CONTROLLED IRREVERSIBLE ELECTROPORATION

Abstract

Electrical pulses are applied to tissue in a manner which destroys targeted cells such as cancerous cells while sparing non-targeted cells such as nerve cells. The electrical pulses are controlled within ranges for voltage, wattage and duration of application. Multiple pulses or groups of pulses may be applied to obtain a desired result while maintaining any temperature increase below a level which destroys cells.

Claims

1.-20. (canceled)

21. A method comprising the steps of: identifying cells to be ablated in a target area, wherein the target area comprises heterogenous tissue comprising nerve tissue surrounded by myelin layers; selecting a size, shape, or relative position of a first electrode and a second electrode; placing the first electrode and the second electrode in the target area; and applying electrical pulses between the first electrode and the second electrode in an amount which compensates for tissue heterogeneity, and is sufficient to irreversibly electroporate the cells in the target area; wherein voltage, wattage and duration of the electrical pulses are maintained within ranges which avoid thermal damage to nerve tissue and the cells in the target area.

22. The method of claim 21, wherein the myelin layers insulate the nerve tissue from thermal damage.

23. The method of claim 21, further comprising: monitoring temperature of the heterogeneous tissue and adjusting the electrical pulses to maintain the temperature at 50 C. or less for a period of time that avoids thermal damage to cells of the heterogeneous tissue.

24. The method of claim 21, further comprising: infusing a material into the heterogenous tissue prior to applying the electrical pulses.

25. The method of claim 24, wherein the material is a chemotherapeutic agent.

26. The method of claim 24, wherein the material is an imaging agent.

27. The method of claim 21, wherein the first electrode and the second electrode are substantially circular in shape; and wherein the first and second electrodes are positioned within less than 2 cm of each other.

28. A method comprising the steps of: identifying a target ablation area, wherein the target ablation area is heterogenous tissue comprising cells and mammary ducts, wherein the mammary ducts are surrounded by myoepithelial cells; placing a first electrode and a second electrode in the target ablation area; and applying electrical pulses between the first electrode and the second electrode in an amount which compensates for tissue heterogeneity, and is sufficient to irreversibly electroporate the cells in the target ablation area; wherein voltage, wattage and duration of the electrical pulses are maintained within ranges which avoid damage to the mammary ducts and the cells in the target ablation area.

29. The method of claim 28, wherein the myoepithelial cells insulate the mammary ducts from thermal damage.

30. The method of claim 28, further comprising: monitoring temperature of the heterogeneous tissue and adjusting the electrical pulses to maintain the temperature at 50 C. or less for a period of time that avoids thermal damage to the cells of the heterogeneous tissue.

31. The method of claim 28, further comprising: infusing a material into the heterogenous tissue prior to applying the electrical pulses.

32. The method of claim 28, wherein the material is a chemotherapeutic agent.

33. The method of claim 31, wherein the material is an imaging agent.

34. The method of claim 31, wherein the first electrode and the second electrode are substantially circular in shape; and wherein the first and second electrodes are positioned within less than 2 cm of each other.

35. A method comprising the steps of: identifying a target ablation area, wherein the target ablation area is comprised of heterogenous tissue comprising cancer cells and nerve tissue, wherein the nerve tissue is surrounded by myelin layers; placing a first electrode and a second electrode in the target ablation area; and applying electrical pulses between the first electrode and the second electrode in an amount which compensates for tissue heterogeneity, and is sufficient to irreversibly electroporate the cancer cells in the target ablation area; wherein voltage, wattage and duration of the electrical pulses are maintained within ranges which avoid damage to the nerve tissue.

36. The method of claim 35, wherein the myelin layers insulate the nerve tissue from thermal damage.

37. The method of claim 35, further comprising: monitoring temperature of the heterogeneous tissue and adjusting the electrical pulses to maintain the temperature at 50 C. or less for a period of time that avoids thermal damage to cells of the heterogeneous tissue.

38. The method of claim 35, further comprising: infusing a material into the heterogenous tissue prior to applying the electrical pulses.

39. The method of claim 38, wherein the material is a chemotherapeutic agent.

40. The method of claim 38, wherein the material is an imaging agent.

41. The method of claim 35, wherein the first electrode and second electrode are substantially circular in shape; and wherein the first and second electrodes are positioned within less than 2 cm of each other.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The invention is best understood from the following detailed description when read in conjunction with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to-scale. On the contrary, the dimensions of the various features are arbitrarily expanded or reduced for clarity. Included in the drawings are the following figures:

[0023] FIGS. 1A and 1B illustrate the mesh used for homogenous (1A) and heterogenous (1B) models.

[0024] FIGS. 2A and 2B show the temperature distribution in the homogeneous (2A) and heterogenous (2B) models for prostate tissue with two electrodes.

[0025] FIG. 3 includes four graphs which show temperature changes where graphs 3A and 3C show the changes with respect to homogeneous tissue and graphs 3B and 3D show temperature changes with heterogeneous tissue.

[0026] FIGS. 4A and 4B show the temperature distribution in the homogeneous (4A) and heterogenous (4B) models for prostate tissue with two electrodes.

[0027] FIG. 5 includes four graphs which show temperature changes where graphs 5A and 5C show the changes with respect to homogeneous tissue and graphs 5B and 5D show temperature changes with heterogeneous tissue.

[0028] FIGS. 6A and 6B show the temperature distribution in the homogeneous (6A) and heterogenous (6B) models for prostate tissue with two electrodes.

[0029] FIG. 7 includes four graphs which show temperature changes where graphs 7A and 7C show the changes with respect to homogeneous tissue and graphs 7B and 7D show temperature changes with heterogeneous tissue.

[0030] FIGS. 8A and 8B illustrate the mesh used for homogenous (8A) and heterogenous (8B) models.

[0031] FIGS. 9A and 9B show the temperature distribution in the homogeneous (9A) and heterogenous (9B) models for prostate tissue with two electrodes.

[0032] FIG. 10 includes four graphs which show temperature changes where graphs 10A and 10C show the changes with respect to homogeneous tissue and graphs 10B and 10D show temperature changes with heterogeneous tissue.

[0033] FIGS. 11A and 11B show the temperature distribution in the homogeneous (11A) and heterogenous (11B) models for prostate tissue with two electrodes.

[0034] FIG. 12 includes four graphs which show temperature changes where graphs 12A and 12C show the changes with respect to homogeneous tissue and graphs 12B and 12D show temperature changes with heterogeneous tissue.

DETAILED DESCRIPTION OF THE INVENTION

[0035] Before the present devices, systems, and methods of treatment and use are described, it is to be understood that this invention is not limited to particular embodiments described, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims.

[0036] Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limits of that range is also specifically disclosed. Each smaller range between any stated value or intervening value in a stated range and any other stated or intervening value in that stated range is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included or excluded in the range, and each range where either, neither or both limits are included in the smaller ranges is also encompassed within the invention, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the invention.

[0037] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, some potential and preferred methods and materials are now described. All publications mentioned herein are incorporated herein by reference to disclose and describe the methods and/or materials in connection with which the publications are cited. It is understood that the present disclosure supercedes any disclosure of an incorporated publication to the extent there is a contradiction.

[0038] It must be noted that as used herein and in the appended claims, the singular forms a, an, and the include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to an electrode includes a plurality of such electrodes and reference to the pulse includes reference to one or more pulses and equivalents thereof known to those skilled in the art, and so forth.

[0039] The publications discussed herein are provided solely for their disclosure prior to the filing date of the present application. Nothing herein is to be construed as an admission that the present invention is not entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided may be different from the actual publication dates which may need to be independently confirmed.

Definitions

[0040] The term reversible electroporation encompasses permeabilization of the cell membrane through the application of electrical pulses across the cell. In reversible electroporation the permeabilization of the cell membrane ceases after the application of the pulse and the cell membrane permeability reverts to normal. The cell survives reversible electroporation. It is used as a means for introducing chemicals, DNA, or other materials into cells.

[0041] The term irreversible electroporation also encompasses the permeabilization of the cell membrane through the application of electrical pulses across the cell. However, in irreversible electroporation the permeabilization of the cell membrane does not cease after the application of the pulse and the cell membrane permeability does not revert to normal. The cell does not survive irreversible electroporation and the cell death is caused by the disruption of the cell membrane and not merely by internal perturbation of cellular components. Openings in the cell membrane are created and/or expanded in size resulting in a fatal disruption in the normal controlled flow of material across the cell membrane. The cell membrane is highly specialized in its ability to regulate what leaves and enters the cell. Irreversible electroporation destroys that ability to regulate in a manner such that the cell can not compensate and as such the cell dies.

Specific Embodiments

[0042] Models described in the Examples below were created and tested to demonstrate the importance of investigating heterogeneous models with NTIRE and to show that NTIRE treatment methods need to consider the heterogeneous nature of the tissue. Both the model of the prostate and the breast demonstrated the substantial difference between homogeneous and heterogeneous cases. Furthermore, unanticipated information about the effects of electroporation was also discovered. The impact electroporation has on biological structures such as nerves, ducts and blood vessels was previously unknown. This investigation has made clear that nerves can be preserved in treated tissue because of the insulating effect of surrounding myelin layers. Additionally, the Examples show that mammary ducts will also be retained because of myoepithelial cells and their ability to regenerate. Therefore, heterogeneous models are not only important to consider in order to generate an accurate simulation, but also to understand the effects of electroporation on all included biological structures and to improve clinical applications.

[0043] A method of targeting cancer cells and subjecting those cells to irreversible electroporation is disclosed. The method involves identifying cancer cells which are to be ablated, killed or in the method of the invention subjected to irreversible electroporation. These cells are identified in a target area wherein the target area comprises an identified nerve tissue. The invention is particularly applicable to killing cancer cells in a target area where the target area comprises nerve tissue which is not cancerous. A first electrode and a second electrode are positioned such that the target area is positioned between the first and second electrodes. Multiple electrodes may be used. Electrical pulses are then applied between the first and second electrodes in sufficient amount to obtain irreversible electroporation of cancer cells in the target area. The voltage, wattage and duration of the electrical pulses are maintained within a distinct range or ranges which avoid damage to nerve tissue in the target area and at the same time avoid thermal damage to cells in the target area and the surrounding area while making it possible to carry out irreversible electroporation of the cancer cells.

[0044] The method used can include calculating a voltage, wattage and duration of electrical pulses to be applied in a manner so as to avoid damage to nerve tissue in the target area and avoid thermal damage to cells in the target area. It is also possible to determine the size, shape and relative position of the first electrode and second electrode in a manner so as to avoid damage to nerve tissue in the target area and avoid thermal damage to cells in the target area while subjecting the cancer cells to irreversible electroporation.

[0045] In one aspect of the invention there is disclosed a method of treating cancer which comprises identifying nerve tissue in a grouping of biological cells in a target area of a mammal and determining cells in the grouping as being cancer cells. Voltage is applied across the targeted tissue. The method can include continuously detecting a ratio of electric current through the targeted tissue to voltage across the targeted tissue as an indication of degree of electroporation of cells in the targeted tissue. With this information it is possible to adjust a determined magnitude of the applied voltage in accordance with changes in detected magnitude of the current-to-voltage ratio to achieve irreversible electroporation of the cancer cells. With this information it is possible to apply the adjusted voltage to a new target tissue at a point in time significantly after the initial steps have been carried out. Specifically, one may carry out initial testing in order to identify cancer cells within the target area and then continuously detect the ratio of electric current through the targeted tissue to voltage across the targeted tissue as an indication of a degree of electroporation of the cancer cells in the targeted tissue. After this is carried out it is possible to adjust the magnitude of the applied voltage in accordance with the changes detecting in the current-to-voltage ratio to achieve irreversible electroporation of the cancer cells. Once this has been achieved it may not be necessary to repeat these processes each time when applying the adjusted voltage to a new target tissue at a point in time after the other steps have been carried out and the proper parameters such as voltage, wattage, duration and number of electrical pulses has been determined.

EXAMPLES

[0046] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to make and use the present invention, and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all or the only experiments performed. Efforts have been made to ensure accuracy with respect to numbers used (e.g. amounts, temperature, etc.) but some experimental errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, molecular weight is weight average molecular weight, temperature is in degrees Centigrade, and pressure is at or near atmospheric.

Example 1

[0047] Models were generated using numerical analysis executed by a commercially available program Comsol Multiphysics (version 3.4). This initial study utilized 2-dimensional models because these were sufficient to demonstrate the significant difference between homogeneous and heterogeneous models. Two equations were solved simultaneously in Comsol. The first of which was the Laplace equation for potential distribution associated with an electric pulse.

.Math.d(VJ.sup.e)=dQ.sub.i(1)

[0048] Where is electrical conductivity, V is voltage, J.sup.e is external current density, d is thickness and Q.sub.j is the current source.

[0049] For all boundaries the external current density and the current source were set to zero, and thickness was set to one. The electric field was solved in order to illustrate the electrical effects of the electroporation in the particular tissue as listed in Tables 1 and 2. The electric field was solved for in the AC/DC Conductive Media module using a static analysis. Each structure was designated a different electrical conductivity, which corresponded to its representative biological entity. The respective values are shown in Tables I and II.

TABLE-US-00001 TABLE I Values of electrical conductivity for the prostate cancer Conductive Media model Electrical Conductivity Structure () [S/m] Reference Prostate tissue 0.42427 Andreuccetii, et al. Myelin 3.45E6 Villapecellin- Cid, et al. Axon 1.44 B. J. Roth et al.

TABLE-US-00002 TABLE II Values of electrical conductivity for the breast cancer Conductive Media model Electrical Conductivity Structure () [S/m] Reference Fatty breast tissue 0.024192 Andreuccetii, et al. Breast myoepithelial cell 10.sup.7 Hassan N et al. Breast gland 0.52427 Andreuccetii, et al. Breast tumor 2.309 A. M. Campbell et al. Blood 0.30709 Andreuccetii, et al.

[0050] The thermal effects of electroporation were determined from the solution of the Pennes bioheat equation, which was solved simultaneously as the electrical potential equation. The Pennes bioheat equation took the following form:

[00001]$\begin{array}{cc}.Math.\left(k.Math.T\right)+{}_b.Math.w_b.Math.c_b\left(T_a-T\right)+q^{}=.Math..Math.c_p.Math.\frac{T}{t}& \left(2\right)\end{array}$

[0051] Where k is the thermal conductivity, T is the temperature, wb is the blood perfusion, cb is the heat capacity of blood, Ta is the arterial temperature, is the tissue density, cp is the tissue heat capacity and q=Q.sub.met+Q.sub.ext. Where Qmet is the metabolic heat generation, which is assumed to be negligible here. Also, Q.sub.ext=||.sup.2, which accounts for Joule heating, where is electrical potential and is electrical conductivity of the tissue.

[0052] Heat transfer in living organisms is more complex than other circumstances. Metabolism and blood flow are important in addition to conduction, convection, radiation and evaporation. For this reason, the bioheat equation, which includes terms that account for blood flow and metabolism, was used. In addition, the bioheat equation solves for the temperature and ascertains the impact of the Joule effect. The result of the bioheat equation determines if the tumor was being treated also by resistive heating, or only irreversible electroporation.

[0053] The values utilized in the bioheat equation for the corresponding structures in the prostate and the breast are shown in Tables III, IV and V.

TABLE-US-00003 TABLE III Values for the prostate cancer Bioheat model Thermal Conductivity Specific Heat Density Structure (k) [W/mk] (c) [J/kgK] () [kg/m.sup.3] Reference Prostate tissue 0.561 3600 1045 Yusheng Feng et al.[21] Nerve 0.503 3600 1043 S. DeMarco (axon and myelin) et al.

TABLE-US-00004 TABLE IV Values for the breast cancer Bioheat model Thermal Conductivity Specific Heat Density Structure (k) [W/mK] (c) [J/kgK] () [kg/m.sup.3] Reference Fatty breast 0.25 2522.5 900 Howorka K. et tissue al.; M. P. Robinson et al.; F. Fidanza Breast gland 0.41 3492 1030 F. O. Dosekun; M. A. Kolka et al.; C. R. Moreira et al. Breast tumor 0.48 2926 1186 Kwok et al.; P. Prakash et al.; B. J. Roth et al.

TABLE-US-00005 TABLE V Values for human blood flow in the prostate and breast cancer Bioheat models Perfusion Thermal Specific Rate Conductivity Heat (c) Density Structure [1/s] (k) [W/mK] [J/kgK] () [kg/m.sup.3] Reference Blood 0.002 0.391 3640 1000 L. Sun et al.; J. Valvano et al.; S. Belov; Elad Maor et al.

Models

[0054] Five models were utilized to demonstrate the differences between heterogeneous and homogeneous tissues treated with electroporation with an application that is typical to the current implementation of the method in animal models (B. Al-Sakere et al., Tumor Ablation with Irreversible Electroporation, PLoS ONE, vol. 2, 2007, p. el 135; R. V. Davalos, B. Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effects during in vivo tissue electroporation, Bioelectrochemistry, vol. 61, October 2003, pp. 99-107). The electrodes were taken to have a diameter of one mm. The electrodes were placed at a distance of one cm, center to center. For boundary conditions, in each case a uniform voltage was imposed on each electrode and a voltage difference of 2000 V was imposed between each electrode.

[0055] Case 1a: (2 cm2 cm) Prostate tissue with two electrodes separated by 1 cm

[0056] Case 1b: A nerve (axon with myelin sheath) in the center of (2 cm2 cm) prostate tissue with two electrodes separated by 1 cm. The nerve is modeled as a structure of a circular axon surrounded by a uniform layer of myelin. The axon radius was 0.1 mm (A. Takenaka et al., Variation in course of cavernous nerve with special reference to details of topographic relationships near prostatic apex: Histologic study using male cadavers, Urology, vol. 65, January 2005, pp. 136-142) and the thickness of the myelin surrounding it was 0.02 mm (J. Schroder, Altered ratio between axon diameter and myelin sheath thickness in regenerated nerve fibers, Brain Research, vol. 45, October 1972, pp. 49-65). The axon and myelin structure was centered within the square section of prostate tissue.

[0057] Case 1c: A blood vessel in the center of (2 cm2 cm) prostate tissue with two electrodes separated by 1 cm. The blood vessel was 5 E-5 m in radius and was placed in the center of a square section of prostate tissue.

[0058] Case 2: (2 cm2 cm) fatty breast tissue with two electrodes separated by 1 cm

[0059] Case 2b: A duct in the center of (2 cm2 cm) fatty breast tissue with two electrodes separated by 1 cm. We used in the model a gland surrounded by myoepithelial. The breast gland was 0.7 mm in radius (J. Rusby et al., Breast duct anatomy in the human nipple: three-dimensional patterns and clinical implications, Breast Cancer Research and Treatment, vol. 106, January 2007, pp. 171-9) and the surrounding layer of myoepithelial cells were 0.13 mm in thickness. The gland and myoepithelial cells were centered within a square section of breast tissue.

[0060] The model includes a rectangular cross section of tissue (4 cm2 for the prostate and the breast), large enough to account for fringe effects of the electric field. Electrodes conductive only at the tips are utilized in vivo, so they were represented as points in the models. All models were evaluated at a voltage potential difference between the electrodes of 2000V. Each model simulated a single voltage pulse of length 0.1 ms, and the temperature evaluated at time steps of 0.1 E-4 s.

[0061] There were two sets of boundary conditions generated; one set for the Laplace equation and another for the Pennes bioheat equation. For the Laplace equation, the edges of the tissue sample were treated as electrically insulating.

[00002]$\begin{array}{cc}\frac{}{n}=0.Math.& \left(3\right)\end{array}$

[0062] Where is potential. The remaining structures were prescribed continuity boundary conditions.

n.Math.(J.sub.1J.sub.2)=0(4)

[0063] Where n is the normal vector and J is the current density. For the bioheat equation, the edges of the tissue were set to body temperature.

T=310.15K(5)

[0064] The remaining structures were prescribed continuity boundary conditions.

Results and Discussion

[0065] FIGS. 1A and 1B illustrate the mesh that was used for the homogeneous and the heterogeneous models. It is important to note that the mesh becomes more defined around the boundaries of the electrodes. This ensures accurate results in the vicinity of the electrodes and captures even the smallest temperature difference on the micron scale. This is also true of the mesh used for the heterogeneous model. The mesh is extra fine around the boundaries of the inhomogeneity as well as the electrodes.

[0066] FIGS. 2A and 2B show the temperature distribution in the homogeneous and heterogeneous models of prostate tissue with two electrodes of voltage potential difference 2000V at the end of the application of a single pulse. The figures plot isothermal lines and the details of the temperature distribution can be found in FIGS. 3A, 3B, 3C and 3D. The elevated temperature reaches a maximum of 313.431K in the homogeneous case. However, this is only within nanometers of the electrode. Nevertheless, even the tissue near the electrode doesn't experience thermal damage. In fact, no tissue in the homogeneous case experiences thermal damage. This is because a temperature of 360.15K represents the upper limit before thermal damage occurs. The highest temperature occurs on either sides of the electrode, as can be seen by FIG. 3A.

[0067] The heterogeneous plot in FIG. 2B includes a nerve (axon and myelin) within the prostate tissue. The axon radius was 0.1 mm (A. Takenaka et al., Variation in course of cavernous nerve with special reference to details of topographic relationships near prostatic apex: Histologic study using male cadavers, Urology, vol. 65, January 2005, pp. 136-142) and the thickness of the myelin surrounding it was 0.02 mm (J. Schroder, Altered ratio between axon diameter and myelin sheath thickness in regenerated nerve fibers, Brain Research, vol. 45, October 1972, pp. 49-65). The axon and myelin structure was centered within the square section of prostate tissue. The difference between the heterogeneous and homogeneous cases can be seen in the temperature range. The homogeneous model ranges from nearly body temperature, 310.234K, to 313.431K. However, the heterogeneous model has a slightly lower temperature throughout, ranging from 310.23K to 313.278K. From the maximum temperature reached in both the heterogeneous cases, it is apparent that it does not experience thermal damage either. Therefore, the prostate tissue in these models only experiences electroporation. It is interesting to note that the main difference between the homogeneous and heterogeneous cases is the dip in the temperature at the center of the plot in the heterogeneous case, where the nerve is located. This dip does not exist in the homogeneous graphs (FIGS. 3A and 3C). The difference in the temperature distribution between these two plots shows the importance of taking heterogeneous models into account for an accurate portrayal.

[0068] The plot in FIGS. 4A and 4B displays lines of constant electrical field in prostate tissue.

[0069] The detailed field distribution can be found in FIGS. 5A, 5B, 5C and 5D.

[0070] The maximum electric field occurs at the electrodes and takes a value of

[00003]$6.964.Math.E.Math..Math.5.Math.\frac{v}{m}.$

The remaining tissue in the rectangular sample above and below the electrodes receives a lessening effect, with the electric field forced to reach nearly

[00004]$0.Math.\frac{v}{m}$

at the edge of the tissue sample. However, it is important to note, in the location between the electrodes, where the nerve would be in the heterogeneous model, that the electric field does not quite reach zero, which is the desired effect. This can be seen in the plot of the electric field along a vertical cross section of the homogeneous model (FIG. 5A). It only reaches a minimum of

[00005]$1.15.Math.E.Math..Math.5.Math.\frac{v}{m}.$

[0071] The electric field in the heterogeneous prostate (FIG. 4B) is exceptionally different than in the homogeneous prostate (FIG. 4A).

[0072] The maximum electric field is

[00006]$1.853.Math.E.Math..Math.6.Math.\frac{v}{m},$

which is more than in the homogeneous model. In the heterogeneous model, the myelin receives the absolute highest levels of electric field in the entire sample. The electrodes themselves have substantially different readings. At

[00007]$1.7.Math.E.Math..Math.6.Math.\frac{v}{m},$

the electric field in the myelin is almost a magnitude more than the maximum in the homogeneous model. The electric field elsewhere is low, beyond the immediate vicinity of the electrodes. The plots (FIGS. 5B and 5D) also show that the axon receives the lowest levels of electric field, reaching zero. This implies that the myelin insulates the axon from the effect of the electric field. Because axons are able to remyelinate themselves (W. F. Blakemore, Remyelination by Schwann cells of axons demyelinated by intraspinal injection of 6-aminonicotinamide in the rat, Journal of Neurocytology, vol. 4, December 1975, pp. 745-757), these results suggest that the nerve structure should be able to fully recover even if the myelin is damaged. This plot demonstrates the importance of heterogeneous models to understand the effect of irreversible electroporation on the nervous system.

[0073] These results explain the outcome in the trials utilizing NTIRE to treat prostate cancer (G. Onik, P. Mikus, and B. Rubinsky, Irreversible electroporation: implications for prostate ablation, Technology in cancer research & treatment, vol. 6, August 2007, pp. 295-300). Nerves surrounding the prostate remained unharmed by the effects of electroporation. It is now understood why the nerves near the prostate survived. The myelin insulates the axons from the electric field. Even if damaged, the axons remyelinate via Schwann cells and all neurological functionality is retained.

Example 2

[0074] The methodology described above in Example 1 was used to analyze the prostate with a blood vessel which had a relatively small radius (e.g. less than 5 mm) which was placed in the center of a square section of prostate tissue. FIGS. 6A, 6B, 7A, 7B, 7C and 7D show the temperature distributions in the same manner as FIGS. 2A, 2B, 3A, 3B, 3C and 3D. The maximum temperature reached was 313.584K, while it was 313.431K for the homogeneous case. The blood vessel model has a temperature distribution between 310.238 and 313.584K. Because the maximum temperature reached is below 360.15K, the entire samples stays well below any temperature necessary for thermal damage. This means that absolutely none of the tissue receives any thermal damage. However, it is important to note that an elevated temperature does exist, but only in the immediate vicinity of the electrodes (FIG. 7A).

[0075] The electrical fields in this case are depicted in FIGS. 7 and 8 in the same manner as FIGS. 4 and 5.

[0076] The maximum electric field of the blood vessel in the prostate (FIG. 7) is lower than the homogeneous case. The homogeneous prostate reached

[00008]$6.964.Math.E.Math..Math.5.Math.\frac{v}{m},$

while the prostate with a blood vessel reached

[00009]$6.87.Math.E.Math..Math.5.Math.\frac{v}{m}.$

Additionally, there is a slight rise in the electric field in the vicinity of the blood vessel. This occurs because the electrical conductivity of the blood vessel is slightly lower than that of prostate tissue. Nevertheless it receives a low level of electric field, indicating that during clinical trials, blood vessels in the vicinity of a tumor would be unharmed by the effects of the electroporation.

Example 3

[0077] The methodology of Example 1 above was used to investigate the effects of electroporation on breast tissue. The model included a section of fatty breast tissue in the homogeneous model. In the heterogeneous model a gland surrounded by myoepithelial cells was included in the breast tissue (FIGS. 8A and 8B). The breast gland was 0.7 mm in radius (J. Rusby et al., Breast duct anatomy in the human nipple: three-dimensional patterns and clinical implications, Breast Cancer Research and Treatment, vol. 106, January 2007, pp. 171-9.) and the surrounding layer of myoepithelial cells were 0.13 mm in thickness. The gland and myoepithelial cells were centered within a square section of breast tissue.

[0078] FIGS. 9 and 10 are presented in the same manner as FIGS. 2 and 3 and FIGS. 11 and 12 in the same manner as FIGS. 4 and 5. FIG. 10 shows that in the vertical plane the highest temperature reached in the homogeneous model is 310.687K, only 0.537 degrees higher than body temperature. In the heterogeneous case, however, the maximum temperature, 310.466K, is even lower. There is no portion of tissue in the entire sample that reaches temperature levels required for thermal damage. The horizontal cross section yields a vast difference between the temperature distribution in the homogeneous and heterogeneous cases (FIG. 10). The homogeneous model reaches a maximum at the location between the electrodes, but the heterogeneous model dips to a minimum.

[0079] In the homogeneous model the maximum electric field reaches

[00010]$9.307.Math.E.Math..Math.5.Math.\frac{v}{m}.$

The maximum electric field in the heterogeneous model,

[00011]$1.935.Math.E.Math..Math.6.Math.\frac{v}{m},$

is slightly higher. However, the electric field between the electrodes is very different.

[0080] In the heterogeneous model the electric field reaches zero at the center of the gland (FIG. 12). However, in the homogeneous model, the electric field only goes as low as

[00012]$2.9.Math.E.Math..Math.5.Math.\frac{v}{m}.$

Additionally, the homogeneous model, the highest electric field occurs at the electrodes. But in the heterogeneous model, the highest electric field is within the myoepithelial cells and is followed distantly by the electric field near the electrodes. This, however, does not pose a threat to the physiological function of the ducts because myoepithelial cells are known to regenerate (S. TAKAHASHI et al., Regeneration of myoepithelial cells in rat submandibular glands after yttrium aluminium garnett laser irradiation, International Journal of Experimental Pathology, vol. 78, 1997, pp. 91-99).

[0081] The preceding merely illustrates the principles of the invention. It will be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and conditional language recited herein are principally intended to aid the reader in understanding the principles of the invention and the concepts contributed by the inventors to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents and equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. The scope of the present invention, therefore, is not intended to be limited to the exemplary embodiments shown and described herein. Rather, the scope and spirit of present invention is embodied by the appended claims.

REFERENCES

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