Bioelectromagnetics 35:607^613 (2014)
Brief Communication Theoretical Analysis of AC Electric Field Transmission Into Biological TissueThrough Frozen Saline for Electroporation Chunyan Xiao1* and Boris Rubinsky2 1
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China 2 Graduate Program in Biophysics, Department of Mechanical Engineering, UC Berkeley, Berkeley, California
An analytical model was used to explore the feasibility of sinusoidal electric field transmission across a frozen saline layer into biological tissue. The study is relevant to electroporation and permeabilization of the cell membrane by electric fields. The concept was analyzed for frequencies in the range of conventional electroporation frequencies and electric field intensity. Theoretical analysis for a variety of tissues show that the transmission of electroporation type electric fields through a layer of frozen saline into tissue is feasible and the behavior of this composite system depends on tissue type, frozen domain temperature, and frequency. Freezing could become a valuable method for adherence of electroporation electrodes to moving tissue surfaces, such as the heart in the treatment of atrial fibrillation or blood vessels for the treatment of restenosis. Bioelectromagnetics 35:607–613, 2014. © 2014 Wiley Periodicals, Inc. Key words: electroporation; AC electric field; arrhythmias treatment; plate electrodes; frozen saline
Electric pulses of sufficient intensity and from microsecond to millisecond in duration, delivered across the cell membrane, can produce electroporation. Electroporation is the electric field-induced permeabilization of the cell membrane through the formation of nanoscale pores or defects in the membrane [Neumann et al., 1982]. Electroporation has been studied intensively since the 1960’s [Sale and Hamilton, 1967; Weaver and Chizmadzhev, 1996; Teissie et al., 2005]. It was observed that for certain pulse parameters, the cell membrane permeabilization is temporary and that the cell survives the procedure. This is referred to as reversible electroporation (RE). For other parameters, the cells do not survive and this is referred to as irreversible electroporation (IRE). Both RE and IRE are used in medicine for diverse applications such as electrochemotherapy [Mir et al., 1991] and tissue ablation [Davalos et al., 2005]. Electroporation is delivered when electrodes are inserted in tissue or brought into contact with the tissue surface. Clinical electroporation has several technical challenges. One is the need for precise and simultaneous placement of several electrodes into soft tissue [Thomson et al., 2011], or onto moving surfaces such as the heart in the treatment of atrial fibrillation [Lavee 2014 Wiley Periodicals, Inc.
et al., 2007] or blood vessels in the treatment of restenosis [Maor, 2009]. Physicians report that the insertion of multiple needle electrodes in a parallel structure into soft and moving tissue or placement of electrodes on a moving surface is a technical challenge, which substantially extends the length of this otherwise short surgical procedure. In addition, the fluid between the electrode and the tissue is a site for electrolysis with gas bubbles forming. They affect the electric contact and sometimes become ionized and induce an electric discharge associated with sound waves, which is very undesirable. This study explores the feasibility of a technical solution to the problems of electrode placement, inspired by cryosurgery.
*Correspondence to: Chunyan Xiao, School of Automation Science and Electrical Engineering, Beihang University, Xueyuan Road 37, Beijing 100191, China. E-mail: [email protected] Received for review 21 June 2013; Accepted 30 July 2014 DOI: 10.1002/bem.21881 Published online 25 September 2014 in Wiley Online Library (wileyonlinelibrary.com).
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Xiao and Rubinsky
Cryosurgery, tissue ablation by freezing, is technically similar to IRE [Lin, 1987]. In cryosurgery, several needle-like cryoprobes are inserted in the tissue to form a frozen shape that encompasses the undesirable tissue [Rubinsky, 2000]. A solution to the surgical technical difficulties of cryosurgery is found in the ability of high subzero freezing temperatures to tightly bind between the probe and tissue by creating ice that sticks the probe to the tissue. In conventional cryosurgery, every probe is inserted separately in its position where it is stuck in place by high subzero freezing. This makes it possible to place every probe separately, in relation to each other. The method can be also used to attach cryoprobes to the outer surface of tissue when treating atrial fibrillation by cryosurgery, on or in the heart. It should be emphasized that at high subzero temperatures, that is, higher than about 20 8C, and for short surgery times typical to cryosurgery, freezing causes little damage to biological tissue [Rubinsky, 2000]. In fact, this is considered a drawback of cryosurgery. We proposed that the technical problems of electroporation concerning the placement of electrodes could be overcome by cooling the electroporation electrodes to a high subzero freezing temperature, similar to what is done in cryosurgery. Specifically, we propose that a cooling system in the electroporation electrodes brings the electrodes to a high subzero temperature once the electrodes come into contact with the tissue. Cooling the electroporation electrodes should: (a) Bind the electrode to tissue by sticking; (b) simplify the electrode placement method; (c) produce good electrical contact with the tissue; and (d) eliminate the fluid between electrode and tissue. The idea of cooling the electroporation electrodes was suggested in the past [Becker and Kuznetsov, 2007]. However, in that study, cooling was done at above freezing temperatures and was used to reduce the Joule heating effects of electroporation. In our study, cooling was done at below freezing temperatures, which introduced additional complexity in the analysis. Ice has a tight crystalline structure and therefore, frozen tissue is a composite of dielectric pure ice with interspersed high concentration conductive saline pockets [Rubinsky and Pegg, 1988]. This structure suggests that it may be preferable to use alternating current (AC) to transmit electroporation electric fields across the frozen layer, into the tissue. The use of AC may have additional benefits. Ziv et al. [2009] showed that AC delivered in pulse form can reduce electrolysis during electroporation. Several recent studies have shown that sinusoidal AC is as effective as direct current (DC) pulses in producing electroporation [Zhan et al., 2012] with the added benefit of reducing electrolysis [Adamo et al., 2012; Hung and Chang, 2012; Liu et al., 2013]. Bioelectromagnetics
The goal of this study was to investigate sinusoidal AC electroporation field transmission across a layer of frozen material into tissue. The feasibility of the concept was explored through an analytical study in a simple one-dimensional Cartesian configuration of three-layered conductor model for the ice and tissue. Analytical harmonic AC electric fields were calculated by the circuit method. The focus of this study was to elucidate the effect of frequency and ice dielectric properties on the electric fields that develop in the tissue. The analysis was relevant to conventional frequencies of 1 kHz–1 MHz, that is, conventional electroporation pulses. It is further assumed that only a thin layer at the surface of contact between the electrode and the tissue is frozen at high subzero temperatures to facilitate sticking. This can be achieved through the use of a temperature control system at the point of contact. The temperature of the tissue to be treated by electroporation will remain physiological, about 37 8C. This assumption on temperature distribution was actually physically correct for the onset of freezing of tissue [Rubinsky and Cravalho, 1979]. Because of the large change of phase enthalpy in tissue and the heating effect of the blood flow in living tissue in any freezing process, and because the electrode temperature was maintained at a high subzero temperature, the change of phase interface propagated very slowly in relation to a typical electroporation procedure and the temperature of the unfrozen tissue would not change much at the onset of freezing [Rubinsky and Cravalho, 1979]. We performed an analysis on a system relevant to electroporation with typical two-plate electrodes. The modeled system was comprised of three layers of different material (Fig. 1). The first and the third layer were ice with the same thickness x, and the second layer was unfrozen tissue with thickness H. The thickness of each layer was much less than its radius, which allowed for a one-dimensional model. Suppose that the top and bottom of the conductor are two facing circular plate electrodes of the same
Fig.1. Three-layered model.The first and the third layer are salty ice, andthesecondlayeristissue.
Alternating Current Electroporation
radius as the layers. voltage between the two pffiffiThe ffi electrodes is V ¼ 2V 0 sinðvtÞ, where V0 is the voltage magnitude, v ¼ 2pf is the angular frequency, and f is the frequency. The following simplifying assumption was made: The material in each layer was homogeneous at a constant temperature. The electromagnetic parameters of materials were a function of the frequency f and temperature T, that is, the permeability is mi(f,T), the conductivity is si(f,T), and the permittivity is ei(f,T), i ¼ 1, 2, 3. The inductances can be ignored for plate conductors because the thickness is far less than the radius, so the equivalent circuit of this model is a series connection of impedance in the ith layer with resistance Ri and capacitance Ci in parallel. The total impedance between upper and bottom electrodes Z can be calculated from Z¼
X3 i¼1
1 1=Ri þ jvC i
ð1Þ
where j2 ¼ 1. For a plate conductor, after ignoring the fringe effect, the resistance and capacitance can be calculated by Ri ¼ shi iS, C i ¼ shiiS : Then the current density on the surface of two electrodes is given by: Js ¼ P3
V0
i¼1
hi =g i
ez
ð2Þ
where the complex conductivity is gi ¼ si þ jvei. The analysis is relevant to the range of interest in conventional electroporation from 1 kHz to 1 MHz. In this frequency range, the electric field is quasi-static, and the electric field intensity in each layer is Ei ¼
Js gi
ð3Þ
The above analysis is valid for the frequency of conventional electroporation but not valid for nanosecond pulses, which requires the solution of the wave equation. Permeability of both biological tissues and ice was approximately equal to vacuum permeability, that is, relative permeability mri 1 (i ¼ 1, 2, 3). Despite an extensive literature search, we were unable to find data for the dielectric properties of frozen tissue or frozen physiological saline solutions in the frequency range from 1 kHz to 1 MHz. There was some data for dielectric properties of frozen tissue at DC or low frequency AC currents [LePivert et al., 1977]. This data was used to monitor the extent of the frozen region during cryosurgery. There was also some data for the dielectric properties of frozen tissue at high MHz radiofrequencies and microwave frequencies [Mahvi, 2007],
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with applications to food processing [Bassaran-Akgul et al., 2008] and thawing during cryopreservation [Macklis et al., 1979]. The lack of available data for the electromagnetic parameters of frozen tissue in the range of frequencies of interest to electroporation, suggested that deriving this data may be of scientific interest. Some limited electromagnetic data for certain frozen aqueous solutions and ice exists [Lamb, 1946; Addison, 1969; Grimm et al., 2008]. However, the most complete data on dielectric parameters in the frequency range of interest was given for sea ice in references [Buchanan, 2010; Buchanan et al., 2011]. While unfrozen sea ice had a conductivity that is about three times as high as physiological saline, Buchanan provided the most complete set of available data closest to frozen physiological saline. Furthermore, such saline concentrations may be used in actual clinical practice. The primary purpose of freezing was to connect the electrodes to tissue. However, freezing substantially reduced the conductivity of the solution because of the formation of ice. Therefore it is quite possible that a freezing composite solution with an electrical conductivity higher than pure ice will produce good contact and provide higher electric field intensity in tissues. The complex conductivity of sea ice as a function of frequency and temperature was given by [Buchanan, 2010; Buchanan et al., 2011]
0 m
s ðv; T Þ ¼ s DC þ Kðjv Þ þ jve0
x þ e1 1 þ jvt
ð4Þ
where v0 is a dimensionless frequency given by v0 ¼ v0 =1 Hz, the conductivity s ¼ Reðs Þ, and the Þ relative dielectric constant er ¼ Imðs 2pf e0 : We matched the data in [Buchanan, 2010] with polynomial fitting and piecewise interpolation. For the temperature in the range of [23, 8 8C], that is, T2[23, 8 8C], the property coefficients for sea ice took the form: s DC ðS m1 Þ ¼ 3:856 106 T 4 þ 2:747 104 T 3 þ 7:223 103 T 2 þ 8:423 102 T þ 3:871 101 ð5Þ K ðS m1 Þ ¼ 1:664 105 T 4 1:178 103 T 3 3:070 102 T 2 3:508 101 T 1:511 ð6Þ m ¼ 1:196 105 T 3 1:215 103 T 2 3:888 102 T 6:978 101
ð7Þ
Bioelectromagnetics
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Xiao and Rubinsky
8 1:151T 2 23:4T þ 9:956 102 > > < 4 3 x ¼ 1:834T þ 82:82T þ 1:378 3 2 > > 10 T þ 1:004 104 T : þ 2:825 104
T 2 ½23; 14 8CÞ T 2 ½14; 8 8C
ð8Þ t ¼ ð0:2T þ 3Þ 106
ð9Þ
e1 ¼ 2:016 102 T 3 þ 1:14T 2 þ 22:42T þ 163:7
ð10Þ
where the unit of T is 8C. The R2 for s DC ; K; m; x; t; and; e1 are respectively 1.00, 0.99, 0.99, 1.00, 1.00, and 1.00. Dielectric properties of biological tissues at 37 8C were taken from Gabriel et al. [1996]. The complex permittivity as a function of frequency was ^e ðvÞ ¼ e1 þ
X n
Den 1 þ ðjvtn Þ
1an
þ
si jve0
ð11Þ
The parameters used in this expression for tissues in the following were also obtained from this reference. The relative dielectric constant was er ¼ Reð^e Þ and the conductivity was s ¼ veo Imð^e Þ: The conductivity of biological tissues increases and the permittivity decreases as the frequency increases. To explore the effect of frozen matter between the electrode and tissue, we assumed the tissue thickness was constant, H ¼ 4 mm. The tissues studied were liver, kidney, muscle, and wet skin. We assumed that the temperature of tissues is constant at 37 8C, while the temperature of sea ice was from 8 to 23 8C. The electric current density and electric field intensity in a layer of tissue such as liver, kidney, muscle, and wet skin bounded by sea ice vary as a function of the temperature of sea ice and frequency (Fig. 2). The voltage across two electrodes is 100 V and x/H ¼ 0.05, 0.1, 0.15, and 0.2. The dimensionless parameter x/H is used for intuitive proportion. The current density versus frequency and temperature panel for the above four kinds of tissues shows that as the thickness of the ice increases and the temperature decreases, the current density will decrease regardless of the increase in frequency (left column, Fig. 2). This is because the ice, which acts as an insulator at lower temperatures, dominates the dielectric constant of the entire system. The electric field intensity in tissue, an important parameter in electroporation, decreases with an increase in the thickness of ice and a decrease in ice temperature (right column, Fig. 2). However, for a very thin layer of ice of x/H ¼ 0.05 and a relative high subzero temperature of 8 8C, the electric field in the liver tissue is comparable to that in liver without ice, 250 V/cm. Increasing the frequency in the analyzed Bioelectromagnetics
range reduced the electric field intensity, but much less than the relative effects of increase in ice thickness and decrease in ice temperature. For a layer of kidney or muscle bounded by sea ice, the pattern of current and electric field intensity as a function of ice temperature and thickness is qualitatively similar to that for the liver. However, there is a quantitative difference that will be discussed with respect to Figure 3. For instance, the electric field intensity for a very thin layer of ice of x/H ¼ 0.05 and a relative high subzero temperature of 8 8C, is lower than that for the liver with the same configuration. For a layer of wet skin bounded by sea ice, it appears that the skin is very different from the previous discussed tissues. The electric field intensity is very high at low frequency and independent of ice temperature and thickness at those frequencies. This is reasonable and should give confidence in our results. The skin at low frequencies has high impedance matching that of ice. However, at higher frequencies, the electric field intensity decreases because the impedance of the skin decreases. Electroporation of the skin is important in treating melanoma as well as in gene therapy. The ice sticking technology introduced here could have particular value in treating the skin with plate electrodes from the surface. For other tissues such as brain (gray matter), brain (white matter), and lung, the pattern of current density and electric field intensity as a function of ice temperature and thickness is also qualitatively similar to that for the liver. However, the electric current density in white matter is substantially lower than that in gray matter. The pattern in lung is similar to that in white matter both qualitatively and quantitatively. Figure 3 shows the combination of ice thickness and temperature and applied voltage frequency that produces an electric field intensity of 104 V/m for different tissues. We chose this value because it is typical to the lower end of reversible electroporation parameters. Furthermore, because the electric field intensity and the electric current density are directly proportional to the voltage magnitude, it is easy to obtain expected values of electric field intensity by applying different voltage. The data in Figure 3 was compiled from Figure 2. The interesting aspect of this compilation of panels is the observation that different tissue types behave differently in the presence of an ice layer. This suggests that careful analysis will be required when designing freeze sticking electroporation protocols to deliver the desired electroporation fields to the treated tissue. Additionally, we simulated the electric field intensity by finite element method (FEM) using Ansoft Maxwell (v. 12, Ansys, Canonsburg, PA). For the same model of liver, analytical solutions in Equation (3) are
Alternating Current Electroporation
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Fig.2. Current density (left column) andelectricfieldintensity (right column) intissuesofliver, kidney, muscle, and wet skin with frequency and sea ice temperature.V0 ¼100 V.The ratio between ice thickness and tissue from top to bottom surfaces is: x/H ¼ 0.05, 0.1, 0.15, and 0.2.The current density willdecrease asthethicknessof theice increases, and the temperature and frequencydecrease. The electric field intensity will increase as the thickness of the ice and the frequency decrease, andthetemperatureincreases. Bioelectromagnetics
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Fig. 3. The combination of ice thickness and temperature and applied voltage frequency that produces an electric field intensity of 104 V/m for different tissues. Data from Figure 2. On the upper left of the level curve, the electric field intensity is more than104 V/m. For Liver (a), kidney (b), and wet skin (d), the electric field intensity can reach104 V/m when x/H ¼ 0.05, 0.10, 0.15, and 0.20. For muscle (c), theelectricfieldintensityislessthan10 4 V/mwhenx/H ¼ 0.15,0.20.
in agreement with the simulation results. For example, when the temperature of salty ice is at 15 8C and x/ H ¼ 0.05, the electric field intensity for liver at 10 kHz is 1.876 104 V/m by analytical method and 1.872 104 V/m by FEM. In conclusion, we studied the feasibility of using a freeze stick method for attaching electrodes to tissue during electroporation. We made a simplified analysis with suboptimal data. Nevertheless, the analysis suggests this technology is feasible. It was possible to deliver electroporation type electric fields to tissue through ice and therefore to use ice as a mean to firmly attach the electroporation probe to the treated tissue. This technique can overcome some of the technical difficulties of electroporation. To generate higher electric fields in the treated tissue, it is advantageous to use thinner layers of ice at a higher subfreezing temperature and at a lower frequency. Our results are restricted to the range of frequencies we examined, from 1 kHz to Bioelectromagnetics
1 MHz. This range is relevant to the field of electroporation. Obviously much work remains to be done both experimentally in gathering relevant fundamental data and testing the feasibility with tissue and in developing new and more accurate models. The recent interest in nanosecond electroporation pulses further suggests the extension of this study to higher frequencies.
REFERENCES Adamo A, Allesandro A, Sharei A, Jenses KF. 2012. Flow-through comb electroporation device for delivery of macromolecules. Anal Chem 85:1637–1641. Addison JR. 1969. Electrical properties of saline ice. J Appl Phys 40:3105–3114. Bassaran-Akgul N, Basaran P, Rasco BA. 2008. Effects of temperature (5 to 130 8C) and fiber direction on the dielectric properties of beef semi-tendinous at radio frequency and microwave frequency. J Food Sci 73:E243–E249.
Alternating Current Electroporation Buchanan ST. 2010. The low frequency electrical properties of sea ice. A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Physics. Wellington, New Zealand: Victoria University of Wellington. pp 77, 79, 82, and 84. Buchanan S, Ingham M, Gouws G. 2011. The low frequency electrical properties of sea ice. J Appl Phys 110:074908. Becker SM, Kuznetsov AV. 2007. Thermal damage reduction associated with in vivo skin electroporation: A numerical investigation justifying aggressive pre-cooling. Int J Heat Mass Transf 50:105–116. Davalos R, Mir L, Rubinsky B. 2005. Tissue ablation with irreversible electroporation. Ann Biomed Eng 33:223–231. Gabriel S, Lau RW, Gabriel C. 1996. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41:2271–2293. Grimm RE, Stillman DE, Dec SF, Bullock MA. 2008. Lowfrequency electrical properties of polycrystalline saline ice and salt hydrates. J Phys Chem B 112:15382–15390. Hung MS, Chang YT. 2012. Single cell lysis and DNA extending using electroporation microfluidic device. Biochip J 6:84–90. Lamb J. 1946. Measurements of the dielectric properties of ice. Trans Faraday Soc 42A:238–253. Lavee J, Onik G, Mikus P, Rubinsky B. 2007. Novel non-thermal energy source for surgical epicardial atrial ablation: Irreversible electroporation. Heart Surg Forum 10:E162–E167. LePivert PJ, Binder P, Ougier T. 1977. Measurements of intratissue bioelectric low frequency impedance: A new method to predict pre-operatively the destructive effect of cryosurgery. Cryobiology 14:245–250. Lin JC. 1987. Electromagnetic heating techniques for organ rewarming. In: Pegg D, Karow A, editors. Biophysics of organ cryopreservation. New York: Plenum Press. pp 315–335. Liu C, Xie X, Zhao W, Liu N, Maraccini PA, Sassoubre LM, Boehm AB, Cui Y. 2013. Conducting nanosponge electroporation for affordable and high efficiency disinfection of bacteria and viruses in water. Nano Lett 13:4288–4293. Macklis JD, Ketterer FD, Cravalho EG. 1979. Temperature dependence of the microwave properties of aqueous solutions of ethylene glycol between þ15 8C and 70 8C. Cryobiology 16:272–286.
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Mahvi DM. 2007. Dielectric properties of human normal, malignant and cirrhotic liver tissue: In vivo and ex vivo measurements from 0.5 to 20 GHz using a precision open-ended coaxial probe. Phys Med Biol 52:4707–4719. Maor E. 2009. Fundamental study on the effects of irreversible electroporation pulses on blood vessels with application to medical treatment. Ph.D. Thesis, University of California Berkeley. pp 169. Mir LM, Orlowski S, Belehradek J Jr, Paoletti C. 1991. Electrochemotherapy potentiation of antitumor effect of bleomycin by local electric pulses. Eur J Cancer 27:68–72. Neumann E, Schaeffer-Ridder M, Wany Y, Hofschneider PH. 1982. Gene transfer into mouse lymphoma cells by electroporation in high electric fields. EMBO J 1:841–845. Rubinsky B. 2000. Cryosurgery. Ann Rev Biomed Eng 2:157– 187. Rubinsky B, Cravalho EG. 1979. The determination of the thermal history in a one-dimensional freezing system by a perturbation method. ASME Trans J Heat Transf 108:326–330. Rubinsky B, Pegg DE. 1988. A mathematical model for the freezing process in biological tissue. Proc R Soc 234:343– 358. Sale AJH, Hamilton WA. 1967. Effects of high electric fields on microorganisms: I. Killing of bacteria and yeasts. Biochim Biophys Acta 148:781–788. Teissie J, Golzio M, Rols MP. 2005. Mechanisms of cell membrane electropermeabilization: A minireview of our present (lack of?) knowledge. Biochim Biophys Acta 1724:270–280. Thomson KR, Cheung W, Ellis SJ, Federman D, Kavnoudias H, Loader-Oliver D, Roberts S, Evans P, Ball C, Haydon A. 2011. Investigation of the safety of irreversible electroporation in humans. J Vasc Interv Radiol 22:611–621. Weaver J, Chizmadzhev Y. 1996. Theory of electroporation: A review. Bioelectrochem Bioenerg 41:135–160. Zhan YH, Cao ZN, Bao N, Li JB, Wang J, Geng T. 2012. Lowfrequency ac electroporation shows strong frequency dependence and yields comparable transfection results to dc electroporation. J Control Release 160:570–576. Ziv R, Steinhardt Y, Pelled G, Gazit D, Rubinsky B. 2009. Microelectroporation of mesenchymal stem cells with alternating electrical current pulses. Biomed Microdevices 11:95–101.
Bioelectromagnetics
Brief Communication Theoretical Analysis of AC Electric Field Transmission Into Biological TissueThrough Frozen Saline for Electroporation Chunyan Xiao1* and Boris Rubinsky2 1
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China 2 Graduate Program in Biophysics, Department of Mechanical Engineering, UC Berkeley, Berkeley, California
An analytical model was used to explore the feasibility of sinusoidal electric field transmission across a frozen saline layer into biological tissue. The study is relevant to electroporation and permeabilization of the cell membrane by electric fields. The concept was analyzed for frequencies in the range of conventional electroporation frequencies and electric field intensity. Theoretical analysis for a variety of tissues show that the transmission of electroporation type electric fields through a layer of frozen saline into tissue is feasible and the behavior of this composite system depends on tissue type, frozen domain temperature, and frequency. Freezing could become a valuable method for adherence of electroporation electrodes to moving tissue surfaces, such as the heart in the treatment of atrial fibrillation or blood vessels for the treatment of restenosis. Bioelectromagnetics 35:607–613, 2014. © 2014 Wiley Periodicals, Inc. Key words: electroporation; AC electric field; arrhythmias treatment; plate electrodes; frozen saline
Electric pulses of sufficient intensity and from microsecond to millisecond in duration, delivered across the cell membrane, can produce electroporation. Electroporation is the electric field-induced permeabilization of the cell membrane through the formation of nanoscale pores or defects in the membrane [Neumann et al., 1982]. Electroporation has been studied intensively since the 1960’s [Sale and Hamilton, 1967; Weaver and Chizmadzhev, 1996; Teissie et al., 2005]. It was observed that for certain pulse parameters, the cell membrane permeabilization is temporary and that the cell survives the procedure. This is referred to as reversible electroporation (RE). For other parameters, the cells do not survive and this is referred to as irreversible electroporation (IRE). Both RE and IRE are used in medicine for diverse applications such as electrochemotherapy [Mir et al., 1991] and tissue ablation [Davalos et al., 2005]. Electroporation is delivered when electrodes are inserted in tissue or brought into contact with the tissue surface. Clinical electroporation has several technical challenges. One is the need for precise and simultaneous placement of several electrodes into soft tissue [Thomson et al., 2011], or onto moving surfaces such as the heart in the treatment of atrial fibrillation [Lavee 2014 Wiley Periodicals, Inc.
et al., 2007] or blood vessels in the treatment of restenosis [Maor, 2009]. Physicians report that the insertion of multiple needle electrodes in a parallel structure into soft and moving tissue or placement of electrodes on a moving surface is a technical challenge, which substantially extends the length of this otherwise short surgical procedure. In addition, the fluid between the electrode and the tissue is a site for electrolysis with gas bubbles forming. They affect the electric contact and sometimes become ionized and induce an electric discharge associated with sound waves, which is very undesirable. This study explores the feasibility of a technical solution to the problems of electrode placement, inspired by cryosurgery.
*Correspondence to: Chunyan Xiao, School of Automation Science and Electrical Engineering, Beihang University, Xueyuan Road 37, Beijing 100191, China. E-mail: [email protected] Received for review 21 June 2013; Accepted 30 July 2014 DOI: 10.1002/bem.21881 Published online 25 September 2014 in Wiley Online Library (wileyonlinelibrary.com).
608
Xiao and Rubinsky
Cryosurgery, tissue ablation by freezing, is technically similar to IRE [Lin, 1987]. In cryosurgery, several needle-like cryoprobes are inserted in the tissue to form a frozen shape that encompasses the undesirable tissue [Rubinsky, 2000]. A solution to the surgical technical difficulties of cryosurgery is found in the ability of high subzero freezing temperatures to tightly bind between the probe and tissue by creating ice that sticks the probe to the tissue. In conventional cryosurgery, every probe is inserted separately in its position where it is stuck in place by high subzero freezing. This makes it possible to place every probe separately, in relation to each other. The method can be also used to attach cryoprobes to the outer surface of tissue when treating atrial fibrillation by cryosurgery, on or in the heart. It should be emphasized that at high subzero temperatures, that is, higher than about 20 8C, and for short surgery times typical to cryosurgery, freezing causes little damage to biological tissue [Rubinsky, 2000]. In fact, this is considered a drawback of cryosurgery. We proposed that the technical problems of electroporation concerning the placement of electrodes could be overcome by cooling the electroporation electrodes to a high subzero freezing temperature, similar to what is done in cryosurgery. Specifically, we propose that a cooling system in the electroporation electrodes brings the electrodes to a high subzero temperature once the electrodes come into contact with the tissue. Cooling the electroporation electrodes should: (a) Bind the electrode to tissue by sticking; (b) simplify the electrode placement method; (c) produce good electrical contact with the tissue; and (d) eliminate the fluid between electrode and tissue. The idea of cooling the electroporation electrodes was suggested in the past [Becker and Kuznetsov, 2007]. However, in that study, cooling was done at above freezing temperatures and was used to reduce the Joule heating effects of electroporation. In our study, cooling was done at below freezing temperatures, which introduced additional complexity in the analysis. Ice has a tight crystalline structure and therefore, frozen tissue is a composite of dielectric pure ice with interspersed high concentration conductive saline pockets [Rubinsky and Pegg, 1988]. This structure suggests that it may be preferable to use alternating current (AC) to transmit electroporation electric fields across the frozen layer, into the tissue. The use of AC may have additional benefits. Ziv et al. [2009] showed that AC delivered in pulse form can reduce electrolysis during electroporation. Several recent studies have shown that sinusoidal AC is as effective as direct current (DC) pulses in producing electroporation [Zhan et al., 2012] with the added benefit of reducing electrolysis [Adamo et al., 2012; Hung and Chang, 2012; Liu et al., 2013]. Bioelectromagnetics
The goal of this study was to investigate sinusoidal AC electroporation field transmission across a layer of frozen material into tissue. The feasibility of the concept was explored through an analytical study in a simple one-dimensional Cartesian configuration of three-layered conductor model for the ice and tissue. Analytical harmonic AC electric fields were calculated by the circuit method. The focus of this study was to elucidate the effect of frequency and ice dielectric properties on the electric fields that develop in the tissue. The analysis was relevant to conventional frequencies of 1 kHz–1 MHz, that is, conventional electroporation pulses. It is further assumed that only a thin layer at the surface of contact between the electrode and the tissue is frozen at high subzero temperatures to facilitate sticking. This can be achieved through the use of a temperature control system at the point of contact. The temperature of the tissue to be treated by electroporation will remain physiological, about 37 8C. This assumption on temperature distribution was actually physically correct for the onset of freezing of tissue [Rubinsky and Cravalho, 1979]. Because of the large change of phase enthalpy in tissue and the heating effect of the blood flow in living tissue in any freezing process, and because the electrode temperature was maintained at a high subzero temperature, the change of phase interface propagated very slowly in relation to a typical electroporation procedure and the temperature of the unfrozen tissue would not change much at the onset of freezing [Rubinsky and Cravalho, 1979]. We performed an analysis on a system relevant to electroporation with typical two-plate electrodes. The modeled system was comprised of three layers of different material (Fig. 1). The first and the third layer were ice with the same thickness x, and the second layer was unfrozen tissue with thickness H. The thickness of each layer was much less than its radius, which allowed for a one-dimensional model. Suppose that the top and bottom of the conductor are two facing circular plate electrodes of the same
Fig.1. Three-layered model.The first and the third layer are salty ice, andthesecondlayeristissue.
Alternating Current Electroporation
radius as the layers. voltage between the two pffiffiThe ffi electrodes is V ¼ 2V 0 sinðvtÞ, where V0 is the voltage magnitude, v ¼ 2pf is the angular frequency, and f is the frequency. The following simplifying assumption was made: The material in each layer was homogeneous at a constant temperature. The electromagnetic parameters of materials were a function of the frequency f and temperature T, that is, the permeability is mi(f,T), the conductivity is si(f,T), and the permittivity is ei(f,T), i ¼ 1, 2, 3. The inductances can be ignored for plate conductors because the thickness is far less than the radius, so the equivalent circuit of this model is a series connection of impedance in the ith layer with resistance Ri and capacitance Ci in parallel. The total impedance between upper and bottom electrodes Z can be calculated from Z¼
X3 i¼1
1 1=Ri þ jvC i
ð1Þ
where j2 ¼ 1. For a plate conductor, after ignoring the fringe effect, the resistance and capacitance can be calculated by Ri ¼ shi iS, C i ¼ shiiS : Then the current density on the surface of two electrodes is given by: Js ¼ P3
V0
i¼1
hi =g i
ez
ð2Þ
where the complex conductivity is gi ¼ si þ jvei. The analysis is relevant to the range of interest in conventional electroporation from 1 kHz to 1 MHz. In this frequency range, the electric field is quasi-static, and the electric field intensity in each layer is Ei ¼
Js gi
ð3Þ
The above analysis is valid for the frequency of conventional electroporation but not valid for nanosecond pulses, which requires the solution of the wave equation. Permeability of both biological tissues and ice was approximately equal to vacuum permeability, that is, relative permeability mri 1 (i ¼ 1, 2, 3). Despite an extensive literature search, we were unable to find data for the dielectric properties of frozen tissue or frozen physiological saline solutions in the frequency range from 1 kHz to 1 MHz. There was some data for dielectric properties of frozen tissue at DC or low frequency AC currents [LePivert et al., 1977]. This data was used to monitor the extent of the frozen region during cryosurgery. There was also some data for the dielectric properties of frozen tissue at high MHz radiofrequencies and microwave frequencies [Mahvi, 2007],
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with applications to food processing [Bassaran-Akgul et al., 2008] and thawing during cryopreservation [Macklis et al., 1979]. The lack of available data for the electromagnetic parameters of frozen tissue in the range of frequencies of interest to electroporation, suggested that deriving this data may be of scientific interest. Some limited electromagnetic data for certain frozen aqueous solutions and ice exists [Lamb, 1946; Addison, 1969; Grimm et al., 2008]. However, the most complete data on dielectric parameters in the frequency range of interest was given for sea ice in references [Buchanan, 2010; Buchanan et al., 2011]. While unfrozen sea ice had a conductivity that is about three times as high as physiological saline, Buchanan provided the most complete set of available data closest to frozen physiological saline. Furthermore, such saline concentrations may be used in actual clinical practice. The primary purpose of freezing was to connect the electrodes to tissue. However, freezing substantially reduced the conductivity of the solution because of the formation of ice. Therefore it is quite possible that a freezing composite solution with an electrical conductivity higher than pure ice will produce good contact and provide higher electric field intensity in tissues. The complex conductivity of sea ice as a function of frequency and temperature was given by [Buchanan, 2010; Buchanan et al., 2011]
0 m
s ðv; T Þ ¼ s DC þ Kðjv Þ þ jve0
x þ e1 1 þ jvt
ð4Þ
where v0 is a dimensionless frequency given by v0 ¼ v0 =1 Hz, the conductivity s ¼ Reðs Þ, and the Þ relative dielectric constant er ¼ Imðs 2pf e0 : We matched the data in [Buchanan, 2010] with polynomial fitting and piecewise interpolation. For the temperature in the range of [23, 8 8C], that is, T2[23, 8 8C], the property coefficients for sea ice took the form: s DC ðS m1 Þ ¼ 3:856 106 T 4 þ 2:747 104 T 3 þ 7:223 103 T 2 þ 8:423 102 T þ 3:871 101 ð5Þ K ðS m1 Þ ¼ 1:664 105 T 4 1:178 103 T 3 3:070 102 T 2 3:508 101 T 1:511 ð6Þ m ¼ 1:196 105 T 3 1:215 103 T 2 3:888 102 T 6:978 101
ð7Þ
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8 1:151T 2 23:4T þ 9:956 102 > > < 4 3 x ¼ 1:834T þ 82:82T þ 1:378 3 2 > > 10 T þ 1:004 104 T : þ 2:825 104
T 2 ½23; 14 8CÞ T 2 ½14; 8 8C
ð8Þ t ¼ ð0:2T þ 3Þ 106
ð9Þ
e1 ¼ 2:016 102 T 3 þ 1:14T 2 þ 22:42T þ 163:7
ð10Þ
where the unit of T is 8C. The R2 for s DC ; K; m; x; t; and; e1 are respectively 1.00, 0.99, 0.99, 1.00, 1.00, and 1.00. Dielectric properties of biological tissues at 37 8C were taken from Gabriel et al. [1996]. The complex permittivity as a function of frequency was ^e ðvÞ ¼ e1 þ
X n
Den 1 þ ðjvtn Þ
1an
þ
si jve0
ð11Þ
The parameters used in this expression for tissues in the following were also obtained from this reference. The relative dielectric constant was er ¼ Reð^e Þ and the conductivity was s ¼ veo Imð^e Þ: The conductivity of biological tissues increases and the permittivity decreases as the frequency increases. To explore the effect of frozen matter between the electrode and tissue, we assumed the tissue thickness was constant, H ¼ 4 mm. The tissues studied were liver, kidney, muscle, and wet skin. We assumed that the temperature of tissues is constant at 37 8C, while the temperature of sea ice was from 8 to 23 8C. The electric current density and electric field intensity in a layer of tissue such as liver, kidney, muscle, and wet skin bounded by sea ice vary as a function of the temperature of sea ice and frequency (Fig. 2). The voltage across two electrodes is 100 V and x/H ¼ 0.05, 0.1, 0.15, and 0.2. The dimensionless parameter x/H is used for intuitive proportion. The current density versus frequency and temperature panel for the above four kinds of tissues shows that as the thickness of the ice increases and the temperature decreases, the current density will decrease regardless of the increase in frequency (left column, Fig. 2). This is because the ice, which acts as an insulator at lower temperatures, dominates the dielectric constant of the entire system. The electric field intensity in tissue, an important parameter in electroporation, decreases with an increase in the thickness of ice and a decrease in ice temperature (right column, Fig. 2). However, for a very thin layer of ice of x/H ¼ 0.05 and a relative high subzero temperature of 8 8C, the electric field in the liver tissue is comparable to that in liver without ice, 250 V/cm. Increasing the frequency in the analyzed Bioelectromagnetics
range reduced the electric field intensity, but much less than the relative effects of increase in ice thickness and decrease in ice temperature. For a layer of kidney or muscle bounded by sea ice, the pattern of current and electric field intensity as a function of ice temperature and thickness is qualitatively similar to that for the liver. However, there is a quantitative difference that will be discussed with respect to Figure 3. For instance, the electric field intensity for a very thin layer of ice of x/H ¼ 0.05 and a relative high subzero temperature of 8 8C, is lower than that for the liver with the same configuration. For a layer of wet skin bounded by sea ice, it appears that the skin is very different from the previous discussed tissues. The electric field intensity is very high at low frequency and independent of ice temperature and thickness at those frequencies. This is reasonable and should give confidence in our results. The skin at low frequencies has high impedance matching that of ice. However, at higher frequencies, the electric field intensity decreases because the impedance of the skin decreases. Electroporation of the skin is important in treating melanoma as well as in gene therapy. The ice sticking technology introduced here could have particular value in treating the skin with plate electrodes from the surface. For other tissues such as brain (gray matter), brain (white matter), and lung, the pattern of current density and electric field intensity as a function of ice temperature and thickness is also qualitatively similar to that for the liver. However, the electric current density in white matter is substantially lower than that in gray matter. The pattern in lung is similar to that in white matter both qualitatively and quantitatively. Figure 3 shows the combination of ice thickness and temperature and applied voltage frequency that produces an electric field intensity of 104 V/m for different tissues. We chose this value because it is typical to the lower end of reversible electroporation parameters. Furthermore, because the electric field intensity and the electric current density are directly proportional to the voltage magnitude, it is easy to obtain expected values of electric field intensity by applying different voltage. The data in Figure 3 was compiled from Figure 2. The interesting aspect of this compilation of panels is the observation that different tissue types behave differently in the presence of an ice layer. This suggests that careful analysis will be required when designing freeze sticking electroporation protocols to deliver the desired electroporation fields to the treated tissue. Additionally, we simulated the electric field intensity by finite element method (FEM) using Ansoft Maxwell (v. 12, Ansys, Canonsburg, PA). For the same model of liver, analytical solutions in Equation (3) are
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Fig.2. Current density (left column) andelectricfieldintensity (right column) intissuesofliver, kidney, muscle, and wet skin with frequency and sea ice temperature.V0 ¼100 V.The ratio between ice thickness and tissue from top to bottom surfaces is: x/H ¼ 0.05, 0.1, 0.15, and 0.2.The current density willdecrease asthethicknessof theice increases, and the temperature and frequencydecrease. The electric field intensity will increase as the thickness of the ice and the frequency decrease, andthetemperatureincreases. Bioelectromagnetics
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Fig. 3. The combination of ice thickness and temperature and applied voltage frequency that produces an electric field intensity of 104 V/m for different tissues. Data from Figure 2. On the upper left of the level curve, the electric field intensity is more than104 V/m. For Liver (a), kidney (b), and wet skin (d), the electric field intensity can reach104 V/m when x/H ¼ 0.05, 0.10, 0.15, and 0.20. For muscle (c), theelectricfieldintensityislessthan10 4 V/mwhenx/H ¼ 0.15,0.20.
in agreement with the simulation results. For example, when the temperature of salty ice is at 15 8C and x/ H ¼ 0.05, the electric field intensity for liver at 10 kHz is 1.876 104 V/m by analytical method and 1.872 104 V/m by FEM. In conclusion, we studied the feasibility of using a freeze stick method for attaching electrodes to tissue during electroporation. We made a simplified analysis with suboptimal data. Nevertheless, the analysis suggests this technology is feasible. It was possible to deliver electroporation type electric fields to tissue through ice and therefore to use ice as a mean to firmly attach the electroporation probe to the treated tissue. This technique can overcome some of the technical difficulties of electroporation. To generate higher electric fields in the treated tissue, it is advantageous to use thinner layers of ice at a higher subfreezing temperature and at a lower frequency. Our results are restricted to the range of frequencies we examined, from 1 kHz to Bioelectromagnetics
1 MHz. This range is relevant to the field of electroporation. Obviously much work remains to be done both experimentally in gathering relevant fundamental data and testing the feasibility with tissue and in developing new and more accurate models. The recent interest in nanosecond electroporation pulses further suggests the extension of this study to higher frequencies.
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Alternating Current Electroporation Buchanan ST. 2010. The low frequency electrical properties of sea ice. A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Physics. Wellington, New Zealand: Victoria University of Wellington. pp 77, 79, 82, and 84. Buchanan S, Ingham M, Gouws G. 2011. The low frequency electrical properties of sea ice. J Appl Phys 110:074908. Becker SM, Kuznetsov AV. 2007. Thermal damage reduction associated with in vivo skin electroporation: A numerical investigation justifying aggressive pre-cooling. Int J Heat Mass Transf 50:105–116. Davalos R, Mir L, Rubinsky B. 2005. Tissue ablation with irreversible electroporation. Ann Biomed Eng 33:223–231. Gabriel S, Lau RW, Gabriel C. 1996. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41:2271–2293. Grimm RE, Stillman DE, Dec SF, Bullock MA. 2008. Lowfrequency electrical properties of polycrystalline saline ice and salt hydrates. J Phys Chem B 112:15382–15390. Hung MS, Chang YT. 2012. Single cell lysis and DNA extending using electroporation microfluidic device. Biochip J 6:84–90. Lamb J. 1946. Measurements of the dielectric properties of ice. Trans Faraday Soc 42A:238–253. Lavee J, Onik G, Mikus P, Rubinsky B. 2007. Novel non-thermal energy source for surgical epicardial atrial ablation: Irreversible electroporation. Heart Surg Forum 10:E162–E167. LePivert PJ, Binder P, Ougier T. 1977. Measurements of intratissue bioelectric low frequency impedance: A new method to predict pre-operatively the destructive effect of cryosurgery. Cryobiology 14:245–250. Lin JC. 1987. Electromagnetic heating techniques for organ rewarming. In: Pegg D, Karow A, editors. Biophysics of organ cryopreservation. New York: Plenum Press. pp 315–335. Liu C, Xie X, Zhao W, Liu N, Maraccini PA, Sassoubre LM, Boehm AB, Cui Y. 2013. Conducting nanosponge electroporation for affordable and high efficiency disinfection of bacteria and viruses in water. Nano Lett 13:4288–4293. Macklis JD, Ketterer FD, Cravalho EG. 1979. Temperature dependence of the microwave properties of aqueous solutions of ethylene glycol between þ15 8C and 70 8C. Cryobiology 16:272–286.
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Mahvi DM. 2007. Dielectric properties of human normal, malignant and cirrhotic liver tissue: In vivo and ex vivo measurements from 0.5 to 20 GHz using a precision open-ended coaxial probe. Phys Med Biol 52:4707–4719. Maor E. 2009. Fundamental study on the effects of irreversible electroporation pulses on blood vessels with application to medical treatment. Ph.D. Thesis, University of California Berkeley. pp 169. Mir LM, Orlowski S, Belehradek J Jr, Paoletti C. 1991. Electrochemotherapy potentiation of antitumor effect of bleomycin by local electric pulses. Eur J Cancer 27:68–72. Neumann E, Schaeffer-Ridder M, Wany Y, Hofschneider PH. 1982. Gene transfer into mouse lymphoma cells by electroporation in high electric fields. EMBO J 1:841–845. Rubinsky B. 2000. Cryosurgery. Ann Rev Biomed Eng 2:157– 187. Rubinsky B, Cravalho EG. 1979. The determination of the thermal history in a one-dimensional freezing system by a perturbation method. ASME Trans J Heat Transf 108:326–330. Rubinsky B, Pegg DE. 1988. A mathematical model for the freezing process in biological tissue. Proc R Soc 234:343– 358. Sale AJH, Hamilton WA. 1967. Effects of high electric fields on microorganisms: I. Killing of bacteria and yeasts. Biochim Biophys Acta 148:781–788. Teissie J, Golzio M, Rols MP. 2005. Mechanisms of cell membrane electropermeabilization: A minireview of our present (lack of?) knowledge. Biochim Biophys Acta 1724:270–280. Thomson KR, Cheung W, Ellis SJ, Federman D, Kavnoudias H, Loader-Oliver D, Roberts S, Evans P, Ball C, Haydon A. 2011. Investigation of the safety of irreversible electroporation in humans. J Vasc Interv Radiol 22:611–621. Weaver J, Chizmadzhev Y. 1996. Theory of electroporation: A review. Bioelectrochem Bioenerg 41:135–160. Zhan YH, Cao ZN, Bao N, Li JB, Wang J, Geng T. 2012. Lowfrequency ac electroporation shows strong frequency dependence and yields comparable transfection results to dc electroporation. J Control Release 160:570–576. Ziv R, Steinhardt Y, Pelled G, Gazit D, Rubinsky B. 2009. Microelectroporation of mesenchymal stem cells with alternating electrical current pulses. Biomed Microdevices 11:95–101.
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