Optimum Conductivity of Gels for Electric Field Homogenization in Tissue Electroporation Therapies A. Ivorra and B. Rubinsky 1

Dept. of Mechanical Eng. and Dept. of Bioengineering, University of California at Berkeley, CA 94720, USA

Abstract— Electroporation is used in tissue for gene therapy, drug therapy and minimally invasive tissue ablation. For the electroporation to be successful, the electrical field that develops during the application of the pulses needs to be precisely controlled. It is desirable to generate a homogeneous electric field in the region of interest and a null electric field in the regions not to be treated. In case of irregularly shaped tissue structures, such as bulky tumors, electric field homogeneity is almost impossible to be achieved with current electrode arrangements. In the past (Bioelectrochemistry, 70:2, 551-60, 2007), we proposed the use of conductive gels, matched to the conductivity of the tissues, to overcome this limitation. Those gels can be used to fill the dead spaces between plate electrodes gripping the tissue so that the electric field distribution becomes homogeneous. Here we analyze, through finite element simulations, how relevant the conductivity mismatches are. We found that conductivity mismatching errors are surprisingly well tolerated by the technique and that it is more convenient to use gels with higher conductivity than the conductivity of tissues rather than gels with lower conductivity. A gel with a conductivity of 5 mS/cm could be a proper solution for most cases. Keywords— Electroporation, electropermeabilization, electro-chemotherapy, gels.

I. INTRODUCTION Electroporation, or electropermeabilization, is the phenomenon in which cell membrane permeability to ions and macromolecules is increased by exposing the cell to short (microsecond to millisecond) high electric field pulses [1]. Reversible electroporation of living tissues is the basis for different therapeutic maneuvers on clinical use or under study [2] such as the in vivo introduction of genes into cells (electrogenetherapy) [3-5] and the introduction of anticancer drugs into undesirable cells (electro-chemotherapy) [6]. More recently, irreversible electroporation has also found a use in tissues as a minimally invasive surgical procedure to ablate undesirable tissue without the use of adjuvant agents [7-9]. Electroporation is a dynamic phenomenon that depends on the local transmembrane voltage. It is generally accepted that for a given pulse duration and shape, a specific transmembrane voltage threshold exists for the manifestation of

the electroporation phenomenon (from 0.5V to1V). This leads to the definition of an electric field magnitude threshold for electroporation (Eth). That is, only the cells within areas where E ≥ Eth are electroporated. If a second threshold (Eth_irr) is reached or surpassed, electroporation will compromise the viability of the cells, i.e., irreversible electroporation. It is obvious, from the above, that precise control over the electric field that develops in tissues is important for electroporation therapies [10-13]. For instance, in reversible electroporation based therapies it is desirable to generate a homogeneous electric field (Eth ≤E < Eth_irr) in the region of interest and a null electric field in the regions not to be treated. Currently, optimization of the electric field distribution during electroporation is done through design of optimal electrode setups [14]. However, there are situations in which an electrode setup alone is not sufficient for obtaining an optimal electrical field, particularly in situations such as the electroporation of irregularly shaped tissues or when the protection of specific tissue regions is required. In [15] we introduced the concept of using gels with specific conductivities in order to optimize the electric field distribution in different electroporation scenarios. One of those scenarios was the treatment of bulky superficial tumors. Although electro-chemotherapy with plate electrodes is achieving impressive results with the treatment of such tumors [2], some failures can be attributed to heterogeneities in the electric field distribution, particularly in the case of hard tumors that cannot be squeezed properly between the electrodes. It is quite easy to realize that if one fills the space between plate electrodes with a gel whose conductivity is equal to that of the tissue to be electroporated, then the whole material between the plates will become homogeneous in electrical terms and the generated electric field distribution will also be homogeneous. Here we show that perfect conductivity matching is not necessary at all. This fact simplifies enormously the application of the technique. We hope that the technique described here will be useful for the treatment of tumors by means of electroporation based therapies. As a matter of fact, this technique is about to be tried in tumors implanted in small animals.

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II. METHODS We employed the finite element method (FEM) to compute the electric field distribution under the assumption of static currents and fields. This modeling methodology has been used by previous researchers in the field [16-18]. Unfortunately, due to a lack of basic knowledge of the electroporation phenomenon in tissues, the models ignore possible effects of multiple pulses and different pulse lengths, periods or shapes. Nevertheless, it has been proven empirically that this methodology is able to predict reasonably well the outcome of the electroporation treatment [9, 11]. In order to improve the realism of the models, here we consider that the tissue conductivity is not constant but it is electric field dependant. This feature was not taken into account until recently by researchers in the field but it has been shown to have significant effect on electric field distribution computations [19]. The key idea of the FEM is the decomposition of an arbitrary geometry into small simple elements in which it is possible to solve the differential equations related to the phenomena under study. Given the appropriate boundary conditions, the solutions are then assembled and an approximate solution for the complete geometry is provided. In our case, the solved equation for each element is the Poisson’s equation:

(

)

− ∇ ⋅ σ∇V − J e = 0

(1)

where σ is the conductivity, V is the voltage and Je is a vector denoting the externally generated current density. The specific FEM tool used here was COMSOL Multiphysics 3.3 (www.comsol.com) and the mode chosen for the simulations was “3D conductive media DC”. The boundary conditions were all insulating on the external surfaces. An unstructured mesh of 10214 tetrahedral elements was automatically generated by the FEM tool. The geometry of the analyzed case is showed in Figure 1. The simulations have been performed assuming that Eth =500 V/cm (reversible electroporation threshold) and Eth_irr = 1000 V/cm (irreversible electroporation threshold). The conductivity of the tissue (σ) was 1 mS/cm at 0 V/cm and 5 mS/cm at 1000 V/cm or larger electric fields; linear interpolation was employed for intermediate electric fields. In the resulting graphs black color indicates E < 500 V/cm (no effect); grey color 500 V/cm ≤ E < 1000 V/cm (reversible electroporation); and white E ≥ 1000 V/cm (irreversible electroporation). Since the tissue conductivity depends on the electric field and the field in turn depends on the conductivity, the model was solved as a sequence of steps in which the conductivity distribution for each step was defined by the electric distri-

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Fig. 1 Model employed in the simulations. A semispherical tumor is “sandwiched” between two electrodes (E+ and E-) and a voltage difference of 600 V is applied. The transparent box between the electrodes represents the location of the conductive gel.

bution in the previous step. Eight steps were employed here although no significant changes were observed after the fourth one. III. RESULTS AND DISCUSSION Even in the ideal case of a homogeneous material slab sandwiched between two parallel plates some electric field distribution heterogeneity must be expected due to the edge effect of the electric field. Nevertheless, electric field distribution is significantly worsened when the material itself, or its geometry, is not homogeneous. A common observable feature is an increase of field magnitude on narrow sections due to an increase of resistance of those sections. It is obvious that a semispherical region between two plates represents one of those non ideal cases. In the vicinity of the electrodes the electrical paths become narrower and hence it can be expected that field will be significantly higher than in central regions of the geometry. On the other hand, if dead spaces are filled with a material whose conductivity is equal to that of the tissue, then the electrical paths are balanced and a more homogenous field distribution should be expected. The simulation result of electroporation in the absence of a gel is shown in Figure 2 a) and b). It can be noticed that the electric field distribution is extremely heterogeneous and that some regions are not reversibly electroporated. If the applied voltage is increased from 600 V to 1200 V then the whole tumor becomes electroporated (Figure 2c and d) but some healthy regions are unnecessarily treated, more-

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Optimum Conductivity of Gels for Electric Field Homogenization in Tissue Electroporation Therapies

Fig. 2. Simulation results without conductive gels. Lateral (a,c) and top views (b,d) when the applied voltage is 600 V (a,b) and 1200 V (c,d). Black color indicates E < 500 V/cm (no effect); grey color 500 V/cm ≤ E < 1000 V/cm (reversible electroporation); and white E ≥ 1000 V/cm (irreversible electroporation)

over, regions subjected to irreversible electroporation are significantly large. Figure 3 shows the simulation when gels of different conductivities are employed. Best results are obtained when gel conductivities are 2 mS/cm (Figure 3a) and 5 mS/cm (Figure 3b). Note that those conductivities are larger than the “small signal conductivity” (i.e. electric field ~ 0 V/cm) of the tissue (1 mS/cm). In fact, if gel conductivity is 1 mS/cm (Figure 3c) the upper part of the tumor is not electroporated. Surprisingly, quite good results are also obtained with gels with much higher conductivities: 10 mS/cm (Figure 3d) and 20 mS/cm (Figure 3f).

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Since some uncertainty about tissue conductivity and its dependence on electric field will always exist, gels with higher conductivity than that of the tissue will be preferable. Small-signal conductivities of most soft animal tissues are in the range from 0.1 mS/cm to 3 mS/cm (http://niremf.ifac.cnr.it/tissprop/). Therefore, a gel with a conductivity of 5 mS/cm seems a proper choice. We have collected and measured some commercial gels intended for medical ultrasonography. We have identified three of them that have conductivities that could be adequate for the present technique: Aquasonic 100 by Parker Laboratories, Inc., Fairfield, NJ, USA (2.2 mS/cm); Ultra/Phonic Conductivity Gel by Pharmaceutical Innovations, Inc., Newark, NJ, USA (~ 1 mS/cm); Eko-Gel by CA.MI.NA, S.r.l., Egna, Bolzano, Italy (~ 2 mS/cm). Use of these gels could be indicated in some cases. However it must be taken into account that their conductivities are not optimum and, since they are intended for ultrasonography, electric conductivity is not a relevant parameter and is not controlled in their fabrication.

ACKNOWLEDGMENT This work was supported in part by the U.S. National Institutes of Health (NIH) under Grant NIH R01 RR018961. BR has a financial interest in Excellin Life Sciences and Oncobionic which are companies in the field of electrical impedance tomography of electroporation and irreversible electroporation.

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Antoni Ivorra University of California at Berkeley 6124A Etcheverry Hall 94720 Berkeley, CA USA [email protected]

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