Influence of Pulsed Electric Field Parameters on Electrical Conductivity in Solanum tuberosum Measured by Electrochemical Impedance Spectroscopy

Abstract

High-voltage unipolar square wave pulsed electric fields (PEFs) can cause cell membrane rupture and cell death during a process termed irreversible electroporation (IRE). PEF effects are influenced by pulse parameters like number of pulses (NP), voltage (PV), width (PW), and interval (PI). This study systematically evaluates their effects on the conductivity and relative conductivity changes between untreated and PEF-treated regions of potato tissue across a frequency range of 1 Hz to 5 MHz by means of electrochemical impedance spectroscopy (EIS), using a custom-made four-point EIS probe with RG58/U coaxial cables. Potatoes were chosen as a plant-based PEF model to reduce animal experiments and untreated tissue showed minimal conductivity variation across regions. Relative conductivity changes were maximal at 1000 Hz. At 1000 Hz, significant conductivity differences between untreated and PEF-treated regions were observed from PV = 200 V, NP = 10, PW = 10 µs, and PI = 50 ms onwards (most significant changes occurred for PV = 700 V; NP = 70; PW = 70 µs; PI = 250 ms and 500 ms). Our results may be beneficial for multiphysics modelling of IRE with specific electrical properties, conductivity mapping with optimal contrast—such as in electrical impedance tomography—and development of IRE procedures.

1. Introduction

High-voltage pulsed electric fields (PEFs) can induce the electrical breakdown and rupturing of cell membranes in biological tissues [1]. PEF treatment transiently increases the plasma membrane permeability by forming nanopores, thereby facilitating the transport of otherwise cell-impermeant molecules, which increases electrical conductivity. This phenomenon is referred to as electroporation or electro-permeabilization [2,3,4]. If the cell succeeds in restoring homeostasis by repairing its plasma membrane, the effect is transient and termed reversible electroporation (RE). However, when the PEF pulse parameters exceed certain thresholds, irreparable damage occurs in the plasma membrane, resulting in cell death. This effect is termed irreversible electroporation (IRE) [5].

A clinical application of RE and IRE is minimally invasive tumour treatment [6,7,8,9,10], with IRE being particularly effective for tumours near critical blood vessels in the liver, pancreas, and brain due to its non-thermal mechanism that preserves vascular structures [11].

Commonly, series of unipolar square wave pulses [12], characterized by parameters such as the number of pulses (NP), pulse voltage (PV), pulse width (PW), and pulse interval (PI) (see Figure 1d for parameter definitions), are locally applied to the treated tissue over a needle applicator [13]. The distance between the straight needle electrodes and the PV determines the maximum applied PEF field strength [14]. Numerous studies have explored the effects of PEF parameters across in vitro [15,16], in vivo [17,18], and in plant-based models [19,20]. Towards higher NP, the PV, PW, and smaller PI favour IRE over RE [5,21,22]. Eventually, if the PEFs start to cause Joule heating, thermal ablation will also contribute [14,23]. However, thresholds between the regimes may not only depend on the above-mentioned pulse parameters, but also on the tissue type [24] and shape of the needle applicator [21,25,26]. Understanding these influences is albeit crucial with respect to patient-specific individual treatment planning [27].

A study in rabbit liver by Sel et al. found thresholds for RE and IRE at applied electric fields of 460 and 700 V/cm, respectively (NP = 8, PW = 100 μs, PI = 1 s) [28]. However, for RE treatment in humans, eight electric pulses with a PW of 100 μs are commonly delivered at an electric field of 1000 V/cm or higher [29]. An optimization study on clinical IRE treatments using a NanoKnife on swine liver found that increasing PW beyond 50 µs and NP beyond 50 did not significantly increase the ablation size due to IRE [30]. Furthermore, PW > 70 µs and NP > 70 caused white necrotic tissue next to the electrode because of thermal coagulation, similar to that seen in radiofrequency and microwave ablation [30]. It should be noted that plant tissues seem to require higher PW of around 100 µs–1000 µs for successful PEF treatment [31].

Importantly, pulse parameter experiments necessitate a substantial quantity of viable tissue, which can be either living animal or plant tissue. PEF effects, especially IRE and RE, were also explored at the single-cell level, but tissues present a more complex scenario due to the proximity of cells and the inherent tissue inhomogeneity [32]. In contrast to animal models, metabolic activity, including cellular respiration, persists in plant models even after harvesting [33]. Studying PEF in plant-based models aligns with the “Three Rs”—Replacement, Reduction, and Refinement—to minimize animal usage [34,35]. Also, the Biomedical Engineer’s Pledge 1.0 encourages minimizing animal experimentation [36]. Potatoes are widely used as a plant-based model for electroporation research, including device testing and the development of new measurement methods, due to their cost-effectiveness, availability, and lack of ethical concerns [37,38,39,40,41,42,43,44].

The effects of PEF in potatoes can be detected by dye staining [38], melanin browning [38,40,45], magnetic resonance imaging [39,46], fluorescence imaging [42,43,44], and electrochemical impedance spectroscopy (EIS) [47]. Compared to other techniques, EIS offers quantitative assessment of the electrical tissue properties, including conductivity and permittivity, which serve as indicators of pore formation and membrane permeabilization [48,49]. EIS perturbs an electrochemical system by applying a sinusoidal signal, typically an alternating voltage or current, across a range of frequencies. It then monitors the system’s response, either current or voltage, to study the frequency-dependant electrical impedance. The system is typically assumed to be linear and time-invariant, meaning its behaviour remains constant over time [50]. Even the slightest changes at the medium-electrode interface are detected by EIS, which finds extensive use in biosensing applications [51].

Accurate estimation of tissue-specific electrical conductivity and permittivity changes following electroporation, has multiple applications in optimizing and predicting PEF-induced ablations by allowing more precise numerical simulations [52,53].

Another application of tissue-specific electrical changes post-electroporation is the optimization of electrical impedance tomography (EIT), a low-cost, non-invasive imaging modality that maps tissue conductivity in real time [54]. EIT is sensitive to the passive electrical properties of tissues altered during electroporation, making it the only imaging modality that directly detects electroporation-mediated conductivity changes through its underlying impedance-based mechanism [55]. However, one must choose a frequency in advance that yields optimal contrast between electroporated and non-electroporated tissue, as tissue conductivity varies with frequency [54,56,57]. EIS with higher accuracy can further assist in identifying optimal frequencies with maximal conductivity changes.

Different electrode configurations can be used in EIS, i.e., two-, three- or four-electrode setups. The four-electrode method offers superior accuracy compared to the others [58]. In this setup, the outer electrodes inject current, while the inner electrodes measure frequency-dependent voltage signals, or vice versa [58]. The four-probe EIS method eliminates electrode polarization [59], which occurs at the tissue-electrode interface due to molecular charge organization forming ionic double layers [60]. Probes using open-ended coaxial cables have demonstrated the capability to rapidly evaluate highly accurate and precise dielectric properties in various materials after calibrating the probe by measuring its cell constant in a solution of known dielectric properties. Also, they only require a small sensing area as small probes can be constructed [61]. Gabriel et al. used an open-ended coaxial cable system to obtain the dielectric properties of biological tissues from EIS [62,63].

A recent systematic review of 18 preclinical studies in both animal and phantom models highlighted the need for research on the optimization of IRE treatment protocols to better predict the effect of specific pulse parameter combinations on treatment response [21]. Yet, to the best of the authors’ knowledge, comprehensive studies integrating PEF for a wide range of the above-mentioned pulse parameters and EIS measurements in plant tissues are so far absent in the literature. A previous study by Zhao et al. analysed impedance changes in potatoes using four 1.15 mm diameter electrodes in a square array, with one diagonal pair applying PEF and the alternating pairs measuring impedance changes from EIS (1 Hz to 1 MHz). It focused solely on impedance, without analysing conductivity and permittivity, and only varied PV and NP [64]. Another PEF study on potatoes by Genovese et al. employed four-point EIS with frequencies from 50 Hz to 1 MHz and copper needle electrodes. Their analysis showed a notable decrease in impedance above a threshold PEF field of 250 V/cm (NP = 8, PW = 100 μs, PI = 1 s). However, PEF parameters other than PV were not examined [47].

Additionally, open-ended coaxial four-point EIS probes have not been employed in the context of electroporation research on plant-based models.

Thus, the aim of this study was to comprehensively assess conductivity changes in response to PEF by EIS in potato samples as a model system. To that purpose, we varied diverse PEF parameters, i.e., PV, PV, PI, and NP, and performed EIS with a custom-designed four-point coaxial probe. We hypothesized that a specific frequency range would show high relative conductivity changes between PEF-treated and non-treated potato regions in EIS, which can be applied to EIT.

2. Materials and Methods

2.1. Fabrication of an Open-Ended Coaxial Four-Point Probe

A four-point EIS probe was custom-designed, as shown in Figure 1a and Supplementary Figure S1, with four open-ended RG58/U coaxial cables (Cnals, Jiangsu Elesun Cable Co., Ltd., Zhenjiang, Jiangsu, China) (45 cm long, copper core diameter of 0.9 mm, polyethylene insulation with an outer diameter of 2.95 mm, maximum capacitance of 101 pF/m, and impedance of 50 ± 2 Ω). BNC connectors were fitted to one end of each cable, while the opposite ends were modified to expose 4 cm of insulation and 1.5 cm of the copper core. These open ends were mounted in a polycarbonate block with evenly spaced holes to maintain a core-to-core distance of 0.3 cm between the exposed cores in a linear arrangement. Likewise, the setup minimized displacement and optimized contact during the measurements.

2.2. EIS Measurement System

EIS measurements were conducted using the ISX3 EIS analyser Version 4 (Sciospec Scientific Instruments GmbH, Bennewitz, Germany). The BNC ends of the four-point probe were connected in linear order to the W (work), WS (working sense), R (reference), and C (counter) connectors on the ISX3 EIS analyser, respectively, as shown in Figure 1a. The excitation voltage was applied between electrodes W and C, while EIS spectra were acquired between WS and R. A representative Nyquist plot of the sample EIS data is shown in Supplementary Figure S2. Prior to EIS measurements, the exposed cores of the four-point probe were inserted 1 cm deep into the samples.

To select an appropriate frequency range for our EIS measurements, we referred to the accuracy contour plot [ScioSpec ISX-3/ISX-3mini manual, version 87, 2021], which indicated an 0.01% error for 1 kΩ impedances from 1 Hz to 1 MHz and an 0.1% error for frequencies above 1 MHz. Also, coaxial cable capacitance, determined by shielding quality, sets an upper frequency limit, while cable inductance, influenced by length, defines a lower frequency limit for accurate impedance measurement [50]. All EIS scans, including calibration scans, were performed over a frequency range of 1 Hz to 5 MHz, using 2048 logarithmically spaced data points per sweep. An excitation voltage of 250.0 mV was applied. Mean and repeat count were set to 1.

The complex impedance ($Z$) at each frequency point was determined based on the measured real ($Re$) and imaginary ($Im$) components of impedance, expressed as:

$$Z=Re\left(Z\right)+j Im\left(Z\right)$$

(1)

where $j$ is the imaginary unit. The equivalent circuit of the sample and electrode system was modelled as a resistor in parallel with a capacitor, assuming negligible contact resistance and inductance between the sample and the EIS probes [65,66]. For a parallel circuit, the admittance ($Y=1/Z$), defined as the inverse of impedance, is given by:

$$Y=G+jB=G+j \mathsf{\omega }\mathrm{C}$$

(2)

Here, $G$ represents the conductance contributed by the resistor, while $B$ denotes the susceptance contributed by the capacitor with capacitance ($C$), proportional to the relative permittivity of the sample (${\epsilon }_r$). The angular frequency is defined as $\omega =2\pi f$, where $f$ is the frequency [47].

For the sample modelled as a parallel RC circuit, the conductance ($G$) and susceptance (B) were calculated from the measured impedance components as

$$G={\displaystyle \frac{Re\left(Z\right)}{{Re\left(Z\right)}^2+{Im\left(Z\right)}^2}} \mathrm{and} B={\displaystyle \frac{-Im\left(Z\right)}{{Re\left(Z\right)}^2+{Im\left(Z\right)}^2}}$$

(3)

The sample’s (real-valued) conductivity ($\sigma$) and relative permittivity (${\epsilon }_r$) were further derived using the following relations: $\sigma =K_{Cell} . G$ and ${\epsilon }_0 {\epsilon }_r=K_{Cell} . C$. Here, $\sigma$ is the conductivity of the sample, ${\epsilon }_0$ is the permittivity of free space (8.85 × 10⁻¹² Fm⁻¹) and $K_{Cell}$ (in m⁻¹) is the cell constant that depends on the geometry and properties of the electrode [67].

2.3. Calibration of the Four-Point Probe

The calibration of the four-point probe for EIS-based conductivity measurements, that is, determining the cell constant for transforming impedance spectra to conductivity, was performed using the HI70031 conductivity standard solution (Hanna Instruments Inc., Woonsocket, RI 02895, USA).

After each set of experiments, the cell constant was determined by performing a calibration EIS scan in 40 mL of the standard solution which had been allowed to equilibrate to room temperature before. The temperature was measured using a Brymen BM235 Multimeter (Brymen Technology Corporation, Taipei, Taiwan) paired with a K type temperature probe, which has an accuracy of ±1 °C. The conductivity of the HI70031 standard solution closest to the measured solution temperature, (${\sigma }_{Solution}$), was read from the provided conductivity chart. At 21 and 22 °C, the provided conductivity values of the solution (${\sigma }_{Solution}$) are 0.1305 ± 0.0005 and 0.1332 ± 0.0005 S/m, respectively. The frequency-dependent cell constant ($K_{Cell}\left(f\right)$) for the four-point probe was calculated according to

$$K_{Cell}\left(f\right)={\sigma }_{Solution}\left(f\right) ÷ G_{Solution}\left(f\right)$$

(4)

Here, “$f$” designates the frequency. Subsequently, $K_{Cell}\left(f\right)$ was utilized to calculate the conductivity of biological samples (${\sigma }_{Sample}\left(f\right)$) [65] as

$${\sigma }_{Sample}\left(f\right)=K_{Cell}\left(f\right)·G_{Sample}\left(f\right)$$

(5)

To compare the relative conductivity change ($∆{\sigma }_{rel}\left(f\right)$) following PEF treatment with respect to an untreated control region with conductivity (${\sigma }_{Ctrl}\left(f\right)$), a relative conductivity change (in percent) was calculated as follows:

$$∆{\sigma }_{rel}\left(f\right)={\displaystyle \frac{{\sigma }_{Sample}\left(f\right)-{\sigma }_{Ctrl}\left(f\right)}{ {\sigma }_{Ctrl}\left(f\right)}}\times 100$$

(6)

Similarly, the permittivity (${\epsilon }_{Sample}\left(f\right)$) and relative permittivity change ($∆{\epsilon }_{rel}\left(f\right)$) of biological samples were calculated as follows:

$${\epsilon }_{Sample}\left(f\right)=B_{Sample}\left(f\right)·K_{Cell}\left(f\right) ÷(2\pi f·{\epsilon }_0)$$

(7)

$$∆{\epsilon }_{rel}\left(f\right)={\displaystyle \frac{{\epsilon }_{Sample}\left(f\right)-{\epsilon }_{Ctrl}\left(f\right)}{ {ϵ}_{Ctrl}\left(f\right)}}\times 100$$

(8)

2.4. Heterogeneity Test of Untreated Potato Tissue

Potatoes (Solanum tuberosum var. Gala) were purchased as a single batch from a local supermarket.

As a pre-experiment, the heterogeneity of potato tissue was assessed. To that purpose, EIS spectra were acquired in different tissue locations, including three randomly selected regions within the perimedulla, and one region per medulla, cortex, and cortical medulla, respectively (c.f. Figure 1c). In total, N = 6 samples were investigated.

After a longitudinal bisection of the potatoes along their central axis, EIS spectra were obtained by inserting the above described four-point probe perpendicularly to the cut-plane into the respective regions. Frequency-dependent conductivity was derived using cell constants obtained from the standard conductivity solution (0.1332 ± 0.0005 S/m) at a solution temperature of 21.5 °C.

2.5. System Setup for PEF Treatment

The PEF treatment of potato samples was conducted using a BTX Gemini X2 Twin Wave Electroporation System (Harvard Apparatus, Holliston, MA, USA) and a dedicated, custom-designed two-needle electrode system (Figure 1b) [39,40]. The core-to-core distance between the parallel stainless steel needle electrodes, each with a 0.9 mm diameter, was 1 cm. The exposed length of the needles was 1 cm, and the remaining portions were insulated with heated PTFE Teflon tubing to prevent any additional contact with the surroundings. The electrodes were embedded into a transparent polycarbonate block to minimize inadvertent movements during needle insertion into the sample.

2.6. Assessment of PEF-Mediated Conductivity Changes

For PEF treatment, the potato samples were bisected along their longitudinal axis. The two-needle electrodes were inserted 1.3 cm deep into the perimedullar area, perpendicularly to the cut plane. A previously established set of IRE pulse parameters was utilized as a standard IRE protocol and starting point for our experiments, which included NP = 70 unipolar pulses with an applied voltage of PV = 1000 V (and, consequently, a maximum electric field strength of 1000 V/cm), a pulse duration of PW = 100 µs, and a pulse interval of PI = 100 ms.

In four sets of experiments, one parameter from the standard irreversible electroporation protocol, i.e., NP, PI, PW, or PV, was varied at a time, while the remaining parameters were kept at the standard values to assess PEF-mediated conductivity changes.

Table 1. Overview of the four sets of experiments, which varied the number of pulses, the pulse interval, the pulse width, and the pulse voltage while keeping other fixed pulse parameters constant in each set. Alongside, the temperature of the standard conductivity solution and corresponding conductivity as measured prior to calibrating the cell constant.

Variable Pulse Parameters			Fixed Pulse Parameters	Standard Conductivity Solution
Pulse Parameters	Variable Values	Units		Solution Temperature (°C)	Conductivity (S/m)
Pulse voltage (PV)	100, 200, 300, 400, 500, 600, 700, 800, 900, 1000	V	NP = 70 PW = 100 µs PI = 100 ms	20.8	0.1305
Number of pulses (NP)	5, 10, 15, 20, 30, 40, 50, 60, 70	-	PI = 100 ms PW = 100 µs PV = 1000 V	21.4	0.1305
Pulse width (PW)	10, 20, 30, 50, 70, 80, 90, 100, 200	µs	NP = 70 PI = 100 ms PV = 1000 V	20.8	0.1305
Pulse interval (PI)	50, 100, 150, 200, 250, 300, 350, 400, 500	ms	NP = 70 PW = 100 µs PV = 1000 V	21.0	0.1305

summarizes the four sets of experiments alongside with the temperature and conductivity of the standard solution. Each set of experiments was performed on six different potatoes (N = 6). Consequently, up to 10 different PEF treatments were conducted per sample, along with two untreated control measurements, on the available perimedullar area. The dimensions of the potatoes were measured using a digital caliper (Forum, E/D/E GmbH, Wuppertal, Germany) with a resolution of 0.01 mm.

To verify that the PEF treatment did not cause any tissue heating, the temperature of the potato tissue close to one of the electroporation needle tips was measured after each PEF treatment by inserting a K-type temperature probe of the Multimeter into the needle hole, approximately 10 s after retracting the electroporation needle. Immediately afterwards, i.e., approximately 30 s after PEF treatment, the EIS spectrum was recorded. To that purpose, the four-point probe was positioned vertically about 1 cm deep in the potato tissue, in between the marks left by the electroporation needles.

2.7. Analysis of EIS Data

Per set of experiments and investigated PEF parameter, N = 6 individual conductivity and permittivity curves were calculated using Equations (3)–(5) and referenced to the ‘Ctrl’ regions according to Equation (6), yielding N = 6 relative conductivity ($∆{\sigma }_{rel}$) and relative permittivity ($∆{\epsilon }_{rel}$) curves, respectively. Subsequently, a mean conductivity and permittivity curve and their standard deviation (SD) as well as the corresponding mean $∆{\sigma }_{rel}$ curves and their SDs were calculated. The maximum relative conductivity ($∆{\sigma }_{rel.max}$) and the corresponding frequency ($f_{∆{\sigma }_{rel.max}}$) were read from the relative conductivity curves. Based on $f_{∆{\sigma }_{rel.max}}$, the optimal decade ($f_{opt10}$) for analyzing PEF-mediated conductivity changes was determined by rounding the logarithm of $f_{∆{\sigma }_{rel.max}}$ to the nearest integer and converting back to the linear scale. The same analysis was repeated for the permittivity data.

The relative standard deviation (RSD) in percent was used to assess the precision of replicate conductivity and permittivity measurements within each sample group. It was calculated as follows:

$$RSD \left(\%\right)={\displaystyle \frac{Standard deviation}{Mean}}\times 100$$

(9)

2.8. Statistical Analysis

Statistical analysis was performed using GraphPad Prism 10.1.1 (GraphPad Software, Inc., San Diego, CA, USA). One-way repeated-measures ANOVA was employed to compare the conductivity and permittivity of potato tissue before and after electroporation with varying pulse parameters. Per set of experiments, conductivity and permittivity were separately compared at six logarithmically spaced frequencies between 10 Hz and 1 MHz (i.e., 10; 100; 1000; 10,000; 100,000; 1,000,000 Hz), respectively. Tukey’s post hoc test was used to obtain multiplicity-adjusted p-values to address the multiple-comparison problem. The family-wise alpha threshold was set to 0.05.

3. Results

3.1. Study Samples Overview

In total, N = 30 potato samples (5 sets of experiments with N = 6 each) were measured in this study. Their average dimensions were 103 ± 10 mm in length, 76 ± 4 mm in width, and 68 ± 4 mm in height.

3.2. Heterogeneity Test

Conductivity in the untreated potato samples increased from approximately 1000 Hz onwards, while at 1 MHz the highest conductivity values were reached within the medulla region (Figure 2a–d). From 100 kHz onwards, a notable increase in standard deviation of conductivity could be observed.

ANOVA at 1000 Hz revealed no significant conductivity differences between the investigated tissue regions (p > 0.9) (Figure 2e). Supplementary Figure S3 and Supplementary Tables S1 and S2 present the mean conductivity values and ANOVA results for the other investigated frequencies. The corresponding permittivity data can be found in Supplementary Figures S4 and S5 and Supplementary Tables S3 and S4. Additionally, ANOVA at 1000 Hz revealed no significant differences in permittivity between the investigated tissue regions (p > 0.9).

3.3. Effect of Different Pulse Voltages on Electrical Conductivity

The pulse voltage significantly influenced the measured conductivity values towards higher pulse voltages (Figure 3a–d). For 8 out of 10 investigated pulse voltages, the highest relative conductivity change was observed near 1000 Hz; the remaining two showed peaks near 10 Hz and 100,000 Hz (

Table 2. Frequencies with highest relative conductivity changes. Per set of experiments and parameter investigated, the highest relative conductivity change observed (${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$), the corresponding frequency at which ${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$ was measured (${\mathit{f}}_{{∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}}$), as well as the optimum decade for detecting PEF-induced conductivity changes (${\mathit{f}}_{\mathit{o}\mathit{p}\mathit{t}10}$) are listed.

Pulse Voltage
	100 V	200 V	300 V	400 V	500 V	600 V	700 V	800 V	900 V	1000 V
${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$ (%)	14	232	671	825	905	1131	1294	1354	1357	1671
${\mathit{f}}_{{∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}}$ (Hz)	185,717	1483	1818	7	1483	1552	1483	1439	1660	1660
${\mathit{f}}_{\mathit{o}\mathit{p}\mathit{t}10}$ (Hz)	100,000	1000	1000	10	1000	1000	1000	1000	1000	1000
Number of Pulses
	5	10	15	20	30	40	50	60	70
${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$ (%)	149	476	771	1049	964	1309	1523	1652	1565
${\mathit{f}}_{{∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}}$ (Hz)	3372	1660	1575	1575	1575	1724	1859	1859	1859
${\mathit{f}}_{\mathit{o}\mathit{p}\mathit{t}10}$ (Hz)	10,000	1000	1000	1000	1000	1000	1000	1000	1000
Pulse Width
	10 µs	20 µs	30 µs	50 µs	70 µs	80 µs	90 µs	100 µs	200 µs
${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$ (%)	732	776	1222	1381	1367	1184	1160	1176	1410
${\mathit{f}}_{{∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}}$ (Hz)	1540	1724	1777	13	19	1975	1975	1975	1975
${\mathit{f}}_{\mathit{o}\mathit{p}\mathit{t}10}$ (Hz)	1000	1000	1000	10	10	1000	1000	1000	1000
Pulse Interval
	50 ms	100 ms	150 ms	200 ms	250 ms	300 ms	350 ms	400 ms	500 ms
${∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}$ (%)	1029	1065	1262	1422	1381	1441	1474	1191	1192
${\mathit{f}}_{{∆\mathit{\sigma }}_{\mathit{r}\mathit{e}\mathit{l}.\mathit{m}\mathit{a}\mathit{x}}}$ (Hz)	1587	1587	1587	1790	1587	1818	13	1587	1587
${\mathit{f}}_{\mathit{o}\mathit{p}\mathit{t}10}$ (Hz)	1000	1000	1000	1000	1000	1000	10	1000	1000

). At 1000 Hz, the relative conductivity increased from 230 ± 85% to 1644 ± 233% as the applied voltage was raised from 200 V to 1000 V.

At 1 kHz, the mean conductivity increased significantly from the control value of 0.025 ± 0.004 S/m to 0.08 ± 0.019 S/m for 200 V (p = 0.0099). At 400 V and above, very significant and extremely significant conductivity changes (p < 0.01) were observed (Figure 4a). The smallest p-value was observed at 700 V, with mean conductivity increasing from the control to 0.337 ± 0.060 S/m (p = 0.0007). The highest mean conductivity was measured at 1000 V, 0.428 ± 0.082 S/m (p = 0.0009).

Table 3. Average conductivity values (N = 6) with standard deviation in S/m at 1000 Hz for different pulse parameters, including number of pulses, pulse voltage, pulse width, and pulse interval. p-value with respect to ‘Ctrl,’ from the one-way repeated-measures ANOVA. Abbreviations. N/A: not applicable, SD: standard deviation. Supplementary Tables S5, S7, S9 and S11 list the similar data for the other frequency decades.

Pulse Voltage
	Ctrl	100 V	200 V	300 V	400 V	500 V	600 V	700 V	800 V	900 V	1000 V
Average	0.025	0.026	0.080	0.183	0.223	0.240	0.296	0.337	0.343	0.346	0.428
SD	0.004	0.003	0.019	0.058	0.032	0.049	0.086	0.060	0.064	0.071	0.082
p value	N/A	0.9971	0.0099	0.0158	0.0002	0.0018	0.008	0.0007	0.0012	0.0017	0.0009
Number of Pulses
	Ctrl	05	10	15	20	30	40	50	60	70
Average	0.030	0.077	0.169	0.257	0.339	0.315	0.420	0.480	0.511	0.491
SD	0.006	0.040	0.063	0.076	0.078	0.115	0.191	0.099	0.134	0.083
p value	N/A	0.2199	0.0333	0.009	0.0023	0.0207	0.0465	0.0012	0.0041	0.0004
Pulse Width
	Ctrl	10 µs	20 µs	30 µs	50 µs	70 µs	80 µs	90 µs	100 µs	200 µs
Average	0.031	0.254	0.267	0.392	0.428	0.427	0.387	0.378	0.376	0.448
SD	0.004	0.086	0.098	0.128	0.111	0.040	0.123	0.123	0.058	0.085
p value	N/A	0.0156	0.0211	0.012	0.004	<0.0001	0.0097	0.0115	0.0004	0.001
Pulse Interval
	Ctrl	50 ms	100 ms	150 ms	200 ms	250 ms	300 ms	350 ms	400 ms	500 ms
Average	0.031	0.350	0.360	0.419	0.470	0.459	0.474	0.482	0.398	0.400
SD	0.003	0.068	0.109	0.066	0.085	0.044	0.072	0.109	0.072	0.032
p value	N/A	0.0011	0.0094	0.0004	0.0007	<0.0001	0.0003	0.002	0.0008	<0.0001

summarizes conductivity at 1 kHz; extended results (mean conductivity values and ANOVA results at other frequencies) are provided in Supplementary Tables S5 and S6.

3.4. Electrical Conductivity Analysis for Different Number of Pulses

In PEF-treated samples, the number of pulses had a significant impact on the measured conductivity (Figure 5a–d). Overall, the (relative) conductivity increased with the number of pulses. For 8/9 investigated NP, the most important relative conductivity changes were observed near 1000 Hz (Table 2). At 1000 Hz, relative conductivity increased from 470 ± 263% to 1535 ± 256% as the number of pulses increased from 10 to 70 (Figure 5c,d).

At 1 kHz, mean conductivity increased significantly from the control value of 0.030 ± 0.006 S/m to 0.170 ± 0.063 S/m after 10 pulses (p = 0.033). Very significant changes (p < 0.01) were observed for 15, 20, 50, and 60 pulses (Figure 4b). The highest mean conductivity was measured for 60 pulses (0.511 ± 0.134 S/m, p = 0.004), while the most significant increase was observed at 70 pulses (0.491 ± 0.083 S/m, p = 0.0004).

Table 3 summarizes the conductivity values at 1 kHz; extended results are presented in Supplementary Tables S7 and S8.

3.5. Effect of Different Pulse Widths on Electrical Conductivity

Pulse width significantly influenced the measured conductivity values, with changes observed starting from the shortest pulse width of 10 µs (Figure 6a–d). For 7 out of 9 investigated pulse widths, the highest relative conductivity changes were observed near 1000 Hz; the remaining two showed peaks near 10 Hz (Table 2).

At 1 kHz, conductivity for PW = 10 µs increased significantly from the control value of 0.031 ± 0.004 S/m to 0.254 ± 0.086 S/m (p = 0.0156), representing a relative increase of 722 ± 214%. Extremely significant conductivity changes were observed at 70 µs (0.427 ± 0.040 S/m, p < 0.0001) and 100 µs (0.376 ± 0.058 S/m, p = 0.0004) (Figure 4c). The highest conductivity was recorded at a pulse width of 200 µs, measuring 0.448 ± 0.085 S/m (p = 0.001), which corresponds to a relative increase of 1385 ± 314%.

Table 3 summarizes the conductivity values at 1 kHz; extended results are provided in Supplementary Tables S9 and S10.

3.6. Effect of Different Pulse Intervals on Electrical Conductivity

The pulse interval also significantly influenced the measured electrical conductivity across various pulse intervals (Figure 7a–d). For 8 out of 9 investigated pulse intervals, the highest relative conductivity changes were observed near 1000 Hz; one showed a peak near 10 Hz (Table 2).

At 1 kHz, starting from the shortest investigated pulse interval of 50 ms, conductivity increased very significantly to 0.350 ± 0.070 S/m (p = 0.0011), representing a relative increase of 1019 ± 224% compared to the control (0.031 ± 0.003 S/m) (Figure 4d). Extremely significant conductivity changes (p < 0.0001) were observed at 250 ms and 500 ms, where conductivities reached 0.459 ± 0.044 S/m and 0.400 ± 0.032 S/m, corresponding to relative increases of 1367 ± 159% and 1177 ± 86%, respectively. The highest conductivity change of 0.482 ± 0.109 S/m (p = 0.002) was observed at a pulse interval of 350 ms, with a relative increase of 1437 ± 346%.

Table 3 summarizes the conductivity values at 1 kHz; extended results are presented in Supplementary Tables S11 and S12.

3.7. Effect of Different PEF Pulse Parameters on Permittivity and Tissue Temperature

The average permittivity values (F/m) and ANOVA results at different frequencies, evaluating the effects of PEF pulse parameters such as pulse voltage, number, width, and interval, are presented in the Supplementary Tables S13–S20 and Supplementary Figures S10–S17. Also, Supplementary Figure S18 and Supplementary Table S21 summarizes the temperatures measured within the samples directly after electroporation for all four sets of experiments.

3.8. Repeatability of Conductivity and Permittivity Measurements

Repeatability of conductivity and permittivity measurements, expressed as RSD (%) across frequencies for heterogeneity tests, is shown in the Supplementary Tables S22–S24. The assessment of repeatability for conductivity and permittivity measurements used to study the effects of PEF pulse parameters is presented in the Supplementary Tables S25 and S26, respectively.

4. Discussion

This study investigated the effects of PEF parameters on the electrical conductivity of potato tissue using open-ended four-probe coaxial cable EIS. We have shown that untreated potato tissue can be considered electrically homogeneous (p > 0.9). By covering a wide range of pulse parameters, our study gives indications for future studies in potato as a plant-based PEF model. Throughout four sets of PEF experiments that varied different treatment parameters, 1000 Hz was found to be the optimal frequency decade in most cases, as it yielded the maximal measured relative conductivity changes. However, in some experiments, 10 Hz resulted in the maximum conductivity changes (Table 2). At 1000 Hz, significant differences between an untreated control region and the PEF-treated regions were found from PV = 200 V, NP = 10, PW = 10 µs, and PI = 50 ms onwards, respectively, which comprised nearly all the investigated pulse parameter ranges. When varying the pulse voltage, the smallest p-value was found for PV = 700 V, corresponding to a mean conductivity increase from 0.025 ± 0.004 to 0.337 ± 0.060 S/m (p = 0.0007). When varying the number of pulses, the smallest p-value (at 1000 Hz) was found for NP = 70, resulting in a mean conductivity increase from 0.030 ± 0.006 S/m to 0.491 ± 0.083 S/m (p < 0.004). When varying the pulse width, the smallest p-value was found for PW = 70 µs, corresponding to a mean conductivity increase from 0.031 ± 0.004 to 0.427 ± 0.04 S/m (p < 0.0001). Lastly, when varying the pulse interval, the smallest p-values were found for PI = 250 ms and PI = 500 ms, corresponding to a mean conductivity increase from 0.031 ± 0.003 S/m to 0.459 ± 0.044 S/m (p < 0.0001) and to 0.400 ± 0.032 S/m (p < 0.0001), respectively.

In this study, we selected pulse parameters around the most reported ones for clinical IRE treatments, which are 100 µs pulse width and 1000 V/cm electric field strength [8,68]. While we intentionally employed “traditional” pulse protocols, recent studies have achieved nanopore formation by using nanosecond pulses with electric field strengths of 15–30 kV/cm (NP = 800, PW = 300 ns) [69]. Studies showed that a single pulse, even with supercritical amplitude, may not cause irreversible membrane rupture, indicating that the number of pulses (NP) is one of several parameters influencing membrane response [1]. This well-known behaviour was replicated with our setup: our results did not show any significant conductivity changes for the smallest number of pulses (NP = 5). In this study, we used high-voltage unipolar square wave pulses in line with other PEF studies [70].

This study focused on pulse intervals greater than 50 ms, although previous studies suggest that shorter intervals (<1 ms) may further enhance PEF treatment efficacy [71]. We observed significant conductivity changes at all pulse intervals up to 500 ms.

The stability of tissue temperature post-PEF treatment, as observed in Supplementary Figure S18, shows an advantage of irreversible electroporation (IRE) over thermal ablation methods such as radiofrequency ablation (RFA). Across varied PEF parameters, tissue temperatures remained close to room temperature, indicating minimal thermal effects. This supports the potential of IRE for applications where heat-induced damage is a concern.

Plant-based models were chosen for this study to accommodate the need for a larger number of samples in line with the 3R policy on animal research [34,35]. Moreover, potatoes were utilized in previous studies focusing on electrochemical EIS-based conductivity analysis [72]. From the non-significant conductivity changes within untreated potato tissue, we conclude that potato tissue is a suitable plant-based model for future EIS-based conductivity experiments to assess PEF effects. However, there may be overall conductivity differences between different potato variants.

The cell membrane behaves as a capacitor at low frequencies (around 1 kHz), preventing electric current flow in the intracellular medium. At higher frequencies (10 to 100 MHz), the membrane conducts electric current with similar impedance values for both intact and ruptured cells [73]. During PEF treatment, PEF exerts a force on ions, potentially disrupting membrane integrity and increasing conductivity. This is due to the formation of membrane nanopores, which enhance membrane permeability to Na⁺, K⁺, Cl⁻ [74], and internal Ca²⁺ ions move to the extracellular matrix [22,75]. The higher standard deviation in electrical conductivity observed at lower frequencies in PEF-treated samples may be due to varying intracellular ionic concentrations and differing cellular responses among samples.

Electrical impedance tomography (EIT) is a recent technique that adds tomographic capacity to EIS. By a conventional EIT measurement, conductivity maps of (biological) samples at a single excitation frequency can be obtained [76]. Previously, researchers used a 5 kHz excitation signal to obtain in vivo EIT maps of irreversibly electroporated tissue [55]. This study rather recommends an excitation frequency closer to 1000 Hz to image PEF effects using EIT, at least for EIT on potato tissue. In the future, optimal frequencies derived from EIS could be employed for EIT to maximize conductivity differences between PEF-treated and untreated tissue, enabling high-contrast imaging.

Our study has limitations. First, we did not examine any time-dependent conductivity changes caused by PEF, but limited EIS analysis to approximately 30 s after treatment. The conductivity of PEF-treated samples is time-dependent. According to the literature, the resealing of pores caused by PEF occurs within 1–100 µs, if electroporation was reversible [77]. However, a study using EIS at 3 kHz to analyse the time-dependent changes of high-voltage PEF-treated potato tissue (PV = 4000 V, PW = 1000 µs) suggested that conductivity reached a plateau after 50 min [73]. Moreover, PEF treatments with smaller PV or PW may require more prolonged resealing times, ranging from seconds to days [77]. Summing up, 30 s after PEF treatment, tissue damage from IRE was likely to be complete, but conductivity changes may not have reached a plateau yet. Second, our study does not provide an external reference such as tissue staining to assess whether RE or IRE has happened, which is why we refrained from assigning the observed conductivity changes to one or the other regime. Third, EIS is inherently limited because it can only provide localized measurements. Future studies should investigate potential synergies between PEF parameters and explore different PEF treatment electrode configurations, as the current study focused on a single electrode setup and isolated parameter effects. Additionally, nuclear magnetic resonance (NMR) and Raman spectroscopy may be used to characterize extracellular chemical changes, alongside high-resolution confocal microscopy to reveal structural alterations.

5. Conclusions

Four-point open-ended coaxial probe EIS, after calibration to a standard reference solution, was identified as a highly suitable platform for estimating the dielectric properties of electroporated potato samples. Additionally, the non-significant conductivity changes between different regions within the potato indicate its suitability for EIS-based PEF pulse parameter optimization studies. The optimal measurement frequency for PEF-mediated changes in potato tissue was found to be 1000 Hz. At this frequency, EIS revealed significant increases in conductivity over a wide range of investigated PEF parameters, which has implications for conductivity mapping methods such as electrical impedance tomography that operate at a single frequency. Our findings indicate the influence of PEF parameters on conductivity changes measured by EIS, offering insights for multiphysics modelling of clinical IRE treatments with tissue-specific electrical properties and for optimizing excitation frequencies to enhance conductivity mapping contrast in applications such as electrical impedance tomography. These results and information may support future needle development and personalized clinical intervention protocols.