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Research Papers

# Endovascular Nonthermal Irreversible Electroporation: A Finite Element Analysis

[+] Author and Article Information

Biophysics Graduate Group, University of California at Berkeley, Berkeley, CA 94720; Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720eladmaor@gmail.com

Boris Rubinsky

Biophysics Graduate Group, University of California at Berkeley, Berkeley, CA 94720; Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720; School of Computer Science and Engineering, Hebrew University of Jerusalem, Israel

1

Corresponding author. Also at Department of Internal Medicine A, Chaim Sheba Medical Center.

J Biomech Eng 132(3), 031008 (Feb 17, 2010) (7 pages) doi:10.1115/1.4001035 History: Received October 04, 2009; Revised December 24, 2009; Posted January 18, 2010; Published February 17, 2010; Online February 17, 2010

## Abstract

Tissue ablation finds an increasing use in modern medicine. Nonthermal irreversible electroporation (NTIRE) is a biophysical phenomenon and an emerging novel tissue ablation modality, in which electric fields are applied in a pulsed mode to produce nanoscale defects to the cell membrane phospholipid bilayer, in such a way that Joule heating is minimized and thermal damage to other molecules in the treated volume is reduced while the cells die. Here we present a two-dimensional transient finite element model to simulate the electric field and thermal damage to the arterial wall due to an endovascular NTIRE novel device. The electric field was used to calculate the Joule heating effect, and a transient solution of the temperature is presented using the Pennes bioheat equation. This is followed by a kinetic model of the thermal damage based on the Arrhenius formulation and calculation of the Henriques and Moritz thermal damage integral. The analysis shows that the endovascular application of 90, $100 μs$ pulses with a potential difference of 600 V can induce electric fields of 1000 V/cm and above across the entire arterial wall, which are sufficient for irreversible electroporation. The temperature in the arterial wall reached a maximum of $66.7°C$ with a pulse frequency of 4 Hz. Thermal damage integral showed that this protocol will thermally damage less than 2% of the molecules around the electrodes. In conclusion, endovascular NTIRE is possible. Our study sets the theoretical basis for further preclinical and clinical trials with endovascular NTIRE.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Endovascular electrode geometry. The figure shows a cage on top of an inflatable balloon, with four legs. Two opposite legs are connected to a positive potential (V), and the remaining two legs are connected to ground.

Figure 2

Finite element mesh. The figure shows the large tissue block (vertical and horizontal axes are in meters), with the center area of the electrodes enlarged in the upper right side. This example includes 3284 triangular elements. Simulations were done with meshes of different sizes (3192–108,864 elements) to validate that the temperature and electric potential simulation did not change in more than 1%.

Figure 3

Electric field distribution. The figure shows two-dimensional finite element simulation of the electric field induced by a potential difference of 600 V. The outermost line corresponds to an electric field of 1000 V/cm.

Figure 4

Minimal electric field as a function of the radius from the center. The figure shows the decreasing electric field magnitude as a function of the distance from the endovascular electrodes. The balloon radius is 0.00125 m, and therefore, only a potential difference of 600 V or above yields electric fields of 1000 V/cm at a distance of 200 μm from the inner surface of the balloon.

Figure 5

Transient solution of the temperature for three different frequencies (1 Hz, 2 Hz, and 4 Hz). The figure shows the temporal behavior of the maximal temperature, solved with COMSOL MULTIPHYSICS 3.5A together with MATLAB 2008RB (version 7.7). The rate of temperature increase is correlated with the pulse frequency. However, the rate of temperature decay is similar and depends on the heat convection of the biological tissue only. The thermal damage integral is calculated by integrating the Arrhenius equation, and is based on the transient solution of the temperature.

Figure 6

Effect of the potential difference and pulse frequency on the maximal temperature. The figure shows the strong correlation between the potential difference, pulse frequency, and maximal temperature in the treated domain. It illustrates the important conclusion that NTIRE can be applied to large volumes by increasing the potential difference together with decreasing the pulse frequency.

Figure 7

The effect of blood perfusion and electric conductivity on the maximal temperature. Parametric analysis of the maximal temperature reached as a function of blood perfusion rate and electric conductivity. Note the minor effect blood perfusion rate has on the temperature, compared with the significant effect of the electric conductivity.

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