Four-electrode liquid impedance spectroscopy analysis method and model

Abstract

The application discloses a four-electrode liquid impedance spectrum analysis method and model, the analysis method comprising: obtaining the original impedance spectrum of the liquid to be measured through a measuring circuit; inputting the electrical parameters of the liquid to be measured into a field-circuit coupling model, and obtaining the simulation impedance spectrum of the liquid to be measured according to the potential distribution, the electric field distribution and the current density distribution output by the field-circuit coupling model; the field-circuit coupling model comprises a finite element field model and a lumped parameter model coupled at an electrical port; the finite element field model is used for solving the potential distribution, the electric field distribution and the current density distribution inside the liquid to be measured according to the electrical parameters of the liquid to be measured; the lumped parameter model is used for providing boundary conditions for the finite element field model; and the simulation impedance spectrum and the original impedance spectrum are subjected to error iterative fitting, and when the error meets preset conditions, the corrected electrical parameters are obtained. The method can improve the analysis precision of the liquid impedance spectrum at a high frequency band, and the intrinsic electrical parameters of the liquid to be measured are obtained without reference calibration.

Description

Technical Field

[0001] This application relates to the field of bioimpedance measurement and multiphysics simulation technology, specifically to a four-electrode liquid impedance spectrum analysis method and model. Background Technology

[0002] Four-electrode impedance measurement technology employs a structure in which an excitation current or voltage is applied to the outer electrode and a differential voltage is detected by the inner electrode. Compared with a two-electrode structure, it can effectively eliminate some polarization errors, and therefore it is widely used in fields such as liquid electrical parameter characterization, impedance analysis of biological samples, and food quality testing.

[0003] However, the hardware parameters of the external measurement circuit in a four-electrode impedance measurement system can cause electric field distortion within the liquid, and this distortion is more significant when the excitation current or voltage is at high frequencies, leading to measurement errors in the liquid impedance. Related techniques compensate for these high-frequency measurement errors by differentiating the test liquid from a standard liquid; however, this method is cumbersome, lacks versatility, and only compensates for errors numerically, failing to reveal and eliminate the fundamental impact of electric field distortion at the physical level. Summary of the Invention

[0004] In view of this, this application provides a four-electrode liquid impedance spectroscopy analysis method and model, which can improve the analysis accuracy of liquid impedance spectroscopy in the high-frequency band and obtain the intrinsic electrical parameters of the liquid under test without the need for reference calibration.

[0005] To solve the above problems, the technical solution provided in this application is as follows:

[0006] In a first aspect of this application, a four-electrode liquid impedance spectroscopy analysis method is provided, the analysis method comprising:

[0007] The original impedance spectrum of the liquid to be tested is obtained by a measuring circuit, which is connected to the liquid to be tested through an electrical port.

[0008] The electrical parameters of the liquid under test are input into the field-circuit coupling model. Based on the potential distribution, electric field distribution, and current density distribution output by the field-circuit coupling model, the simulated impedance spectrum of the liquid under test is obtained. The field-circuit coupling model includes a finite element field model and a lumped parameter model coupled at the electrical port. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution based on the electrical parameters of the liquid under test. The lumped parameter model is used to provide boundary conditions for the finite element field model.

[0009] The simulated impedance spectrum and the original impedance spectrum are iteratively fitted to obtain the corrected electrical parameters when the error meets the preset conditions.

[0010] One possible implementation also includes:

[0011] Based on the electrical and structural parameters of the liquid under test, a finite element field model of the liquid under test is constructed.

[0012] The electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test; the structural parameters include the sample cell geometry of the liquid under test, the position of the electrode, and the size of the electrode.

[0013] One possible implementation also includes:

[0014] Based on the hardware parameters of the measurement circuit, the lumped parameter model is constructed;

[0015] The measurement circuit includes: an AC excitation source, an excitation electrode, and three detection electrodes;

[0016] The hardware parameters include: the voltage or current of the AC excitation source, the equivalent impedance of the excitation electrode channel, the equivalent impedance of each of the detection electrode channels, the parasitic capacitance of the excitation electrode channel, and the parasitic capacitance of each of the detection electrode channels.

[0017] One possible implementation involves performing an error iterative fitting between the simulated impedance spectrum and the original impedance spectrum to obtain the corrected electrical parameters, specifically including:

[0018] Input the electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum;

[0019] The updated electrical parameters are obtained iteratively until the error loss function is less than a threshold, at which point the corrected electrical parameters are obtained.

[0020] In one possible implementation, the original impedance spectrum is the impedance spectrum obtained by the measurement circuit sweeping the frequency of the liquid under test under a preset frequency band, and the original impedance spectrum is used to reflect at least the relaxation characteristics of the liquid under test.

[0021] In a second aspect of this application, a four-electrode liquid impedance spectroscopy analytical model is provided, comprising:

[0022] A measurement module is used to obtain the original impedance spectrum of the liquid to be tested through a measurement circuit, wherein the measurement circuit is connected to the liquid to be tested through an electrical port;

[0023] The simulation module is used to input the electrical parameters into the field-circuit coupling model and obtain the simulated impedance spectrum of the liquid under test based on the potential distribution, electric field distribution, and current density distribution. The field-circuit coupling model includes a finite element field model coupled at the electrical port and a lumped parameter model. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution based on the electrical parameters of the liquid under test. The lumped parameter model is used to provide boundary conditions for the finite element field model.

[0024] The calculation module is used to use the electrical parameters as parameters to be optimized, perform error iterative fitting between the simulated impedance spectrum and the original impedance spectrum, and output the corrected electrical parameters when the error meets the preset conditions.

[0025] One possible implementation also includes: a modeling module;

[0026] The modeling module is used to construct the finite element field model of the liquid under test based on the electrical and structural parameters of the liquid under test.

[0027] The electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test; the structural parameters include the sample cell geometry of the liquid under test, the position of the electrode, and the size of the electrode.

[0028] In one possible implementation, the modeling module is further configured to:

[0029] Based on the hardware parameters of the measurement circuit, the lumped parameter model is constructed;

[0030] The measurement circuit includes: an AC excitation source, an excitation electrode, and three detection electrodes;

[0031] The hardware parameters include: the voltage of the AC excitation source, the current of the AC excitation source, the equivalent impedance of the excitation electrode channel, the equivalent impedance of each of the detection electrode channels, the parasitic capacitance of the excitation electrode channel, and the parasitic capacitance of each of the detection electrode channels.

[0032] In one possible implementation, the computing module is specifically used for:

[0033] Input the electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum;

[0034] The updated electrical parameters are obtained iteratively until the error loss function is less than a threshold, at which point the corrected electrical parameters are obtained.

[0035] In one possible implementation, the original impedance spectrum is the impedance spectrum obtained by the measurement circuit sweeping the frequency of the liquid under test under a preset frequency band, and the original impedance spectrum is used to reflect at least the relaxation characteristics of the liquid under test.

[0036] The four-electrode impedance spectroscopy analytical method provided in this application solves for the measurement circuit and the internal electric field of the liquid in a unified manner through a field-circuit coupling model, which includes a finite element field model and a lumped parameter model coupled at the electrical ports. The finite element field model can realistically solve for the distribution of potential, electric field, and current density within the liquid; the introduction of real lumped parameters from the external measurement circuit through the electrical ports accurately characterizes the frequency domain electric field distortion over a wide frequency range. Compared with traditional equivalent circuits, the field-circuit coupling model of this application can dynamically describe the evolution of the spatial electric field, with a clearer physical mechanism and more accurate high-frequency analysis, providing a reliable foundation for precise fitting and absolute quantitative measurement of broadband impedance spectra. The analytical method provided in this application can accurately characterize the frequency domain electric field distortion over a wide frequency range, achieve precise fitting between simulated and measured impedance spectra, and obtain absolute quantitative electrical parameters of the liquid under test without high-frequency calibration, thereby significantly improving measurement accuracy and reliability. Attached Figure Description

[0037] Figure 1 A schematic diagram of a four-electrode impedance measurement system;

[0038] Figure 2 A schematic diagram of the lumped parameter equivalent model of a four-electrode impedance measurement system;

[0039] Figure 3 A schematic diagram of simulation data for the lumped parameter equivalent model;

[0040] Figure 4 A flowchart illustrating a four-electrode liquid impedance spectroscopy analysis method provided in this application embodiment;

[0041] Figure 5 A schematic diagram of the field-circuit coupling equivalent model of a four-electrode impedance measurement system provided in this application embodiment;

[0042] Figure 6 A comparison of the current density distribution in the liquid under ideal boundary conditions and under actual measurement circuit conditions;

[0043] Figure 7 A schematic diagram of simulation data for the field-circuit coupling model provided in the embodiments of this application;

[0044] Figure 8 This is a schematic diagram of a four-electrode liquid impedance spectrum analytical model provided in an embodiment of this application. Detailed Implementation

[0045] To enable those skilled in the art to fully understand the application scenarios of the four-electrode impedance spectroscopy analysis method provided in the embodiments of this application, a brief introduction to the four-electrode impedance measurement system is given below.

[0046] See Figure 1 The figure shows a schematic diagram of a four-electrode impedance measurement system.

[0047] Figure 1 The measurement system shown includes a sample cell 100 for holding the liquid to be tested and peripheral measurement circuitry. The measurement circuitry includes a detection circuit 200 and an impedance detection instrument 300 for obtaining the impedance spectrum. The detection circuit 200 includes: an excitation electrode P1 for input excitation; a first detection electrode P2 for detecting voltage; a second detection electrode P3 for detecting voltage; a third detection electrode P4 for detecting current; a parasitic capacitance C1 to ground for a first channel corresponding to the excitation electrode P1; a parasitic capacitance C2 to ground for a second channel corresponding to the first detection electrode P2; a parasitic capacitance P3 to ground for a third channel corresponding to the second detection electrode P3; and a parasitic capacitance C4 to ground for a fourth channel corresponding to the third detection electrode P4. The excitation electrode P1, the first detection electrode P2, the second detection electrode P3, and the third detection electrode P4 are in contact with the liquid to be tested through electrical ports. The first detection electrode P2 is used to detect a first voltage u1, the second detection electrode P3 is used to detect a second voltage u2, and the third detection electrode P4 is used to detect current u1.

[0048] In related technologies, lumped parameter models are used to... Figure 1 The four-electrode impedance measurement system shown is equivalent. See [link / reference]. Figure 2 The figure shows a schematic diagram of the lumped parameter equivalent model of a four-electrode impedance measurement system.

[0049] Figure 2 In this model, the impedance detection instrument 300 is equivalent to an AC excitation source B1 located in the first channel, an output impedance Z1 located in the first channel, a first input impedance Z2 located in the second channel, a second input impedance Z3 located in the third channel, and a third input impedance Z4 located in the fourth channel. The impedance of the liquid to be tested between the excitation electrode P1 and the first detection electrode P2 is equivalent to a model of a first resistor R1 and a first capacitor C11 connected in parallel; the impedance of the liquid to be tested between the first detection electrode P2 and the second detection electrode P3 is equivalent to a model of a second resistor R2 and a second capacitor C12 connected in parallel; and the impedance of the liquid to be tested between the second detection electrode P3 and the third detection electrode P4 is equivalent to a model of a third resistor R3 and a third capacitor C13 connected in parallel.

[0050] However, when the AC excitation source B1 outputs a high-frequency AC excitation, Figure 2 The provided lumped parameter equivalent model suffers from severe distortion, leading to significant errors in the calculated impedance of the liquid under test. See also... Figure 3 The figure shows a schematic diagram of simulation data for the lumped parameter equivalent model.

[0051] Figure 3 In (a), the horizontal axis f represents the frequency of the AC excitation source, in Hz; the vertical axis A represents the impedance amplitude of the liquid under test, in Ω. Figure 3 In (b), the horizontal axis f represents the frequency of the AC excitation source, in Hz; the vertical axis φ represents the impedance phase of the liquid under test, in °. Figure 3 The study compared real experimental data, simulation data considering only the lumped parameters of the liquid, and simulation data considering both the lumped parameters of the liquid and the external circuit. Figure 3 It can be seen that the average absolute errors of impedance amplitude and impedance phase between the liquid lumped parameter simulation and the actual experiment are 16.27Ω and 4.30°, respectively. The average absolute errors of impedance amplitude and impedance phase between the liquid and external circuit lumped parameter simulation and the actual experiment are 42.49Ω and 16.90°, respectively. This indicates that the existing traditional lumped parameter analysis techniques, regardless of whether the external circuit is considered, cannot solve the problem of high-frequency impedance distortion in a four-electrode system.

[0052] To address the high-frequency distortion problem in four-electrode liquid impedance measurement over a wide frequency range, this application provides a four-electrode liquid impedance spectrum analysis method and model. By constructing a frequency domain field-path coupling system that combines the liquid-electrode spatial field with the actual detection circuit, the influence of the external circuit dynamic response on the effective electric field path inside the liquid and the resulting impedance nonlinear frequency domain distortion mechanism are revealed, thereby achieving accurate modeling and analysis of the broadband impedance spectrum of the four-electrode system.

[0053] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the embodiments of this application will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0054] The four-electrode liquid impedance spectroscopy analysis method and model provided in this application are applicable not only to biological liquids but also to other complex electrolytes.

[0055] See Figure 4 The figure is a flowchart of a four-electrode liquid impedance spectroscopy analysis method provided in an embodiment of this application.

[0056] Figure 4 The parsing methods provided in the embodiments include:

[0057] S1: Obtain the original impedance spectrum of the liquid to be tested through the measuring circuit, which is connected to the liquid to be tested through an electrical port.

[0058] One possible implementation is that the original impedance spectrum is the impedance spectrum obtained by sweeping the measurement circuit to measure the liquid under test in a preset frequency band. The original impedance spectrum is used to reflect at least the relaxation characteristics of the liquid under test.

[0059] For example, the detection circuit 200 and the impedance detection instrument 300 can be used to perform frequency sweep measurement on the liquid to be tested in the sample cell 100 to obtain the actual original impedance spectrum of the liquid to be tested.

[0060] This application does not specifically limit the frequency of AC excitation during the impedance detection instrument 300 sweep frequency measurement. In order to obtain various characteristics of the liquid under test, such as the dielectric relaxation of the liquid under test, the liquid under test can be measured over a wide frequency range. For example, the preset frequency band can be 10kHz to 10MHz, that is, AC excitation with a frequency of 10kHz to 10MHz can be used to perform sweep frequency measurement on the liquid under test.

[0061] S2: Input the electrical parameters of the liquid under test into the field-circuit coupling model. Based on the potential distribution, electric field distribution, and current density distribution output by the field-circuit coupling model, obtain the simulated impedance spectrum of the liquid under test. The field-circuit coupling model includes a finite element field model coupled at the electrical ports and a lumped parameter model. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution inside the liquid under test based on the electrical parameters of the liquid under test. The lumped parameter model is used to provide boundary conditions for the finite element field model.

[0062] For example, the electrical parameters of the liquid under test can be input into the field-circuit coupling model. The field-circuit coupling model performs frequency sweeping solution on the liquid under test over a wide frequency band and outputs the potential distribution, electric field distribution and current density distribution of the liquid under test under the current electrical parameters, thereby obtaining the simulated impedance spectrum of the liquid under test.

[0063] See Figure 5 The figure is a schematic diagram of the field-circuit coupling equivalent model of a four-electrode impedance measurement system provided in an embodiment of this application.

[0064] Figure 5 In the field-circuit coupling equivalent model provided in the embodiment, 11 is the double-layer interface of the excitation electrode P1, 12 is the double-layer interface of the first detection electrode P2, 13 is the double-layer interface of the second detection electrode P3, and 14 is the double-layer interface of the third detection electrode P4. The double-layer interface is used to characterize the contact impedance characteristics of the electrode-liquid interface, which can accurately simulate the influence of interface effects on the impedance spectrum in the low-frequency range. Thus, the four-electrode impedance spectrum analysis method provided in this application embodiment can achieve accurate analysis in both the low-frequency and high-frequency ranges, improving the versatility of the analysis method in a wide frequency range.

[0065] and Figure 2Unlike the simplified model in the previous embodiment, which represented a series of parallel resistors and capacitors with lumped parameters, the finite element field model in this application does not equate the liquid region to discrete impedance elements and capacitors. Instead, it constructs a realistic geometric space field model that includes the liquid region, four electrodes, the liquid-electrode interface, and electrical ports, thereby accurately reproducing the potential distribution, electric field distribution, and current density distribution within the liquid. The lumped parameter model of the measurement circuit applies the lumped parameters of the measurement circuit to the boundary of the finite element field model through the electrical ports, accurately reflecting the changes in the boundary conditions of the electrode ports caused by the external measurement circuit. This, in turn, characterizes the frequency domain electric field distortion of the liquid under test caused by the lumped parameters of the external measurement circuit over a wide frequency band.

[0066] S3: Iteratively fit the error between the simulated impedance spectrum and the original impedance spectrum, and obtain the corrected electrical parameters when the error meets the preset conditions.

[0067] For example, the error between the simulated impedance spectrum of the liquid under test and the original impedance spectrum obtained in step S1 can be calculated. The error can be iteratively fitted between the simulated impedance spectrum and the original impedance spectrum until the error meets the preset conditions. At this point, the corrected electrical parameters output by the field-circuit coupling model are the absolute quantitative electrical parameters of the liquid under test that do not require high-frequency calibration.

[0068] Compared to related technologies that rely on differential compensation with standard liquids for numerical compensation, this embodiment uses a field-circuit coupling model to realistically reproduce the frequency-domain electric field distortion caused by the external circuit. This corrects high-frequency measurement deviations from the physical essence of the potential distribution, electric field distribution, and current density distribution of the test liquid. Through iterative fitting of the simulated impedance spectrum with the original impedance spectrum, the fundamental influence of frequency-domain electric field distortion is eliminated mechanistically, enabling the acquisition of absolute quantitative electrical parameters of the test liquid. Compared to related technologies that use differential compensation between the test liquid and a standard liquid to obtain relative correction values, the analytical method provided in this application saves on the detection and differential comparison operations of the standard liquid, simplifying the operation process and reducing experimental costs. Moreover, the analytical method provided in this application does not rely on a standard liquid with similar characteristics to the test liquid; instead, it uses a field-circuit coupling model for wide-band, adaptive iterative fitting, making it widely applicable and highly versatile.

[0069] The four-electrode impedance spectroscopy analytical method provided in this application solves for the measurement circuit and the internal electric field of the liquid in a unified manner through a field-circuit coupling model, which includes a finite element field model and a lumped parameter model coupled at the electrical ports. The finite element field model can realistically solve for the distribution of potential, electric field, and current density inside the liquid; the actual lumped parameters of the external measurement circuit introduced through the electrical ports can accurately characterize the frequency domain electric field distortion over a wide frequency range. Compared with traditional equivalent circuits, the field-circuit coupling model of this application can dynamically describe the evolution of the spatial electric field, with a clearer physical mechanism and more accurate high-frequency analysis, providing a reliable foundation for accurate fitting and absolute quantitative measurement of broadband impedance spectra. The analytical method provided in this application can accurately characterize the frequency domain electric field distortion over a wide frequency range, achieve accurate fitting between simulated and measured impedance spectra, and obtain the absolute quantitative electrical parameters of the liquid under test without high-frequency calibration, thereby significantly improving measurement accuracy and reliability.

[0070] One possible implementation of the four-electrode impedance spectroscopy analysis method provided in this application further includes:

[0071] S4: Based on the electrical and structural parameters of the liquid under test, construct a finite element field model of the liquid under test.

[0072] Electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test; structural parameters include the sample cell geometry of the liquid under test, the position of the electrodes, and the size of the electrodes.

[0073] Specifically, the liquid region under test satisfies the electric field control equation shown in equation (1):

[0074] (1).

[0075] in, Represents the total current density. Represents a volume current source; under the condition that there is no volume current source inside the liquid being measured, .

[0076] Total current density Obtained from the following formula (2):

[0077] (2).

[0078] in, Represents conduction current, satisfying , The conductivity of the liquid to be measured is... Electric field strength; Represents displacement current, satisfying , The imaginary unit, Angular frequency, It is the electric displacement vector. The vacuum permittivity, The relative permittivity of the liquid being measured; This represents the applied current density term.

[0079] Electric field strength in the liquid region to be measured Potential distribution of the liquid being measured The following equation (3) must be satisfied between them:

[0080] (3).

[0081] The geometric dimensions of the sample cell 100, the positions and dimensions of the four electrodes are used as the geometric boundary definition parameters of the finite element model. The conductivity of the liquid to be measured is then used. and relative permittivity By inputting material parameters into the electric field control equations shown in equations (1) to (3), and using the lumped parameters of the measuring circuit as the boundary conditions of the finite element field model, the potential distribution within the liquid to be measured can be obtained. Furthermore, the electric field distribution, current density distribution, and electrical port response within the liquid under test are obtained.

[0082] This application does not specifically limit the type of model used to simulate the liquid to be tested in the sample pool 100. The model of the liquid to be tested can be a three-dimensional model provided in this application, or a two-dimensional axisymmetric model or a verified reduced-order model to calculate the effective impedance of the liquid to be tested.

[0083] Figure 4 The dual-electrode interface in this embodiment is simulated by introducing anisotropic boundary conditions (such as an equivalent thin layer with tangential conductivity and normal insulation) with interfacial contact impedance characteristics onto the electrode surface. This embodiment does not elaborate further. This embodiment does not specifically limit the type of model used to simulate electrode interface characteristics. One possible implementation is that the electrode interface characteristics can be achieved using the dual-layer anisotropic thin-layer model provided in this embodiment, or other equivalent models such as interfacial contact impedance and electrode surface capacitance.

[0084] The four-electrode impedance spectrum analysis method provided in this application, by constructing a finite element field model including the electric field control equation, can realistically solve the potential distribution, electric field distribution, and current density distribution inside the liquid under test, accurately reflecting the broadband electric field variation law inside the liquid under test; by using the lumped parameters of the external real measurement circuit as the boundary conditions of the finite element field model, it can accurately characterize the influence of the introduction of the external measurement circuit on the electric field of the liquid under test, thereby improving the simulation accuracy and physical reliability of the broadband impedance spectrum.

[0085] One possible implementation of the four-electrode impedance spectroscopy analysis method provided in this application further includes:

[0086] S5: Construct a lumped parameter model based on the hardware parameters of the measurement circuit.

[0087] The measurement circuit includes an AC excitation source B1, an excitation electrode P1, and three detection electrodes, namely the first detection electrode P2, the second detection electrode P3, and the third detection electrode P4.

[0088] The hardware parameters include: the voltage of the AC excitation source B1; the current of the AC excitation source B1; the equivalent impedance of the excitation electrode P1 channel, i.e., the output impedance Z1 of the first channel; the equivalent impedance of each detection electrode channel, namely the first input impedance Z2 of the second channel, the second input impedance Z3 of the third channel, and the third input impedance Z4 of the fourth channel; the parasitic capacitance of the excitation electrode P1 channel, i.e., the parasitic capacitance to ground C1 of the first channel; and the parasitic capacitance of each detection electrode channel, namely the parasitic capacitance to ground C2 of the second channel, the parasitic capacitance to ground P3 of the third channel, and the parasitic capacitance to ground C4 of the fourth channel.

[0089] See Figure 6 The figure shows a comparison of the current density distribution in the liquid under ideal boundary conditions and under actual measurement circuit conditions.

[0090] Figure 6 At three representative frequencies of 10 kHz, 2 MHz, and 10 MHz, the changes in the internal current path of the liquid under test were compared under ideal boundary conditions without considering the influence of external measurement circuits, and with considering the influence of external measurement circuits. Figure 6 The streamlines in the diagram represent the conduction current density. Figure 6 (a) shows the current density distribution under ideal boundary conditions. Figure 6 (b) shows the current density distribution under actual measurement circuit conditions. Figure 6 It can be seen that the dynamic response of the external measurement circuit will change the effective electric field path inside the liquid, especially in the high-frequency band where there is significant frequency domain electric field distortion.

[0091] The four-electrode impedance spectrum analysis method provided in this application constructs a lumped parameter model based on the hardware parameters of the actual measurement circuit. It can accurately characterize the equivalent impedance and parasitic capacitance characteristics of the excitation channel and each detection channel, and provide boundary conditions for the finite element field model that fit the actual measurement scenario. This allows for a more realistic reflection of the influence of the external circuit on the impedance spectrum of the liquid under test, thereby improving the accuracy and reliability of broadband impedance analysis.

[0092] One possible implementation of the four-electrode impedance spectrum analysis method provided in this application includes step S3, which iteratively fits the simulated impedance spectrum to the original impedance spectrum to obtain the corrected electrical parameters. Specifically, this includes:

[0093] S31: Input electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum.

[0094] For example, inputting the initial conductivity of the liquid under test into the field-path coupling model. and relative permittivity The simulated impedance spectrum of the liquid to be tested is obtained, and the error loss function between the simulated impedance spectrum and the original impedance spectrum is calculated.

[0095] S32: Iterate to obtain the updated electrical parameters until the error loss function is less than the threshold, and obtain the corrected electrical parameters.

[0096] For example, updating the conductivity of the liquid being measured based on the error loss function. and relative permittivity And update the conductivity of the liquid to be tested. and relative permittivity Input the field-circuit coupling model to obtain the updated simulated impedance spectrum. Iterative updates are performed to gradually approximate the original impedance spectrum until the error loss function is less than a threshold. This yields a corrected conductivity of the measured liquid that highly matches the actual measurement conditions. and relative permittivity .

[0097] This application does not specifically limit the selection of the threshold, and it can be adaptively set according to the actual measurement accuracy requirements, the type of liquid to be measured, and the analysis target.

[0098] The four-electrode impedance spectroscopy analysis method provided in this application can adaptively optimize conductivity and relative permittivity using the original impedance spectrum as the target, ensuring that the simulation results output by the field-circuit coupling model closely match the measured data. This iterative process automatically corrects measurement deviations caused by external hardware parameters and frequency-domain electric field distortion, obtaining stable and reliable corrected electrical parameters without relying on a standard reference liquid for differential calibration. This enables absolute quantitative extraction of the conductivity and relative permittivity of the liquid under test. Furthermore, this method possesses strong versatility and adaptability, applicable to liquid samples with different conductivity and dielectric properties, ensuring impedance analysis accuracy over a wide frequency range and improving the accuracy and repeatability of measurement results.

[0099] The four-electrode liquid impedance spectroscopy analysis method provided in this application will be further explained below with reference to a specific embodiment.

[0100] In this embodiment, a Zurich HF2LI lock-in amplifier is selected as the impedance detection instrument 300 to build a four-electrode impedance measurement system. The output impedance Z1 of the lock-in amplifier is 50Ω, the parameters of the first input impedance Z2 and the second input impedance Z3 are both 1 MΩ|| 20 pF, and the third input impedance Z4 is 50Ω. The measurement circuit is connected to the four-electrode liquid sample cell 100 via a coaxial cable, and the parasitic capacitance to ground of each measurement channel has been calibrated in advance to obtain the lumped parameters of the actual measurement circuit. In this embodiment, a standard solution with known nominal electrical parameters is selected as the sample to be tested to verify the accuracy and reliability of this analytical method.

[0101] First, based on the parasitic capacitance of the coaxial cable to ground obtained from calibration, and the hardware parameters such as the output impedance Z1, first input impedance Z2, second input impedance Z3, and third input impedance Z4 of the lock-in amplifier, a lumped parameter model corresponding to the measurement circuit is constructed.

[0102] A four-electrode impedance measurement system was used to perform broadband sweep measurements on the standard solutions to be tested. The measurement frequency range was set from 10 kHz to 10 MHz to obtain raw impedance spectrum data without any high-frequency compensation, numerical calibration, or standard solution differential correction. This broadband band can completely cover the dielectric polarization and relaxation characteristic range of various complex liquid samples, such as biological cell suspensions. It can simultaneously capture low-frequency electrode interface effects, mid-frequency bulk liquid conductivity characteristics, and high-frequency dielectric relaxation characteristics. It is a core frequency band for accurate quantitative analysis of liquid electrical parameters and is crucial for sample characterization.

[0103] Then, a finite element field model of a four-electrode liquid sample pool 100 matching the real measurement scenario is constructed. This finite element field model can completely replicate the actual measurement structure of the four-electrode impedance measurement system. The modeling region includes at least the liquid region to be measured, the four-electrode structure, the liquid-electrode contact interface, and the electrical port for connecting to external circuits. Among them, the liquid region is described by the frequency domain electric field control equations shown in equations (1) to (3), which accurately characterize the coupling response of the conduction current and displacement current inside the liquid. At the same time, anisotropic equivalent boundary conditions with interface contact impedance characteristics are set on the electrode surface to simulate the liquid-electrode double-layer interface effect under the real measurement scenario, effectively making up for the deficiency of traditional models in characterizing low-frequency interface impedance characteristics, and ensuring the authenticity of the full-band field domain solution.

[0104] Furthermore, the completed lumped parameter model of the peripheral circuit and the four-electrode finite element field model are dynamically coupled at the electrical ports corresponding to each electrode, thus constructing a field-circuit coupling model adapted to real measurement conditions. This field-circuit coupling model, relying on the lumped parameter model of the peripheral measurement circuit, can accurately output the actual voltage and current loading boundary conditions at different frequencies at the electrode ports, replacing the traditional ideal port boundary assumptions. Based on these real boundary conditions, the finite element field model solves for the potential distribution inside the liquid under test at each frequency point. The electric field distribution and current density distribution are combined with the port electrical response to complete iterative calculations, and finally output a simulated impedance spectrum that matches the real physical scene.

[0105] Finally, using the measured original impedance spectrum as a benchmark, the simulated impedance spectrum is compared point-by-point with the original impedance spectrum to construct the corresponding error loss function. The conductivity of the liquid under test is continuously updated through an iterative optimization method. With relative permittivity The electrical parameters are optimized, and the simulated impedance spectrum is continuously corrected until the error loss function is less than the preset accuracy threshold, satisfying the iterative convergence condition. At this point, the electrical parameters output by the field-circuit coupled forward analytical model are the absolute quantitative intrinsic electrical parameters of the liquid under test, eliminating frequency domain electric field distortion interference and requiring no high-frequency compensation or standard liquid calibration.

[0106] See Figure 7 The figure is a schematic diagram of simulation data of the field-circuit coupling model provided in the embodiment of this application.

[0107] Figure 7 In (a), the horizontal axis f represents the frequency of the AC excitation source, in Hz; the vertical axis A represents the impedance amplitude of the liquid under test, in Ω. Figure 7 In (b), the horizontal axis f represents the frequency of the AC excitation source, in Hz; the vertical axis φ represents the impedance phase of the liquid under test, in °. Figure 7 The data were compared with real experimental data, simulation data under traditional ideal electrode boundary conditions, and global simulation data of field-circuit coupling under the field-circuit coupling model provided in this application. The average absolute errors between the impedance amplitude and impedance phase of the simulation data under ideal boundary conditions and the real experimental data were 16.27Ω and 4.30°, respectively, while the average absolute errors between the impedance amplitude and impedance phase of the simulation data obtained through the field-circuit coupling model provided in this application and the real experimental data were 2.36Ω and 0.71°, respectively. Figure 7 This further demonstrates that the four-electrode liquid impedance spectroscopy analysis method provided in this application can accurately describe the changing trend of experimental impedance spectra over a wide frequency band.

[0108] Based on the four-electrode liquid impedance spectroscopy analysis method provided in the above embodiments, this application also provides a four-electrode liquid impedance spectroscopy analysis model. The four-electrode liquid impedance spectroscopy analysis model provided in this application applies any of the four-electrode liquid impedance spectroscopy analysis methods provided in this application.

[0109] See Figure 8 The figure is a schematic diagram of a four-electrode liquid impedance spectrum analytical model provided in an embodiment of this application.

[0110] Figure 8 The four-electrode liquid impedance spectroscopy analytical model provided in the embodiment includes a measurement module 10, a simulation module 20, and a calculation module 30.

[0111] The measurement module 10 is used to obtain the original impedance spectrum of the liquid to be tested through the measurement circuit, which is connected to the liquid to be tested through an electrical port.

[0112] One possible implementation is that the original impedance spectrum is obtained by sweeping the measurement circuit to measure the impedance spectrum of the liquid under test within a preset frequency band. The original impedance spectrum is used to at least reflect the relaxation characteristics of the liquid under test. For example, the preset frequency band can be from 10 kHz to 10 MHz.

[0113] Simulation module 20 is used to input electrical parameters into the field-circuit coupling model and obtain the simulated impedance spectrum of the liquid under test based on the potential distribution, electric field distribution, and current density distribution. The field-circuit coupling model includes a finite element field model coupled at the electrical ports and a lumped parameter model. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution inside the liquid under test based on its electrical parameters; the lumped parameter model is used to provide boundary conditions for the finite element field model.

[0114] The calculation module 30 is used to use electrical parameters as parameters to be optimized, perform error iterative fitting between the simulated impedance spectrum and the original impedance spectrum, and output the corrected electrical parameters when the error meets the preset conditions.

[0115] The four-electrode impedance spectrum analytical model provided in this application provides a field-circuit coupling model that unifies the solution of the measurement circuit and the internal electric field of the liquid through a unified solution. The finite element field model can realistically solve for the distribution of potential, electric field, and current density within the liquid; the introduction of real lumped parameters from the external measurement circuit through the electrical ports accurately characterizes the frequency domain electric field distortion over a wide frequency range. Compared with traditional equivalent circuits, the field-circuit coupling model of this application can dynamically describe the evolution of the spatial electric field, with a clearer physical mechanism and more accurate high-frequency analysis, providing a reliable foundation for precise fitting and absolute quantitative measurement of broadband impedance spectra. The analytical method provided in this application can accurately characterize the frequency domain electric field distortion over a wide frequency range, achieving precise fitting between simulated and measured impedance spectra. It can obtain the absolute quantitative electrical parameters of the liquid under test without high-frequency calibration, thereby significantly improving measurement accuracy and reliability.

[0116] One possible implementation of the four-electrode impedance spectrum analytical model provided in this application embodiment further includes: a modeling module.

[0117] The modeling module is used to construct a finite element field model of the liquid under test based on its electrical and structural parameters. The electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test. The structural parameters include the sample cell geometry, electrode positions, and electrode dimensions.

[0118] The four-electrode impedance spectrum analytical model provided in this application, by constructing a finite element field model including the electric field control equation, can realistically solve the potential distribution, electric field distribution, and current density distribution inside the liquid under test, accurately reflecting the broadband electric field variation law inside the liquid under test; by using the lumped parameters of the external real measurement circuit as the boundary conditions of the finite element field model, it can accurately characterize the influence of the introduction of the external measurement circuit on the electric field of the liquid under test, improving the simulation accuracy and physical reliability of the broadband impedance spectrum.

[0119] In one possible implementation, the four-electrode impedance spectrum analytical model provided in this application embodiment, the modeling module, is further used for:

[0120] Based on the hardware parameters of the measurement circuit, a lumped parameter model is constructed. The measurement circuit includes an AC excitation source, an excitation electrode, and three detection electrodes. The hardware parameters include the voltage of the AC excitation source, the current of the AC excitation source, the equivalent impedance of the excitation electrode channel, the equivalent impedance of each detection electrode channel, the parasitic capacitance of the excitation electrode channel, and the parasitic capacitance of each detection electrode channel.

[0121] The four-electrode impedance spectrum analysis model provided in this application embodiment is based on the hardware parameters of the actual measurement circuit to construct a lumped parameter model. It can accurately characterize the equivalent impedance and parasitic capacitance characteristics of the excitation channel and each detection channel, and provide boundary conditions for the finite element field model that fit the actual measurement scenario. This allows it to more realistically reflect the influence of the external circuit on the impedance spectrum of the liquid under test, and improve the accuracy and reliability of broadband impedance analysis.

[0122] In one possible implementation, the computing module 30 is specifically used for:

[0123] Input electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum;

[0124] The updated electrical parameters are obtained iteratively until the error loss function is less than the threshold, at which point the corrected electrical parameters are obtained.

[0125] The four-electrode impedance spectroscopy analytical model provided in this application can adaptively optimize conductivity and relative permittivity using the original impedance spectrum as the target, ensuring that the simulation results output by the field-circuit coupling model closely match the measured data. This iterative process automatically corrects measurement deviations caused by external hardware parameters and frequency domain electric field distortion, obtaining stable and reliable corrected electrical parameters without relying on a standard reference liquid for differential calibration. This enables absolute quantitative extraction of the conductivity and relative permittivity of the liquid under test. Furthermore, this method possesses strong versatility and adaptability, applicable to liquid samples with different conductivity and dielectric properties, ensuring impedance analysis accuracy over a wide frequency range and improving the accuracy and repeatability of measurement results.

[0126] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0127] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A four-electrode liquid impedance spectroscopy analysis method, characterized in that, The parsing method includes: The original impedance spectrum of the liquid to be tested is obtained by a measuring circuit, which is connected to the liquid to be tested through an electrical port. The electrical parameters of the liquid under test are input into the field-circuit coupling model. Based on the potential distribution, electric field distribution, and current density distribution output by the field-circuit coupling model, the simulated impedance spectrum of the liquid under test is obtained. The field-circuit coupling model includes a finite element field model coupled at the electrical port and a lumped parameter model. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution based on the electrical parameters of the liquid under test. The lumped parameter model is used to provide boundary conditions for the finite element field model. The simulated impedance spectrum and the original impedance spectrum are iteratively fitted to obtain the corrected electrical parameters when the error meets the preset conditions.

2. The method according to claim 1, characterized in that, Also includes: Based on the electrical and structural parameters of the liquid under test, a finite element field model of the liquid under test is constructed. The electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test; the structural parameters include the sample cell geometry of the liquid under test, the position of the electrode, and the size of the electrode.

3. The method according to claim 1, characterized in that, Also includes: Based on the hardware parameters of the measurement circuit, the lumped parameter model is constructed; The measurement circuit includes: an AC excitation source, an excitation electrode, and three detection electrodes; The hardware parameters include: the voltage or current of the AC excitation source, the equivalent impedance of the excitation electrode channel, the equivalent impedance of each of the detection electrode channels, the parasitic capacitance of the excitation electrode channel, and the parasitic capacitance of each of the detection electrode channels.

4. The method according to any one of claims 1-3, characterized in that, The simulated impedance spectrum and the original impedance spectrum are subjected to error iterative fitting to obtain the corrected electrical parameters, specifically including: Input the electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum; The updated electrical parameters are obtained iteratively until the error loss function is less than a threshold, at which point the corrected electrical parameters are obtained.

5. The method according to any one of claims 1-3, characterized in that, The original impedance spectrum is the impedance spectrum obtained by the measurement circuit sweeping the frequency of the liquid under test under a preset frequency band. The original impedance spectrum is used to reflect at least the relaxation characteristics of the liquid under test.

6. A four-electrode liquid impedance spectroscopy analytical model, characterized in that, include: A measurement module is used to obtain the original impedance spectrum of the liquid to be tested through a measurement circuit, wherein the measurement circuit is connected to the liquid to be tested through an electrical port; The simulation module is used to input the electrical parameters into the field-circuit coupling model and obtain the simulated impedance spectrum of the liquid under test based on the potential distribution, electric field distribution, and current density distribution. The field-circuit coupling model includes a finite element field model coupled at the electrical port and a lumped parameter model. The finite element field model is used to solve for the potential distribution, electric field distribution, and current density distribution based on the electrical parameters of the liquid under test. The lumped parameter model is used to provide boundary conditions for the finite element field model. The calculation module is used to use the electrical parameters as parameters to be optimized, perform error iterative fitting between the simulated impedance spectrum and the original impedance spectrum, and output the corrected electrical parameters when the error meets the preset conditions.

7. The model according to claim 6, characterized in that, Also includes: Modeling module; The modeling module is used to construct the finite element field model of the liquid under test based on the electrical and structural parameters of the liquid under test. The electrical parameters include conductivity and relative permittivity, which are used to solve for the intrinsic impedance of the liquid under test; the structural parameters include the sample cell geometry of the liquid under test, the position of the electrode, and the size of the electrode.

8. The model according to claim 6, characterized in that, The modeling module is also used for: Based on the hardware parameters of the measurement circuit, the lumped parameter model is constructed; The measurement circuit includes: an AC excitation source, an excitation electrode, and three detection electrodes; The hardware parameters include: the voltage of the AC excitation source, the current of the AC excitation source, the equivalent impedance of the excitation electrode channel, the equivalent impedance of each of the detection electrode channels, the parasitic capacitance of the excitation electrode channel, and the parasitic capacitance of each of the detection electrode channels.

9. The model according to any one of claims 6-8, characterized in that, The calculation module is specifically used for: Input the electrical parameters into the field-circuit coupling model to obtain the simulated impedance spectrum of the liquid under test, and calculate the error loss function between the simulated impedance spectrum and the original impedance spectrum; The updated electrical parameters are obtained iteratively until the error loss function is less than a threshold, at which point the corrected electrical parameters are obtained.

10. The model according to any one of claims 6-8, characterized in that, The original impedance spectrum is the impedance spectrum obtained by the measurement circuit sweeping the frequency of the liquid under test under a preset frequency band. The original impedance spectrum is used to reflect at least the relaxation characteristics of the liquid under test.

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