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Research Papers

Electrical Field and Temperature Model of Nonthermal Irreversible Electroporation in Heterogeneous Tissues

[+] Author and Article Information
Charlotte Daniels1

Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720daniels.charlotte@gmail.com

Boris Rubinsky

Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720; Center for Bioengineering in the Service of Humanity and Society, School of Computer Science and Engineering, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel

1

Corresponding author.

J Biomech Eng 131(7), 071006 (Jul 16, 2009) (12 pages) doi:10.1115/1.3156808 History: Received November 10, 2008; Revised May 21, 2009; Published July 16, 2009

Nonthermal irreversible electroporation (NTIRE) is a new minimally invasive surgical technique that is part of the emerging field of molecular surgery, which holds the potential to treat diseases with unprecedented accuracy. NTIRE utilizes electrical pulses delivered to a targeted area, producing irreversible damage to the cell membrane. Because NTIRE does not cause thermal damage, the integrity of all other molecules, collagen, and elastin in the targeted area is preserved. Previous theoretical studies have only examined NTIRE in homogeneous tissues; however, biological structures are complex collections of diverse tissues. In order to develop electroporation as a precise treatment in clinical applications, realistic models are necessary. Therefore, the purpose of this study was to refine electroporation as a treatment by examining the effect of NTIRE in heterogeneous tissues of the prostate and breast. This study uses a two-dimensional finite element solution of the Laplace and bioheat equations to examine the effects of heterogeneities on electric field and temperature distribution. Three different heterogeneous structures were taken into account: nerves, blood vessels, and ducts. The results of this study demonstrate that heterogeneities significantly impact both the temperature and electrical field distribution in surrounding tissues, indicating that heterogeneities should not be neglected. The results were promising. While the surrounding tissue experienced a high electrical field, the axon of the nerve, the interior of the blood vessel, and the ducts experienced no electrical field. This indicates that blood vessels, nerves, and lactiferous ducts adjacent to a tumor treated with electroporation will survive, while the cancerous lesion is ablated. This study clearly demonstrates the importance of considering heterogeneity in NTIRE applications.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Top row, geometry of homogeneous prostate model and electrodes (left) and geometry of heterogeneous prostate model, nerve and electrodes (right) in a cross section of prostate tissue. Bottom row, mesh utilized for homogeneous prostate models that includes two circular electrodes (left). Right, mesh utilized for heterogeneous prostate models that includes a cross section of a nerve between two circular electrodes. Note that the mesh is extra fine in the vicinity of the heterogeneities in order to capture the change in electric field and temperature over such a small distance.

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Figure 2

Plots illustrating the temperature distribution in the prostate after the application of a single pulse at V=2000 V. The figure on the left illustrates the homogeneous case with two electrodes within a square of prostate tissue. The figure on the right illustrates the heterogeneous case with a nerve between two electrodes within a square of prostate tissue.

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Figure 12

The graphs above illustrate vertical and horizontal transects of the temperature distribution in the two cases in Fig. 1. Top left, vertical homogeneous; top right, vertical heterogeneous. Bottom left, horizontal homogeneous; bottom right, horizontal heterogeneous. Note that in both heterogeneous cases the temperature drops at the location of the duct.

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Figure 3

The graphs above illustrate vertical and horizontal transects of the temperature distribution in the two cases from Fig. 2. Top left, vertical homogeneous; top right, vertical heterogeneous. Bottom left, horizontal homogeneous; bottom right, horizontal heterogeneous. Note that in both heterogeneous cases the temperature drops drastically at the location of the nerve.

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Figure 4

Electric field distribution in the prostate from a single pulse of V=2000 V. The left figure depicts homogeneous prostate tissue with two electrodes. The right figure depicts the heterogeneous case with a nerve between to electrodes in prostate tissue. Note that in the heterogeneous case the electric field reaches near zero at the location of the nerve, whereas in the same location for the homogeneous model it is 1.45×105 V/m.

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Figure 5

A closeup of the electric field distribution in the axon and myelin structures in the prostate as a result of a single pulse of V=2000 V at 0.1 ms. Note that the electric field lines are concentrated inside the myelin and that there are no field lines inside the axon.

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Figure 6

The graphs above illustrate vertical and horizontal transects of the electric field distribution in the two cases in Fig. 4. Top left, vertical homogeneous; top right, vertical heterogeneous. Bottom left, horizontal homogeneous; bottom right, horizontal heterogeneous. Note that the highest electric field in the heterogeneous cases (two right hand graphs) occurs in the location of the myelin, and the lowest electric field (0) at the axon.

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Figure 7

Temperature and electric field distribution in the prostate with a blood vessel after a single pulse at 2000 V. The left figure illustrates the temperature distribution in the heterogeneous case with a blood vessel between two electrodes in a square of prostate tissue. The right figure illustrates the electric field distribution for the same case.

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Figure 8

Closeup of the electric field distribution around the blood vessel in the prostate after a single pulse at 2000 V. Note that there are no electric field lines inside the blood vessel.

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Figure 9

The graphs above illustrate the vertical and horizontal transects of the temperature and electric field distribution in the two heterogeneous cases from Fig. 7. Top: temperature in prostate with blood vessel; left, vertical; right, horizontal. Bottom: heterogeneous electric field in prostate with blood vessel; left, vertical; right horizontal.

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Figure 10

Top row, geometry of homogeneous breast model and electrodes (left) and heterogeneous breast model, lactiferous ducts and electrodes (right) in a cross section of breast tissue. Bottom row, mesh utilized for homogeneous breast model that includes two circular electrodes (left). Right, mesh utilized for heterogeneous breast models that includes a cross section of a lactiferous duct between two circular electrodes. Note that the mesh is extra fine in the vicinity of the heterogeneities in order to capture the change in electric field and temperature over the small distance.

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Figure 11

Plots illustrating the temperature distribution in the breast after the application of a single pulse at V=2000 V. The figure on the left illustrates the homogeneous case with two electrodes in a square of breast tissue. The figure on the right illustrates the heterogeneous case with a duct between two electrodes in a square of breast tissue.

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Figure 13

Plots illustrating the electric field distribution in breast tissue after a single pulse at 2000 V. The left figure depicts the homogeneous case with two electrodes in a square of breast tissue. The right figure illustrates the heterogeneous case, with a duct between two electrodes.

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Figure 14

The graphs above illustrate vertical and horizontal transects of the electric field distribution in the two cases in Fig. 1. Top: breast tissue vertical electric field. Left, homogeneous; right, heterogeneous. Bottom: breast tissue horizontal electric field. Left, homogeneous; right, heterogeneous. Note that the electric field reaches zero at the location of the duct.

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Figure 15

Close up of the electric field distribution around the duct in the breast after a single pulse at 2000 V. Note that electric field lines are concentrated inside the layer of myoepithelial cells, but that there are absolutely none inside the duct.

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