# Multi-parametric study of temperature and thermal damage of tumor exposed to high-frequency nanosecond-pulsed electric fields based on finite element simulation

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## Abstract

High-frequency nanosecond-pulsed electric fields were recently introduced for tumor or abnormal tissue ablation to solve some problems of conventional electroporation. However, it is necessary to study the thermal effects of high-field-intensity nanosecond pulses inside tissues. The multi-parametric analysis performed here is based on a finite element model of liver tissue with a tumor that has been punctured by a pair of needle electrodes. The pulse voltage used in this study ranges from 1 to 4 kV, the pulse width ranges from 50 to 500 ns, and the repetition frequency is between 100 kHz and 1 MHz. The total pulse length is 100 μs, and the pulse burst repetition frequency is 1 Hz. Blood flow and metabolic heat generation have also been considered. Results indicate that the maximum instantaneous temperature at 100 µs can reach 49 °C, with a maximum instantaneous temperature at 1 s of 40 °C, and will not cause thermal damage during single pulse bursts. By parameter fitting, we can obtain maximum instantaneous temperature at 100 µs and 1 s for any parameter values. However, higher temperatures will be achieved and may cause thermal damage when multiple pulse bursts are applied. These results provide theoretical basis of pulse parameter selection for future experimental researches.

## Keywords

Multi-parameters Temperature Thermal damage Tumor High-frequency nanosecond-pulsed electric fields Finite element method## 1 Introduction

Electroporation, as an intrinsically nonthermal phenomenon, is reversible when electric fields are used up to a specific level, but becomes irreversible at higher field levels. An irreversible electroporation (IRE) treatment includes electrode placement within the target region and delivery of a series of electric pulses of microsecond-scale single pulse duration with a low frequency. These microsecond-long high-voltage pulses can not only cause IRE on a cell membrane and then changes in the cell function, but can also induce biomedical effects such as apoptotic effects, anti-angiogenic effects and immune responses [35, 38]. Ultimately, IRE can achieve the goal of tumor ablation. IRE has recently also been considered as a nonthermal treatment modality to destroy tumors [14, 47, 55]. The most significant advantage of IRE is that it only affects the cell membrane while keeping the extracellular matrix (ECM) around the targeted cells intact by reducing Joule heating [47]. However, statistics from clinical trials show that muscle contraction appears during the pulsed electric field process and the patients suffer from muscle contraction discomfort during the treatment [7, 24]. When the width of the applied electric field pulse is reduced to the ns level, the electric field strength increases to the MV/m level, and the biological effects induced by nanosecond-pulsed electric fields (nsPEFs) are different from those of the aforementioned IRE. While no apparent irreversible electroporation phenomenon occurs on the cell membrane, a series of functional changes occur inside the cell, and then, apoptosis is induced [50, 51]. However, because of the high intensity of the pulsed electric fields that are applied to the electrodes, the treatment may cause surface discharges on the targeted tissue and skin burns.

To combine the advantages of both microsecond pulsed electric field (μsPEF) and nsPEF treatments, we introduced a high-frequency nsPEF protocol for treatment of tumors. Studies have shown that when a high-repetition-rate nsPEF is applied, the number of pulses makes a greater contribution to the killing effects than the field strength and the pulse width. In fact, an increase in the electric field pulse repetition frequency can inhibit patient muscle contraction [1, 10, 37, 39, 46, 57]. Therefore, we forecast that a high-repetition-frequency nsPEF increased to the 100 kHz level will effectively restrain patient muscle contraction. In addition, when the field strength is reduced to less than the breakdown field strength of air (10 kV/cm level), it will also effectively solve the problem of skin burns caused by the electrode discharge during nsPEF treatment. Consequently, the protocols that are proposed in this study can solve the problems of μsPEF and nsPEF treatments in cancer therapy, but also, through a synergistic effect, simultaneously perform the tasks and enhance the effects of inducing tumor cell necrosis and apoptosis. In addition, the high-frequency pulses can produce a more uniform electric field distribution to prevent tumor recurrence [2, 5]. Thus, this protocol is expected to provide a better outcome from cancer treatments.

Finally, it should be noted that high intensity pulsed electric fields will cause Joule heating, which should be avoided in electroporation applications, because temperature control is important even in IRE treatments. Lackovic et al. simulated the temperature distribution of a liver with needle electrodes during and after eight 100 μs, 1500 V/cm pulses and eight 50 ms, 250 V/cm pulses, with a repetition frequency of 1 Hz. The simulation results show that the Joule heating depends on the conductance of the tissue and the pulse parameters [32]. They also found that when the repetition rate increased from 1 Hz to 1 kHz, it could cause the tissue temperature to increase, but still by less than 3 °C [34]. Davalos et al. [15] elaborated on the determination of the temperature distribution and how to assess the thermal effects. They also investigated the temperature distribution and the thermal damage in the brain based on numerical models. The temperature was measured at the same time [21]. Thus, it is essential to pay greater attention to the thermal effects when tissue is exposed to high-frequency nsPEF treatment with a field strength that is greater than 1 kV/cm but less than 10 kV/cm. However, recent studies with regard to the temperature increase aspects of thermal damage are mainly concerned with the thermal effect under a given pulse parameter, or are simply research on the influence of a single parameter on tissue heating [12, 15, 21, 31, 32, 34, 41]. Therefore, in this study, we provide a multi-parameter analysis method to determine the relationship between the thermal effects and the pulse parameters (e.g., pulse width, pulse amplitude, repetition rate) and then to predict the temperature increase and the thermal damage. The results of this work can provide theoretical guidance for parameter selection in future tumor treatments using high-frequency nsPEFs.

## 2 Methods

### 2.1 Finite element model

### 2.2 Parameter model

Material properties

Mass density [ | Heat capacity [Cp (J kg | Thermal conductivity [ | Electrical conductivity [ | Blood perfusion [ | Metabolic heat [ | |
---|---|---|---|---|---|---|

Electrodes | 70 | 1045 | 0.026 | 1e–5 | – | – |

Insulation | 6450 | 840 | 18 | 1e8 | – | – |

Liver | 1080 | 3540 | 0.52 | 0.067 (initial) | 0.0005 | 4200 |

Tumor | 1220 | 4180 | 0.6 | 0.135 (initial) | 0.002 | 42,000 |

With regard to the blood perfusion and metabolic heat generation in biological heat transfer, the blood density and the heat capacity were *ρ* _{b} = 1000 kg/m^{3} and *c* _{b} = 4200 J/(kg K), respectively [28, 36]. Different values for blood perfusion and the metabolic heat of both the liver and the tumor are also listed in Table 1. The value of the blood perfusion and the metabolic heat of the tumor were both larger than that of the liver because of the specific characteristics of the tumor [16, 28, 36]. The temperature coefficient of electrical conductivity was 1.5%. Finally, the initial temperature and the arterial blood temperature were both 37 °C.

### 2.3 Computing method

*T*is the temperature,

*t*is the time,

*ρ*,

*c*and

*k*are the density, the heat capacity and the thermal conductivity of the tissue,

*ω*

_{b}is the blood perfusion,

*ρ*

_{b}and

*c*

_{b}are the density and the heat capacity of blood,

*T*

_{ b }is the temperature of the arterial blood,

*Q*

_{m}is the metabolic heat, and

*Q*is the Joule heating caused by the electric field.

*E* is the electric field and *J* is the current density. The Pennes equation is a thermal–electric coupled field calculation, from which we can obtain the temperature of the biological tissue.

The electrical boundary condition at one electrode–tissue interface was set to be *φ* = *φ*(*t*), and *φ*(*t*) was the time-varying voltage. The other electrode–tissue interface was set at *φ* = 0. The remaining boundaries were treated as electrical insulation and are described by \(\frac{{{\text{d}}\varphi }}{{{\text{d}}n}} = 0\). The outer surface of the liver tissue was set to be thermal insulation.

*Ω*accumulated for time

*t*is represented by the following equation [17]:

*A*(1/s) is the pre-exponential factor,

*E*(J/mol) is the activation energy,

*R*(= 8.314 J/(mol K)) is the universal gas constant and

*T (K)*is the absolute temperature. The damage process and the parameters are listed in Table 2. The parameters used in this computation are the pre-exponential factor

*A*of 7.39e39 (1/

*s*) and the activation energy

*E*of 2.577e5 (J/mol), which represent protein coagulation [23].

Parameters of damage process

Damage process | | |
---|---|---|

Microvascular blood flow stasis | 6.67e5 | 1.98e106 |

Cell death | 5.064e5 | 2.984e80 |

Protein coagulation | 2.577e5 | 7.39e39 |

In terms of finite element modeling of the thermal damage, the value of *Ω* = 1 corresponds to a 63% probability of cell death, while the value of *Ω* = 4.6 represents a 99% probability of cell death due to the thermal effects. And the value of 0.53 is used as the threshold needed for thermal damage [21].

The computations use parameter scanning and transient solutions. Because the elapsed pulse time is very short (the total pulse length is 100 μs), particular attention was paid to the control of the time steps in the variable-step solver. We introduced time steps of 10 ns during the first 100 μs, and then extended the time step to 1 ms up to a total time of 1 s.

## 3 Results

### 3.1 Simulation results for temperature and thermal damage

*P*) with time, and Fig. 4f shows the enlargement of Fig. 4e. They were so much like the figure of thermal damage; just the value of

*P*(%) is 100 times larger than thermal damage.

The maximum instantaneous temperature at 100 µs and maximum instantaneous thermal damage at 1 s that can be acquired are 49.26 °C and 0.0016, respectively.

### 3.2 Relationship between thermal effects and pulse parameters

### 3.3 Determination of pulse parameters without causing thermal damage

By calculating the electric field coupling with the thermal fields based on finite element simulations, the temperature and thermal damage profiles were obtained. On this basis, the data were analyzed to draw these figures and to pave the way for subsequent data fitting and estimation processes.

## 4 Discussion

### 4.1 Prediction of temperature and thermal damage under high-frequency nanosecond pulse bursts

*T*

_{m}(°C) and

*T*

_{f}(°C) are the maximum instantaneous temperature at 100 µs and the maximum instantaneous temperature at 1 s in the tumor, respectively,

*T*

_{0}(= 37 °C) is the initial temperature,

*p*

_{w}(ns) is the pulse width,

*f*(kHz) is the repetition frequency,

*V*is the voltage applied to the electrodes and

*N*is the number of pulse bursts. In this simulation, we run for only one pulse burst. However, it can be roughly estimated that the temperature will increase after multiple pulse bursts by a factor of

*N*.

*x*-axis represents the number of pulse bursts and the

*y*-axis represents the temperature increase in the tumor. The curve is when pulse voltage is 4000 V, pulse width is 500 ns, and pulse repetition is 1 MHz. From Fig. 9, we can see when increase the number of pulse burst to 8, temperature will reach to 75 °C, which may cause instantaneous thermal damage in tumor. According to this method, we can get the temperature rise under multiple pulse bursts. However, in fact, the temperature rise after each pulse burst is not the same as the number of pulses increases. When the temperature of biological tissue continues to rise, the cooling process is also become more obvious. If we assume that the temperature rise is same after each pulse burst, we can get an upper bound on the maximum temperature. Because the thermal damage is associated with the time integral of the temperature, it will reach such heights to cause the thermal damage when subjected to several bursts of pulses. This demonstrates the cumulative effect of the temperature and is related to the enclosed area below the curve. Consequently, we can roughly estimate the temperature increase in the tumor for a parameter choice that does not cause thermal damage. It should also be noted that when the treatment outcome is taken into consideration, we should impose more bursts of pulses. We should then wipe out a portion of the area near the electrodes because of the hot spots that always exist when performing an analysis of the thermal effects for parameter selection. However, it has still to be determined whether the removed segment is sufficient to meet the clinical requirements.

### 4.2 Limitations of the simulations

- 1
First, this paper studies the influence of multiple parameters (voltage, pulse width and frequency) of high-frequency nanosecond pulses on the thermal effects. The number of values for each parameter that we discussed is only four. Even so, 64 parameter combinations are sufficient for a study of the rules, and more parameters could greatly increase the difficulty of the calculations. Unlike other studies in the literature, in which only a few parameters are studied [6, 19–24 31], this analysis was designed to be based on a multi-parameter perspective to determine the rules for fitting and estimating these parameters.

- 2
Second, some measurements have been performed to study the nonlinear increase in the tissue conductivity during IRE and nsPEF therapies when the tissues are exposed to sufficiently high electric fields [22, 26, 40, 45, 52]. However, few studies have been performed on the changing conductivity characteristics of tissue when subjected to high-frequency composite pulses. Bhonsle et al. [6] measured the conductivity before and after application of high-frequency bipolar pulses. The protocols in this simulation used high-frequency unipolar pulses and the changes in conductivity remain unclear. To simplify the calculations, we used a simple model of conductivity changes instead. The initial electrical conductivity of the rat liver that we used in this study was 0.067 S/m and the conductivity of the tumor was 0.135 S/m. When the tissue was electroporated, the electrical conductivity of the liver increased to 0.241 S/m and that of tumor increased to 0.426 S/m. Neal et al. used an equivalent circuit of a cell to analyze the bioimpedance behavior. A variable resistance was introduced to represent the macroscopic behavior of tissue under the influence of pulsed electric fields. When effective electric fields are applied, the resistance is a function of only the intra- and extracellular resistances because the variable resistance is short-circuited. The same effect is produced when the frequency of the pulses is high enough to make the capacitive component of the cell membrane short circuit [52]. The behavior of a single cell can be scaled to represent that of a larger tissue sample [18, 19]. In this way, we can obtain a method to estimate the increase in electrical conductivity that occurs when electroporation and the high-frequency components of the pulses produce a synergistic effect for further study.

- 3
Third, the threshold field for electroporation that was used in this study was 800 V/cm [4, 14]. However, as the pulse frequency increases, the permeabilization thresholds also increase [25, 49]. Different protocols may cause different increases in the threshold value. We can hardly set an increased electric field threshold for high-frequency nsPEF treatment casually without performing a great deal of preparatory experimental research. This article is intended to provide a simulation method to study the thermal effects, and therefore, it is acceptable to use the threshold field for irreversible electroporation.

- 4
Finally, this study of temperature and thermal damage has been performed on the basis of numerical simulations and thus lacks experimental verification. Despite this, the study is useful from the perspective of using multiple parameters to investigate the relationship between the thermal effect and the pulse parameters (voltage, pulse width and repetition frequency) under application of high-frequency nanosecond composite pulses.

### 4.3 Future work

It is important to obtain accurate values of the changes in conductivity to calculate the electric field distribution and predict the outcomes of use of high-frequency pulses and the thermal effects. There are many studies that have measured the increases in tissue conductivity during electroporation-based protocols [9, 11, 26, 27, 29, 45]. The feasibility of using electrical impedance tomography [11, 13] and magnetic resonance electrical impedance tomography [29, 30] to monitor the electric field distributions has also been suggested. Our next work is to measure the conductivity of tissue when subjected to high-frequency nanosecond pulses, and to verify the effects of the high-frequency components on the electrical conductivity.

Temperature measurement is also vital to verify the accuracy of the models by comparing the experiment results with those of the theoretical calculations. Garcia et al. used a fiber optic temperature sensor to measure the temperature inside the tissue [12, 22]. A thermocouple was used by Pliquett et al [44]. for bulk temperature measurements, while temperature-sensitive liquid crystal was also used to measure the surface temperature. A thermal camera can also be used to capture the surface temperatures [6].

From a local viewpoint, the protocol proposed in this study can be viewed as use of high-frequency nanosecond pulses, but it also has the characteristics of microsecond pulses overall. Further research is necessary to assess the treatment outcomes, including the mechanism when a tumor is exposed to such pulses. In general, when applying IER pulses, it will appear on the cell membrane of several nanometers to several tens of nanometers pores. The poles with several nanometers size will recover while pores with tens of nanometers size will continue to expand to several hundred nanometers or micrometers, which are irreversible. But when applying low-frequency nsPEF, it will also appear on pores of several nanometers size, which are reversible. So when apply high-frequency nsPEF, it will produce some small nanopores at the beginning, and then, because the total pulse time is 100 μs, the nanopores may be expanded like IRE. We assume that nsPEFs can produce nanopores on the cell membrane, which will promote irreversible electroporation on the cell membrane by μsPEF. When the outer membranes have been corrupted, this will have beneficial effects for electroporation of the organelle membrane to induce apoptosis. There is a hypothesis that nsPEFs combined with μsPEFs are applied on both the inner and outer membrane, inducing tumor cell necrosis and apoptosis by a direct killing effect and slow indirect regulation, but numerous experiments are still required to verify this hypothesis.

## 5 Conclusions

In this study, we have presented a type of pulse protocol for electroporation-based therapies. The pulse voltage used is in the range from 1 to 4 kV, and the pulse width ranges from 50 ns to 500 ns, while the repetition frequency is in the range between 100 kHz and 1 MHz. The total pulse length is 100 μs, and the repetition rate of the pulse bursts is 1 Hz. To analyze the thermal effect on the tumor, simulation models were developed based on finite element methods. Results from the simulations indicate that the maximum instantaneous temperature at 100 µs is up to 49.26 °C, and the maximum instantaneous temperature at 1 s and maximum instantaneous thermal damage at 1 s reach values of 40.4 °C and 0.0016, respectively, during a single pulse burst. Through multi-parameter analysis, we can obtain rules on how the pulse parameters affect the temperature and the thermal damage. By parameter fitting, maximum instantaneous temperature at 100 µs and 1 s for any parameter value after a single pulse burst or multiple pulse bursts can be calculated. In addition, higher temperatures are likely to be achieved and may cause thermal damage, based on parameter estimation when several bursts of pulses are applied. The results of temperature and thermal damage calculations performed using different high-frequency nsPEF parameters can provide a theoretical basis for selection of parameter options for experimental research.

## Notes

### Acknowledgements

This study was funded by the National Natural Science Foundation of China (51477022, 51321063), the Natural Science Foundation Project of CQ CSTC (cstc2014jcyjjq90001) and the Fundamental Research Funds for the Central Universities (No. 106112015CDJZR158804).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- 1.Arena CB, Sano MB, Rossmeisl JH, Caldwell JL, Garcia PA, Rylander MN, Davalos RV (2011) High-frequency irreversible electroporation (H-FIRE) for non-thermal ablation without muscle contraction. Biomed Eng Online 10:102CrossRefPubMedPubMedCentralGoogle Scholar
- 2.Arena CB, Sano MB, Rylander MN, Davalos RV (2011) Theoretical considerations of tissue electroporation with high frequency bipolar pulses. IEEE Trans Bio-med Eng 58(5):1474–1482CrossRefGoogle Scholar
- 3.Arena CB, Szot CS, Garcia PA (2012) A three-dimensional in vitro tumor platform for modeling therapeutic irreversible electroporation. Biophys J 103(9):2033–2042CrossRefPubMedPubMedCentralGoogle Scholar
- 4.Bertacchini C, Margotti PM, Bergamini E et al (2007) Design of an irreversible electroporation system for clinical use. Technol Cancer Res Treat 6(4):313–320CrossRefPubMedGoogle Scholar
- 5.Bhonsle SP, Arena CB, Davalos RV (2015) A feasibility study to mitigate tissue-tumor heterogeneity using high frequency bipolar electroporation pulses. 6th European conference of the international federation for medical and biological engineering, vol 45. Springer international publishing, pp 565–568Google Scholar
- 6.Bhonsle SP, Arena CB, Sweeney DC, Davalos RV (2015) Mitigation of impedance changes due to electroporation therapy using bursts of high-frequency bipolar pulses. Biomed Eng Online 14(Suppl 3):S3CrossRefPubMedPubMedCentralGoogle Scholar
- 7.Breton M, Mir LM (2012) Microsecond and nanosecond electric pulses in cancer treatments. Bioelectromagnetics 33:106–123CrossRefPubMedGoogle Scholar
- 8.Chang IA, Nguyen UD (2004) Thermal modeling of lesion growth with radiofrequency ablation devices. Biomed Eng Online 3:27CrossRefPubMedPubMedCentralGoogle Scholar
- 9.Cima LF, Mir LM (2004) Macroscopic characterization of cell electroporation in biological tissue based on electrical measurements. Appl Phys 85:4520–4522Google Scholar
- 10.Daskalov I, Mudrov N, Peycheva E (1999) Exploring new instrumentation parameters for electrochemotherapy—Attacking tumors with bursts of biphasic pulses instead of single pulses. IEEE Eng Med Biol 18(1):62–66CrossRefGoogle Scholar
- 11.Davalos RV, Rubinsky B, Otten DM (2002) A feasibility study for electrical impedance tomography as a means to monitor tissue electroporation for molecular medicine. IEEE Trans Biomed Eng 49(4):400–403CrossRefPubMedGoogle Scholar
- 12.Davalos RV, Rubinsky B, Mir LM (2003) Theoretical analysis of the thermal effects during in vivo tissue electroporation. Bioelectrochemistry 61(1–2):99–107CrossRefPubMedGoogle Scholar
- 13.Davalos RV, Otten DM, Mir LM, Rubinsky B (2004) Electrical impedance tomography for imaging tissue electroporation. IEEE Trans Biomed Eng 51(5):761–767CrossRefPubMedGoogle Scholar
- 14.Davalos RV, Mir ILM, Rubinsky B (2005) Tissue ablation with irreversible electroporation. Ann Biomed Eng 33(2):223–231CrossRefPubMedGoogle Scholar
- 15.Davalos RV, Garcia PA, Edd JF (2010) Thermal aspects of irreversible electroporation. In: Irreversible electroporation. Springer, Berlin, pp 123–154Google Scholar
- 16.Deng ZS, Jing L (2004) Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics. Comput Biol Med 34(6):495–521CrossRefPubMedGoogle Scholar
- 17.Diller KR, Valvano JW, Pearce JA (2000) The CRC handbook of thermal engineering. CRC Press LLC, Boca RatonGoogle Scholar
- 18.Esser Axel T, Smith Kyle C, Gowrishankar Thiravallur R, Weaver JC (2007) Towards solid tumor treatment by irreversible electroporation: Intrinsic redistribution of fields and currents in tissue. Technol Cancer Res Treat 6:261–273CrossRefPubMedGoogle Scholar
- 19.Fricke H (1924) A mathematical treatment of the electric conductivity and capacity of disperse systems: I. The electric conductivity of a suspension of homogeneous spheroids. Phys Rev 24:575CrossRefGoogle Scholar
- 20.Garcia PA, Rossmeisl JH, Ii REN, Ellis TL, Olson JD, Henao-Guerrero N et al (2010) Intracranial nonthermal irreversible electroporation: in vivo analysis. J Membr Biol 236(1):127–136CrossRefPubMedGoogle Scholar
- 21.Garcia PA, Rossmeisl JH Jr, Neal RE 2nd, Ellis TL, Davalos RV (2011) A parametric study delineating irreversible electroporation from thermal damage based on a minimally invasive intracranial procedure. Biomed Eng Online 10:34CrossRefPubMedPubMedCentralGoogle Scholar
- 22.Garcia PA, Neal RE, Sano MB, Robertson JL, Davalos RV (2011) An experimental investigation of temperature changes during electroporation. In: General assembly and scientific symposium, 2011 XXXth URSI. IEEE, Istanbul, Turkey, pp 1–4Google Scholar
- 23.Garcia PA, Davalos RV, Miklavcic D (2014) A numerical investigation of the electric and thermal cell kill distributions in electroporation-based therapiesin tissue. PLoS ONE 8(9):1–12Google Scholar
- 24.Golberg A, Yarmush ML (2013) Nonthermal irreversible electroporation fundamentals, applications, and challenges. IEEE Trans Biomed Eng 60(3):707–714CrossRefPubMedGoogle Scholar
- 25.Ibey BL, Xiao S, Schoenbach KH, Murphy MR, Pakhomov AG (2009) Plasma membrane permeabilization by 60- and 600-ns electric pulses is determined by the absorbed dose. Bioelectromagnetics 30(2):92–99CrossRefPubMedPubMedCentralGoogle Scholar
- 26.Ivorra A, Rubinsky B (2007) In vivo electrical impedance measurements during and after electroporation of rat liver. Bioelectrochemistry 70(2):287–295CrossRefPubMedGoogle Scholar
- 27.Ivorra A, Al-Sakere B, Rubinsky B, Mir LM (2009) In vivo electrical conductivity measurements during and after tumor electroporation: conductivity changes reflect the treatment outcome. Phys Med Biol 54(19):5949–5963CrossRefPubMedGoogle Scholar
- 28.Jamil M, Ng EYK (2013) To optimize the efficacy of bioheat transfer in capacitive hyperthermia: a physical perspective. J Therm Bio 38(5):272–279CrossRefGoogle Scholar
- 29.Kranjc M, Bajd F, Sersa I, Miklavcic D (2011) Magnetic resonance electrical impedance tomography for monitoring electric field distribution during tissue electroporation. IEEE Trans Med Imaging 30(10):1771–1778CrossRefPubMedGoogle Scholar
- 30.Kranjc M, Bajd F, Sersa I, Woo EJ, Miklavcic D (2012) Ex vivo and in silico feasibility study of monitoring electric field distribution in tissue during electroporation based treatments. PLoS ONE 7(9):e45737CrossRefPubMedPubMedCentralGoogle Scholar
- 31.Kurata K, Nomura S, Takamatsu H (2014) Three-dimensional analysis of irreversible electroporation: estimation of thermal and non-thermal damage. Int J Heat Mass Transf 72(5):66–74CrossRefGoogle Scholar
- 32.Lackovic I, Magjarević R, Miklavcic D (2007) Analysis of tissue heating during electroporation based therapy: a 3D FEM model for a pair of needle electrodes. 11th mediterranean conference on medical and biomedical engineering and computing 2007. Springer, Berlin, Heidelberg, pp 631–634Google Scholar
- 33.Lackovic I, Magjarevic R, Miklavcic D (2009) Three-dimensional finite-element analysis of joule heating in electrochemotherapy and in vivo gene electrotransfer. IEEE Trans Dielectr Electr Insul 16(5):1338–1347CrossRefGoogle Scholar
- 34.LackoviĆ I, Magjarević R, Miklavčič D (2009) A multiphysics model for studying the influence of pulse repetition frequency on tissue heating during electrochemotherapy. 4th European conference of the international federation for medical and biological engineering. Springer, Berlin, Heidelberg, pp 2609–2613Google Scholar
- 35.Luo X (2007) An experimental study of energy controllable steep pulse in the treatment of rat with subcutaneous transplantive tumor. J Biomed Eng 24(3):492–495Google Scholar
- 36.Lv YG, Deng ZS, Liu J (2005) 3-d numerical study on the induced heating effects of embedded micro/nanoparticles on human body subject to external medical electromagnetic field. IEEE Trans Nanobiosci 4(4):284–294CrossRefGoogle Scholar
- 37.Marty M et al (2006) Electrochemotherapy—An easy, highly effective and safe treatment of cutaneous and subcutaneous metastases: results of ESOPE study. Eur J Cancer Suppl 4(11):3–13CrossRefGoogle Scholar
- 38.Mi Y (2007) Effect of steep pulsed electric fields on the immune response of tumor-bearing wistar mice. J Biomed Eng 24(2):253–256Google Scholar
- 39.Miklavčič D, Pucihar G, Pavlovec M, Ribarič S, Mali M, Maček-Lebar A, Petkovšek M, Nastran J, Kranjc S, Čemažar M, Serša G (2005) The effect of high frequency electric pulses on muscle contractions and antitumor efficiency in vivo for a potential use in clinical electrochemotherapy. Bioelectrochemistry 65:121–128CrossRefPubMedGoogle Scholar
- 40.Neal RE II, Garcia PA, Robertson JL, Davalos RV (2012) Experimental characterization and numerical modeling of tissue electrical conductivity during pulsed electric fields for irreversible electroporation treatment planning. IEEE Trans Biomed Eng 59:1076–1085CrossRefPubMedGoogle Scholar
- 41.Pavšelj N, Miklavčič D (2011) Resistive heating and electropermeabilization of skin tissue during in vivo electroporation: a coupled nonlinear finite element model. Int J Heat Mass Trans 54:2294–2302CrossRefGoogle Scholar
- 42.Pearce JA (2009) Relationship between Arrhenius models of thermal damage and the CEM 43 thermal dose. In: Proceedings of SPIE, Energy-based treatment of tissue and assessment V, vol 7181, p 718104. doi: 10.1117/12.807999
- 43.Pennes HH (1998) Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 85:5–34PubMedGoogle Scholar
- 44.Pliquett U, Nuccitelli R (2014) Measurement and simulation of joule heating during treatment of b-16 melanoma tumors in mice with nanosecond pulsed electric fields. Bioelectrochemistry 100:62–68CrossRefPubMedGoogle Scholar
- 45.Pliquett U, Schoenbach K (2009) Changes in electrical impedance of biological matter due to the application of ultrashort high voltage pulses. IEEE Trans Dielectr Electr Insul 16:1273CrossRefGoogle Scholar
- 46.Pucihar G, Mir LM, Miklavčič D (2002) The effect of pulse repetition frequency on the uptake into electropermeabilized cells in vitro with possible applications in electrochemotherapy. Bioelectrochemistry 57:167–172CrossRefPubMedGoogle Scholar
- 47.Rubinsky B (2007) Irreversible electroporation in medicine. Technol Cancer Res Treat 6(4):255–260CrossRefPubMedGoogle Scholar
- 48.Sahakian Alan V, Al-Angari Haitham M, Adeyanju Oyinlolu O (2012) Electrode activation sequencing employing conductivity changes in irreversible electroporation tissue ablation. IEEE Trans Biomed Eng 59(3):604–607CrossRefPubMedGoogle Scholar
- 49.Sano MB, Arena CB, DeWitt MR, Saur D, Davalos RV (2014) In vitro bipolar nano-and microsecond electro-pulse bursts for irreversible electroporation therapies. Bioelectrochemistry 100:69–79CrossRefPubMedGoogle Scholar
- 50.Schoenbach KH, Beebe SJ, Buescher ES (2001) Intracellular effect of ultrashort electrical pulses. Bioelectromagnetics 22(6):440–448CrossRefPubMedGoogle Scholar
- 51.Schoenbach KH, Hargrave B, Joshi RP, Kolb JF, Nuccitelli R, Osgood C, Pakhomov A, Stacey M, Swanson RJ, White JA, Xiao S, Zhang J, Beebe SJ, Blackmore PF, Buescher ES (2007) Bioelectric effects of intense nanosecond pulses. IEEE Trans Dielectr Electr Insul 14(5):1088–1109CrossRefGoogle Scholar
- 52.Sel D, Cukjati D, Batiuskaite D, Slivnik T, Mir LM et al (2005) Sequential finite element model of tissue electropermeabilization. IEEE Trans Biomed Eng 52:816–827CrossRefPubMedGoogle Scholar
- 53.Shafiee H, Garcia PA, Davalos RV (2009) A preliminary study to delineate irreversible electroporation from thermal damage using the arrhenius equation. J Biomech Eng 131:074509CrossRefPubMedGoogle Scholar
- 54.Thomsen S, Pearce JA (2011) Thermal damage and rate processes in biologic tissues. In: Welch AJ, van Gemert MJC (eds) Optical-thermal response of laser irradiated tissue, 2nd edn. Springer Science + Business Media B.V, Berlin, pp 487–549Google Scholar
- 55.Thomson KR, Cheung W, Ellis SJ, Park 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(5):611–621CrossRefPubMedGoogle Scholar
- 56.Yao CG, Zhao YJ, Dong SL, Chen R, Liao RJ (2015) Optimization of the treatment planning for the tumor ablation of irreversible electroporation based on genetic algorithm. High voltage engineering
**(in press)**Google Scholar - 57.Zupanic A, Ribaric S, Miklavcic D (2007) Increasing the repetition frequency of electric pulse delivery reduces unpleasant sensations that occur in electrochemotherapy. Neoplasma 54(3):246–250PubMedGoogle Scholar

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