604 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 59, NO. 3, MARCH 2012

Electrode Activation Sequencing EmployingConductivity Changes in Irreversible

Electroporation Tissue AblationAlan V. Sahakian, Fellow, IEEE, Haitham M. Al-Angari∗, and Oyinlolu O. Adeyanju

Abstract—Irreversible electroporation (IRE) uses high-voltagepulses applied to tissue, which cause dielectric breakdown of cellmembranes resulting in cell death. IRE is a promising techniquefor ablation of nonresectable tumors because it can be configuredto spare critical structures such as blood vessels. A consequence ofpulse application is an increase in tissue electrical conductivity dueto current pathways being opened in cell membranes. We proposea novel IRE method introducing electrode switching and pulsesequencing in which tissue conductivity is first increased usingpreparatory pulses in order to form high-conductivity zones, whichthen helps provide higher electric field intensity within the targetedtissue as subsequent pulses are applied, and hence, enhances theefficiency and selectivity of the IRE treatment. We demonstratethe potential of this method using computational models on simplegeometries.

Index Terms—Ablation, electrical conductivity, finite-elementmodeling (FEM), irreversible electroporation (IRE), tumor.

I. INTRODUCTION

IRREVERSIBLE electroporation (IRE) is a novel nonthermalablation technique. Studies have shown that IRE holds great

potential in the treatment of cancer [1]–[5] as well as other uses,including cardiac ablation [6], angioplasty [7]–[10], and foodtreatment [11]–[13]. Preliminary work has shown that IRE caneradicate cancer cells in vitro (e.g., HepG2, a liver cancer cellline [5], and PC3, a prostate cancer cell line [4]). Studies in a ratmodel of liver cancer [14] and a mouse model with cutaneoustumors [2] have shown IRE’s ability to shrink tumors, whilestudies in pigs have shown the clinical feasibility of guiding andmonitoring IRE therapy in real time [15], [16] using ultrasound.Other preclinical work has shown that IRE can ablate liver, lung,and kidney cancer in humans [17].

IRE uses short duration (microsecond to millisecond), highamplitude electric pulses applied via electrodes to ablate tissue.The current understanding of the underlying mechanism in IRE

Manuscript received August 2, 2011; revised October 21, 2011 andDecember 1, 2011; accepted December 12, 2011. Date of publication December21, 2011; date of current version February 17, 2012. Asterisk indicates corre-sponding author.

A. V. Sahakian is with the Department of Electrical Engineeringand Computer Science and the Department of Biomedical Engineering,Northwestern University, Evanston, IL 60208 USA (e-mail: sahakian@eecs.northwestern.edu).

∗H. M. Al-Angari is with the Department of Electrical Engineering andComputer Science, Northwestern University, Evanston, IL 60208 USA (e-mail:hangari@northwestern.edu).

O. O. Adeyanju is with the Department of Biomedical Engineering, North-western University, Evanston, IL 60208 USA (e-mail: lolu@northwestern.edu).

Digital Object Identifier 10.1109/TBME.2011.2180722

is that the application of a high electric field increases the trans-membrane potential of cells, causing structural rearrangementsin the lipid bilayer, promoting the formation of semipermanentto permanent aqueous pores in the cellular membrane. Thesepores allow the abnormal flux of ions across the cellular mem-brane, which disrupts the cell’s homeostatic mechanisms andinduces cell death [2].

There are many advantages to IRE, including but not limitedto: 1) it works quickly [15]; 2) IRE lesions resolve quickly; [16]and 3) it leaves intact tissue structural elements (e.g., bile ducts,blood vessels, connective tissue) [16], and there is a sharp demar-cation between ablated and nonablated regions [6], [18], [19],indicating the possibility of very specific targeting of IRE. Cur-rently, areas of development in IRE revolve around targeting theelectric field to the desired structure of ablation and minimizingthe potentially harmful effects of thermal ablation [20], [21].

We propose a new technique for improving IRE via the useof a predetermined electrode pulse sequence to structure theablation zone and enhance the homogeneity of the effectiveelectric field in the target area while minimizing the necessaryapplied voltage. The proposed technique uses preparatory IREpulses to alter tissue electric conductivity to enhance the ho-mogeneity of the electric field generated by subsequent pulses.Other researchers have recognized the necessity of a homoge-neous electric field within the desired target structure [22], [23].Rebersek et al. introduced the principle of pulse sequencingto improve reversible electroporation in electrochemotherapy[24]. The first part of the pulse sequence is designed to in-crease the electrical conductivity of the outer part of the tumor,and the second part of the sequence is designed to electropo-rate the inner tumor tissue by utilizing the elevated conduc-tivity of the outer regions. Previous studies have shown thatthe electric conductivity increases nonlinearly with the appliedelectric field during IRE treatment [25]–[28]. Sel et al. has mod-eled this variation in the conductivity with a unidirectional sig-moidal function [25]. Although the conductivity drops to lowervalues within a few microseconds after the termination of thepulse, it stays relatively higher than its value before the firstpulse for tens to hundreds of milliseconds. The resultant con-ductivity value, measured 500 ms after the termination of thelast pulse in rat healthy liver IRE, has shown to be 43% higherthan the baseline with a pulse protocol of 1500 V/cm, 8–100 μspulses applied at a rate of 10 Hz [27]. On the other hand and forthe same applied pulse protocol, the increase in conductivity formice sarcoma cells was only around 10%, measured 50 ms afterthe last pulse. This percentage can be increased by increasing

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the applied electric field, the pulse duration, and/or the num-ber of pulses [28]. Studies of finite element modeling (FEM)that incorporate the effect of dynamic conductivity on electricfield distribution in IRE have been presented [25], [26], [29].However, these studies have not explored the effect of pulsesequencing with different electrode activation patterns on im-proving the treatment. Such a study requires adding a modelof conductivity drop during the OFF period of the activationsequence. In this paper, we incorporate ON- and OFF-pulsevariations of conductivity together with pulse sequencing in aFEM to test the possible improvement of the IRE treatment.

II. METHODS

To test the effect of conductivity changes, a 3-D electropora-tion model of rabbit liver with a four-electrode configuration wasimplemented. The liver was modeled as a 32 × 32 × 25 mm3 .The electrodes, metal needles with 1 mm diameter and an ex-posed length of 1 cm, were placed to form a 1 cm2 and insertedinside the tissue. A sequence consisting of two 100 μs durationpulses, the first of 1000 V and the second of 1200 V amplitude,was applied with different electrode activation patterns. An OFFperiod between the two pulses was introduced to simulate theswitching time for the electrode activation. Two time durations:10 ms and 10 μs were tested for the OFF period to study itseffect on conductivity drop and the resultant overall ablationarea at the end of the second pulse. During the first pulse, thetwo electrodes on the left side of the square were active whilethe other two electrodes on the right side were grounded. Theconductivity during this pulse was modeled from Sel et al. [25]as follows:

σpulse1(t) = S (t) + 0.067 (1)

where S(t) is a sigmoid function defined as follows:

S(t) =0.241 − 0.067

1 + 10 exp(−(E(t) − A)/B)(2)

where E(t) is the electric field distribution (in V/cm) computed atevery time step, and A and B are fitting parameters. The conduc-tivity value before the first pulse is 0.067 S/m and the maximumvalue, which the ON-pulse conductivity can reach, is 0.241 S/m.The conductivity during the OFF period was modeled from ex-perimental data of rat healthy liver taken from [27] and rescaledto fit the maximum and the conductivity value before the firstpulse for the rabbit model:

σOFF = max [0.067, σpulse1(t1)(0.28 − 0.03 ln(t − t1))](3)

where t1 is the duration of the first pulse.During the second pulse, the electrodes on the topside of the

square were active while the bottom two were grounded. Theconductivity during the second pulse is computed as follows:

σpulse2(t) = min [0.241, S(t) + σOFF] . (4)

The activation pattern is shown schematically in Fig. 1. Thesimulation was repeated while introducing a spherical tumorwith 1.6 cm diameter inserted 1 cm deep into the liver. Theexposed length of electrodes was increased to 2 cm and themidline of the exposed length was aligned with the tumor center.

Fig. 1. Activation pattern for the four-electrode configuration during the (a)first pulse and (b) second pulse. The active electrodes are represented by theblack-filled circles and the ground electrodes are represented by the white-filledcircles. The arrows indicate the electric field direction.

Conductivity computation of the tumor was done similar to theliver using equations derived from experimental measures ofconductivity for mice sarcoma cells from Ivorra et al. [28] asfollows:

σtp u l s e 1 (t) = St(t) + 0.135 (5)

St(t) = 0.291 exp(−e−0.0012(|E (t)|−1500)) (6)

σtO F F = max [0.135, σtp u l s e 1 (t1)(0.64

− 0.017 ln(t − t1))] (7)

σtp u l s e 2 (t) = min[0.426, St(t) + σ(tO F F ) ]. (8)

The amplitude of both pulses was 1000 V. To get a useful effectof conductivity changes in the liver–tumor case, we needed toshorten the first pulse to about 25 μs while the duration of thesecond pulse was kept as 100 μs. The reason for this is discussedin the results. To simulate the electroporation procedure, we usedCOMSOL Multi-Physics (version 4.1), an FEM software. Dis-tribution of the electric field intensity due to the electroporationpulse is determined by solving the Laplace equation:

∇(σ∇φ) = 0 (9)

where φ is the electric potential. The boundary condition fortissues contacting the active electrodes is

φ = V0 (10)

where V0 is the applied voltage, while boundary condition fortissues contacting the ground electrodes is

φ = 0. (11)

A predefined fine-sized mesh with 112 957 elements was se-lected. The simulations were conducted on a Dell M6500 com-puter with 1.73 GHz Core(TM) i7 processor and 8 GB of RAMoperating on Microsoft Windows 7.

III. RESULTS

Fig. 2 shows the conductivity map and the ablated area at theend of the first and second pulses for the liver model. As the firstpulse is applied, the conductivity of the path between active andground electrodes increases [see Fig. 2(a)]. If the conductivitychange is not included during the OFF period, the overall ablatedarea will be the aggregate sum of two ablated areas achieved byeach pulse separately [see (Fig. 2(d)]. With conductivity change

606 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 59, NO. 3, MARCH 2012

Fig. 2. Conductivity map (in S/m) and ablated zone (electric field intensity ≥ 700 V/cm) for the liver model: (a) shows conductivity map at the end of the firstpulse, while (b) and (c) show conductivity map at the end of the second map for 10 ms and 1μs switching time, respectively. The ablated area with no conductivitychange during the OFF period is shown in (d), while (e) and (f) show ablation area with conductivity change and 10 ms and 10 μs switching time, respectively.The conductivity is evaluated 1 μs before the pulse termination.

Fig. 3. Slice plots of conductivity map and ablated zones (E ≥ 700 V/cm) for the liver–tumor model at the center of the tumor. (a) and (b) show the conductivitymap at the end of the first and second pulses, respectively. The overall ablated zone is shown with and without conductivity changes during the OFF period (c) and(d), respectively. Switching time between the two pulses is 10 μs.

considered, the rise in conductivity due to the first pulse dropslogarithmically to a lower value yet is still higher than the valuebefore the first pulse, depending on the switching time betweenthe two pulses. This new conductivity distribution works as thesecond pulse is applied to increase the electric field in the centralregion surrounded by the electrodes, which results in increasingits conductivity [see Fig. 2(b) and (c)] and ablated area, whichwas defined as area with electric field intensity ≥ 700 V/cm[see Fig. 2(e) and (f). However, the central area was not com-pletely ablated. The effect of the switching time was tested as the10 μs switching time [see Fig. 2(c) and (f)] gave slightly higherconductivity and more ablation than the 10 ms switching time[see Fig. 2(b) and (e)].

Fig. 3 shows slice plots for the conductivity map and ablationzone at the center of the tumor for the liver–tumor model. Atthe end of the first pulse (25 μs), the transient conductivity ofthe liver near the edge of the tumor was higher than the conduc-tivity inside the tumor [see Fig. 3(a)]. This helps drive a higherelectric field inside the tumor and hence increase its conductiv-ity as the second pulse is applied [see Fig. 3(b)]. The overall

ablation is shown in Fig. 3(c), while Fig. 3(d) shows the ablationzone when no conductivity changes during the OFF period areincluded. The reduction of the first pulse duration was essentialas a longer first pulse would increase the conductivity inside thetumor and prevent the second pulse from forcing higher electricfield lines inside the tumor. Even with a 10 ms switching time,the ablated area was about the same achieved with the 10 μsswitching time (plots are not shown). To quantify the differencebetween including and not including the OFF-period changein conductivity to the model, we evaluated the percentage ofthe ablated tumor volume. With the 1000 V pulse sequenceand OFF-period change, 96% of the tumor was ablated com-pared with 91% when the OFF-period change was not included.To completely ablate the tumor, the model with OFF-periodchanges needed 1200 V compared with 1250 V with no OFF-period changes. The volume of the ablated normal tissue was8.2% less when the OFF-period changes were included. Thispercentage was increased for tumors with bigger size (it was12.5% for a tumor with a 3 cm diameter; a required pulse am-plitude of 2750 V to completely ablate the tumor in both cases).

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IV. DISCUSSION

The goal of this paper is to propose a novel method for apulse sequence and electrode activation pattern to improve theIRE treatment. A first pulse (or sequence of pulses) with apredefined electrode activation pattern is used to ablate certainregions of the tissue, causing them to have higher conductivity.Although these higher conductivities in these regions declinein time, they are still higher than the baseline, which resultsin ablating more area in the central region surrounded by theelectrodes. The ablation of the central area increases with short-ening of the switching time between the electrodes. Switchingtime of 10 μs can be implemented with current technology forthese pulse amplitudes using insulated gate bipolar junctiontransistors. Although no complete ablation was achieved in thehomogenous liver model when applying sequences of relativelylow-amplitude pulses, more promising results were achievedwith the liver–tumor model, which is of more importance. Inour opinion, this might be due to the high increase in the liverconductivity compared to the tumor conductivity when applyingthese relatively low voltages. This can be observed from the sig-moid functions modeled from the experimental data. Althoughour model results show a small improvement, combination ofthe conductivity OFF-period modeling with proper electrodeconfiguration and activation pattern might provide better re-sults. Although variation of conductivity with temperature wasnot directly included in the model, we believe it was intrinsi-cally accounted for as the experimental values of conductivitythat we used in the model were measured at the end of theON pulse, where the rise in the conductivity value is due toa summation of changes because of the temperature rise andelectric field distribution. Similarly, drops in the measured con-ductivity during the OFF-pulse period are due to other factorssuch as membrane resealing and cooling down of the tissue.However, it should be considered that the rise in temperaturedue to electroporation will cause inhomogeneous conductivitychange in the liver and in the tumor, which is originally an inho-mogeneous tissue. Different combinations of electrode numberand placement, activation patterns, and pulse sequences need tobe tested in phantom experiments and animal studies togetherwith FEM to verify these findings and find optimum electrodeconfigurations for different tumor sizes and locations.

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