We have designed a cylindrical dielectric property measuring cell tailored for biological soft tissues, as shown in Figure 1, to meet the requirements of both two-electrode and four-electrode methods. The measuring cell is made of transparent organic glass, with the inner diameter is 5mm, the outer diameter is 8mm, and the length is 15 mm. At both ends, two circular silver electrodes with a thickness of 0.4 mm are fixed to the organic glass box cover and can be conveniently removed with the cover for filling the tissue to be measured or for cleaning.

An O-ring made of rubber is placed between the box cover and the box body to prevent leakage. Two annular silver electrodes with a thickness of 0.4 mm are embedded in the middle section of the box, with the inner side of the rings maintaining the same cylindrical surface as the inner cavity of the box. The two annular electrodes are spaced 7.5 mm apart. The box body features two round holes with a diameter of 1mm, which can be used for liquid injection and gas release.

During dielectric property measurements, the excitation signal is injected through the two circular electrodes at the ends, and the response signal can be directly measured from these two electrodes (two-electrode method), or it can be measured through the intermediate annular electrodes embedded in the box (four-electrode method).

Before measuring, it is necessary to immerse the electrodes in 75% medical alcohol for more than 10 min to perform sterilization. Then, soak them in saline solution for more than 30 min to maintain a relatively stable polarization state of the electrodes. This procedure ensures that the electrodes are clean and free from contaminants that could affect the accuracy of the measurements, and it helps to stabilize the electrode polarization, which is crucial for obtaining consistent and reliable results in dielectric property measurements.

The four-electrode measurement system presented in Figure 2, comprises a Solartron 1260A frequency response analyzer and a Solartron 1,294 impedance measurement interface (Schlumberger, United Kingdom). The excitation terminals of the Solartron 1,294 are connected to the circular electrodes at both ends of the measuring cell, while the measurement terminals are connected to the annular electrodes in the middle section of the cell (Figure 2B). The entire process of sample installation and measurement is conducted in an infant incubator to maintain a stable temperature (37°C) and humidity (90%) environment within 30 min.

The system is connected to the main control computer via USB-GPIB, and measurement methods and parameter settings are selected and configured using the Zplot measurement software. This software allows for the measurement of the real part, imaginary part, modulus, and phase of the complex impedance of the target under test. Additionally, these parameters can be mathematically converted into equivalent capacitance and admittance of the target and saved to the computer.

Due to the significant impact of the distributed parameters of electrode leads at high frequencies, this system is primarily used for dielectric property measurements in the frequency range of 1Hz to 1 MHz. Since the Solartron 1,294 impedance measurement interface supports true differential four-terminal connections, it has high input impedance and sensitivity to both voltage and current. Therefore, this system can more effectively suppress the influence of high electrode impedance caused by electrode polarization, achieving high-precision measurements in the low frequencies.

As shown in Figure 3, the two-electrode measurement system is primarily based on the Agilent 4294A Impedance Analyzer (Agilent Technologies, United States). The Agilent 42942A Terminal Adapter is used to transform the four-terminal configuration of the impedance analyzer’s measurement ends into a 7 mm two-terminal configuration (Figure 3A). The Agilent 16092A clamp serves as the interface to connect the circular electrodes at both ends of the dual-purpose measuring cell to the measurement system. The Agilent 16092A clamp, along with the measuring cell, is installed together in a temperature-controlled incubator to maintain the sample temperature (37°C). The system is connected to the main control computer via GBIP, and Intuilink software is integrated within Office software, allowing measurement data to be imported into Excel for analysis (Figure 3B).

The two-electrode measurement system is used to measure the real and imaginary parts of the impedance of biological tissues in the frequency range of 40Hz to 100 MHz. Then mathematically convert them into equivalent conductance and capacitance. Before measurement, Agilent 42942A and Agilent 16092A are calibrated with standard calibration terminals provided by the manufacturer to ensure accuracy and reliability of the data obtained.

In dielectric property measurements, there are some sources of systematic error, including the dimensions of the measuring cell, the nonlinearity of the measuring instruments, and the distributed parameters of electrodes and connecting wires. To improve the accuracy of the measurements, these errors need to be corrected. Corrections for both four-electrode and two-electrode methods are based on the 12.88 m/cm (25°C) standard conductivity solution produced by Mettler Toledo.

The dielectric properties of the measured material were obtained using the four-electrode method for the frequency range of 10Hz to 1 MHz and the two-electrode method for the frequency range of 40Hz to 100 MHz. To verify the accuracy of the results and the valid frequency range of the measured data, we analyzed the conductivity of NaCl solutions at 0.01 Mol/L and 0.05 Mol/L, as well as the conductivity and permittivity of the porcine liver tissue.

Figures 5A, B present the measurement results and theoretical calculations for the conductivity of NaCl solutions. It can be observed that the conductivity measured via the four-electrode method below 1 MHz closely aligns with theoretical values. The conductivity measured via the two-electrode method above 10 kHz shows close agreement with theoretical values, while significant deviations are observed below 10 kHz, with the deviation increasing rapidly as the frequency decreases. This suggests that the measurements using two-electrode method in this frequency range are greatly affected by electrode polarization, leading to poor credibility of the results.

Figures 5C, D shows the measured conductivity and permittivity of porcine liver tissue. Below 4 kHz, due to the influence of contact impedance, the conductivity measured by the two-electrode method is lower than that measured by the four-electrode method. While the permittivity measured by the two-electrode method exceeds that obtained by the four-electrode method, with the difference widening as the frequency decreases. Above 400 kHz, the conductivity and permittivity measured by the four-electrode method begin to deviate from those obtained by the two-electrode method due to the impact of distributed parameters. Between 4 kHz and 400 kHz, and particularly within the frequency range of 50 kHz–200 kHz, there is a complete concordance between the results from both measurement methods.

Given the insights from our study, we have established the following guidelines for determining the dielectric properties of the target in our future research. For frequencies below 50 kHz, we will rely on the measurement results from the four-electrode method. This decision is informed by the pronounced effects of contact impedance at these lower frequencies, which can significantly bias the results from the two-electrode method, leading to lower conductivity and higher permittivity.

For frequencies ranging from 50 kHz to 200 kHz, we will utilize a weighted average of the measurements from both the four-electrode and two-electrode methods. This approach is justified by the fact that, within this frequency band, both methods provide consistent results. By using a weighted average, we can leverage the combined precision and reliability of both techniques, thereby enhancing the overall accuracy of our dielectric property determinations.

For frequencies above 200 kHz, we will rely on the measurement results from the two-electrode method. This decision stems from the observation that the four-electrode method’s measurements begin to deviate from those of the two-electrode method at these higher frequencies. The deviation is likely attributed to the effects of distributed parameters, which can impair the accuracy of the four-electrode method’s readings.

Following the established protocols, we have determined the conductivities of NaCl solutions with concentrations of 0.01, 0.03, 0.05, and 0.07 Mol/L. Figure 6 depicts the frequency-dependent variation of both the measured and theoretical conductivity values for these four NaCl solutions. Notably, the comparison indicates a high degree of correspondence between the measured and theoretical values.

Furthermore, the average standard deviations for the four different concentrations were 1.76 × 10⁻³, 2.68 × 10⁻³, 4.66 × 10⁻³, and 5.95 × 10⁻³, representing 1.79%, 0.92%, 0.96%, and 0.88% of the mean values, respectively. Given that the measurement samples of the same concentration all came from the same solution and that sodium chloride solutions can maintain their chemical stability at 37°C, the average standard deviations were mainly attributed to the measurement system and method. This minimal variability suggested the high stability and accuracy of our measurement system and methods.

Relative error E r was used to evaluate the accuracy of our methods for determining tissue conductivity across different measurement frequency ranges. Relative error quantifies the discrepancy between measured values and theoretical values, providing insight into measurement accuracy. E r f i = σ m f i − σ t f i σ t f i × 100 %

Where, σ m and σ t represent measured and theoretical conductivity at the measured frequency f i , respectively. The average and maximum value of E r are shown in Table 1. NaCl solution with concentrations of 0.01 Mol/L exhibits the highest average relative error E r a v e and maximum relative error E r   max , peaking at 1.46% and 6.34%. With an increase in the concentration of NaCl solutions, both E r a v e and E r   max progressively diminish, dropping to 0.47% and 1.27% when the solution concentration reaches 0.07 Mol/L. This might be attributed to the ions in the solution. At lower concentrations, fewer ions are available, resulting in a weaker signal and greater susceptibility to various interfering factors, which in turn leads to a larger E r . As the concentration increases, the ion count rises, enhancing the signal and consequently reducing the E r . The regression coefficients R 2 for the four concentrations of sodium chloride solution are all above 0.98, indicating an exceptionally strong linear relationship between the measured values and the theoretical values. This suggests that the experimental data is highly reliable and accurate.

Figures 7A, B display the measured conductivity and permittivity of six porcine liver tissue samples, while Figure 7C summarizes the mean value and standard deviation for both conductivity and permittivity. Notably, the dielectric properties of these samples are found to be close to each other. To assess the consistency of these measurements, we calculated the relative deviation (standard deviation as a percentage of the mean) for conductivity across all six samples at each frequency (Figure 7D). The observed deviations, ranging from 3% to 6%, which is relatively small, indicating good repeatability of our measurement method. This consistency suggests that the method is reliable for accurately determining the dielectric properties of the tissue.

The measuring cell designed in this study is a novel approach that addresses specific challenges associated with in vivo tissue measurements. It is engineered to provide a controlled environment for tissue samples, ensuring that the electric field is distributed uniformly and predictably. This design not only minimizes the effects of tissue boundary changes and the influence of surrounding tissues on the electric field, but also prevents tissue from being subjected to undue pressure during the measurement process, thus avoiding deformation that can skew results.

What’s more important is that this versatile device can swiftly and flexibly switch between the two-electrode and four-electrode methods, accommodating the measurement requirements for dielectric characteristics across a broad spectrum of frequencies. It is beneficial for diminishing the impact of electrode polarization and the distributed parameters of the measurement system on these properties, thereby ensuring the acquisition of accurate dielectric characteristics.

In pursuit of more precise dielectric properties of biological tissues up to 100 MHz, we have synergized the four-electrode method with the two-electrode method. The four-electrode method was used to measure the impedance below 1 MHz to eliminate the polarization effects of the electrodes and contact resistance. The two-electrode method was used to measure the impedance above 1 MHz to eliminate the effect of stray capacitance and inductance.

To accommodate the measurement demands of four-electrode and two-electrode methods, we have implemented specific enhancements for each. For the four-electrode impedance measurement system, we have integrated the Solartron 1,294 impedance interface, which boasts higher input impedance and greater measurement precision. This addition significantly reduces the effects of electrode polarization, leading to improved accuracy in low-frequency measurements.

For the two-electrode method, we have designed a measurement system with minimal lead length using the Agilent 4294A impedance analyzer, along with the Agilent 42942A terminal adapter and Agilent 16092A clamps. Additionally, we have developed advanced calibration techniques to further mitigate the impact of distributed parameters, thereby enhancing the reliability of high-frequency measurement outcomes.

Based on the analysis of the optimal frequency range (Figure 5), we have proposed recommendations for measuring the dielectric properties of biological tissues across the frequency range from 10 Hz to 100 MHz. The four-electrode method is found to be most effective for frequencies below 50kHz, whereas the two-electrode method demonstrates superior performance at frequencies above 200 kHz. For the intermediate frequencies, an optimal result can be achieved by utilizing a weighted average of the two methods.

The integrated methodology allows us to maintain a low level of measurement deviation across the entire spectrum up to 100 MHz. For NaCl solution, the maximum relative deviation observed is 6.34%, and the average deviation is less than 1.5% (Figure 6; Table 1). For porcine liver tissue, the relative deviation is kept below 6% overall (Figure 7). These improvements are significantly lower than the 10% deviation reported in literature (25), highlighting the superior performance of our method in meeting the stringent demands for measuring biological tissues. This synergy approach not only broadens the frequency range for accurate measurements but also ensures that the results are consistent and reliable across the entire spectrum of frequencies. It provides a robust framework for accurate impedance measurements, particularly in the context of biological applications where precision is paramount.

As documented in various studies, measurement conditions such as temperature, humidity, and the duration that tissue is kept ex vivo can significantly influence the measurement results of dielectric property of biological tissues (Di Meo et al., 2022; Fallahi, Sebek, and Prakash, 2021; Halonen et al., 2022; Wang et al., 2023). In this study, we have adopted the following measures to make the environment of the tissue samples as similar as possible to their in vivo conditions, thereby ensuring that the dielectric properties of the ex vivo tissues closely approximate those in vivo.

The samples are maintained in incubator with the same temperature and humidity as in vivo. The samples are immersed in physiological saline to replicate the in vivo interstitial and tissue fluid environment. All sample measurements were completed within 30 min after clamping the hepatic portal vessels and stopping blood supply to the liver. The short period of tissue ischemia ensures that the tissue remains in an active state similar to that in vivo (Wang et al., 2021).

As we look to the future, the implementation of automated sampling and specimen preparation has the potential to significantly reduce the duration of ex vivo measurements. This innovation not only streamlines the process but also promises to bridge the gap between ex vivo and in vivo data, enhancing the correlation between the two. Such progress is expected to yield more reliable and accurate measurement outcomes, thereby reinforcing the significance of the measuring cell as an indispensable tool in biological tissue analysis. Furthermore, by integrating the dielectric property measurement techniques with magnetic property techniques, a more comprehensive understanding of the biophysical characteristics of diseases can be achieved, which in turn provides more accurate guidance for clinical diagnosis and treatment (O'Callaghan et al., 2017; Winkler R et al., 2023).

In the future, we will develop the automated sampling and specimen preparation technologies to reduce the duration of ex vivo measurements. Concurrently, we will focus on refining our calibration methods to further minimize system measurement errors. Furthermore, we recognize the importance of considering the sensitivity of the measurement method. This involves not only assessing the method’s reproducibility but also its ability to detect subtle changes in dielectric properties. These efforts will significantly enhance the reliability of the measurement system and methods employed in this study, paving the way for more advanced and reliable dielectric property measurement of active biological tissues across the 10 Hz to 100 MHz frequency range.

In summary, this study has introduced an innovative measurement technique for determining the dielectric properties of active biological tissues within the frequency range of 10Hz to 100MHz, leveraging a newly developed two/four-electrode dual-purpose measuring cell. The efficacy of this method was confirmed by assessing the dielectric properties of NaCl solutions with varying concentrations and porcine liver tissues. The findings highlight the method’s aptness for quantifying dielectric properties in active biological tissues and underscore its potential to serve as a solid foundation for future research in this critical field.