# Development of an endothermic electrode for electroporation-based therapies: A simulation study: Applied Physics Letters: Vol 117, No 14

Irreversible electroporation (IRE) is regarded as a non-thermal, focal tumor ablation technology that has been applied to a variety of cancers.11. K. N. Aycock and
R. V. Davalos, Bioelectricity 1, 214–234 (2019). doi.org/10.1089/bioe.2019.0029
IRE employs a series of intensive and short duration pulsed electric fields (PEFs) to induce a critical transmembrane potential (TMP) across cell membranes, which leads to the formation of unrecoverable defects, and causes an increase in cell membrane permeability and eventually promotes cell death because of the loss of cell homeostasis.22. T. Kotnik,
L. Rems,
M. Tarek, and
D. Miklavcic, Annu. Rev. Biophys. 48, 63 (2019). doi.org/10.1146/annurev-biophys-052118-115451
As the applied PEFs are of low energy, cell death is mediated by non-thermal mechanisms, thereby discerning IRE as a non-thermal tumor therapy. With this non-thermal advantage, IRE can be used to treat thermal-sensitive organs with unresectable tumors encasing large blood vessels or ducts, which remains a challenge for thermal ablation technologies.33. A. Golberg and
M. L. Yarmush, IEEE Trans. Biomed. Eng. 60(3), 707 (2013). doi.org/10.1109/TBME.2013.2238672
In practical application, it is necessary to determine treatment protocols before applying pulses according to the geometry and properties of the target tissue,44. J. F. Edd and
R. V. Davalos, Technol. Cancer Res. Treat 6(4), 275 (2007). doi.org/10.1177/153303460700600403
termed as treatment planning. Treatment planning is an optimization of pulse parameters and arrangement of needle electrodes with the goal of providing sufficient electric field coverage of the tumor, while Joule heating is minimized to avoid thermal damage.5,65. A. Zupanic,
B. Kos, and
D. Miklavcic, Phys. Med. Biol. 57(17), 5425 (2012). doi.org/10.1088/0031-9155/57/17/5425
6. A. Županič,
S. Čorović, and
D. Miklavčič, Radiol. Oncol. 42(2), 93 (2008). doi.org/10.2478/v10019-008-0005-5
However, the temperature rise near the electrodes is often higher than that at the center of the ablation zone and induces some thermal effects in the vicinity of the electrodes,77. P. Agnass,
E. van Veldhuisen,
M. J. C. van Gemert,
C. W. M. van der Geld,
K. P. van Lienden,
T. M. van Gulik,
M. R. Meijerink,
H. P. Kok, and
J. Crezee, Int. J. Hyperthermia 37(1), 486 (2020). doi.org/10.1080/02656736.2020.1753828
especially in cases where aggressive pulsing protocols are desired for larger ablations.88. E. Ben-David,
L. Appelbaum,
J. Sosna,
I. Nissenbaum, and
S. N. Goldberg, Am. J. Roentgenol. 198(1), W62 (2012). doi.org/10.2214/AJR.11.6940
Neglecting to consider thermal damage can induce some complications if the electrodes are placed adjacent to critically sensitive structures,99. B. Geboers,
H. J. Scheffer,
P. M. Graybill,
A. H. Ruarus,
S. Nieuwenhuizen,
R. S. Puijk,
P. M. van den Tol,
R. V. Davalos,
B. Rubinsky,
T. D. de Gruijl,
D. Miklavčič, and
like vessel damage and coagulative necrosis of venules and bile ducts.1010. J. Zmuc,
G. Gasljevic,
G. Sersa,
I. Edhemovic,
N. Boc,
A. Seliskar,
T. Plavec,
M. Brloznik,
N. Milevoj,
E. Brecelj,
B. Kos,
J. Izlakar,
T. Jarm,
M. Snoj,
M. Stukelj,
D. Miklavcic, and
M. Cemazar, Sci. Rep. 9(1), 3649 (2019). doi.org/10.1038/s41598-019-40395-y
Also, a greater thermal dose could lead to less capase-3 production, preventing activation of apoptotic pathways.1111. M. Faroja,
M. Ahmed,
L. Appelbaum,
E. Ben-David,
M. Moussa,
J. Sosna,
I. Nissenbaum, and
These were reported in previous electroporation-based therapies, such as electrochemotherapy (ECT),1010. J. Zmuc,
G. Gasljevic,
G. Sersa,
I. Edhemovic,
N. Boc,
A. Seliskar,
T. Plavec,
M. Brloznik,
N. Milevoj,
E. Brecelj,
B. Kos,
J. Izlakar,
T. Jarm,
M. Snoj,
M. Stukelj,
D. Miklavcic, and
M. Cemazar, Sci. Rep. 9(1), 3649 (2019). doi.org/10.1038/s41598-019-40395-y
electrogene therapy (EGT),1212. I. Lackovic,
R. Magjarevic, and
D. Miklavcic, IEEE Trans. Dielectr. Electr. Insul. 16(5), 1338 (2009). doi.org/10.1109/TDEI.2009.5293947
and IRE.1313. P. A. Garcia,
R. V. Davalos, and
D. Miklavcic, PLoS One 9(8), e103083 (2014). doi.org/10.1371/journal.pone.0103083
In addition, the temperature rise during treatment can cause significant increases in tissue conductivity.1414. F. A. Duck, Physical Properties of Tissues: A Comprehensive Reference Book (
Higher conductivity can induce a higher output current, which may initiate unintended treatment termination because of the protection mechanisms embedded in the equipment.1515. C. Bertacchini,
P. M. Margotti,
E. Bergamini,
A. Lodi,
M. Ronchetti, and
R. Cadossi, Technol. Cancer Res. Treat. 6(4), 313 (2007). doi.org/10.1177/153303460700600408
These issues are also critical for high-frequency IRE (HFIRE) treatment—with benefits of mitigating muscle contraction—which requires the application of higher PEFs to get similar ablation zones to IRE.1616. M. B. Sano,
C. B. Arena,
K. R. Bittleman,
M. R. DeWitt,
H. J. Cho,
C. S. Szot,
D. Saur,
J. M. Cissell,
J. Robertson,
Y. W. Lee, and
R. V. Davalos, Sci. Rep. 5, 14999 (2015). doi.org/10.1038/srep14999
Therefore, reducing thermal effects during IRE treatment is an important aspect that needs to be improved.
Recently, a cycled pulsing approach for multi-electrode IRE was reported in which pulses were split into individual pulse cycles and a delay was inserted between cycles; the optimization of this sequence enabled a preservation of ablation volume for a given pulse protocol while substantially reducing thermal effects.1717. T. J. O'Brien,
M. F. Lorenzo,
Y. Zhao,
R. E. Neal Ii,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 36(1), 953–963 (2019). doi.org/10.1080/02656736.2019.1657187
This is a methodology to reduce thermal effects by adjusting only the pulse parameters or the pulse delivery scheme, which is similar to the previous study by manipulating the pulse timing.1818. C. Jiang,
Q. Shao, and
J. Bischof, Ann. Biomed. Eng. 43(4), 887 (2015). doi.org/10.1007/s10439-014-1133-2
Aside from these, others have investigated reducing thermal effects by using modified electrodes. Electrodes with an embedded phase change material (PCM) can store heat as the PCM transitions from solid to liquid, which can limit temperature rise during treatment.19,2019. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, Appl. Phys. Lett. 101(8), 083902 (2012). doi.org/10.1063/1.4747332
20. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, J. Biomech. Eng. 135(11), 111009 (2013). doi.org/10.1115/1.4025334
However, the melting point for a specific material is fixed, and the PCM remains inactivated until the temperature reaches that critical value. Thus, PCM electrodes are passive and depend upon creating a pulsing protocol which maximizes the time above this critical temperature. Electrodes with an internal cooling system were also proposed to mitigate thermal effects, and this system can work throughout the whole treatment process.2121. T. J. O'Brien,
M. Bonakdar,
S. Bhonsle,
R. E. Neal,
C. H. Aardema, Jr.,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 35(1), 44 (2018). doi.org/10.1080/02656736.2018.1473893
However, it needs an external perfusion system which increases the complexity of operation. This might be feasible for one bipolar probe, but it would be cumbersome with 4–6 probes, which are usually used in the clinic. Notably, PCM electrodes or actively cooled electrodes can be used in conjunction with cycled pulsing to further amplify thermal reduction effects during IRE.
In this study, we propose the use of endothermic reactions within a hollow electrode to absorb the Joule heating generated during IRE; such a chemical reaction is controllable and free of other assistant systems. Endothermic reactions/processes absorb heat from their ambient environment and historically have been used to cooldown electronics.2222. J. O. Coulter, U.S. patent US 10,063,270 B2 (2018). The dissolution of ammonium nitrate (NH4NO3) in water is a typical endothermic reaction. The absorbed energy from the environment to break the ionic bond within the salt is greater than the heat released while solvating those ions in water, making the entire process absorb energy from the surrounding environment.2323. B. Z. Shakhashiri, Chemical Demonstrations: A Handbook for Teachers of Chemistry (
University of Wisconsin Press, 1985).
Here, we made a cavity out of hollow needle electrodes and investigated the effect of electrode dimension, dissolving rate, and time point of dissolving on thermal mitigation in liver tissue during IRE.
The numerical simulation was performed in COMSOL MULTIPHYSICS 5.5 (COMSOL Inc. Stockholm, Sweden). An ellipsoid with dimensions

$15×15×11.25$

cm3 was used to represent the liver tissue. Two hollow electrodes filled with an NH4NO3 solution were constructed, and the dimensions are shown in Fig. 1. We assume the tip of the electrode was filled with NH4NO3, and water, which could be stored in the insulation part of the electrode, was used to dissolve NH4NO3 during the IRE treatment. To investigate how the amount of NH4NO3 affects the temperature profile, three electrode diameters, 1 mm, 1.5 mm, and 2 mm, were included in this study. The spacing of the two electrodes was fixed to 1.5 cm (center to center), and the thickness of the hollow electrode wall was set to 0.15 mm. 70 pulses with a pulse width of 90 μs, a repeat frequency of 1 Hz, and a voltage–distance ratio of 2000 V/cm were applied. One electrode surface was energized (3000 V) and the other was set to ground (0 V). The inner boundaries are treated as continuity, while the outer boundaries are set as electrically and thermally insulating.

The endothermic reaction of dissolving NH4NO3 shown in Eq. (1) was selected in here to absorb heat during IRE treatment.

 $NH4NO3s→NH4+aq+NO3−aq,ΔH=25.69 kJ/mol.$ (1)

It should be noted that a positive

$ΔH$

means this process will absorb heat from the ambient environment.

The dissolving process of NH4NO3 was described using the Noyes–Whitney model24,2524. A. A. Noyes and
W. R. Whitney, J. Am. Chem. Soc. 19(12), 930 (1897). doi.org/10.1021/ja02086a003
25. A. Dokoumetzidis and
P. Macheras, Int. J. Pharm. 321(1–2), 1 (2006). doi.org/10.1016/j.ijpharm.2006.07.011
where

$C$

is the concentration of NH4NO3 at time

$t$

,

$Cs$

is the concentration of the saturated NH4NO3 solution, and

$k$

is used to quantify the dissolving rate and the value is set to 0.01, 0.05, 0.1, and 0.5 s−1 (details can be found in the supplementary material) in this study.

$Cs$

is a function of temperature where

$T$

is the temperature; the acquisition of this function can be found in the supplementary material.

The electric field distribution in the tissue domain was solved by the modified Laplace equation where

$σ$

is the tissue conductivity as a function of both local electric field

$E$

and temperature

$T$

, and

$φ$

is the electric potential. The following conductivity function was used:2626. Y. Zhao,
S. Bhonsle,
S. Dong,
Y. Lv,
H. Liu,
A. Safaai-Jazi,
R. V. Davalos, and
C. Yao, IEEE Trans. Biomed. Eng. 65(8), 1810 (2018). doi.org/10.1109/TBME.2017.2778101

 $σE,T=σ0(1+A·flc2hsE−Edel, Erange+α(T−T0)),$ (5)

where

$σ0$

is the initial conductivity,

$A$

is the increase factor,

$flc2hs$

is the Heaviside function with a continuous second derivative, and

$Edel$

and

$Erange$

define the transition zone of conductivity from the initial value to the electroporated value, respectively. Finally,

$α$

is the temperature coefficient and

$T0$

is the initial temperature of the tissue.

Heat transfer was obtained using the follow equation:

 $−ρcp∂T∂t=∇·kl∇T+QJ+Qrec,$ (6)

where

$ρ$

is the tissue density,

$cp$

is the specific heat capacity of the tissue, and

$kl$

is the thermal conductivity of the tissue. Additional heat sources include Joule heating (QJ), and endothermic heat absorption (Qrec) on the electrode core. According to previous research, blood perfusion was severely reduced after the first pulse was delivered.2727. T. Jarm,
M. Cemazar,
D. Miklavcic, and
G. Sersa, Expert Rev. Anticancer Ther. 10(5), 729 (2010). doi.org/10.1586/era.10.43
Therefore, to get conservative results, the perfusion term was neglected here. The thermal conductivity, specific heat capacity, and density of the NH4NO3 solution are approximated as similar to the value of water: Equation (7) is used to calculate the Joule heating, while Eq. (8) is the heat absorbed by the reaction—

$mss$

is the molar mass of the solute.

Finally, thermal damage was quantified by the Arrhenius equation

 $Ωt=∫ξe−Ea/(RT(t))dt,$ (9)

where

$Ωt$

is the damage integral,

$ξ$

is the frequency factor,

$Ea$

is the activation energy,

$R$

is the universal gas constant, and

$T(t)$

is the temperature at time t. All parameters for the simulation can be found in the supplementary material.

The commercial electrodes for electroporation-based treatment used in clinic have diameters of 1 mm,1717. T. J. O'Brien,
M. F. Lorenzo,
Y. Zhao,
R. E. Neal Ii,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 36(1), 953–963 (2019). doi.org/10.1080/02656736.2019.1657187
1.2 mm,1010. J. Zmuc,
G. Gasljevic,
G. Sersa,
I. Edhemovic,
N. Boc,
A. Seliskar,
T. Plavec,
M. Brloznik,
N. Milevoj,
E. Brecelj,
B. Kos,
J. Izlakar,
T. Jarm,
M. Snoj,
M. Stukelj,
D. Miklavcic, and
M. Cemazar, Sci. Rep. 9(1), 3649 (2019). doi.org/10.1038/s41598-019-40395-y
and 1.6 mm.1313. P. A. Garcia,
R. V. Davalos, and
D. Miklavcic, PLoS One 9(8), e103083 (2014). doi.org/10.1371/journal.pone.0103083
To get a better sense of how the clinically used electrode size affects the results, we picked electrode sizes of 1, 1.5, and 2 mm in this study to compare the thermal mitigation between solid and endothermic electrodes. With a larger diameter electrode, more substance can be placed in the core of the electrodes, which can absorb more heat. In addition, a thicker solid electrode can dissipate more heat because of its high thermal conductivity. The location of the highest temperature rise is the interface between the electrode and tissue during IRE treatment. Here, the temperature profiles at the center point along the electrode–tissue interface were chosen to compare these two types of electrodes, and the results are shown in Fig. 2(a).

As expected, electrodes with a larger diameter are good for both solid and endothermic electrodes to mitigate temperature rise, while this benefit is more pronounced for endothermic electrodes. However, when picking the electrode diameter, one should make a trade-off between the thermal mitigation and increased invasiveness. Compared to solid electrodes, the temperature for endothermic electrodes is lower throughout the pulsing process. The temperature drop at the beginning indicates that the endothermic reaction absorbed more heat than the treatment generated. As the treatment continues, more Joule heating is generated, and the temperature starts to increase when the Joule heating is larger than the heat absorbed by the endothermic reaction. In this simulation, the specific heat capacity of the solution was approximated to water which is higher than the solid electrodes (stainless steel), making the temperature rise rate slower than solid electrodes.

The thermal mitigation is also affected by how long this reaction can last for. The rate of dissolution plays a critical role in the reaction duration. Figure 2(b) shows the dependency of NH4NO3 concentration on time at different dissolving rates. The process can be regarded as stopped when the concentration is saturated. The period for which this reaction lasts varies from tens to hundreds of seconds at different dissolution rates with solubility at

$37 °C$

[Eq. (3)]. It should be noted that the reaction duration can be even longer in clinical applications, since the solubility will increase because of the temperature rise during treatment.

The dissolving rate will affect the heat absorption speed and the duration of the process. Therefore, the effect of the dissolving rate should be considered. The calculated rate is about 0.09 s−1 (supplementary material) and several factors affect this rate, e.g., temperature, agitation, exposed surface area, etc. In consideration of this, a parametric study with four different dissolving rates (0.01, 0.05, 0.1, and 0.5 s−1) was implemented. To investigate the effect of dissolving rate on thermal mitigation, we fixed the diameter of the electrode to 1.5 mm. Figure 3(a) shows the change of NH4NO3 concentration in the solution at different dissolving rates. With a higher dissolving rate, the NH4NO3 concentration increases more rapidly and therefore more heat is absorbed at the early stage. It should be noted that the solubility of NH4NO3 is temperature-dependent (higher solubility at a higher temperature, see the supplementary material), therefore, with increased temperature throughout the treatment, the same amount solvent can dissolve more solute. It is of interest to note that the concentration of NH4NO3 still increases a little after pulsing, then starts to decrease. This can be explained by the fact that the NH4NO3 solution is not saturated at the end of pulsing because of the increased solubility at higher temperature; therefore, more NH4NO3 can still be dissolved. However, temperature starts to decrease after pulsing which makes the NH4NO3 precipitate out due to its temperature-dependent solubility.
The temperature distribution at different time points for solid electrodes and endothermic electrodes with different dissolving rates is given in Fig. 3(b). Since the endothermic reaction occurs inside the electrodes, the temperature is much lower in the core of the electrodes. This is more pronounced for the reaction with a faster dissolving rate at an early time point (k = 0.5 s−1, t = 10 s). The temperature distribution at the end of the treatment (t = 70 s) is similar for all endothermic electrodes and is altogether better than solid electrodes. This can also be found from Fig. 3(c). The maximum temperature at the chosen point for the endothermic electrodes is about 5 °C lower than that for the solid electrode. At the beginning when NH4NO3 is dissolving, the temperature difference between solid and endothermic electrodes with faster dissolving rates is even larger. Figure 3(d) presents the temperature profile along the line connecting the two electrode centers. The results show that the decrease in temperature in the vicinity of the electrodes is more pronounced than the area between the two electrodes. However, the temperature rise mainly concentrates near the electrodes [Fig. 3(d)] and decreases rapidly away from the electrodes because of the distribution of the current density and electric field. The potential thermal damage incurred from IRE occurs within millimeters of the tissue/electrode interface and would, therefore, benefit from the endothermic electrodes.
When the endothermic reaction happens at the beginning of the treatment, the heat absorbed causes the temperature to drop below the initial tissue temperature (37 °C). To take full advantage of this process, we purposely initiate the reaction at different time points after applying the first pulse. Figure 4 shows the temperature development if the endothermic reaction occurs at different time points during the treatment. At a lower dissolving rate, dissolving at different time points did not reduce the maximum temperature. The maximum temperature is slightly lower at dissolving rates of 0.1 and 0.5 s−1 if the reaction starts 30 s after pulsing. The maximum temperature reduction compared to the solid electrode happened at the beginning of the reaction and was about 10 °C, which is comparable to the internal cooling electrodes (about 9–10 °C at the end of pulsing)2121. T. J. O'Brien,
M. Bonakdar,
S. Bhonsle,
R. E. Neal,
C. H. Aardema, Jr.,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 35(1), 44 (2018). doi.org/10.1080/02656736.2018.1473893
and better than the PCM electrode (about 2 °C for Φ = 1.5 mm).1919. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, Appl. Phys. Lett. 101(8), 083902 (2012). doi.org/10.1063/1.4747332
Since the thermal mitigation of the irrigated electrode was driven by an external perfusion system, the effect can last longer than our design. However, according to existing studies, electroporation effects will be saturated by a certain number of pulses;2828. Y. Zhao,
S. Zheng,
N. Beitel-White,
H. Liu,
C. Yao, and
R. V. Davalos, Front. Bioeng. Biotechnol. 8, 396 (2020). doi.org/10.3389/fbioe.2020.00396
therefore, the pulse number needs to be further optimized in the future, which will make our design without any external assistant system more competitive.
Thermal damage is a dose-dependent phenomenon determined by both temperature and the time at which the tissue experiences elevated temperatures. Therefore, the Arrhenius Eq. (9) was introduced to evaluate thermal damage for different conditions (Fig. 5). Since Ω = 1 empirically marks tissue whitening,1919. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, Appl. Phys. Lett. 101(8), 083902 (2012). doi.org/10.1063/1.4747332
here we calculated the volume of the tissue where Ω > 1. Following the last pulse administered, the thermal damage may still accumulate during this process since the temperature is still relatively high. Therefore, Ω was calculated 300 s after treatment ended (370 s from the beginning) since the relative increase in the thermal damage volume is less than 0.1% afterward (data are not shown here). The results show that the endothermic electrodes can reduce the thermal damage volume compared to solid electrodes at any dissolution rate. Higher dissolving rates (k >0.01 s−1) have better performance at reducing thermal damage than the lower rate (k =0.01 s−1), however, trends might change if a longer treatment/more-pulse process is applied. For k =0.05, 0.1, and 0.5 s−1, the dissolving rates are high enough so that the solution is almost saturated at the end of the treatment. Therefore, the effect of the thermal mitigation for these dissolving rates at different starting points is close (except t = 50 s). With the condition in this study, an endothermic reaction beginning at an early stage gives us lower thermal damage when k =0.01 s−1. This is because NH4NO3 does not become saturated with this slow rate, so beginning earlier in treatment allows for the maximum amount to be dissolved. The thermal damage levels of t = 0, 10, and 30 s are similar for k =0.05 and 0.1 s−1, and lower than t = 50 s. When k =0.05, or 0.1 s−1, the NH3NO4 becomes saturated if t = 0, 10, or 30 s but not t = 50 s, making the thermal damage for the first three time points similar but lower than t = 50 s. When k =0.5 s−1, the rate is high enough to make the solution saturated and the thermal damage level to be similar for all cases even for t = 50 s. However, the maximum temperatures for these cases are different (Fig. 4). These results indicate that the best time to start the reaction could be optimized according to the reaction process and the treatment time.

This proof-of-concept numerical study shows that thermal mitigation can be achieved by incorporating an endothermic process to the therapeutic electrodes for electroporation-based treatment. However, the engineering challenge of realizing this design clinically still remains. The main structure of the electrode should be similar to the PCM probe. However, some details must be addressed, such as separating the chemicals before treatment and mixing them when they are expected to be activated. These details will be the focus of future efforts. For the configuration used in our simulation, the chemicals could be placed at the tip of the electrode, while the water is stored in a bag and released by a trigger on the handle or injected by an external syringe directly. Since the amount of solute is small, with enough water, the efficient mixing of the salt should not be difficult.

The dynamic process of dissolution is simplified in this study, which needs to be optimized in a specific case. For example, in most IRE applications, more pulses (∼100–300 pulses total) are delivered as sets – each with 10 pulses and separated from each other by a 3.5 s delay. Also, the repetition rate in clinical application is synchronized to the ECG to avoid arrhythmia rather than a fixed 1 Hz here. All of these will make the treatment longer. Therefore, it is important that the endothermic process is extended, and this can be realized by manipulating the dissolution rates, as shown in Fig. 2(b). It can last hundreds of seconds when k =0.01 s−1. Modifying the dissolving rate could be realized by using different sizes of particles to adjust the exposed surface area, or agitate the solution. From a safety standpoint, the proposed design only requires a small amount of NH4NO3, and the NH4NO3 aqueous solution is safe.2929. G. B. Kauffman and
C. A. Ferguson, J. Chem. Educ. 65(3), 267 (1988). doi.org/10.1021/ed065p267
Additionally, compared to the PCM electrode in which the melting process is reversible, the endothermic process we proposed here is irreversible. Nevertheless, this should not be a limitation for clinical application since the electrodes are often of one-time use. Some new endothermic processes or reactions could be introduced in the future for this application. In this study, we only considered using the tip of the electrode as the reaction chamber. To make full use of the whole electrode, we could sequence a small amount of chemical and water bag alternately and mix them simultaneously or in a specific order, maximizing the endothermic effect and reducing the temperature in the future design. Beside the simulation work, experimental work is necessary in the future to validate this method. For different tissues, the reaction rate and the work time point still need to be optimized. Finally, in this study, only the typically used needle electrode was involved. Other electrodes, like flat plate electrodes used in ECT or EGT, are also suitable for this method, and it might be easier to design the structure for separating and mixing the chemicals with these electrodes. Also, the approach proposed here is not limited to electroporation-based treatments, but should also work for other applications where thermal mitigation is desired.

In summary, this study proposed an endothermic electrode for thermal mitigation of electroporation-based therapies. We demonstrated numerically that temperature rise in the tissue during IRE treatment can be mitigated, especially near the electrodes, and the thermal damage volume is also reduced by using this electrode. This is critical for some ablations near sensitive structures in which thermal damage must be negligible. Also, with these benefits, it may be possible to apply higher voltages to achieve larger ablation volumes.

See the supplementary material for the acquisition of the dissolving rate, temperature-dependent solubility, and parameters used in the simulation.

This work was supported by the National Institutes of Health Award No. R01 CA240476. The authors acknowledge support from the Institute for Critical Technology and Applied Science (ICTAS) and the Center for Engineered Health (CEH) at Virginia Tech for their support of this research.

The data that support the findings of this study are available within the article and its supplementary material.

#### REFERENCES

1. 1. K. N. Aycock and
R. V. Davalos, Bioelectricity 1, 214–234 (2019). doi.org/10.1089/bioe.2019.0029, Google ScholarCrossref
2. 2. T. Kotnik,
L. Rems,
M. Tarek, and
D. Miklavcic, Annu. Rev. Biophys. 48, 63 (2019). doi.org/10.1146/annurev-biophys-052118-115451, Google ScholarCrossref
3. 3. A. Golberg and
M. L. Yarmush, IEEE Trans. Biomed. Eng. 60(3), 707 (2013). doi.org/10.1109/TBME.2013.2238672, Google ScholarCrossref
4. 4. J. F. Edd and
R. V. Davalos, Technol. Cancer Res. Treat 6(4), 275 (2007). doi.org/10.1177/153303460700600403, Google ScholarCrossref
5. 5. A. Zupanic,
B. Kos, and
D. Miklavcic, Phys. Med. Biol. 57(17), 5425 (2012). doi.org/10.1088/0031-9155/57/17/5425, Google ScholarCrossref
6. 6. A. Županič,
S. Čorović, and
7. 7. P. Agnass,
E. van Veldhuisen,
M. J. C. van Gemert,
C. W. M. van der Geld,
K. P. van Lienden,
T. M. van Gulik,
M. R. Meijerink,
H. P. Kok, and
J. Crezee, Int. J. Hyperthermia 37(1), 486 (2020). doi.org/10.1080/02656736.2020.1753828, Google ScholarCrossref
8. 8. E. Ben-David,
L. Appelbaum,
J. Sosna,
I. Nissenbaum, and
S. N. Goldberg, Am. J. Roentgenol. 198(1), W62 (2012). doi.org/10.2214/AJR.11.6940, Google ScholarCrossref
9. 9. B. Geboers,
H. J. Scheffer,
P. M. Graybill,
A. H. Ruarus,
S. Nieuwenhuizen,
R. S. Puijk,
P. M. van den Tol,
R. V. Davalos,
B. Rubinsky,
T. D. de Gruijl,
D. Miklavčič, and
10. 10. J. Zmuc,
G. Gasljevic,
G. Sersa,
I. Edhemovic,
N. Boc,
A. Seliskar,
T. Plavec,
M. Brloznik,
N. Milevoj,
E. Brecelj,
B. Kos,
J. Izlakar,
T. Jarm,
M. Snoj,
M. Stukelj,
D. Miklavcic, and
M. Cemazar, Sci. Rep. 9(1), 3649 (2019). doi.org/10.1038/s41598-019-40395-y, Google ScholarCrossref
11. 11. M. Faroja,
M. Ahmed,
L. Appelbaum,
E. Ben-David,
M. Moussa,
J. Sosna,
I. Nissenbaum, and
12. 12. I. Lackovic,
R. Magjarevic, and
D. Miklavcic, IEEE Trans. Dielectr. Electr. Insul. 16(5), 1338 (2009). doi.org/10.1109/TDEI.2009.5293947, Google ScholarCrossref
13. 13. P. A. Garcia,
R. V. Davalos, and
D. Miklavcic, PLoS One 9(8), e103083 (2014). doi.org/10.1371/journal.pone.0103083, Google ScholarCrossref
14. 14. F. A. Duck, Physical Properties of Tissues: A Comprehensive Reference Book (
15. 15. C. Bertacchini,
P. M. Margotti,
E. Bergamini,
A. Lodi,
M. Ronchetti, and
R. Cadossi, Technol. Cancer Res. Treat. 6(4), 313 (2007). doi.org/10.1177/153303460700600408, Google ScholarCrossref
16. 16. M. B. Sano,
C. B. Arena,
K. R. Bittleman,
M. R. DeWitt,
H. J. Cho,
C. S. Szot,
D. Saur,
J. M. Cissell,
J. Robertson,
Y. W. Lee, and
R. V. Davalos, Sci. Rep. 5, 14999 (2015). doi.org/10.1038/srep14999, Google ScholarCrossref
17. 17. T. J. O'Brien,
M. F. Lorenzo,
Y. Zhao,
R. E. Neal Ii,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 36(1), 953–963 (2019). doi.org/10.1080/02656736.2019.1657187, Google ScholarCrossref
18. 18. C. Jiang,
Q. Shao, and
J. Bischof, Ann. Biomed. Eng. 43(4), 887 (2015). doi.org/10.1007/s10439-014-1133-2, Google ScholarCrossref
19. 19. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, Appl. Phys. Lett. 101(8), 083902 (2012). doi.org/10.1063/1.4747332, Google ScholarScitation, ISI
20. 20. C. B. Arena,
R. L. Mahajan,
M. N. Rylander, and
R. V. Davalos, J. Biomech. Eng. 135(11), 111009 (2013). doi.org/10.1115/1.4025334, Google ScholarCrossref
21. 21. T. J. O'Brien,
M. Bonakdar,
S. Bhonsle,
R. E. Neal,
C. H. Aardema, Jr.,
J. L. Robertson,
S. N. Goldberg, and
R. V. Davalos, Int. J. Hyperthermia 35(1), 44 (2018). doi.org/10.1080/02656736.2018.1473893, Google ScholarCrossref
22. 22. J. O. Coulter, U.S. patent US 10,063,270 B2 (2018). Google Scholar
23. 23. B. Z. Shakhashiri, Chemical Demonstrations: A Handbook for Teachers of Chemistry (
University of Wisconsin Press, 1985). Google Scholar
24. 24. A. A. Noyes and
W. R. Whitney, J. Am. Chem. Soc. 19(12), 930 (1897). doi.org/10.1021/ja02086a003, Google ScholarCrossref
25. 25. A. Dokoumetzidis and
P. Macheras, Int. J. Pharm. 321(1–2), 1 (2006). doi.org/10.1016/j.ijpharm.2006.07.011, Google ScholarCrossref
26. 26. Y. Zhao,
S. Bhonsle,
S. Dong,
Y. Lv,
H. Liu,
A. Safaai-Jazi,
R. V. Davalos, and
C. Yao, IEEE Trans. Biomed. Eng. 65(8), 1810 (2018). doi.org/10.1109/TBME.2017.2778101, Google ScholarCrossref
27. 27. T. Jarm,
M. Cemazar,
D. Miklavcic, and
G. Sersa, Expert Rev. Anticancer Ther. 10(5), 729 (2010). doi.org/10.1586/era.10.43, Google ScholarCrossref
28. 28. Y. Zhao,
S. Zheng,
N. Beitel-White,
H. Liu,
C. Yao, and
R. V. Davalos, Front. Bioeng. Biotechnol. 8, 396 (2020). doi.org/10.3389/fbioe.2020.00396, Google ScholarCrossref
29. 29. G. B. Kauffman and
C. A. Ferguson, J. Chem. Educ. 65(3), 267 (1988). doi.org/10.1021/ed065p267, Google ScholarCrossref