is introduced in Patent Document 1.

[0003] Safety or hazard assessment is essential for substances used in the development of chemicals, cosmetics, medical devices, and pesticides.

[0004] Animal testing has been used for such evaluations, but animal models have limitations in confirming efficacy and effects in the human body due to differences between species. In addition, as ethical issues regarding animal testing increase, research on alternative animal testing methods continues.

[0005] Recently, the FDA enacted a bill, signed by the US President, that would eliminate the need for animals to be used in new drug testing, and the demand for alternative testing methods is expected to grow further in the future.

[0006] Meanwhile, non-destructive real-time cell analysis technology overcomes the limitations of existing dye-based end-point cytotoxicity assessment methods and enables faster / more accurate cell analysis.

[0007] Non-destructive real-time cell analysis technologies include electrical cell-to-substrate impedance measurement and local field potential measurement.

[0008] Electrical cell-substrate impedance sensing (ECIS) is a cell analysis technique developed by Giaver and Keese. By applying an alternating electric field to a cell covering an electrode and measuring in-phase and out-of-phase potentials, frequency-dependent electrical impedance can be obtained. This method of electrical cell-substrate impedance sensing enables long-term measurements without affecting cellular function, making it an ideal cell analysis technique for biological research.

[0009] Local field potential (LFP) measurement technology can be used to measure signals with a constant pulse, such as from cardiomyocytes, or to measure various electrical signal changes in nerve cells. It is a cell analysis technology that enables monitoring of cellular changes in response to chemicals, drugs, and anticancer treatments.

[0010] Impedance measurement and local field potential measurement are suitable for non-destructive, real-time cell analysis monitoring. However, simultaneous measurement of impedance and local field potential has presented a challenge: interference occurs between them when detecting changes in cell electrical properties, making simultaneous measurement impossible. Specifically, the reference voltage for the local field potential can lead to errors in impedance measurements. Conversely, the AC signal used for impedance measurement can cause unacceptable interference in local field potential measurements.

[0011] Patent Document 1 introduces a device and method for parallel recording of impedance spectrum and field potential. Patent Document 1 also introduces a problem when performing impedance measurement and EPR measurement simultaneously, and to solve the problem, proposes a technology to perform impedance measurement and EPR measurement in a time-division manner, while improving the switching device to reduce noise generated during the process of switching measurement methods. However, Patent Document 1 also could not solve the noise problem when performing impedance measurement and LFP measurement at the same point in time.

[0012] One aspect of the present invention can provide an electrical non-destructive real-time cell monitoring technology capable of simultaneously monitoring cell impedance and local field potential.

[0013] The technical problems of the present invention are not limited to the technical problems mentioned above, and other technical problems not mentioned will be clearly understood by those skilled in the art from the description below.

[0014] According to an exemplary embodiment of the present invention, an electrical non-destructive real-time cell monitoring device comprises: a first electrode with which a cell is in contact; a second electrode provided at a position spaced apart from the first electrode; an impedance measuring unit connected to the first electrode and the second electrode; an LFP measuring unit connected to the first electrode and the second electrode; and a collection signal processing unit connected to the impedance measuring unit and the LFP measuring unit to receive and process a measurement result; wherein the impedance measuring unit applies an alternating current to the second electrode to measure an impedance between the first electrode and the second electrode, the LFP measuring unit measures a local field potential between the first electrode and the second electrode and outputs a first digital signal, and the impedance measuring unit and the LFP measuring unit operate simultaneously, and the collection signal processing unit processes the first digital signal to obtain a second digital signal, wherein the second digital signal is a signal obtained by removing noise generated by the impedance measuring unit from the first digital signal.

[0015] At this time, the collection signal processing unit can convert the first digital signal into a frequency domain, filter out noise, and then convert it into a time domain to obtain a second digital signal.

[0016]

[0017] In addition, the above-mentioned collection signal processing unit can convert the first digital signal into a frequency domain by applying mathematical expression 1.

[0018] [Mathematical Formula 1]

[0019]

[0020] At this time, the X(k) is a signal in the frequency domain, the x(n) is a signal in the time domain, the k is a frequency, the n is a time, the e is a natural constant, and the i may mean an imaginary unit.

[0021] In addition, the collection signal processing unit may include an MCU connected to the impedance measurement unit and the LFP measurement unit; and a computer connected to the MCU.

[0022] Additionally, a main switch may be further included to optionally connect or ground the second electrode to the impedance measuring unit.

[0023] In addition, a third electrode provided at a position spaced apart from the first electrode and the second electrode; and a stimulation signal generating unit for applying an electric stimulation signal to the third electrode may be further included.

[0024]

[0025] An electrical non-destructive real-time cell monitoring method according to an exemplary embodiment of the present invention is characterized by including: a step A for simultaneously measuring impedance and LFP and outputting the first digital signal; a step B for converting the first digital signal into a frequency domain; a step C for filtering the signal converted into the frequency domain with a low-pass filter (LPF) or a notch filter; and a step D for converting the signal processed in step C into a time domain to generate a second digital signal.

[0026] According to one embodiment of the present invention, cell impedance and local field potential can be monitored simultaneously. Consequently, since both impedance and local field potential can be measured simultaneously for the same specimen, various parameters can be extracted to more accurately understand the electrical activity and characteristics of the cell. For example, impedance measurements can monitor cell adhesion and viability as well as spontaneous contraction, while local field potential measurements can analyze electrical signals, such as changes in cell ion channels, through analysis of the size and cycle of cell spikes. Furthermore, cell experiments involving a wider variety of events can be performed using microcurrent stimulation signals.

[0027] FIG. 1 is a schematic diagram illustrating an electrical non-destructive real-time cell monitoring device according to one embodiment of the present invention;

[0028] FIG. 2 is a drawing for explaining an electrical non-destructive real-time cell monitoring device according to one embodiment of the present invention;

[0029] FIG. 3 is a drawing for explaining the front end of an electrical non-destructive real-time cell monitoring device according to one embodiment of the present invention.

[0030] Figure 4 is a flowchart schematically illustrating an electrical non-destructive real-time cell monitoring method according to one embodiment of the present invention.

[0031] FIG. 5 is a drawing for explaining a first digital signal and its conversion signal in an electrical non-destructive real-time cell monitoring device according to one embodiment of the present invention.

[0032] FIG. 6 is a drawing for explaining a signal subjected to noise filtering and its conversion signal in an electrical non-destructive real-time cell monitoring device according to one embodiment of the present invention.

[0033] Figure 7 is a drawing for explaining the results of impedance measurement for skin keratinocytes.

[0034] Figure 8 is a drawing for explaining the results of impedance measurement for skin keratinocytes.

[0035] Figure 9 is a drawing for explaining the LFP measurement results.

[0036] The advantages and features of the present invention, and the methods for achieving them, will become clearer with reference to the embodiments described in detail below with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below and may be implemented in various different forms. These embodiments are provided to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention. Like reference numerals may refer to like elements throughout the specification.

[0037] The terms used herein are for the purpose of describing embodiments and are not intended to limit the present invention. In this specification, the singular also includes the plural unless specifically stated otherwise. As used herein, the words "comprise" and / or "comprising" refer to components, steps, operations, and / or elements, and do not exclude the presence or addition of one or more other components, steps, operations, and / or elements.

[0038]

[0039] Unless otherwise defined, all terms used herein have the same meaning as commonly understood by those of ordinary skill in the art to which this invention pertains. Terms defined in commonly used dictionaries should be interpreted to be consistent with their meaning within the context of the relevant technology, and should not be interpreted as having an idealized or overly formal meaning unless explicitly defined herein.

[0040]

[0041] Hereinafter, the configuration and operation effects of the present invention will be described in more detail with reference to the attached drawings.

[0042]

[0043] ​​FIG. 1 is a schematic diagram illustrating an electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention, FIG. 2 is a diagram for explaining an electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention, FIG. 3 is a diagram for explaining a front end (210) of an electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention, FIG. 4 is a flowchart schematically illustrating an electrical non-destructive real-time cell monitoring method according to an embodiment of the present invention, FIG. 5 is a diagram for explaining a first digital signal and a conversion signal thereof in an electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention, FIG. 6 is a diagram for explaining a signal subjected to noise filtering and a conversion signal thereof in an electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention, FIG. 7 is a diagram for explaining an impedance measurement result for keratinocytes, and FIG. 8 is a diagram for explaining an impedance measurement result for keratinocytes. It is a drawing, and Fig. 9 is a drawing for explaining the LFP measurement results.

[0044]

[0045] An electrical non-destructive real-time cell monitoring device (1000) according to one embodiment of the present invention includes an impedance measurement unit (200), an LFP measurement unit (300), and a collection signal processing unit. Furthermore, an electrical non-destructive real-time cell monitoring device (1000) according to one embodiment of the present invention may further include a cell chip (100), a main switch (SW1), a stimulation signal generation unit (600), a computer (800), etc.

[0046]

[0047] In one embodiment, the first electrode (121) is provided to be in contact with the cell, and the second electrode (122) is provided at a position spaced apart from the first electrode (121). In one embodiment, the third electrode (123) may be provided at a position spaced apart from the first electrode (121) and the second electrode (122). In one embodiment, the first electrode (121), the second electrode (122), and the third electrode (123) may be implemented on the cell chip (100), and in particular, may be implemented in the cell well (110). In one embodiment, the first electrode (121) may be referred to as a measuring electrode or a working electrode, the second electrode (122) may be referred to as a reference electrode, and the third electrode (123) may be referred to as a stimulation electrode. In one embodiment, the first terminal (T1) and the second terminal (T2) connected to the impedance measurement unit (200) and the LFP measurement unit (300) may be connected to the first electrode (121) and the second electrode (122), respectively, and the third terminal (T3) connected to the stimulus signal generation unit (600) may be connected to the third electrode (123).

[0048] In one embodiment, a cell chip (100) may be provided with a plurality of cell wells (110). In FIG. 1, an impedance measurement unit (200), an LFP measurement unit (300), and a stimulation signal generation unit (600) are connected to the first electrode (121), the second electrode (122), and the third electrode (123) of one cell well (110) as an example, but an impedance measurement unit (200), an LFP measurement unit (300), and a stimulation signal generation unit (600) may be connected to other cell wells (110) in a similar manner.

[0049]

[0050] In one embodiment, the impedance measuring unit (200) is connected to the first electrode (121) and the second electrode (122), and applies an alternating current to the second electrode (122) to measure the impedance between the first electrode (121) and the second electrode (122).

[0051] In one embodiment, the impedance measurement unit (200) may include a front end (210) and a multiplexer (220). At this time, the front end (210) may include a driving power source (211), a current meter (212), switches (213, 214), etc., and the impedance between the first electrode (121) and the second electrode (122) of the cell well (110) may be measured by switching the switches (213, 214). In one embodiment, the impedance of the cell well (110) measured by the current meter (212) may be converted into a digital signal through an analog-to-digital converter, etc., and may undergo a signal amplification or filtering process as needed.

[0052]

[0053] In one embodiment, the LFP measurement unit (300) is connected to a first electrode (121) and a second electrode (122) and measures a local field potential between the first electrode (121) and the second electrode (122). In one embodiment, the LFP measurement unit (300) may include an amplifier (310), a filter (320), and an ADC (330).

[0054]

[0055] In one embodiment, the collection signal processing unit is connected to the impedance measurement unit (200) and the LFP measurement unit (300), and can receive measurement results output from the impedance measurement unit (200) and the LFP measurement unit (300). In one embodiment, the collection signal processing unit may include an MCU (400), and the MCU (400) may be connected to the impedance measurement unit (200), the LFP measurement unit (300), the electric stimulus generation unit (600), the main switch (SW1), etc. In one embodiment, the collection signal processing unit may process the measurement results received from the impedance measurement unit (200) and the LFP measurement unit (300). In particular, the collection signal processing unit may receive a first digital signal output from the LFP measurement unit (300), and then obtain a second digital signal.

[0056] When the impedance measurement unit (200) and the LFP measurement unit (300) operate simultaneously to perform measurements, the influence of the AC power applied to the second electrode (122) for impedance measurement is reflected in the LFP measurement results. That is, the first digital signal output by the LFP measurement unit (300) includes noise caused by the AC power, and the electrical non-destructive real-time cell monitoring device (1000) according to an embodiment of the present invention can obtain a second digital signal from which this noise has been removed. To this end, the acquisition signal processing unit can obtain the second digital signal by converting the first digital signal into a frequency domain, filtering out the noise, and then converting it into a time domain. The process of converting the first digital signal into a frequency domain can be performed by a Fourier transform using mathematical equation 1.

[0057]

[0058] Here, X(k) is a signal in the frequency domain, x(n) is a signal in the time domain, k is frequency, n is time, e is a natural constant, i is an imaginary unit, and ∑ represents a partial sum of the sequence.

[0059] In one embodiment, the collection signal processing unit may be implemented with the aforementioned MCU (400) and memory, etc.

[0060] In another embodiment, a process of processing a first digital signal and obtaining a second digital signal may be performed in a computer (800) connected to the aforementioned MCU (400). In this case, the collection signal processing unit may include the MCU (400) and the computer (800). At this time, the computer (800) and the MCU (400) may be connected using various data cables such as a USB cable. Meanwhile, the MCU (400), the power supply unit (700), the impedance measuring unit (200), the LFP measuring unit (300), the stimulus signal generating unit (600), the main switch (SW1), etc. may be referred to as a measuring main body (MB). This measuring main body (MB) may be individually packaged by a separate housing (not shown), and may be connected to the computer (800) by a USB cable, etc., and various cell chips (100) may be connected to the measuring device body.

[0061] In one embodiment, the measuring body (MB) may be controlled by a separate driving program running on the computer (800) or data received from the measuring body (MB) may be processed. In one embodiment, data collected from the measuring body (MB) may be transmitted to the computer (800) via a USB cable and processed to be displayed to the user in various indices such as numbers and graphs. For example, FIGS. 7 and 8 illustrate the results of measuring impedance at a frequency of 100 kHz while varying the injection concentration of keratinocytes, and FIG. 9 illustrates the results of detecting electrical signals after administering various drugs to human-derived myocardial cells. By analyzing the graphs illustrated in FIG. 9, it is possible to determine whether an arrhythmia occurs.

[0062]

[0063] In one embodiment, a main switch (SW1) for selectively grounding the second terminal (T2) may be further provided. For example, in cases where impedance measurement is unnecessary but LFP measurement is required, LFP measurement can be performed more easily by grounding the second electrode (122) using the main switch (SW1). That is, when the second electrode (122) is grounded, it can be operated in the same manner as a conventional LFP measuring device.

[0064] In one embodiment, the main switch (SW1) may connect the second electrode (122) to an AC power source. That is, when impedance measurement and LFP measurement are performed simultaneously, the main switch (SW1) may cause the second electrode (122) to be supplied with AC power. Meanwhile, the selective connection of the main switch (SW1) may be determined according to a control command of the MCU (400) or the computer (800).

[0065] In one embodiment, when LFP measurement is performed alone, the second electrode (122) may be grounded. In one embodiment, when LFP measurement and impedance measurement are performed simultaneously, an AC signal having a higher frequency than the frequency of the local field potential signal of the target cell may be applied to the second electrode (122). Accordingly, interference in impedance measurement due to LFP measurement can be minimized. However, when simultaneous measurement is performed, noise is generated in the local field potential measurement due to the influence of the AC signal used for impedance measurement, making it difficult to analyze the index with the original data. According to one embodiment of the present invention, the problem in LFP measurement due to the AC signal used for impedance measurement is solved, and index analysis is possible.

[0066]

[0067] In one embodiment, the stimulus signal generation unit (600) may perform a function of applying an electrical stimulus signal to the third electrode (123) and may include a DAC (610) and a constant current circuit (620).

[0068] In one embodiment, a user can set the characteristics of a stimulus signal through a computer (800) or the like.

[0069] In one embodiment, the preset stimulus signal may be a digital signal, and the stimulus signal generation unit (600) may receive the digital signal, convert it into an analog signal through a DAC (610), stabilize it through a constant current circuit (620), and then provide it to the third electrode (123). Typically, a balanced two-phase pulse waveform is used as the stimulus signal, and the timing and amplitude of the two-phase pulse may be controlled by software and a built-in algorithm.

[0070]

[0071] A method for electrical non-destructive real-time cell monitoring according to one embodiment of the present invention may include the steps of simultaneously measuring impedance and LFP and outputting the first digital signal; converting the first digital signal into a frequency domain; filtering the signal converted into the frequency domain with a low-pass filter (LPF) or a notch filter; and converting the signal into a time domain to generate a second digital signal.

[0072] Referring to Fig. 4, first, impedance measurement and LFP measurement are performed simultaneously (S110).

[0073] Next, the measured result is output, and at this time, the LFP measurement result is output as a first digital signal (S120).

[0074] Next, the first digital signal is converted into the frequency domain (S130). Fig. 5 (a) illustrates the first digital signal, and Fig. 5 (b) illustrates the result of converting the first digital signal into the frequency domain. Noise (NS) can be observed in Fig. 5 (b). This noise is caused by the AC power used during the impedance measurement process.

[0075]

[0076] Next, a noise filtering process (S140) is performed. In one embodiment, the noise filtering process may be performed by filtering a signal converted to the frequency domain using a low-pass filter (LPF) or a notch filter.

[0077] Next, a second digital signal is generated by converting the noise-removed signal back into the time domain (S150).

[0078] As a result, the existing problem of difficulty in simultaneous measurement due to mutual interference when measuring impedance and local field potential simultaneously in detecting changes in the electrical characteristics of cells has been solved, and since impedance and local field potential can be measured simultaneously for the same test specimen, various parameters can be extracted to more accurately understand the electrical activity and characteristics of cells.

[0079]

[0080] While representative embodiments of the present invention have been described in detail above, those skilled in the art will appreciate that various modifications to the above-described embodiments are possible without departing from the scope of the present invention. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be defined not only by the claims set forth below but also by equivalents thereof.

[0081] 1000: Electrical non-destructive real-time cell monitoring device

[0082] 100: Cell Chip

[0083] 110: Cellwell

[0084] 121: First electrode

[0085] 122: Second electrode

[0086] 123: Third electrode

[0087] 200: Impedance measurement unit

[0088] 210: Frontend

[0089] 211: Driving power

[0090] 212: Current Meter

[0091] 220: Multiplexer

[0092] 300: LFP measurement unit

[0093] 310: Amplifier

[0094] 320: Filter

[0095] 330: ADC

[0096] T1: Terminal 1

[0097] T2: Second terminal

[0098] T3: Third terminal

[0099] 400: MCU

[0100] 500: Main switch

[0101] 600: Stimulus signal generation unit

[0102] 610: DAC

[0103] 620: Constant current circuit

[0104] 700: Power supply

[0105] 800: Computer

[0106] MB: Measuring body

Claims

1. In an electrical non-destructive real-time cell monitoring device that monitors cell impedance and local field potential (LFP), A first electrode with which the cell is in contact; A second electrode provided at a position spaced apart from the first electrode; An impedance measuring unit connected to the first electrode and the second electrode and applying AC power; An LFP measuring unit connected to the first electrode and the second electrode; and It includes a collection signal processing unit that is connected to the impedance measurement unit and the LFP measurement unit and receives and processes the measurement results; The above impedance measuring unit applies an alternating current to the second electrode to measure the impedance between the first electrode and the second electrode, The above LFP measuring unit measures the local field potential between the first electrode and the second electrode and outputs a first digital signal, The above impedance measurement unit and the above LFP measurement unit operate simultaneously to measure impedance and LFP at the same physical time, The above-mentioned collection signal processing unit processes the first digital signal to obtain a second digital signal, An electrical non-destructive real-time cell monitoring device, characterized in that the second digital signal is a signal obtained by removing noise generated by the impedance measuring unit from the first digital signal.

2. In claim 1, The above collection signal processing unit, An electrical non-destructive real-time cell monitoring device characterized in that the first digital signal is converted into a frequency domain, noise is filtered out, and then converted into a time domain to obtain a second digital signal.

3. In claim 2, The above-mentioned collection signal processing unit converts the first digital signal into a frequency domain by applying mathematical expression 1, [Mathematical Formula 1] An electrical non-destructive real-time cell monitoring device, characterized in that the above X(k) is a signal in the frequency domain, the above x(n) is a signal in the time domain, the above k is a frequency, the above n is a time, the above N is an arbitrary real number greater than 0, the above e is a natural constant, and the above i is an imaginary unit.

4. In claim 1, The above collection signal processing unit, An MCU connected to the impedance measurement unit and the LFP measurement unit; and An electrical non-destructive real-time cell monitoring device, characterized in that it comprises a computer connected to the above MCU.

5. In claim 1, An electrical non-destructive real-time cell monitoring device, characterized in that it further comprises a main switch for optionally connecting or grounding the second electrode to the impedance measuring unit.

6. In claim 1, A third electrode provided at a position spaced apart from the first electrode and the second electrode; and Further comprising a stimulation signal generating unit that applies an electrical stimulation signal to the third electrode; The above stimulation signal generating unit, An electrical non-destructive real-time cell monitoring device comprising a DAC for converting a received digital signal into an analog signal and a constant current circuit for providing the stabilized analog signal to the third electrode.

7. In a method for electrical non-destructive real-time cell monitoring using a device according to claim 1, Step A for simultaneously measuring impedance and LFP and outputting the first digital signal; Step B of converting the first digital signal into a frequency domain; Step C of filtering the signal converted to the frequency domain with a low-pass filter (LPF) or a notch filter; and An electrical non-destructive real-time cell monitoring method characterized by comprising a D step for converting the signal obtained in the above C step into a time domain to generate a second digital signal.

8. In claim 7, In the above step B, the first digital signal is converted into the frequency domain by applying mathematical expression 1, [Mathematical Formula 1] An electrical non-destructive real-time cell monitoring method, characterized in that the above X(k) is a signal in the frequency domain, the above x(n) is a signal in the time domain, the above k is a frequency, the above n is a time, the above N is an arbitrary real number greater than 0, the above e is a natural constant, and the above i is an imaginary unit.

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