## Abstract

While the primary goal of focal therapy for prostate cancer (PCa) is conserving patient quality of life by reducing oncological burden, available modalities use thermal energy or whole-gland radiation which can damage critical neurovascular structures within the prostate and increase risk of genitourinary dysfunction. High-frequency irreversible electroporation (H-FIRE) is a promising alternative ablation modality that utilizes bursts of pulsed electric fields (PEFs) to destroy aberrant cells via targeted membrane damage. Due to its nonthermal mechanism, H-FIRE offers several advantages over state-of-the-art treatments, but waveforms have not been optimized for treatment of PCa. In this study, we characterize lethal electric field thresholds (EFTs) for H-FIRE waveforms with three different pulse widths as well as three interpulse delays in vitro and compare them to conventional irreversible electroporation (IRE). Experiments were performed in non-neoplastic and malignant prostate cells to determine the effect of waveforms on both targeted (malignant) and adjacent (non-neoplastic) tissue. A numerical modeling approach was developed to estimate the clinical effects of each waveform including extent of nonthermal ablation, undesired thermal damage, and nerve excitation. Our findings indicate that H-FIRE waveforms with pulse durations of 5 and 10 μs provide large ablations comparable to IRE with tolerable levels of thermal damage and minimized muscle contractions. Lower duration (2 μs) H-FIRE waveforms exhibit the least amount of muscle contractions but require increased voltages which may be accompanied by unwanted thermal damage.

## 1 Introduction

Prostate cancer (PCa) is the most commonly diagnosed and second most deadly cancer in males, accounting for one in five new cancer cases globally [13]. Despite its prevalence, diagnosis and treatment of PCa presents a challenge for patients and clinicians. Because PCa is insidious in nature and often does not threaten life expectancy, early detection has led to unnecessary overtreatment, reducing quality of life (QoL) for countless patients [4]. The 2012 guidelines of the U.S. Preventative Services Task Force even recommended against prostate-specific antigen screening with the hopes of preventing overtreatment [5], but recent evidence suggests this recommendation may be partly responsible for the recent plateau in PCa mortality, which had been in steady decline for over two decades [6]. Declining QoL after treatment of local-stage low-risk PCa is perhaps the most salient motive behind recommendations against prostate-specific antigen screening. Standard-of-care options like radical prostatectomy (RP) and radiotherapy can damage critical stromal neurovasculature, diminishing QoL by creating urinary and sexual problems for patients [4]. More specifically, ∼20% of men who undergo RP experience long-term urinary incontinence, while both RP and radiotherapy cause long-term erectile dysfunction in over half of men treated [7]. For these reasons and due to improved diagnostics allowing for regional localization of disease, focal therapy has garnered attention as a low-risk treatment option that can prevent or delay the transition of low-grade PCa to a more aggressive state [8]. The main goal of these modalities is to treat tumor (index) foci without injury to the urethra, ejaculatory vesicles, neurovascular bundle, rectum, and other sensitive structures within and adjacent to the treatment region. Cryotherapy, high-intensity focused ultrasound, and laser ablation are currently the most widely utilized local interventions for treating prostate tumors [9]. However, these therapies rely on thermal mechanisms that cause indiscriminate and sometimes extensive stromal damage within the treatment region [8,10].

Irreversible electroporation (IRE) is an emerging nonthermal pulsed field ablation modality with the potential to overcome these limitations. IRE treatment is performed by delivering several high-amplitude electric pulses through pairs of needle electrodes inserted directly into the treatment region. The induced electric field increases the transmembrane potential of targeted cells, forming nanoscale membrane defects (pores) that cumulatively lead to cell death. Unlike the aforementioned focal therapies, IRE's unique nonthermal mechanism allows it to be administered near critical structures such as nerves and vasculature. Preclinical work has demonstrated the ability of IRE to ablate malignant tissue immediately adjacent to the urethra while preserving microvasculature [11,12], with clinical studies showing that the 5-yr survival rate with IRE is comparable to radical prostatectomy [13]. However, the long monopolar pulses used during IRE can stimulate excitable cells including cardiomyocytes, skeletal muscle fibers, and peripheral nerves; if ignored, this can lead to the potential for cardiac arrhythmias, intense muscle contractions, and pain. Thus, patients must undergo general anesthesia, pulses are electrocardiogram synchronized, and neuromuscular blocking agents are administered to limit skeletal muscle contractions [1416].

High-frequency irreversible electroporation (H-FIRE), or next-generation IRE, was introduced to provide the benefits of IRE while mitigating its disadvantages. While IRE employs 70–100 μs monopolar pulses, H-FIRE uses bursts of short (1–10 μs), bipolar pulses repeated with small delays (1–10 μs) between them. These short pulses enable current flow through both intracellular and extracellular spaces prior to electroporation [17], so the electric field distribution is not as reliant on cell morphology or tissue architecture as compared to IRE [1820]. This simplifies treatment planning and improves predictability of ablation geometries. The alternating polarity of H-FIRE also reduces muscle contractions, obviating the need for neuroparalytics and reducing the risk of cardiac arrhythmias. H-FIRE has been examined in vitro and in preclinical in vivo studies for a range of visceral cancers [15,2124]. Additionally, several recent works have reported the use of H-FIRE waveforms for the treatment of cardiac arrhythmias [25,26]. Despite these generally promising results, aside from an initial clinical trial assessing feasibility, H-FIRE has not been evaluated for ablation of prostate cancer [27].

It is generally unknown which H-FIRE waveforms are best for ablating large tissue volumes while maintaining acceptable levels of nerve stimulation and thermal damage. It is well established that pulse width is the dominant waveform parameter affecting the size of H-FIRE ablations. Longer pulse durations lead to improved ablation volumes [14,28,29], but these also increase the likelihood of muscle contractions. Short pulse widths theoretically favor selective ablation of malignant cells [30] but require higher electric field strengths to generate cell death [20], making it difficult to generate the targeted lesion size while avoiding thermal damage [3133]. A second waveform parameter that may impact treatment outcomes is the delay between subsequent pulses. Pilot in vitro cuvette studies have demonstrated that inclusion of longer delays can reduce lethal ablation thresholds for “continuous” H-FIRE bursts [28]. However, theoretical work has shown that waveforms with longer symmetric delays could cause more intense nerve stimulation [33]. Thus, waveform choice is not a trivial task, and specifically for PCa, little progress has been made toward determining the optimal combination of pulse width and interpulse delay.

In this paper, we use immortalized and primary malignant prostate cells as well as a non-neoplastic prostate cell line to examine the ablative electric field thresholds (EFTs) for nine H-FIRE waveforms (three pulse widths × three interpulse delays) as well as conventional IRE. In parallel, we develop a numerical approach to objectively compare the risk of muscle contractions and heat generation for different waveforms. Experimentally, we characterize lethal EFTs for each cell type in a well-characterized three-dimensional (3D) culture platform that preserves cellular morphology, which is thought to play an important role in mediating waveform efficacy [34,35]. Computationally, we use a modified spatially extended nonlinear node nerve fiber model to estimate stimulation thresholds for each waveform. These two thresholds, along with waveform-specific dynamic electrical conductivity, are then used to predict the volumes of tissue undergoing ablation, nerve stimulation, and thermal damage with standard dose-matched protocols. Finally, voltage is adjusted for each waveform such that ablation volume is consistent across each H-FIRE waveform, and at this equivalent voltage, we examine the extent of thermal damage and nerve stimulation.

## 2 Materials and Methods

### 2.1 Experimental Approach.

Cells were seeded in 3D tumor mimics and incubated for 24 h prior to treatment with H-FIRE or conventional IRE. Cell size and morphology were assessed by confocal microscopy, and ablated lesions were visualized through live–dead fluorescence microscopy 24 h after treatment. A numerical model of pulse delivery to the tumor mimics was constructed as previously described [34], allowing us to correlate lesion areas to the electric field distribution and calculate a lethal threshold.

Table 1

Lethal electric field thresholds determined for the H-FIRE and IRE waveforms examined in this study, with nerve stimulation thresholds and conductivity curve data [46]

WaveformTissue representedCell typeNST (V/cm)EFT (V/cm)Conductivity curve origin
2–5–2Non-neoplastic prostateRWPE-157.01358.5Estimated
Prostate tumor22Rv11297.3Estimated
PDX997.8
5–5–5Non-neoplastic prostateRWPE-125.4873Experimental data
Prostate tumor22Rv1815.7Experimental data
PDX893.7
10–1–10Non-neoplastic prostateRWPE-116.0761.3Experimental data
Prostate tumor22Rv1750Estimated
PDX835.3
IRENon-neoplastic prostateRWPE-11.2635.2Experimental data
Prostate tumor22Rv1602.9Experimental data
PDX546.4
WaveformTissue representedCell typeNST (V/cm)EFT (V/cm)Conductivity curve origin
2–5–2Non-neoplastic prostateRWPE-157.01358.5Estimated
Prostate tumor22Rv11297.3Estimated
PDX997.8
5–5–5Non-neoplastic prostateRWPE-125.4873Experimental data
Prostate tumor22Rv1815.7Experimental data
PDX893.7
10–1–10Non-neoplastic prostateRWPE-116.0761.3Experimental data
Prostate tumor22Rv1750Estimated
PDX835.3
IRENon-neoplastic prostateRWPE-11.2635.2Experimental data
Prostate tumor22Rv1602.9Experimental data
PDX546.4

NST—nerve stimulation threshold; EFT—electric field threshold for cell death.

### 2.2 Cell Lines.

Three cell lines were tested in this study. The non-neoplastic immortalized prostate epithelial cell line RWPE-1 (CRL-11609, American Type Culture Collection (ATCC), Manassas, VA) was cultured in keratinocyte serum-free medium (17005-042, Life Technologies, Carlsbad, CA) supplemented with 0.05 mg/ml bovine pituitary extract (Life Technologies) and 5 ng/ml human recombinant epidermal growth factor (Life Technologies). The prostate carcinoma cell line 22Rv1 (CRL-2505, ATCC) was cultured in Roswell Park Memorial Institute 1640 medium with 10% fetal bovine serum (ATCC) and 1% penicillin–streptomycin (Fisher Scientific, Waltham, MA). Finally, primary human prostate tumor cells were isolated from mice bearing patient-derived xenografts (PDX). These xenograft cells were extracted using common techniques [37] and cultured in complete F medium [38] containing Rho-associated kinase inhibitor Y-27632. This formulation has been introduced to allow the indefinite proliferation of primary epithelial cells derived from heterogenous tissue samples. PDX prostate cells were confirmed by flow cytometry analysis using fluorescein isothiocyanate-conjugated prostate stem cell antigen antibody (Santa Cruz Biotechnology, Dallas, TX) as a human prostate cell marker and R-phycoerythrin-conjugated CD140a (BioLegend, San Diego, CA) as a mouse cell marker. Human PDX prostate cells were used at early passage numbers (3 to 7). Flow cytometry analysis showed that at higher passage number (8+), mouse feeder cells (L929) become overgrown. All cells were incubated at 37 °C and 5% CO2 and passaged regularly at ∼80% confluency.

### 2.3 Hydrogel Platform.

Collagen was extracted from rat tails and stored as a lyophilized solid as previously described [39]. Working stocks of 10 mg/ml were prepared by dissolution in sterile 0.1% acetic acid. Dissolved collagen was mixed with 10× Dulbecco’s modified eagle medium (10% v/v), and 1 N NaOH was used to adjust pH to ∼7.4 to arrive at a final collagen concentration of 5 mg/ml. Cells suspended in their respective culture medium were introduced into the collagen mixture, which was homogenized and injected into prefabricated cylindrical polydimethylsiloxane (PDMS) wells ($∅$ = 1 cm and $h$ = 1 mm) within a 24-well tissue culture plate. Cylindrical PDMS lids were placed on each well to ensure uniform cylindrical geometries. Culture plates were incubated at 37 °C for 25 min to allow the collagen to fully polymerize. PDMS lids were removed, and 600 μl of complete media was added to each well. Hydrogels were incubated for 24 h prior to treatment.

### 2.4 Pulse Delivery.

Electrical treatment and recording equipment were set up according to the schematic in Fig. 1(a). Conventional IRE (100 μs monopolar pulses, Fig. 1(b)) was delivered using a BTX ECM 830 (Harvard Apparatus, Cambridge, MA) pulse generator. H-FIRE waveforms (Fig. 1(b)) were generated using an EPULSUS FBM1-5 solid-state Marx generator (Energy Pulse Systems, Lisbon, Portugal) with digital triggering. Bursts consisted of a series of bipolar pulses with pulse widths of 2, 5, or 10 μs and interpulse delays of 1, 5, or 10 μs. Within a single burst, pulses of alternating polarity were repeated until a total energized time of 100 μs was achieved. For both IRE and H-FIRE, 100 pulses/bursts were delivered at a rate of 1 Hz using a two-needle electrode setup ($∅$ = 0.9144 mm) with center-to-center separation of 4 mm and a voltage-to-distance ratio of 1500 V/cm (Fig. 1). Treatments were performed within a sterile, humidified incubator at 37 °C to increase physiologic relevance of the data [22,40].

Fig. 1
Fig. 1
Close modal

### 2.5 Confocal Imaging of Tumor Mimics.

Approximately 24 h after pulsing, cell-laden hydrogels were incubated for 30 min with 2 μM Calcein green AM (Life Technologies, Carlsbad, CA) and 15 μM propidium iodide (Life Technologies) in Dulbecco's phosphate buffered saline (Fisher Scientific). This timepoint is informed by prior studies showing that H-FIRE lesions develop over the course of 24 h [41]. Images were taken using a confocal microscope (LSM 800, Carl Zeiss, Oberkochen, Germany) with a 5× objective and a 10× eyepiece. Lesion areas were measured using FIJI (National Institutes of Health, Bethesda, MD). The green filter channel was used to measure the ablation region (live cells). For morphology staining, hydrogels were fixed with 10% neutral buffered formalin, permeabilized by incubation with 0.5% Triton X-100 (Sigma-Aldrich, St. Louis, MO) for 10 min and blocked with 1% bovine serum albumin (Sigma-Ald for 60 min. We used an Alexa Fluor™ 568 Phalloidin (Fisher Scientific) stain to mark F-actin and 4’,6-diamidino-2-phenylindole (Fisher Scientific) to stain nuclei. Cell morphology was visualized via confocal microscopy. We computed cell and nuclear areas as well as nucleus-to-cellular area ratio (NCR) to determine if morphology had a bearing on cell death thresholds [30,42]. Z-stack images acquired by a confocal microscope were projected onto a two-dimensional plane, then the spline function in Zen Blue (Carl Zeiss) was used to determine the cell and nuclear areas (n ≥ 20).

### 2.6 Numerical Estimation of Lethal Electric Field Thresholds.

The hydrogel geometry (Fig. 1(c)) was constructed in comsolmultiphysics software (v5.6, COMSOL Inc., Burlington, MA) to model the electric field distribution, as previously described [34,43]. The hydrogel domain was assigned an initial electrical conductivity of 1.25 S/m, which was experimentally determined using a conductivity meter (data not shown). Changes in gel conductivity due to heating were captured through the thermal coefficient of conductivity ($α$), which was set to 2%/° C. An electric potential of 600 V was applied to one electrode boundary, while the other was set to zero. A time-dependent simulation was used to account for Joule heating due to the application of multiple pulses. During the last (100th) pulse, electric field contours at varying magnitudes were plotted, and the surface area contained within each contour was integrated. The curve fitting tool in matlab (MathWorks Inc., Natick, MA) was used to fit a two-term exponential equation to the resulting area versus electric field data (Fig. 1(d)). Finally, measured cell areas were used as inputs in this equation to compute thresholds.

### 2.7 Predictive Modeling of Clinical Prostate Treatments.

To estimate the efficacy of each waveform, outcomes of clinical treatment protocols were numerically computed. First, the spatially extended nonlinear node model proposed in Ref. [36] was constructed in matlab (MathWorks Inc.) and used to approximate the electric field magnitude required to stimulate a nerve fiber terminus in the vicinity of the electrodes for a given waveform. Next, this threshold and the lethal field threshold determined in vitro were used as inputs into a clinically representative numerical simulation to determine volumes of tissue undergoing ablation, thermal damage, and nerve stimulation.

The spatially extended nonlinear node model construction and boundary conditions followed well-established approaches [33,36]. An externally applied electric field with the given temporal characteristics was constructed in matlab with 5 ns time resolution and applied in parallel to a six-node myelinated nerve terminus. Waveforms were modeled with 100 μs of energized time and rise/fall times of 100 ns each. The electric field was sequentially increased by 0.25% until an action potential was detected, and this field was considered the field required for stimulation.

Using the experimentally determined lethal EFTs and numerically computed nerve stimulation thresholds, outcomes of a typical clinical procedure were estimated. A representative domain was constructed in comsolmultiphysics. Prostate tissue was modeled as a sphere with a radius of 10 cm to avoid boundary effects, and comsol's default “extra fine” meshing option was employed for all simulations. Two-needle electrodes with center-to-center spacing of 1.5 cm, exposure of 1.0 cm, and diameter of 1 mm were centered in the domain (Fig. S4(a) available in the Supplemental Materials on the ASME Digital Collection). Models considered treatment with 100 bursts (or 100 pulses for IRE), each with 100 μs on-time, delivered at the desired repetition rate. To accurately account for the capacitors recharging, a 3.5 s delay was included after every set of 10 bursts/pulses. Computation of the electric potential, temperature, and thermal damage within the domain followed well described methods [44,45]. Dynamic conductivity due to electroporation was considered by using the sigmoidal dynamic conductivity functions from Ref. [46] at 37 °C. In some cases, dynamic conductivity curves were estimated (see Supplemental Materials on the ASME Digital Collection). For non-neoplastic prostate models, conductivity curves were from normal porcine prostate, and RWPE-1 thresholds were used to compute ablation volumes. In prostate tumor models, conductivity curves originated from primary human tumor tissue propagated in mice, and ablation volumes were calculated using lethal EFT data from either 22Rv1 cells or PDX cells (Table 1). Electrical conductivity was assumed to increase at a rate 2%/°C increase in temperature [47]. Material properties of the electrodes and other thermal properties of prostate tissue can be found in Table 2.

Table 2

Material properties for electrodes and tissues utilized in the numerical model

MaterialSymbolDescriptionValueUnitsReference
Stainless steel
ρMass density7850kg/m3
σElectrical conductivity4.032 × 106S/m
kThermal conductivity44.5W/(m K)
cpHeat capacity475J/(kg K)
Prostate tissue
ρMass density1045kg/m3[48]
αConductivity thermal coefficient2%/°C[44]
kThermal conductivity0.51W/(m K)[48]
cpHeat capacity3760J/(kg K)[48]
ωbAverage blood perfusion rate6.86 × 10−31/s[48]
ρbBlood density1050kg/m3[48]
cbBlood heat capacity3617J/(kg K)[48]
MaterialSymbolDescriptionValueUnitsReference
Stainless steel
ρMass density7850kg/m3
σElectrical conductivity4.032 × 106S/m
kThermal conductivity44.5W/(m K)
cpHeat capacity475J/(kg K)
Prostate tissue
ρMass density1045kg/m3[48]
αConductivity thermal coefficient2%/°C[44]
kThermal conductivity0.51W/(m K)[48]
cpHeat capacity3760J/(kg K)[48]
ωbAverage blood perfusion rate6.86 × 10−31/s[48]
ρbBlood density1050kg/m3[48]
cbBlood heat capacity3617J/(kg K)[48]
Volumes of tissue exposed to values of $Ω$ equal to or above 1 were considered thermally damaged. Similarly, at the end of treatment, tissue exposed to fields above the thresholds for ablation and nerve stimulation was considered ablated and stimulated, respectively. Initially, models representative of three H-FIRE waveforms (2–5–2, 5–5–5, and 10–1–10) as well as IRE were performed assuming an applied voltage of 3 kV, as this is representative of current clinical IRE treatments in prostate. Subsequently, a parametric sweep of V0 was performed at values of 3.5 kV, 4 kV, 4.5 kV, and 5 kV, providing trends in ablation volume versus V0 for each H-FIRE waveform. An exponential curve was fit to the dataset for each waveform with the form
$QPEF=a·(V0)b$
(1)

where $QPEF$ is the volume of tissue undergoing (nonthermal) ablation due to the applied treatment, and $a$ and $b$ are fitting terms. For a given repetition rate and cell line, $QPEF$ achieved with conventional IRE applied at 3 kV was inserted into Eq. (1), which was then solved for $V0$. This was considered the equivalent voltage for that waveform, or in other words, the voltage needed with a given H-FIRE treatment to match the ablation volume achieved with a standard IRE procedure. Finally, for each H-FIRE waveform, one final simulation was performed in which $V0$ was set to the equivalent voltage, allowing for examination of thermal effects, energy deposition, and nerve stimulation with equivalent ablation volumes across waveforms.

### 2.8 Statistical Methods.

prism version 9 (GraphPad Software, San Diego, CA) was employed for all statistical analyses with α = 0.05. Cellular morphology data were analyzed using a one-way analysis of variance with post-hoc Tukey's test. For comparison of ablation areas and EFT data, a two-way analysis of variance was used. Šídák's multiple comparison's test was used to examine the effect of temperature across different waveforms. Tukey's honestly significant difference test was used to compare ablation sizes and EFTs across different cell types, while Dunnett's test was employed to compare each waveform to IRE.

## 3 Results

### 3.1 Experimental Results

#### Cell Morphology.

Measured cytoplasmic and nuclear areas for each cell type under study are shown in Fig. S1(a) available in the Supplemental Materials on the ASME Digital Collection. The calculated NCR is shown in Fig. S1(b) available in the Supplemental Materials, and representative confocal images are shown in Figs. S1(c)–S1(e) available in the Supplemental Materials. Qualitatively, all three cell types appeared relatively elliptical with large nuclei and 22Rv1 cells exhibited a wide array of cell sizes. From a quantitative perspective, RWPE-1 cells appeared larger than PDX and 22Rv1 cells but were only significantly larger than PDX cells. All three cell types exhibited similar nuclear areas, and thus RWPE-1 cells had the lowest NCR. While measured areas were relatively consistent across PDX and RWPE-1 cells, 22Rv1 cells demonstrated significant heterogeneity in terms of cell and nuclear size.

#### Malignant Prostate Cells Are More Sensitive to Treatment Temperature Than Non-Neoplastic Cells.

Recent work has revealed that H-FIRE lethal thresholds may be temperature dependent, and some studies have used mild hyperthermia within the treatment region to enhance lesion sizes [40,49,50]. To study the extent to which treatment temperature may impact effectiveness of H-FIRE in prostate cancer ablations, RWPE-1 and 22Rv1 cells were treated with each waveform at room temperature (∼23 °C) as well as physiologic temperature (37 °C) using a benchtop incubator (Fig. 2). For non-neoplastic prostate cells (RWPE-1), ablation areas were relatively unaffected by treatment temperature. Statistically relevant differences in lesion size were observed only for the 10–1–10 H-FIRE waveform as well as IRE. These did not translate into significant differences in lethal EFT, however, as none of the H-FIRE waveforms nor IRE showed a statistically significant difference in EFT as a function of temperature. On the other hand, most H-FIRE waveforms generated significantly larger ablations in 22Rv1 cells when treated at 37 °C compared to 23 °C. Specifically, all H-FIRE waveforms apart from the 2–5–2 and 2–10–2 exhibited lower EFTs when applied at physiologic temperature. Like the RWPE-1 cells, IRE lesion areas were different at the two temperatures, but lethal EFTs were similar.

Fig. 2
Fig. 2
Close modal

#### High-Frequency Irreversible Electroporation Waveforms With Longer Pulse Durations and Interpulse Delays Are Similarly Lethal to Irreversible Electroporation.

Lesion areas as well as lethal electric field thresholds as a function of H-FIRE waveform are shown in Fig. 3. Pulse widths of 5 μs were more effective at generating lesions that 2 μs pulse durations for all cell types, as anticipated (Fig. 3(a)). Increasing the pulse width further, to 10 μs, however, produced a smaller effect which could be dependent upon the interpulse delay. While differences are seen between 5–1–5 and 10–1–10 lethal EFTs for all three cell types, with interpulse delays of 5 or 10 μs, lethal EFTs are nearly identical regardless of pulse width (Fig. 3(b)). Notably, the 5–10–5 waveform exhibited similar lethality in cancer cells (22Rv1 and PDX) as compared to conventional IRE. Waveforms with 10 μs pulse durations also exhibited lethal EFTs similar to IRE, but no other single waveform was particularly efficient across both cancer cell types. H-FIRE lethal thresholds in RWPE-1 cells were consistently higher than those achieved with IRE except for with the 10–1–10 waveform (Fig. 3(b)). This suggests that non-neoplastic prostate cells are more resistant to H-FIRE waveforms than to IRE, regardless of waveform composition.

Fig. 3
Fig. 3
Close modal

#### High-Frequency Irreversible Electroporation Waveforms With Short Pulse Widths Display Signs of Selectivity in Heterogeneous Patient-Derived (Xenograft) Primary Cells.

With 2 μs pulse durations, PDX cells were significantly more vulnerable to H-FIRE treatment than non-neoplastic RWPE-1 cells. Patient-derived cells treated with these waveforms exhibited EFTs approximately 400 V/cm lower than immortalized non-neoplastic prostate cells (Fig. 3(b)). The separation in EFTs between non-neoplastic and patient-derived cells was no longer significant for 5 μs and 10 μs pulse durations, save the 5–10–5 (Fig. 3(b)). Interestingly, 22Rv1 cells were also slightly more susceptible to 2 μs duration H-FIRE waveforms than RWPE-1 cells, but not significantly. Across all H-FIRE waveforms, malignant cells consistently showed a lower EFT than the normal cell line, while PDX cells trended toward lower EFTs than the 22Rv1 cell line (Fig. 3(b)). Both the 5–10–5 and 10–10–10 exhibited significantly lower EFTs in immortalized cancer cells compared to their non-neoplastic counterpart, suggesting the interpulse delay may be an important mediator of selectivity (Fig. 3(b)). Finally, despite the trends noted for different H-FIRE waveforms, IRE demonstrated similar lethal EFTs across all cell types (Fig. 3(b)).

### 3.2 Modeling and Simulation

#### Modeled Outcomes of Standard Clinical Treatment With Irreversible Electroporation and High-Frequency Irreversible Electroporation.

Clinical prostate ablations were numerically modeled to estimate outcomes for each H-FIRE waveform as well as IRE when delivered with 3 kV applied across two-needle electrodes (Fig. 4). Simulations considered ablations performed within either prostate tumor tissue or non-neoplastic prostate to understand the interplay of tissue-specific conductivity and lethal electric field thresholds. As anticipated, models predicted an increase in ablation volume as a function of pulse width, with IRE producing the largest ablation volumes. For a given waveform, relatively minor differences in ablation volume were predicted across different cell types. Further, the tissue-specific dynamic conductivity functions influenced the electric field distribution during treatment, so lethal EFT was not a direct predictor of ablation volume. Thermal damage was more pronounced in non-neoplastic prostate tissue, especially when treated with H-FIRE, presumably due to the increased electrical conductivity of normal prostate compared to prostate tumor (Fig. S2 available in the Supplemental Materials on the ASME Digital Collection). More specifically, thermal damage volumes in all tumor models and non-neoplastic prostate treated with IRE were ∼0.4 cm3, while thermal damage in non-neoplastic prostate was ∼1 cm3 for 2–5–2 and just over 2 cm3 for the 5–5–5 and 10–1–10 (Fig. 4(b)). Modeled volumes of nerve stimulation were also heavily dependent upon applied waveform (Fig. 4(c)). The 2–5–2 produced the least amount of nerve stimulation, with volumes hovering near 100 cm3. The 5–5–5 gave volumes of ∼200 cm3 and the 10–1–10 produced volumes close to 300 cm3, while predicted nerve stimulation volumes for IRE were just above 3000 cm3 (Fig. 4(c)).

Fig. 4
Fig. 4
Close modal

For each waveform, predicted volumes were used to calculate a summary ratio—a dimensionless metric normalizing ablation volume by the predicted volumes of thermal damage and nerve stimulation (Fig. 4(d)). This provides an objective measure of the efficacy of a given waveform. Overall, the summary ratio for each waveform was higher in tumor tissue (22Rv1 or PDX) than in non-neoplastic prostate (RWPE-1). For non-neoplastic tissue, summary ratios were low (∼0.04) and nearly identical regardless of waveform. The highest summary ratio (0.41) was observed for the 2–5–2 using the lethal EFT of PDX cells, but both the 5–5–5 and 10–1–10 produced consistent values near 0.2 in tumor tissue represented by either tumor cell type.

#### Clinical Outcomes of Ablation-Matched High-Frequency Irreversible Electroporation Treatments.

A final series of models was performed in which applied voltage was adjusted such that each H-FIRE waveform produced an ablation volume identical to IRE in either non-neoplastic prostate or tumor tissue (Figs. 5 and S4). The equivalent voltage, or the voltage needed with a given H-FIRE waveform to match the ablation size achieved with the standard IRE protocol, is shown in Fig. 5(a). Waveforms with 2 μs pulse durations required the highest voltages to achieve this large ablation size (4.5–5 kV), while longer duration H-FIRE waveforms required only a few hundred volts more than IRE in RWPE-1 and 22Rv1 simulations. However, equivalent voltages for the 5–5–5 and 10–1–10 in PDX cells were just over 4 kV. The error between the targeted (IRE) ablation volume for a given H-FIRE waveform and the actual modeled volume at the equivalent voltage is shown in Fig. 5(b) and was less than 1.5% across all cases as seen in the near-identical ablation volumes achieved with different waveforms in each cell/tissue type (Fig. 5(c)). With these matched ablation sizes, thermal damage was strongly dependent upon applied pulse duration and somewhat dependent upon tissue type (Fig. 5(d)). Likewise, even with the high potentials applied with shorter H-FIRE waveforms, nerve stimulation trends retained their sharp reliance on pulse width (Fig. 5(e)). Overall, the 5–5–5 and 10–1–10 exhibited the strongest summary ratios overall, with the 2–5–2 in PDX tumor tissue again standing out as the most optimal case using this approach. For a given cell type, summary ratios for all H-FIRE waveforms outperformed those achieved with IRE (Fig. 5(f)).

Fig. 5
Fig. 5
Close modal

## 4 Discussion

H-FIRE is an electroporation-based technology with several potential benefits over conventional IRE and—owing to its nonthermal nature—is well-suited for focal ablation of prostate tumors. Despite its success in preliminary studies for other cancer types and in its first PCa trial in humans, the overall effect of different burst parameters on clinical outcomes is still poorly understood. Thus, in this study, we examined effects of H-FIRE treatment parameters on 3D tumor mimics and compared them to traditional IRE. Immortalized prostate cell lines representative of non-neoplastic and malignant tissue were studied. Primary cells were also isolated from a patient-derived PCa xenograft to determine the effects of these fields on a more physiologically relevant heterogenous sample. We used the experimental lethal EFT data to inform a clinically relevant numerical model to estimate the overall efficacy of different waveforms. This model was used to predict ablation volume, thermal damage, and nerve stimulation under standard settings. Subsequently, voltage was adjusted to match ablation volume across waveforms and side effects including thermal damage and nerve stimulation were analyzed, and a nondimensional parameter was used to objectively compare waveforms.

As expected, hydrogel lesion sizes increased and their corresponding EFTs were reduced with increasing pulse width, as has been described in prior works studying other cell and tissue types [41,51,52]. On the other hand, varying the interpulse delay from 1 to 10 μs had a minimal effect on lesion size, but is known to affect nerve stimulation thresholds (Fig. S3 available in the Supplemental Materials on the ASME Digital Collection) [33,53]. Thus, shorter values of dip may provide the best balance of ablation size relative to nerve stimulation volume. It is also possible that waveforms could be further optimized by varying the delay within each bipolar pulse and between subsequent bipolar pulses independently, but such a comprehensive study is outside the scope of this work.

While the dependence of electroporation on temperature has been documented for decades [5457], it has recently been suggested that H-FIRE is a thermally mediated ablation modality, especially for short (∼1 μs) pulse durations [22,40]. In line with these results, we found that conventional IRE lethal EFTs did not change with variations in experimental temperature in non-neoplastic or malignant prostate cells. Further, H-FIRE treatment in non-neoplastic prostate cells was essentially unaffected by changing the ambient environment from room temperature to physiologic temperature. On the other hand, malignant (22Rv1) prostate cells were significantly more vulnerable to H-FIRE therapy when applied at 37 °C versus 23 °C, consistent with recent literature investigating malignant brain and pancreatic cells [22,40]. Unlike trends reported for malignant astrocytes, however, we found that 2 μs duration waveforms were less temperature dependent than waveforms with pulse durations of 5 or 10 μs. This result suggests that with proper waveform selection, modulating local tissue temperature could offer an opportunity to selectively target malignant prostate cells without inflicting further damage on nearby non-neoplastic cells. This approach would require optimization to maximize H-FIRE induced ablative benefits without eliciting thermal damage. Finally, the high thresholds of nonmalignant cells in the tumor periphery must be considered when planning for adequate treatment margins, as the high thresholds of peripheral non-neoplastic cells may require adjustments to the treatment voltage. Thus, future work is needed to elucidate the interplay of cell type, waveform selection, and local tissue temperature toward optimizing cell death outcomes for different applications.

At physiologic temperature, malignant cells (22Rv1 and PDX) consistently showed similar or lower EFTs than normal cells. PDX cells generally exhibited slightly lower EFTs than 22Rv1 cells, which were especially pronounced with 2 μs pulse durations. With pulse widths of 5 μs or longer, lethal EFTs were similar for PDX and immortalized 22Rv1 cell lines, despite the heterogenous nature of cells within PDX samples. These results suggest that immortalized cancer cell lines can be used in place of primary tumor cells for calculation of lethal EFTs in vitro. Using EFTs from these immortalized cells to numerically estimate clinical ablation sizes should thus represent the minimum ablation size likely to result from the modeled treatment. In practice, underestimation of ablation size is much more favorable than overestimation and may be beneficial to H-FIRE development by implicitly building in treatment margins.

Cell morphology is hypothesized to influence susceptibility to applied electric fields [58] depending on the waveform applied [59]. Cell size is thought to play a major role in electroporation particularly for longer pulse durations. However, capacitive and dielectric properties of the membrane [60] vary between cell lines and likely contribute substantially to lethal EFT values [42]. RWPE-1 cells were slightly larger than 22Rv1 cells and significantly larger than PDX cells (Fig. S1 available in the Supplemental Materials on the ASME Digital Collection). However, because EFTs were overall mostly higher in RWPE-1 cells, our data do not indicate that larger cells are more susceptible to IRE and H-FIRE, as seen in Fig. 3(b). Nuclear area was similar across all cell types, but 22Rv1 and PDX cells displayed larger NCRs than RWPE-1 cells. NCR has been implicated as a mediator of selectivity, mostly for waveforms with extremely short pulse durations [30], but it is possible that the higher NCR of PDX cells is contributing to their low EFT for waveforms with 2 μs pulse durations. These trends indicate that for shorter duration pulses, H-FIRE lethal thresholds may be dependent on NCR in addition to factors other than morphology (biochemical or biophysical) [61] for higher frequency waveforms.

Numerical simulation of a standard clinical ablation protocol demonstrated that pulse width is the dominant factor determining ablation size with different waveforms, as anticipated. For a given H-FIRE waveform, predicted ablation sizes for a given waveform were relatively consistent regardless of tissue or cell type. Because dynamic conductivity functions for each waveform have relatively unique profiles, anticipated ablation volumes for a given cell type and waveform did not directly correlate with the lethal EFT. For instance, the lethal EFTs for 22Rv1 cells treated with a 5–5–5 or 10–1–10 were slightly lower than RWPE-1 cells treated with the same waveforms. However, models predict larger ablation volumes in non-neoplastic tissue with these waveforms, presumably due to changes in electrical conductivity which modulate electric field redistribution and can expand ablation sizes (Fig. S2 available in the Supplemental Materials on the ASME Digital Collection). Heat generation also causes increases in electrical conductivity, particularly near the electrodes, which may be contributing to the larger modeled ablations in non-neoplastic tissue. On the same note, normal prostate tissue is more conductive than neoplastic prostate, so it is also more vulnerable to thermal damage, as reflected in our models (Fig. 4(b)). Because H-FIRE is intended to provide nonthermal ablation volumes, these results highlight the importance of ensuring pulse delivery does not produce thermally damaging temperatures, which can be achieved through thermal mitigation strategies, or by reducing the rate at which energy is delivered [6265]. Modeled nerve stimulation volumes were almost entirely dominated by waveform selection, suggesting tissue type is a negligible factor. Summary ratios were highest in models with low levels of thermal damage and nerve stimulation, so H-FIRE waveforms outperformed conventional IRE in all cases, and tumor tissue was especially favored.

Similar results were observed when the equivalent voltage method was used. As seen in Figs. 5(b) and 5(c), ablation volumes were successfully matched across waveforms by scaling voltage. As anticipated, in some cases this resulted in unacceptable levels of thermal damage (Fig. 5(d)), especially when higher voltages were necessary in non-neoplastic tissue. Overall, nerve stimulation and summary ratio trends remained consistent, suggesting H-FIRE waveforms are more advantageous in terms of their ability to maximize ablation size relative to nerve stimulation and thermal injury. In particular, the 5–5–5 and 10–1–10 waveforms stood out due to their high summary ratios in both malignant cell types (Fig. 5(f)).

This paper provides a first step toward optimizing H-FIRE waveform selection in prostate cancer ablations, but it is important to point out limitations of our investigation. First, due to limited PDX tissue availability, some PDX datapoints provided in this paper contain only one or two replicates. Future analyses will be necessary to add relevance to these results and confirm reported trends. Second, the in vitro collagen hydrogel model is designed specifically to isolate electric field effects without thermal damage; while we assume that cell death behavior is similar between the in vitro model and the simulated in vivo cases, thermal dynamics are much different and could impact cell death behavior. Further, clinical simulations only considered three H-FIRE waveforms and IRE due to lack of experimental conductivity data. Thus, we did not model the full array of waveforms investigated experimentally, so it is possible some waveform exhibits a unique conductivity and lethal EFT profile that make it even more ideally suited for prostate ablation than those included in models. It is worth noting that other pulse parameters and technologies can be implemented to reduce the high levels of thermal damage seen at the higher voltages needed in some models, but the goal of this paper is to demonstrate the necessary increase in energy to achieve similar ablations across waveforms as a scaling factor, rather than tune each waveform independently. Finally, we acknowledge the importance of following this study with in vivo work seeking to validate trends reported herein and further optimize H-FIRE voltage waveforms.

## 5 Conclusion

The effect of H-FIRE treatment with a variety of pulse widths and interpulse delays on 3D tumor mimics was examined in vitro. No differences between patient-derived and immortalized malignant cell lines were noticed, indicating the latter as a suitable replacement for complicated PDX models. Malignant cells were more significantly affected by variations in ambient temperature than their non-neoplastic counterparts, suggesting a potential window for selective exploitation. Among different H-FIRE waveforms, pulse duration had the largest impact on EFT, while interpulse delay had a relatively ambiguous effect. In silico modeling was used to match ablation volumes to IRE, and nondimensional parameters were used to quantify the extent of thermal damage and nerve excitation relative to nonthermal ablation volumes. Among the waveforms under study, 5–10–5 and 10–1–10 were found to provide the largest nonthermal ablations relative to induced side effects.

## Acknowledgment

The authors acknowledge support from the Institute for Critical Technology and Applied Science as well as the Center for Engineered Health at Virginia Tech. We would also like to thank Dr. John Robertson, Zaid Salameh, Sofie Saunier, and Kailee David for assistance in reviewing the paper.

## Funding Data

• This study was funded by AngioDynamics, Inc.

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