Introduction

The National Cancer Institute estimates that 12% of women born today will be diagnosed with breast cancer at some point during their lifetime, and the Centers for Disease Control and Prevention states that breast cancer is the second most common cause of cancer death in women. Typical treatment techniques include a combined approach of surgical resection via mastectomy or lumpectomy, irradiation, and adjuvant chemotherapy.20 Breast conserving therapies that use lumpectomy have shown equivalent survival relative to mastectomy,15 creating incentive for the utilization of minimally invasive focal ablation techniques such as radiofrequency ablation and cryosurgery.26,41,44

Although great strides have been made in breast conserving therapy, the invasive nature of surgical resection oftentimes results in significant scarring and disfigurement, with approximately 20% of patients undergoing breast-conserving therapy unsatisfied with their final breast cosmetic outcome.13,16 Such cases may undergo additional reconstructive procedures to improve aesthetic outcome.13,16,20 The improvement of oncoplastic techniques may help to curb this high percentage.5 However, of greater prognostic concern is the internal scarring that results from invasive procedures. Intramammary scar tissue may form spiculated lesions that resemble various benign or malignant entities when viewed mammographically.17,43 This scarring complicates monitoring for residual tumors and carcinoma recurrence, often requiring additional ultrasound, clinical examination, or magnetic resonance mammography to interpret the nature of these lesions.39 Such additional diagnostics are cumbersome, inaccessible, expensive, and often still require a biopsy to ascertain a true lesion assessment.17,39,43 From this evidence, the reduction of scarring from invasive techniques in the treatment of primary breast cancers would yield a great benefit to patient quality of life as well as monitoring for residual cancerous tissue and recurrence.

Tissue electroporation uses electrodes to deliver short-length, high voltage electric pulses to destabilize the cellular membrane, leading to increased membrane permeability, presumably due to the creation of nano-scale pores.47 Pulse application is typically done through small needle electrodes, making treatment minimally invasive and localized. Electrode placement may be facilitated by ultrasound guidance.29 The effect of these pulses is primarily dependent on the local electric field to which the tissue is exposed.32,48 If the energy from the pulses is below an electric field threshold, pores in the cell membrane close following the offset of the pulses and the effect is known as reversible electroporation. Reversible electroporation is a phenomenon that has been used for almost two decades in the implementation of procedures such as electrochemotherapy and electrogenetransfer.33–35 However, if the strength of the electric field is above this threshold, the cell cannot repair the damage and dies in a phenomenon known as irreversible electroporation (IRE).28

It has recently been shown that substantial volumes of tissue and cutaneous tumors may be ablated in a non-thermal manner using irreversible electroporation.1,6 The mechanism for tissue ablation is unique because the electric fields applied to induce IRE only affect the membrane of the cell, leaving all other tissue molecules intact. The non-thermal characteristic of IRE has been shown to exhibit numerous benefits over other minimally invasive focal tissue ablation techniques. These include that it is unaffected by blood flow, may be administered quickly (several minutes), spares the extracellular matrix and sensitive structures such as the urethra and myelin sheaths, preserves the major tissue vasculature, and exhibits rapid lesion resolution to a minimal scar in approximately 2 weeks.11,31,37,40 This scar may further resolve in the following weeks. In addition to aiding follow-up monitoring, reducing scarring leaves the extracellular matrix and structures available for the potential regeneration of the region with healthy cells and tissue.

An additional advantage is that the electric field induced by the pulses, and thus treatment outcomes, may be predicted through numerical modeling,6,10 allowing reliable treatment planning and outcome prediction in a clinical setting. IRE treatments are not dependent on a functioning immune system,2 but they have been found to promote an immune response,37 including areas experiencing reversible electroporation.34 An immune response may help treat the cancer even after the electric pulses are removed, and selectively increase the treatment volume beyond what was originally ablated by IRE. Due to immediate changes in the treated tissue’s permeability, the affected regions may be monitored in real-time using ultrasound.29 Finally, there is a high resolution demarcation between treated and normal regions,11 and the treated volume exhibits rapid lesion creation and resolution,37 which may allow for the repopulation of the region with healthy cells.

We hypothesize that the previously mentioned advantages from its unique, non-thermal mechanism to cause cell death may prove IRE to be an effective surgical modality for the treatment of certain breast carcinomas. Other focal ablation techniques such as cryosurgery, laser interstitial therapy, and radiofrequency ablation have been investigated for treating these carcinomas. Unfortunately, these thermal techniques present complications, including inconsistencies between the predicted or visualized heated/cooled zone and true cell death regions,41 thermal dissipative properties (the blood perfusion “heat sink” effect) of vascularized tissue, charring at the electrode interface,26 required treatment depth of at least a 1 cm to prevent skin injury,9,44 and the production of significant scar tissue,22 reducing accurate follow-up. These challenges have prevented widespread acceptance of thermal techniques as a viable alternative to lumpectomy in breast conserving therapy. In order for IRE to be an advantageous alternative to surgical resection, it must be shown that substantial volumes of tumor tissue may be treated by IRE before the onset of significant thermal effects and scarring. In this paper we show that IRE is, in fact, a suitable candidate for minimally invasive treatment of primary breast tumors.

Adapting IRE to breast carcinomas encompasses several characteristics that must be taken into account when assessing the feasibility of such a treatment and when planning optimized protocols. Among these are the diverse and dynamic physical and electrical properties of connective and fatty breast tissue, whose low water content significantly reduces the electrical conductivity and permittivity relative to glandular carcinomas.46 The electrical conductivity plays a role in electric field and temperature distribution while permittivity also affects the electric field. It has been shown that the higher conductivity of tumor tissue reduces the electric field it experiences relative to the surrounding, lower conductivity tissue when the electrodes are placed surrounding the targeted region.10 In order to understand if IRE is an attractive alternative for the treatment of breast cancer, it must be shown that treatment-relevant protocols can be developed capable of treating the entire targeted tumor region over a range of heterogeneous conductivities without inducing significant thermal damage.

In this manuscript, we test our hypothesis by determining a baseline in vitro electric field threshold for IRE for MDA-MB-231 cells, a human cancerous mammary epithelial cell line. To the best of our knowledge, no such in vitro study has been conducted on cancerous mammary epithelial cells to experimentally determine a baseline treatment to kill such cells. This electric field was then applied to a heterogeneous breast cancer tumor computational model that numerically predicts treatment outcome values.

The numerical model was adjusted to optimize treatment protocols until the desired treatment volume was achieved with IRE while minimizing thermal damage. The optimization was done for a range of heterogeneous electrical conductivities as a means to determine a range of conductivity ratios between the targeted and peripheral tissue (σt/σp) where IRE is most effective. The results for the range of conductivity ratios studied may be applied to many various heterogeneous tissue scenarios, such as high conductivity tumors within low conductivity tissue, as with typical breast carcinomas, lower conductivity tumors within more conductive surrounding tissue, which may be the case in some brain and spinal carcinomas, or for situations where the conductivity within the targeted region may be manipulated, such as injecting saline prior to treatment. The results of this study found that IRE may be a viable focal ablation technique for the treatment of breast cancer without inducing significant scarring, while presenting non-thermal characteristics and the benefits of minimally invasive procedures.

Materials and Methods

Electric Field Threshold Determination

In vitro suspension studies were conducted on MDA-MB-231 mammary gland epithelial adenocarcinoma cells in order to establish a baseline electric field to induce IRE. This was completed using trypan blue as a determinant of cell membrane integrity, and thus viability. Cells were suspended at a concentration of ~7.5 × 105 cells/mL in DMEM/F12 media (Mediatech, Inc, Manassas, VA), with 125 μL samples (n = 12) placed into a 96-Well Electroporation Plate System (Model No. 96/100-830, Harvard Apparatus, Holliston, MA). The cells were then subjected to 80 square wave pulses lasting 100 μs at a rate of 1 pulse per second; based on parameters found to cause the complete regression in 12 of 13 aggressive cutaneous tumors in an immunodeficient mouse model.1 The applied electric field was adjusted to determine the minimum field required to induce 95% cell death. Following treatment, the cells were incubated for 10 min at 37 °C with 5% CO2 to eliminate transient electroporation effects.21 After this, 100 μL samples of the suspensions were extracted from each well and cell viability was assessed using the Vi-Cell Cell Viability Analyzer (Beckman-Coulter, Fullerton, CA).

The induction of IRE from electrical pulses and experimental outcome has been shown to be dependent on several factors, including pulse repetition rate, pulse shape and length, number of pulses, cell or tissue type, and electric field strength.6,27,32,33 Electroporation procedures depend heavily on the electric field, which induces a transmembrane potential, V m, on the cell membrane. For a cell in suspension, this may be determined by:

$$ V_{\text{m}} = \lambda rE_{\text{a}} \cos (\theta ) \cdot \left[ {1 + \left( {{\frac{f}{{f_{\text{s}} }}}} \right)^{2} } \right]^{ - 0.5} $$
(1)

where λ is the shape factor of the cell (1.5 for a spherical cell), r is the cell radius, E a is the applied electric field, θ is the angle between the electric field and a vector from the cell to any point on its surface, f s is the frequency where the beta dielectric dispersion occurs, and f is the frequency of the applied electric field.30 Because the electroporation pulses used are much longer than the membrane charging time, the transient term ((f/f s)2) may be neglected. It is believed that IRE typically occurs from a transmembrane potential of roughly 1 V.48 This equation shows that different cell types of various sizes and shapes may have distinct susceptibilities to IRE treatment.

Numerical Model of Primary Breast Cancer

A three-dimensional numerical model was constructed to represent the treatment of a targeted region located within a peripheral region. The properties were selected to simulate a breast cancer tumor embedded within a fatty connective tissue matrix. An arrangement of two monopolar electrodes, one charged and one grounded, were used. This composition allows the practitioner flexibility for electrode layout when performing a procedure in order to optimize treatment of a targeted region while minimizing undesirable effects. A convective boundary condition was applied at the electrode-tissue interface to represent the heat dissipative effects of the electrode, which were considered to be infinite fins (h f = 50 W/(m2·K)).

It has been estimated that nearly two thirds of women presenting breast cancer will do so with the disease localized to the breast.23 In addition, it has been predicted that by the year 2010, 50% of newly diagnosed breast cancers will be <1 cm in diameter.4 Therefore, the tumor dimensions chosen for the computational model in this study were a sphere 1 cm in diameter. Various conductivity ratios (σt/σp) were used while electrode placement relative to the targeted region was manipulated in order to obtain a reasonable electric field distribution at practical voltages. A schematic of the three-dimensional model with the electrodes, tumor, and surrounding fatty tissue may be seen in Fig. 1.

Figure 1
figure 1

Schematic of the three-dimensional model. The targeted tissue can be seen as a small sphere within a larger outer sphere of peripheral tissue. The charged surfaces of the electrodes have been placed primarily within the targeted tissue near the periphery

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Tissue properties were taken from the literature and may be found in Table 1. Due to the large variation found within breast carcinoma and the surrounding tissue,46 and the role of conductivity on electric field distribution10 and thermal effects, each tissue’s conductivity was varied between 0.025 and 0.25 S/m, incorporating a range of conductivities that may be found in typical breast tumors as well as the surrounding fatty and connective tissues.25,46

Table 1 Tissue properties for numerical model
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Electric Field Distribution

The electric field distribution for the computational model was determined by solving the Laplace equation:

$$ \nabla \cdot \left( {\sigma \nabla \Upphi } \right) = 0 $$
(2)

where Φ represents the electric potential, σ is the direct current electrical conductivity of the tissue. The boundaries of the charged and grounded electrode surface were taken to be Φ = V 0 and Φ = 0, respectively. The targeted region was placed within an 8 cm diameter sphere peripheral region. This external boundary was found to be large enough not to influence model outcome, and was set as electrically insulating. The electrodes were separated by a 0.8 cm gap, with placement near opposite boundaries of the targeted volume. The electrodes’ diameters were chosen to be 1 mm, a size smaller than that of typical cryoablation and radiofrequency probes,26,41 with 3 mm long steel tips connected by an insulating material.

The conductivities of the targeted, σt, and peripheral breast tissue, σp, were varied with a tumor/peripheral conductivity ratio (σt/σp) between 0.1 and 10. It should be noted that the electric field distribution will not change for different absolute tissue conductivities for a given conductivity ratio. Therefore, the object of interest for treatment prediction in heterogeneous tissues is the ratio of conductivity between the two volumes. The IRE treated and thermally damaged volumes were analyzed for nine of these ratios.

Thermal Effects

The thermal behavior of the tissue due to electroporation may be assessed using the following modified Pennes Bioheat equation with an additional Joule heating term as described in Davalos et al.7:

$$ \nabla (k\nabla T) + w_{\text{b}} c_{\text{b}} (T_{\text{a}} - T) + q^{\prime\prime\prime} + \sigma \left| {\nabla \Upphi } \right|^{2} = \rho c_{\text{p}} {\frac{\partial T}{\partial t}} $$
(3)

where k is the thermal conductivity of the tissue, T is the temperature, c b and c p are blood and tissue heat capacity, respectively, T a is arterial temperature, ρ is tissue density, σ|∇Φ|2 is the joule heating term, q′′′ is metabolic heat generation, and w b is blood perfusion. The tumor metabolic heat generation term was determined based on its dimensions as described by Ng and Sudharsan.36 The initial condition for the temperature of the entire tissue was taken to be 310 K (37 °C). The external tissue thermal boundaries were treated as adiabatic.

Thermal damage is a time-dependent process, thus to calculate regions undergoing thermal necrosis the thermal dose concept was applied, which determines an equivalent amount of time for the tissue to be held at a reference temperature, taken as 43 °C.42 This was calculated for the entire time domain of the modeled treatment according to the equation:

$$ t_{43} = \sum\limits_{{{\text{t}}_{\text{0}} }}^{{{\text{t}}_{\text{final}} }} {R^{{(43 - T_{\text{t}} )}} \Updelta t} $$
(4)

where T t is the average temperature during Δt with R = 0.25 when T t ≤ 43 °C and R = 0.5 when T t > 43 °C. A t 43 thermal dose of 90 min was taken to represent the onset of thermal damage, a value required to produce a thermal lesion in a murine mammary carcinoma.14,38

Results

In Vitro Electric Field Threshold Determination

After performing experiments, it was found that 1000 V/cm was a suitable electric field threshold to estimate IRE induced cell death. As seen in Fig. 2, there is a clear decrease in cell viability corresponding to the higher electric fields. Viability continues to decrease and asymptotically approach 0% for electric fields well beyond this baseline threshold estimate. Therefore, it may be assumed that all cells experiencing electric fields ≥1000 V/cm may be considered to be killed by IRE. Taking the shape factor, λ, to be 1.5, the value for spherical cells, and assuming a cell diameter of 12 μm, the applied electric field of 1000 V/cm corresponds to a transmembrane voltage of V m = 1.8 V. This potential is well above the 1 V found to typically induce IRE,48 supporting the use of this electric field as a conservative estimate to that which would be required for treatment protocol designs in vivo.

Figure 2
figure 2

In vitro results (n = 12) of MDA-MB-231 cell viability vs. applied electric field. 5% viability was observed at 1000 V/cm

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Numerical Model

The computational model was solved for determine the minimum applied voltage necessary to fully expose the tumor volume to the electric field determined from the in vitro experiments to induce IRE. This was repeated for conductivity ratios (σt/σp) between 0.1 and 10 to assess the presence of a threshold for the conductivity ratio where IRE loses its efficacy and to see if the effective range corresponds to physiologically relevant tissue properties.

After simulating various scenarios for electrode geometry and placement around the tumor, it was determined that placing the electrodes within the targeted tissue near its boundary yielded the best results for conductivity ratios (σt/σp) of ≥1, which are more physiologically relevant to breast carcinomas and many other in situ pathologies, while maintaining reasonable results for conductivity ratios <1. It was ultimately determined that placing the electrodes within 0.5 mm of the tissue margin at opposing sides yielded the best results for the range of ratios studied. The exposed surfaces of the electrodes were 5.75 mm excluding the steel tip, which was found to be adequate for treating the entire targeted volume.

Outputs from the model with conductivity ratios (σt/σp) of 0.1, 1, and 10 for an applied voltage of 4.2 kV may be seen in Fig. 3. This applied voltage was found to be large enough to treat the entire targeted region (solid black outline) when the conductivity ratio was 1, providing a qualitative comparison for the electric field and temperature distribution response to changing conductivity ratios for a constant applied voltage. The electric field distribution seen in Figs. 3a–3f is constant during the entirety of the 100 μs pulse; then rapidly decays to zero. The temperature of the tissues increases during the application of the pulse, and then spreads throughout the tumor and peripheral tissue via conduction. The temperature distribution at the end of the first second may be seen in Figs. 3g–3i, where the greatest thermal effects are observed to occur immediately at the charged and grounded surfaces and the steel tips. Other contours are depicted of electric fields that have previously shown to lead to irreversible (650 V/cm) and reversible (360 V/cm) electroporation from in vivo studies on rabbit livers.32

Figure 3
figure 3

Numerical model outputs with same voltage. The outputs with a 4.2 kV applied voltage for conductivity ratios (σt/σp) of 0.1 (a, d, g), 1 (b, e, f), and 10 (c, f, i); showing electric field (a–f) during the pulse and temperature (g–i) distributions 1 s after the first pulse. The higher conductivity ratios show progressively more area treated by IRE with less thermal effects. Targeted tissue boundary may be seen as the solid black line

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Outputs from the model with conductivity ratios (σt/σp) of 0.1, 1, and 10 and applied voltages of 6.85, 4.20, and 2.95 kV, respectively, may be seen in Fig. 4. These applied voltages were found to be capable of exposing the entire targeted region (solid black outline) to an electric field of 1000 V/cm. From this, treatment-relevant distributions of the electric field may be seen for the three conductivity ratios when the required voltage is applied. In addition, more treatment-relevant temperature increases after the initial second of treatment are depicted in Figs. 4g–4i, where the higher required voltage of lower conductivity ratio (σt/σp) systems are seen to contribute to significantly more thermal effects.

Figure 4
figure 4

Numerical model output with applied required voltage for complete lesion ablation for conductivity ratios (σt/σp) of 0.1 (a, d, g) (6.85 kV), 1 (b, e, f) (4.20 kV), and 10 (c, f, i) (2.95 kV); showing electric field (a–f) during the pulse and temperature (g–i) distributions 1 s after the application of the first pulse. The higher applied voltage for σt/σp = 0.1 shows significantly more thermal effects than for homogeneous tissue and conductivity ratios, σt/σp, > 1. Targeted tissue boundary may be seen as the solid black line

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From these results, several effects of the varied conductivity ratios can be observed. For targeted regions that are more conductive than their surrounding tissue (σt/σp > 1), a common scenario for many cancers, the dramatically lower voltage allows for complete exposure of the targeted region without exposing the tissues to large volumes of higher electric fields, such as 2500 V/cm. Such conditions lead to a significantly lower temperature increases, which primarily occur within the tumor. For σt/σp < 1, the less conductive targeted region requires much higher voltages to treat the targeted region with 1000 V/cm, leading to larger volumes of tissue experiencing high electric fields of 2500 V/cm. These higher electric field regions coincide with much higher thermal effects, much of which preside outside of the targeted boundary in accordance to the joule heating behavior with more conductive tissues.

Conductivity and Thermal Effects

The numerical model was solved for tissue conductivity ratios (σt/σp) between 0.1 and 10 to understand how variation in this ratio changes the required voltage to treat the entire targeted volume and the behavior of the thermal effects. A plot of the required voltage for each conductivity ratio may be found in Fig. 5a. From this, it may be seen that for the electrode geometry used, higher conductivity ratios lead to significantly lower required applied voltages decreasing from 6.85 to 2.95 kV.

Figure 5
figure 5

Required voltage and thermal volume consequences. (a) Voltage necessary for complete tumor IRE. (b) Ratio of tissue experiencing thermal damage to tissue treated with IRE for a range of conductivity ratios (σt/σp). The lowest voltages were observed where the tumor is more conductive than the peripheral tissue. This led to less than 5% IRE vs. thermal damage for all conductivity ratios above 0.5

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The t 43 thermal dose values for the modeled 80 pulse treatment were evaluated throughout both tissues to determine what volume (V_Thermal) experienced a thermal dose of 5400 s. This was a dose sufficient to thermally kill murine mammary carcinoma cells.14,38 In addition, the total volume experiencing an electric field of at least 1000 V/cm (V_IRE) was evaluated for both tissues. The ratio of V_Thermal to V_IRE was computed for each conductivity ratio (σt/σp) in order to compare these volumes, which may be found in Fig. 5b. From this figure, it can be seen that less than 5% of the volume experiencing IRE would be subjected to thermal effects for all σt/σp > 0.5. Figure 5b shows a nonlinear trend due to the layered variables described by the figure. One such reason for the non-linearity is that, in addition to changing conductivity ratios, the required voltage was adjusted in order to expose the entire targeted volume to electric fields of 1000 V/cm. Furthermore, the different volumes of the two tissue types studied (targeted and peripheral) and the prevalence of thermal effects in the more conductive regions may also affect the behavior of the trend shown in Fig. 5b.

It is important to note that the analysis conducted in Fig. 5b compared thermal damage to irreversible electroporation and was conducted to understand what volume of tissue may be killed through the IRE mechanism alone. This means that the thermal dose technique used to estimate volumes experiencing thermal damage may assess regions that do not experience protein denaturation or permanent scarring, which typically occurs when tissue reaches temperatures between 50 and 60 °C,8 and are the key concerns for treatment complications and follow-up monitoring. Accounting only for thermal scarring would decrease the thermal to IRE volume ratios (V_Thermal/V_IRE) beyond those investigated here to further improve the efficacy of IRE treatment.

Discussion

These results present supporting evidence for the feasibility of using IRE for the treatment of breast cancer. The in vitro experiments showed a conservative electric field threshold to achieve cell death through IRE. Because it has been shown that reversibly electroporated pores re-seal in the range of nanoseconds to ~100 s,49 it may be assumed that the 10-min incubation period prevented trypan blue from entering any cells that survived the procedure. It is important to note that there are significant differences in the conditions between in vitro and in vivo responses to pulsed electric fields. If it is found in vivo that mammary carcinomas experience IRE at an electric field other than 1000 V/cm, the effects from the heterogeneous tissue conditions on electric field and thermal behavior will remain unaltered. What will change is the required voltage to obtain the electric field capable of treating the entire targeted region. For in vivo situations, the cells have different geometries and arrangements that may play a significant role in altering their transmembrane potential.27 In addition, the interaction of neighboring cells and the extracellular matrix as well as longer-term responses to the electric pulses, such as inflammatory and immune responses, may also play a role in lesion creation and resolution. These effects tend to create larger IRE lesions at lower electric fields than in the in vitro experiments shown here.32

The in vitro experiments conducted in this study were done to obtain a conservative baseline estimate of the electric field necessary for IRE treatment of breast carcinomas in order to demonstrate the feasibility of such a procedure using numerical models. For future in vivo experiments and clinical applications, timing the electric pulses with a patient’s cardiac rhythm will prevent arrhythmia associated with high electric fields in close proximity to the heart.40

The conductivity ratio (σt/σp) manipulations presented some interesting results regarding internally placed electrodes relative to electrodes placed surrounding the targeted region. Previous studies into heterogeneous effects on electric field distribution show that a region of higher conductivity placed between electrodes will experience reduced electric fields.10 However, it was found that for the electrode dimensions used, by placing the electrodes within the targeted region, the required voltage for complete lesion ablation was actually lower for heterogeneous tissues when the targeted region was more conductive than the surrounding tissue. This provides very strong evidence for the ability of IRE treatments to overcome heterogeneous tissue issues present in many cancers.

The measurements conducted by Jossinet25 and Surowiec et al.46 for infiltrating ductal and lobular breast carcinomas showed possible conductivity ratios from 0.68 to 23 between breast tumors and their surrounding tissue structures, with more common values between 1 and 5. These ratios occurred for tumor conductivities ranging from 0.268 to 0.58 S/m and surrounding structure conductivities between 0.0245 and 0.407 S/m.25,46 It should be noted that although the electric field distribution will not change with absolute tissue conductivities for a given conductivity ratio, the thermal effects will change proportionally to the different absolute conductivities, which may affect the amount of thermal damage done. The physiological conductivities in the literature are similar to the values used in the model, so it is possible to apply the study’s findings to clinical settings.

The implications of this work also provide evidence for the need to account for and determine tissue conductivities prior to treatment in order to accurately predict lesion margins, and thus treatment outcome. This may be done by first delivering a low energy pulse, measuring the current induced, and calculating the conductivity. This process may be repeated for as many different tissues as desired by changing electrode placement or exposed region, facilitated by ultrasound guidance.

A key aspect of the effects from heterogeneous tissues to consider from this study is the distinct redistribution of the electric field in response to the conductivity ratios (σt/σp) greater than or less than 1. The limiting margin is defined here as the final border of the targeted region to experience IRE-relevant electric fields when the applied voltage was insufficient to produce complete tumor IRE. This margin will change by altering electrode placement within the targeted region (more central or closer to the perimeter). The geometry used, where the electrodes were placed within and beside the targeted region boundaries, was selected for ease of guidance during application, and because this geometry was found to yield tumor ablation at practical voltages. For many electrode arrangements, when the peripheral tissue is more than or as conductive as the inner tissue (conductivity ratio ≤1), the limiting margin is the border between the electrodes. However, when the peripheral tissue is less conductive than the targeted region (conductivity ratio >1), the limiting margins were more likely to be the regions closest to each electrode. These effects hold great implications for electrode design and use in the treatment of various heterogeneous tissues.

For heterogeneous tissues with a conductivity ratio, σt/σp < 1, the required voltage and thermal effects may be reduced by increasing the diameter of the electrodes relative to the diameter of the targeted region.32 The targeted region/electrode diameter ratio (d t/d e) used in this study was 1/10, which was derived from typical primary tumor characteristics and currently used minimally invasive surgical devices. Also, the electric field may be more accurately aimed at the limiting margin by reducing the separation between the electrodes, moving each closer to the center of the targeted tissue.

The heterogeneous effects also bring the regions of healthy tissue killed by IRE into consideration when designing IRE protocols. This study focused on treating to the boundary of the targeted region. In conventional breast conserving therapies and other surgical resection treatments, a margin of healthy tissue of approximately 0.5 cm beyond the targeted region is often removed to increase the certainty of removing all cancerous cells related to the tumor.13 For IRE treatments of cancer, killing a similar margin beyond the targeted region would likely be desirable.

To further reduce the required voltage for all scenarios investigated, electrodes can first be initially placed immediately within the perimeter of opposite borders of the targeted region. Pulses would be applied at a lower voltage that may not treat the entire targeted region. Following this, the electrodes would be re-inserted, with their location rotated 90° relative to the center of the targeted region. Alternatively, four electrodes could be placed in the arrangement simultaneously. Such a technique does require additional electrode insertions, increasing invasiveness of the procedure and promoting the chances for inaccurate electrode placement, and thus treatment region. However, because tumor location and electrode placement may be accurately visualized using ultrasound guidance,29 multiple insertions should not significantly increase error in electrode placement. The application of such a technique is ultimately dependent on the scenario and should be evaluated for use on a case-by-case basis.

Although this analysis was conducted for a simple arrangement of two single-pole needle electrodes, more complex electrodes and arrangements may be used to customize the shape of the electric field distribution to more efficiently treat the targeted region while sparing the peripheral tissue. This principle may be applied when accounting for tissue heterogeneities as well as for planning and targeting treatments of irregularly shaped tumors. For such situations, ultrasound guidance can ensure accurate electrode placement prior to treatment. By adjusting electrode type, size, shape, placement, and arrangement in response to heterogeneous conductivities and irregular tumor geometries, it is possible to increase the accuracy of the desired electric field relative to the treatment, and thus decrease the required voltage and thermal effects, improving the practicality and efficacy of treatment.

A final aspect to note of the electrodes is the effect of the sharpened tip required for tissue penetration. The use of surgical steel makes this portion of the electrode highly conductive, producing thermal effects and altering the electric field, redistributing it distally. However, for some scenarios where only a very narrow electrode is required or the tissue is very soft, such as the brain, an electrode may be used without the sharpened steel tip to obtain a more uniform electric field distribution.

This study focused on interpreting the behavior of electric field and temperature distributions when planning IRE treatments on tissues with bulk heterogeneities, such as the scenario involving the unique conductive properties of mammary tumors within a fatty connective tissue matrix. To further expand upon this study as treatment planning protocols become more refined, it may be desirable to account for the multiple tissues interacting at a finer scale. For instance, different breast tumors, such as infiltrating ductal and infiltrating lobular carcinomas, can occur in many unique locations relative to the connective, glandular, and adipose tissues that compose the majority of breast tissue, each with unique electrical and physical characteristics.25 In addition, in some cases it may be appropriate to further refine the heterogeneities considered down to the level of distinct cell geometries and organization within the extracellular matrix. At such scales, distinct electrical behaviors for the interaction between cells and their surrounding interstitial matrix have been shown.12

The thermal effects produced by treatments investigated with conductivity ratios (σt/σp) > 0.5 may be considered negligible, since the volume of tissue experiencing thermal damage is less than 5% of the volume treated by IRE, a relatively small value. This allows for the ablation of significant portions of targeted tissue without inducing thermal damage. Furthermore, these effects were studied in order to delineate the mechanism of cell death between IRE and thermal damage, which is likely to occur at temperatures below those that induce thermal scarring. Additional investigation comparing IRE ablation to thermal scarring would likely show even larger amounts of tissue capable of being treated by IRE for a given amount of thermal damage. It should be noted that the greatest temperatures occur at the electrode-tissue interface, where IRE treatment is strongest, ensuring that any scarring will occur in an area of tissue that has received sufficient treatment, decreasing any negative impact on monitoring treatment outcome. Finally, the thermal effects may be reduced even more with the use of an internally cooled electrode.

A significant portion of the volume treated by IRE occurs outside of the targeted region. However, this is consistent with typical breast conserving therapies, where a margin is produced beyond the primary tumor to ensure complete treatment. This volume may be further increased using higher voltages as well as re-inserting the electrodes with a different arrangement. The rapid lesion resolution exhibited by IRE procedures suggests that all healthy cells killed by the IRE procedure will be replaced with an in-growth of new healthy cells and tissue, further reducing scarring and aesthetic effects.

Conclusion

This study has investigated various aspects related to the application of irreversible electroporation to the treatment of breast carcinomas and other applications involving heterogeneous tissue systems. This was completed with regard to ensuring therapy for the entire targeted region from physiologically and anatomically relevant treatment parameters. In vitro experiments determined a conservative electric field estimate to induce IRE on mammary adenocarcinoma cells, which was then adapted into a numerical treatment prediction model. The model simulated procedures using two monopolar electrodes, showing numerous unique treatment characteristics and implications of heterogeneous tissue. It was found that IRE is capable of fully treating targeted heterogeneous volumes of tissue without inducing thermal effects significant enough to cause substantial thermal damage, decreasing the likelihood of significant scarring and allowing for improved treatment outcome and recurrence monitoring while minimizing aesthetic effects. It was shown that this is possible for a range of conductivity ratios (σt/σp) between the two tissue types, showing the applicability of IRE treatments for a range of such heterogeneous tissue scenarios common in clinical settings. Rapid lesion resolution would allow for healthy cells to repopulate the originally afflicted area and treatment margins. These factors, in combination with the additional benefits exhibited by the non-thermal and minimally invasive nature of IRE, provide strong evidence in support of IRE as an advantageous treatment modality for breast cancer and other localized pathologies containing heterogeneous tissue, where distinct tissue and tumor properties may alter treatment parameters and outcome.