WO2000004949A1 - Electroporation electrodes - Google Patents

Abstract

Electrodes, electrode array apparatus (A), and systems improve the therapeutic effects of in vivo delivered electrical waveform by utilizing an arrangement wherein the electrode plates satisfy particular ratios of electrode surface areas to separation distances between the electrode plates (X1, X2).

Description

Description

Electroporation Electrodes

Technical Field

The present invention relates to the delivery of electrical waveforms and, more particularly, to the design of electrodes and electrode arrays for efficient delivery of electrical waveforms in vivo.

Background of the Invention

There exists a broad range of potential applications for the delivery of electrical waveforms in vivo. Certain known techniques utilizing such electrical waveforms are generally referred to as iontophoresis, electro-osmosis, electroporation, and electropermeabilization. As there is limited understanding of the phenomenon known as electroporation, the terms electroporation and electropermeabilization are often used interchangeably. All of these procedures utilize the application of electrical signals to tissue and require some conductive means to transmit these signals. Electroporation refers to the application of electric fields of sufficient intensity and duration as to induce transient increases in cell membrane permeability in the affected tissue. The cell membrane is a selectively permeable barrier that greatly inhibits the penetration of many molecules into the cytosol. The application of brief electric fields of sufficient intensity causes cell membranes to destabilize, increasing the exchange of molecules between cells and their environment. Thus, electroporation can be used to temporarily overcome the membrane barrier and greatly increase the intracellular concentration of normally impermeant substances.

Rols et al. (Biophysical J ^'. 58: 1089-1098 (1990)) describe electroporation as a threshold dependent phenomenon, in that the electric field intensity must be higher than a critical threshold to induce cell permeability. The extent to which the cell membrane is permeabilized is dependent on many factors which include the physical properties of the cell as well as the parameters of the electroporation protocol. Provided that the electric field strength is not too high and the pulse duration not too long, cells can be permeabilized without a significant decrease in viability (Zimmerman in "Rev. Physiol. Biochem. Pharmacol. " 105:177, Springer- Verlag, New York,(1986)).

Electroporation was first applied as a method of inserting normally impermeable molecules into the cytosol of cells in culture. The most common techniques utilize a cuvette with large conductive plate electrodes which produce the required electric field within an ionic buffer solution. This buffer solution is a suspension of the cells to be porated as well as the molecules to be inserted into the cell cytosol. The parameters of the electroporation sequence (e.g. waveform, number, intensity, and duration) are determined based on the characteristics of the cells as well as the type of molecule to be inserted. As the size of the cell is decreased, the electric field strength must be increased in order to achieve the critical voltage difference across the membrane. A first order approximation of the required electric field intensity is given by the equation:

E = ΔΦ 1.5 r cos θ where ΔΦ = critical voltage, r = cell radius, θ = angle of electric field (Mir et al. , Exp. Cell Research 175:15-25 (1988)). This equation assumes that the cell is of the spherical shape normally associated with cells in suspension. If the cell is of irregular shape, membrane permeability is achieved at much lower field strengths. Mammalian cells in culture typically require electric field strengths of approximately 0.2kV/cm to

3kV/cm. Research has indicated that significant permeabilization of the cell can occur if a threshold potential difference of approximately one volt can be established across the plasma membrane (Chang, D. et al. in "Guide to Electroporation and Electrofusion" D. Chang ed., Academic Press, San Diego, pp. 1-6 (1992)). It is important to note that, although electroporation is a threshold phenomena, when cells are exposed to excessively high field strengths cell lysis (death) can result. Many studies (Mir et al. (1988), Zimmerman (1986), Rols et al , (1990), Poddevin et al , Biochem Pharmacol 42 Suppl:S67-S75 (1991)) have indicated that, for many mammalian cell lines, a rapid decrease in cell viability occurs at field strengths above 1500V/cm. It appears that every type of cell has a voltage threshold for cell permeability as well as a voltage threshold for cell death. Therefore, the permeabilization of cell membranes by electroporation would more accurately be characterized as having a specific window of effect, rather than simply a threshold.

The use of relatively large conductive plates with ionic buffer solutions assures that the field strength applied to the electroporation cuvette is equivalent to the field strengths generated uniformly throughout the cell suspension. The transmission of electric fields is completely confined to the buffer solution with little loss in electric field intensity due to fringe effects. Figure 1 illustrates the voltage potential and electric field strength generated between two plates in an electroporation cuvette. While there is a negligible loss in field strength at the plate buffer interface, the generated electric field intensity is constant throughout the buffer solution and equivalent to the applied electric field.

The use of in vitro electroporation has been extremely successful in potentiating the intracellular insertion of normally impermeant or semi-permeant substances such as dyes (Mir et al. (1988)), genes (Neumann et al, EMBO J 1:841-845 (1982)), and drugs (Poddevin et al (1991)). As an illustrative example, Mir et al. (C.R. Acad. Sci. Paris, t. 314, 3:539-544 (1992)) report that significant cytotoxicity was observed in cancer cells treated with electroporation and the chemotherapeutic bleomycin at drug concentrations 10, 000-fold less than would normally be required. The development of electroporation continued with experiments which demonstrated that this process could also be applied to cells in living tissue (Okino et al, Jpn J. Cancer Res. 78: 1319-1321 (1987)). Okino inserted two 0.5mm iron needles, spaced 2cm apart, into the tissue surrounding an AH-109A tumor established in a Donryu rat. After an intravenous injection of bleomycin a capacitive discharge of amplitude 10,000 volts and decay constant 2 ms was applied to the bipolar electrodes.

The researchers determined that this procedure resulted in a significant reduction in tumor growth rate when compared to control animals. However, significant necrosis was observed in the electrode region as well as in neighboring tissue.

Based on these results, there exists a need for the use of electroporation as a means to deliver therapeutic substances to diseased tissue. In order to achieve therapeutic benefit, the electric fields propagated in tissue by the delivery of specific electrical waveforms must apply sufficient transmembrane voltage and pulse duration to induce cell membrane permeability, yet not exceed inherent limits leading to cell death. Until recently, most of the applications of electroporation in tissue consisted of simple two electrode systems or conductive metal plates to generate the electric fields.

U.S. Patent Nos. 5,273,525 to Hofmann and 5,389,069 to Weaver describe two electrode (bipolar) systems for acute placement during tissue electroporation. Nishi et al, Cancer Res. 56: 1050-1055 (1996), Ceberg et al, Anti-Cancer Drugs 5:463-466 (1994), Salford et al, Biochem. Biophys. Res. Comm. 194, 2:938-943 (1993) and Okino et al. (1987) also utilized bipolar electrode systems for tissue electroporation.

These systems are described as having electrodes of needle type construction acutely placed in tissue, and spaced approximately 0.5 - 2cm apart. The voltage applied to these electrodes is based on this spacing. The authors often describe the field strengths required as volts per centimeter (V/cm) of spacing. Therefore, to achieve a field strength of lOOOV/cm between a pair of electrodes 0.5cm apart, it is suggested that a voltage of 500V would need to be applied.

In U.S. Patent No. 5,439,440 to Hofmann, an apparatus of spaced plate electrodes used to grasp the target tissue is described. Mir et al, Eur J Cancer 27:68- 72 (1991), Domenge et al , Cancer 77:956-963 (1996), and Heller et al , Cancer 77:964-966 (1996) detail the results of clinical trials where plate electrodes and bleomycin were utilized to treat various skin cancers. The electric pulses were delivered through plate electrodes described as 10mm wide stainless steel strips placed approximately 6mm apart, pinching the skin on either side of a tumor nodule. The voltage applied between the electrode plates is also based on the spacing between the electrodes according to the same method described earlier. U.S. Patent No. 5,439,440 to Hofmann details a feedback control system which assures that voltage is applied proportionate to the distance between the electrodes.

Further testing of plate electrode systems leads to the conclusion that these plates were inefficient at generating the electric fields required for electroporation in tissue. Domenge et al. (1996) conclude that instances in which the treatment of a tumor nodule was ineffective were due to poor electric field distribution. Problems with field distribution were attributed to the high resistance of the outer layers of skin as well as the difficulty of field transmission to deeper areas of the tissue. Figure 2 illustrates the problems associated with electric field delivery using plates to pinch the skin around a tumor nodule.

It was also determined that bipolar electrode systems were inefficient for the delivery of electric fields for the purpose of tissue electroporation. As depicted in Figure 3A, the electric field propagated in tissue by a two electrode system as described in the prior art would weaken considerably in the region of tissue that is proximal to the midpoint between the electrodes (represented as the dashed box). In fact, the field strength in the tissue will weaken geometrically as the distance from either electrode is increased (Figure 3B), and the field strength in the mid-region of tissue will also weaken geometrically as the distance "L" between the two electrodes is increased. As electroporation is considered to be a threshold-dependent phenomenon, with inherent upper limits due to the risk of cell lysis, a two electrode system is poorly suited to establish uniform electric field coverage, i.e., uniform electroporation, in the tissue targeted for treatment.

Recently, more complex electrode systems have been developed which can more efficiently generate the necessary fields for electroporation in tissue. In U.S. Patent No. 5,439,440, Hofmann describes spaced apart parallel arrays of needle electrodes mounted on a dielectric support member. This design allows adjustments in needle depth and spacing between the parallel arrays (separated by distance L), but not the . spacing of needles within each array. Also disclosed is a device which senses the distance between the two arrays and adjusts the applied voltage accordingly. U.S. Patent No. 5,674,267 to Mir describes an array consisting of individually addressed needles which can be pulsed in bipolar pairs. This design still uses the traditional two electrode system with its inherent weaknesses, but it is able to cover a much larger area of tissue merely by adding more needles. Mir also describes a pulse applicator which applies a voltage proportional to the distance separating the two needles. If the needles are not spaced too far apart, then the problem of field divergence in a bipolar system can be minimized. Mir discloses that a spacing of 0.65cm between each pair of electrodes is considered optimal.

Recently, the testing and application of two further improvements in electrode array design have been reported (Hofmann et al. , IEEE Eng Med and Biol, 124-132 (Nov/Dec 1996), Jaroszeski et al, Biochim. Biophys. Ada 1334: 15-18 (1997), Gilbert et al , Biochim. Biophys. Ada 1334:7-14 (1997)). One improved array is described as a hexagon with six 28 gauge (0.35mm) stainless steel needles spaced equidistant around the circumference of a tumor mass. Opposed pairs of needles are pulsed together in order to provide a convergence of the electric fields within the target region. After pulsing a pair of needles, a switch is rotated 60° to the next active pair. Rotation of the switch is continued until all of the opposed pairs have been pulsed. The author describes this array as significantly limited because it is difficult to treat large volumes of tissue efficiently. As the distance "L" between the electrodes is increased, a correspondingly higher voltage must be applied between them (Hofmann et al, 1996). Based on its geometry, it can be concluded that this array cannot easily be expanded by the addition of electrodes to form a grid of hexagons.

Hofmann et al. (1996) propose a second configuration to address this issue. An array consisting of needle electrodes oriented at 90° angles and spaced 0.65cm apart. This forms an array of squares, each with two pairs of opposed needles which are pulsed simultaneously to achieve more homogeneous fields within the region. After each pulse, the polarity relationship between electrodes is rotated by 90°, and the needles are pulsed again. Each rotation produces a new pair of opposed needles and. continues until all four configurations have been pulsed. Larger volume tumors are treated by adding additional needles in a repetitive geometric pattern. Like the original two electrode systems, the voltage applied between each pair of needles is based solely on the intra electrode distance.

In all of the arrays described above, including both plate and needle systems, the applied voltages are determined based on the same "Volts/cm" paradigm described for the plate electrode system. The required field strength is determined for the application and the applied voltage is calculated based solely on the electrode spacing. In order to provide an electrode array for the clinical use of electroporation, the array must be efficient in the application of fields to the large volumes of tissue required for many treatments. Depending on the tumor site, the region required for the treatment of a solid tumor can often have a diameter of three centimeters or more (Jain, R. , Scientific American 271(l):58-65 (1994)). The volume of tissue treated by an electrode array can be increased by two methods: (1) Increasing the intra electrode distance, and (2) Increasing the number of electrodes in the array. Each of these methods has limitations which act to restrict efficient expansion of the array. As previously described, increasing the distance between electrodes requires an increase in applied voltage commensurate with the increase in spacing. However, higher voltages can result in unacceptable damage to the tissue near the electrodes. Also, there are practical and anatomical considerations which limit the use of large numbers of electrodes. Due to an incremental risk of surgical complication associated with each electrode placement, the number of electrodes should be kept to the minimum necessary. In order to achieve the optimal array size, the intra-electrode spacing, the number of electrodes, and the risks associated with each need to be considered. In achieving these ends, it is considered desirable to provide a means to propagate electric fields of adequate intensity for a three dimensional region of tissue so as to achieve uniform electroporation while mitigating electric field-induced cell lysis, local heating of the tissue, and complications associated with treatment. In addition, there is a need to confine therapeutic field effect to the targeted region of tissue.

Disclosure of the Invention

The present invention provides an electrode apparatus and system which facilitate the efficient delivery of electrical waveforms, and in particular, delivery to a predetermined three dimensional region of tissue within a patient. Electrical waveforms of certain parameters, comprising many different therapeutic objectives and techniques, may be efficiently delivered through the present invention while mmimizing the risk of trauma to the patient.

In one aspect, the invention provides an array comprised of electrodes with a cross section optimized so that therapeutic field strengths can be generated in tissue with the lowest possible applied voltage. This aspect of the invention comprises an electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising a plurality of individually-addressable elongate electrodes, each independently having a cross sectional surface dimension of E_s, are located within a predetermined three-dimensional space in a patient. The ratio of the cross-sectional surface dimension of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula

X = (E_S+ + E,)²/L wherein X is a value greater than approximately 2mm²/mm. Where the array consists of at least three individually -addressable elongate electrodes, X will have a value greater than approximately 0.75mm²/mm. An electrical impulse generating means will be operatively connected to the individually-addressable electrodes for generating electroporation-inducing electrical fields between the electrodes.

In another aspect of the invention, a method is provided to determine the optimal electrode cross section for a given array based on the geometric relationship of the component electrodes. Use of this method will allow the array parameters (e.g. electrode spacing "L", number of electrodes, applied voltage) to be adjusted and optimized for more efficient generation of the necessary electric fields. The result of this optimization would be an array which could more closely approximate the perfectly homogeneous distribution of electric fields observed during in vitro applications. Brief Description of the Drawings

Figure 1A is a three dimensional perspective view of a pair of plate electrodes and the electric field generated between them, and Figure IB is a graph depicting the electric field strength and voltage generated by the plate electrodes and their relationship to locations between the plate electrodes;

Figure 2A is a depiction of a pair of plate electrodes applied to a tumor mass in the epidermal region, and Figure 2B illustrates the typical voltage and electric field profile generated between electrode plates in the relationship depicted in Figure 2A; Figure 3A is a two dimensional schematic view depicting the field lines and approximate electric field intensity for a two electrode model, wherein the intra- electrode distance is L and the dashed box positioned midway between the two electrodes indicates the region of lowest electric field strength, and Figure 3B is a graphic representation of the relationship between the distance from the electrode and the electric field strength; Figure 4 is a graphic representation of the improvement in electric field distribution obtained when needle electrodes are combined into more complex arrays, in which Figure 4A depicts the electric field strengths measured over 1mm increments for a bipolar electrode system, Figure 4B depicts the field strength profile of electrodes establishing a square configuration, and Figure 4C depicts the field strength profile of electrodes establishing a rectangular configuration characteristic of a hexagonal array;

Figure 5 is a two dimensional depiction of the approximate change in the density of field lines for one of the electrodes in a bipolar system, wherein the scale representations are of electrodes with a diameter of 0.3 and 1.0mm;

Figure 6 is a graphical representation of the voltage and electric field profile generated between a bipolar needle electrode system with a intra electrode spacing of

2cm and an electrode diameter of 0.3mm;

Figure 7 is a graphical representation of the voltage profile generated by various bipolar electrode systems with an intra electrode distance of 2cm and electrode diameter ranging from 0.3mm to 2.4mm; Figure 8 is a graphical representation of the relationship between intra electrode spacing and the applied voltage required to generate an electric field of 50 V/mm in the center of a bipolar electrode system;

Figure 9 is a graphical representation of the results produced by a system as described in Example 4, illustrating the percentage of the applied voltage measured over one millimeter in the center of a bipolar electrode system for electrodes of various diameters;

Figure 10 is a graphical representation of the results produced by a system as described in Example 5, illustrating the decrease in voltage 2mm from the pulse electrode for bipolar systems with electrodes of various diameters;

Figure 11 depicts the improvement in electric field distribution when 1.1mm diameter electrodes are incorporated into more complex arrays, wherein Figure 11A depicts the electric field profile generated by a bipolar system, Figure 1 IB depicts the electric field profile generated by a square configuration, and Figure 11C depicts the electric field profile generated by a rectangular configuration characteristic of a hexagonal array; and

Figure 12 is a graphic description of the improvement in field uniformity derived from the use of a conductive solution around each of the electrodes in a bipolar system.

Detailed Description of the Invention

The present invention provides apparatus and methods which facilitate the efficient delivery of electrical waveforms, and in particular waveform delivery to a predetermined three dimensional region of tissue within a patient. Electrical waveforms of certain parameters employed in many different therapeutic techniques may efficiently be delivered through the present invention. These techniques can be performed while minimizing the risk of associated trauma in the patient.

The present invention provides an array of individual electrodes which efficiently deliver electrical waveforms to a predetermined region of tissue within a patient. One aspect of this efficiency is to maximize the electrical waveform intensity and uniformity for a given intra-electrode distance while minimizing the actual number of electrodes which will ensure complete coverage of the predetermined treatment region. This aspect of the invention comprises an electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising a plurality of individually-addressable elongate electrodes, each independently having a cross sectional surface dimension of E_s, are located within a predetermined three-dimensional space in a patient. The ratio of the cross-sectional surface dimension of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula X = (E_s++ E,)²/L wherein X is a value greater than approximately 2mm²/mm. Where the array consists of at least three individually-addressable elongate electrodes, X will have a value greater than approximately 0.75mm²/mm. An electrical impulse generating means will be operatively connected to the individually-addressable electrodes for generating electroporation-inducing electrical fields between the electrodes.

Electric fields will be established within the target tissue by delivery of electrical waveforms to preselected electrodes, desirably such electrodes will be individually-addressable so as to provide the ability to focus and concentrate the electrical fields to insure substantial uniformity throughout the region of tissue to be treated. The parameters of the waveform, geometry of the electrode array, and electrode characteristics will define the electric field strength E (in V/mm) at any given point within the tissue. Each tissue system will have its own characteristics which determine the critical field strength for optimum therapeutic effect. Variation between different types of tissue are due to cell size, cell type, and the electrical properties of the tissue itself. Generally, the field strength varies inversely with the size of the cells contained within the tissue. Mammalian tissue generally requires field strengths of between approximately 200V/cm to 3000V/cm for electroporation. If the tissue has abnormal resistive values or if it is very susceptible to damage, then the waveform parameters are desirably adjusted accordingly. The voltage applied to electrodes is reported in the literature as a function of the distance between those electrodes ("L"), typically in V/cm. Based upon the literature pertaining to tissue electroporation, it appears that a higher voltage commensurate with larger L becomes problematic compared to a lower voltage and the proportionately smaller L. This suggests that one practicing in vivo electroporation cannot simply expand L to any desired distance and expect an overall satisfactory therapeutic effect.

Cell lysis due to high electric field strengths around the electrode tract should be considered, as well as the weakened state of the electric field established at substantial distances between electrodes (see Figure 3).

Given that electroporation of cells is known to require a threshold voltage across the cell membrane, it is important to achieve this threshold field strength throughout the target region. However, it is not desirable be achieve this result by elevating the field strengths in some regions beyond the threshold for cell lysis and death. Ideally, threshold level electric field strengths generated by the electrodes would be evenly distributed across, and completely confined to, the target area. This ideal distribution would be similar to that of the electroporation cuvette illustrated in Figure 1.

Unfortunately, neither plate type or needle type electrodes have demonstrated the capability of generating these completely homogenous fields in tissue. Therefore, a more realistic goal is to optimize both electrode and array parameters in order to maximize the volume of target tissue permeabilized by safe and effective electric field strengths. Plate electrodes, which pinch the skin, must generate electric fields through the highly resistive outer layers of the skin. Applying the voltages necessary for the electroporation of tissue can often result in burning and scarring of the dermal layers. Another significant limitation of the plate electrodes is that the tissue which is accessible for treatment by this method is limited to surface regions. Deeper regions of tissue, for which the use of electroporation treatment would be most relevant, could not easily be treated with this method, both because of the voltage considerations stated above and because this application would involve treating regions of tissue far beyond those for which treatment is indicated. Figure 2 illustrates the typical voltage and electric field profile generated by plate electrodes applied to skin. As can be seen from the figure, there is a significant drop in voltage at the electrode skin interface due to the drastic change in resistance, as well as the poor electrical contact between the electrode plates and the skin. Even when conductive paste or gel is utilized to improve the interface between the electrode plates and the skin, a significant portion of the voltage is dissipated in the outer layers of the skin.

The use of needle-type electrodes to generate electroporation fields has also proven problematic. The field strengths generated in the tissue near the needle electrodes are much higher than those in the more central region between electrodes. Also, a significant dissipation of the field occurs because it is difficult to confine the electric fields to the target region. This occurs due to the radial propagation of fields characteristic to bipolar needle type electrodes (see Figure 5).

The development of more complex arrays of penetrating electrodes alleviated certain of these field distribution problems. These arrays utilize the convergence of fields produced by the simultaneous pulsing of three or more electrodes. Complete coverage of the target tissue is obtained by altering the electrical state of given electrodes in an array, thus changing the orientation of the electric field. Such variable state electrodes, which can be changed singly or in conjunction with other electrodes, are defined as individually addressable. The use of individually addressable electrodes has allowed arrays such as the square grid to be reasonably effective at an electrode spacing of 0.65cm. Figure 4 illustrates the improvements in field distribution possible using square and hexagonal arrays in this configuration. These improvements in electrode arrays create a more homogeneous field distribution, allowing larger volumes of tissue to be treated with a lower applied voltage. However, while these needle type arrays have an improved field distribution characteristics, they cannot approach the uniform nature of the electric fields produced by ideal plate-type electrodes.

Consequently, in order to provide above-threshold-level field strengths throughout the target region, the applied voltage should be sufficient to achieve threshold in the weakest areas. Unfortunately, such increases in electric field strength in the weaker regions often result in excessively high voltages near the electrodes. The prior art does not address the importance of this concept in the application of electroporation to tissue. In Patent No. 5,702,359 Hofmann discloses that applied field strengths for in vivo applications should be determined by in vitro testing of the particular cell line, and proposes that a rough equivalence exists between the optimal applied electric field required for each situation. This method is believed erroneous for several reasons. First, cells in tissue and cells in suspension are in a completely different environment and tend to have different shapes, which can affect the threshold for permeability. More importantly, the needle type electrodes traditionally used in tissue applications cannot produce the homogeneous fields provided by the relatively large plate electrodes found in electroporation cuvettes. In addition, the experimental results represented in Figure 4 demonstrate that different array configurations generate quite different electric field distributions. Therefore, the required field strength for an array cannot be determined without first considering the geometric relationship of the component electrodes.

It is generally acknowledged that the phenomena of electroporation is due to a potential difference established across an individual cell membrane. The use of relatively large plate electrodes for in vitro applications of electroporation made it possible to assume equivalence between the electric field intensity applied to a cuvette and that experienced by the individual cells in suspension. In other words, one could assume that if 1200V/cm was applied to the cell suspension then the potential measured across any one millimeter increment (perpendicular to the plates) would be 120V. Therefore, it could be concluded that each cell in the suspension experienced the same field strength as any other.

However, the prior art does not recognize that this assumption cannot be made for the non-ideal electrode systems utilized in tissue applications. As a result, the terminology developed for in vitro electroporation protocols which describes the required field strengths only in terms of V/cm should be considered inaccurate for in vivo tissue applications. If the electric field strength is averaged over the entire tissue area it is roughly equivalent to the applied field. However, as illustrated in Figure 3, the electric field generated in any given increment of tissue varies widely depending on its position relative to the electrodes. Hence, one cannot develop an effective tissue electroporation system based solely on the applied field strength. An analysis of the behavior at the electrode/tissue interfaces as well as the electric field distribution produced by the particular electrode array will be taken into account before determining an appropriate applied field strength. In one aspect, the present invention provides an array comprised of elongate rod type electrodes which have an optimized cross section. This cross section is predetermined and based on the applications for which the array will be used. One application for which this type of array is particularly suited is in the generation of electric fields in tissue for the purposes of electroporation. An optimal electrode array is one that can generate the necessary electric fields throughout the target tissue with the fewest number of electrodes, lowest applied voltage, and least amount of collateral tissue damage. This corresponds to an array which can efficiently generate homogenous, threshold level fields throughout a target region of tissue.

The use of electrodes with a larger cross section (and a commensurate increase in surface area) would decrease the current density at the electrode tissue interface. A significantly smaller voltage drop would be observed at this more efficient interface, creating a more homogeneous electric field throughout the target region. Figure 5 illustrates the change in density of the electric field lines when the same voltage is applied to electrodes of different diameter. This improvement in the electric field distribution would allow a lower applied voltage to generate the same effective field strengths in the tissue.

Tissue damage due to high field strengths and local heating is the limiting factor for the amount of voltage which can be applied to an electrode array. This tissue damage always occurs first in the region of high current density immediately surrounding the electrodes. This is due to the high electric field strengths generated at the electrode/tissue interface. Therefore, with an increase in the electrode diameter, higher voltages could be applied without the risk of tissue damage, because the field strengths near the electrodes have been distributed across a larger surface area. If higher voltages can be applied to the electrodes, while maintaining safe field strengths in the tissue, then the intra-electrode distance "L" can be increased. As discussed earlier, with an increase in "L", fewer electrodes are necessary to treat a given region of tissue and establish electric fields of sufficient strength for electroporation.

Examples of this invention have indicated that the relationship between the cross section of the electrode, the electrode spacing, and the applied voltage determines the field strengths present in the target region. These tests suggest that the threshold electric fields necessary for electroporation are not generated efficiently when spacing and applied voltage are the only variables taken into consideration. If traditional needle type electrodes (diameter s 0.3mm) are used to generate an electric field, there is a nonlinear relationship between the electric field strength and the position between the electrodes. Testing related to this concept demonstrates that rapid changes in voltage (i.e. electric field strength) occur near the electrodes while a much slower rate of change occurs in the intermediate region (see Figure 6) . This implies that a target field strength of 50 V/mm cannot be generated in the center region by applying a 500V/cm electric field between the electrodes. In fact, the present invention demonstrates that an applied voltage of 650V is used to generate a potential difference of 50V across one mm precisely between two needle electrodes spaced 0.5cm apart. When the intra electrode distance is increased to 0.65cm, the voltage will be 850V. This figure corresponds to an applied voltage of approximately 1300V/cm. It should be noted that the measurements were taken on the center line in the middle of the electrode pair, which is not the weakest point in the region (electric field strength at a given point decreases with the square of the average distance from the two electrodes) .

As discussed earlier, ideally the applied voltage would be distributed evenly throughout the tissue. This ideal distribution corresponds to uniform field strengths across equivalent volumes of tissue. If the diameter of the electrodes is increased, the applied voltage required to generate a target field strength is reduced. This corresponds to a more linear distribution of the electric field (see Figure 7) . As the electrode diameter is increased, the electric field distribution begins to approach the flat profile characteristic of plate electrodes. This indicates that the electric field strength is more evenly distributed across the entire tissue. Thus, the present invention provides that sufficient voltages can be achieved throughout the tissue without excessively high field strengths near the electrodes.

It can be seen in Figure 8 that substantial benefit is derived from the use of larger diameter electrodes. When the 0.3mm diameter bipolar electrodes described above are replaced with larger electrodes, the applied voltage requirements rapidly decrease from 1300V/cm. When 1.13mm diameter electrodes are used, 920V/cm will be applied to generate a 50V/mm electric field in the center. As the electrode diameter is increased to 1.57mm, the desired applied voltage is 900V/cm. A continuing improvement is observed with 2.38mm (820V/cm) and 3.18mm diameter electrodes (570V/cm) . It should also be noted that such electrode dimensions do not conflict with the mechanical norms for surgical procedures.

Based on these results, it can be concluded that the use of needle electrodes of the type described in the prior art has led to inefficient electric field generation for the purposes of tissue electroporation. In the literature, Hofmann et al. (1996) described an array of needle electrodes arranged in repeating squares with an intra electrode spacing of 0.65mm. The typical applied voltage level for this array is 650V (lOOOV/cm). If the diameter of these electrodes was increased to approximately 1.0mm the applied voltage would need to be roughly 520V. With a 22% reduction in applied voltage and a more homogeneous distribution, the electric fields generated near the electrodes would be much safer for the tissue. An improvement in field distribution is also observed when larger diameter electrodes are incorporated into more complex arrays. As discussed earlier, each type of electrode array has a characteristic field distribution based on the geometric relationship of the electrodes and the typical pulsing pattern. As indicated by the results illustrated in Figure 4, improvement in field distribution can be derived through the use of more efficient arrays and pulsing patterns. The applied voltage used for each array will be dependent on its characteristic field distribution as well as the electrode spacing and cross section. The utilization of larger diameter electrodes with such complex electrode arrays results in a substantial improvement in field distribution, which can approach that of the plate type electrodes. The electrode diameter useful to generate an acceptable field profile is dependent on the geometric relationship (i.e. intra electrode distance and spatial orientation) and pulsing pattern of the electrodes. The use of efficient array designs will provide adequate field uniformity with electrodes of smaller diameter. Due to their inefficiency, bipolar electrodes require a much larger electrode diameter to produce an acceptable electric field profile.

It is useful to note that an improvement in electric field distribution can also be derived by altering the conductivity of the medium near the electrodes. Experiments indicate that the infusion of a highly conductive (relative to the medium) solution near both electrodes in a bipolar array can lead to a more effective distribution of the electric fields throughout the medium. By increasing the conductivity of the medium in the electrode region a less drastic drop in voltage is observed near the electrode, leading to a more homogeneous distribution of fields over the entire area of the array. This concept could be clinically useful for tissue which cannot accommodate electrodes with larger cross sections. A saline solution with ionic strength optimized to be effective as well as bio-compatible could be infused through or around array electrodes to shunt high field strengths away from the adjacent tissue region. The timing of this procedure is important because the array should be pulsed after a conductivity gradient has developed, but before the conductive solution has diffused too far into the tissue. In U.S. patent application serial no. 08/845,553, incorporated herein by this reference, similar methods for altering tissue conductivity are disclosed. In order to develop efficient electrode arrays which maximize therapeutic effect and minimize the attendant side effects, all of the array parameters including electrode cross section should be optimized. Optimization of the array parameters is a complicated process in which many factors are taken into account. For clinical applications, electrode diameter is limited by the properties of the tissue being treated.

If the electrode diameter is too large it may result in mechanical damage to the tissue. Depending on the application, electrodes of 4mm or larger in diameter could safely be employed. However, the most common electrode diameters employed in the practice of the invention will be between 0.5 and 2.5mm. After the treatment region has been established, a surgeon or someone skilled in the art will determine the type of array to be used. Based on the type of tissue to be treated, the surgeon will then select an approximate electrode cross section. The electrodes will be selected by balancing the benefits of a larger diameter with treatment objectives and safety issues. After an appropriate electrode diameter has been selected, the intra-electrode spacing "L" can be determined as well as applied voltages known to be safe and effective. In order to provide substantial improvement in electric field uniformity the following general formula should be applied to determine an acceptable relationship between the intra-electrode spacing and electrode cross sectional surface dimension of E_s (calculated as the cross sectional circumference): X = (E_s++ E_s.)²/L wherein the ratio of the cross-sectional surface dimension of any selected pair of adjacent electrodes having opposite polarity (+/-) to the distance (L) separating said adjacent wherein X is a value greater than approximately 2mm²/mm. Where the array consists of at least three individually-addressable elongate electrodes, X will have a value greater than approximately 0.75mm²/mm. This formula recognizes that the cross section of the electrode will vary as the shape of the cross section changes, although typically the cross section will be curvilinear. It should also be noted that the cross- sectional surface dimension should be relatively uniform along the relevant length of the elongate electrode, otherwise some adjustment should be made for this variation as well. In the typical case where the cross section of the elongate electrode is substantially circular, the formula give above can be restated as:

X = π(E_r+ ² + E_r.²)/L where E_r+ and E_r. are the radii of two opposite polarity electrodes in electrical communication with each other. These relationships provides guidance for the design of more efficient electrode systems. In order to maintain a uniform voltage distribution, as the intra-electrode distance "L" is increased for a given array, there will desirably be a commensurate increase in the cross sectional area of the electrodes. In order to provide adequate field distribution for a bipolar electrode system this ratio, X, in the more limited case should exceed 0.1mm² electrode area per mm intra-electrode distance (mm²/mm). Due to the improvements in field uniformity provided by more efficient array geometry, reasonably good field distribution can be achieved with more complex arrays comprised of smaller diameter electrodes where X exceeds 0.03mm²/mm. However, depending on the specific application, most arrays will have an X value of greater than 0.15.

Analysis of the formula reveals that for electrode spacings likely to be clinically useful (i.e. > 5mm) electrodes should have a diameter of greater than 0.5mm. Due to the relative inefficiency of the bipolar system, electrodes employed in this fashion should have a diameter of greater than 0.7mm. For some applications, such as the local infusion of treatment related compounds, it may be deemed desirable to use hollow core needle electrodes. In these cases the electrode efficiency calculation, X, should be based on a solid core electrode of identical dimension. Improvements in electrode efficiency are provided at the electrode/tissue interface and are therefore related to the external profile of the electrode, regardless of the interior shape.

If necessary, fine tuning of the spacing and diameter can be performed so that the electrode array efficiently covers the predetermined treatment area. After the typical electrode and array parameters have been determined for a given application, a range of optimized arrays will be available for the surgeon to choose from. Desirably, electrodes in the array will be of surgical quality, bio-compatible, and capable of withstanding the demands of implantation and use in a patient. Materials commonly employed in the construction of such electrodes include nickel titanium, gold, silver, stainless steel, platinum, platinum iridium alloys, graphite, ceramic, and the like. The electrodes will be elongate with a tip shaped so as to simplify the surgical implantation of the electrode in the patient. The electrode material should be rigorously tested in conditions similar to that which it will be used. For instance, testing has shown that corrosion begins to occur on the anodic (electron collecting) electrode when some grades of stainless steel are pulsed 5-10 times in a conductive saline solution.

Experimentation has also revealed that high intensity pulses delivered to physiological saline can result in the formation of hydrogen gas bubbles near the surface of the cathodic (electron distributing) electrode. This is due to a reaction involving the reduction of water through the addition of electrons. The amount of hydrogen produced is proportional to the current delivered to the system. These bubbles coat the surface of the electrode and could lead to less efficient transmission of the electric signal to the target tissue. The use of larger diameter electrodes leads to a reduction in the thickness of the bubble layer on the electrode, potentially leading to better current flow. Another concern with the use of high intensity fields is the potential for electrical arcing near the electrodes. Testing indicates that the arcing is due to excessively high current densities generated at the electrodes. It has been found that the relatively sharp points may provoke arcing of the electric field, particularly at the electrode delivering the electrons in the propagation of the electric field (i.e. the cathodic electrode). Thus, it is desirable to provide a rod electrode where the point of the electrode distal from the source of electrical signals includes a radius of curvature sufficient to substantially eliminate arcing at the electric field strengths utilized in the practice of the present invention, for example in the range of 0.1 to 1mm. Another source of electrical arcing between electrodes is due to an imbalance between the cathodic and anodic electrodes. If there is a significant difference in the surface areas of the cathodic and anodic portions of the circuit there is an increased risk of arcing at the electrode with the smaller surface area. Electrode parameters such as effective length, electrode material, and diameter can drastically effect the arcing behavior and should be considered in the design of the electrode array. For the purposes of electroporation these electrodes will be connected to a electrical impulse generating means including a suitable power supply capable of generating the proper electrical signals. The most common signal employed in tissue electroporation is a square wave pulse of amplitude 0.1 - 3 kV. The BTX T-820 pulser (Genetronics, San Diego, CA) is sufficient for generating this type of signal. Depending on the application, various other pulse generators (e.g Cytopulse model PA-

2000 electroporation pulse generator, Cytopulse, Inc., Hanover, MD) could also be connected to these electrodes, providing other electrical signals which result in electroporation of cells in a tissue system.

When an electrode array consists of individually addressed electrodes, a high voltage switching mechanism will be provided in order to change the state of the electrodes. Such a mechanism would generally either be mechanically or digitally controlled and capable of changing the electrical state of an electrode singly or in conjunction with other electrodes in the array.

The following examples serve to illustrate certain preferred embodiments and aspects of the present invention and are not to be construed as limiting the scope thereof.

Experimental

In the experimental disclosure which follows, all linear measurements are given in centimeters (cm), millimeters (mm), micrometers (μm), or nanometers (nm), and all electrical potentials are given in volts (V), unless otherwise indicated.

The following examples demonstrate the practice of the present invention in delivering electrical waveforms to tumor tissue. Example 1 : System to Measure Electric Field Strengths

In order to measure the properties of the electric fields generated between electrodes in an array the following system was be developed: The electrodes consist of stainless steel rods (source) of 2cm length and diameter ranging from 0.3mm to 3.18mm. Knox gelatin dissolved in a 0.45 % saline solution is used to create a conductive gel. After it begins to solidify the saline gel is molded around the electrodes and used as a conductive medium for the electric pulses.

A Cytopulse model PA-2000 electroporation pulse generator (Cytopulse, Inc.,

Hanover, MD) is used for the generation of electric fields in the conductive gel. Measurements can be taken with a Tektronix TD700 digital oscilloscope and Tektronix

10X probes.

After connecting the electrodes to the PA-2000 pulse generator and applying pulses, the probes are placed at different locations within the conductive gel. By measuring the electric potential at two probes separated by a known distance the voltage difference (i.e. the electric field strength) between the two points can be determined.

Rxample 2: Electric Field Distribution For Bipolar Electrodes

In order to determine the characteristics of the electric field generated by a bipolar electrode system the method described in Example 1 can be employed.

Two stainless steel electrodes of 0.3mm diameter are spaced exactly 2.0cm apart. One electrode is designated the pulse electrode and the other a ground electrode.

One of the Tektronix 10X probes will be attached to the pulse electrode for the entire test. The second probe is then attached to a stereotaxic device. In this way the second probe can be placed in precise locations between the electrodes.

The testing consists of measuring the voltage differences between the two probes at different positions. The stereotaxic apparatus moves a probe in 1mm increments from the pulse electrode to the ground electrode. A voltage difference measurement is taken at each increment.

Figure 7 illustrates the results of this evaluation. It can be concluded from this example that there is a nonlinear relationship between the electric field strength and the position between the electrodes. A majority of the voltage drop occurs in the regions surrounding the two electrodes. In Figure 7 it can be seen that roughly 25% of the total voltage drop occurs within 2.0mm of the pulse electrode. Another 25 % of the total voltage drop is experienced in the 2.0mm near the ground electrode. Therefore approximately 50% of the total voltage applied to the electrodes is lost in regions which comprise only 20% of the area between the electrodes.

This example indicates that if this array configuration was used to generate a threshold field strength for electroporation in tissue, the electric fields near the electrodes could become dangerously high before threshold was achieved in the remaining target tissue. Example 3: Electric Field Distribution of Larger Diameter Electrodes

Electrodes of larger diameter are evaluated according to the procedure outlined in Example 2 to determine the effect of diameter on distribution of electric fields. Stainless steel electrodes, spaced at 2.0cm, with diameters of 1.13mm, 1.57mm, and 2.38mm are evaluated and compared to the 0.3mm electrodes which have been used in the prior art.

Figure 7 illustrates the results of this evaluation, with the linear voltage distribution of ideal plate electrodes included as a reference. It can be seen that with an increase in electrode diameter, the voltage position relationship becomes more linear, indicating a more homogeneous distribution of the field strengths. For example, with an electrode diameter of 2.38mm one finds that only 30% of the applied voltage is lost in the region around the electrodes (20% of the total). This compares favorably to the 50% voltage drop observed in the same area for the 0.3mm electrodes in Example 2.

Example 4: Effect of Electrode Diameter and Spacing on Electric Field Distribution Experiments are performed in order to determine how the generation of electric fields is affected by the diameter and spacing of the electrodes. Using the system outlined in Example 1 , electrodes of various diameters and spacing can be tested to determine the applied voltage useful to generate a target field strength over 1mm on the center line between to electrodes. The two probes described in Example 1 are placed exactly 1mm apart in the stereotaxic apparatus. In this way, the probes can easily be moved to a specific location in relation to the electrode while maintaining a 1.0mm separation. Electrodes of 0.3mm, 1.13mm, 1.57mm, 2.38mm, and 3.18mm are tested at spacings ranging from 4mm to 34mm. It should be noted that electrode spacing is measured from the inside edge of each electrode to insure that any difference in the electric fields between different diameters is not due to the electrodes being placed in closer proximity.

Evaluations are conducted by measuring the voltage difference across 1mm in the center of the electrode pair. Seven different applied voltages are tested for each spacing and diameter. Figure 9 illustrates the resulting incremental (over the 1mm probe distance) voltages which are averaged and converted into a percent of applied voltage (i.e. the incremental voltage expressed as a percentage of any applied voltage). Preliminary investigations indicate that a target field strength of approximately 50V/mm of tissue is effective for electroporation of certain cell membranes. Figure 8 illustrates the applied voltage necessary to generate this 50V/mm target field strength with any given electrode diameter and spacing. Based on these results, it can be concluded that there is a substantial improvement in field distribution when larger diameter electrodes are used.

Also, it appears that over this range of operation, there is a linear relationship between an increase in electrode spacing and the commensurate increase in applied voltage required to generate a given field strength. The slope of these lines indicates the field strength in V/cm required to generate a 50V/mm field in the center of a bipolar electrode system. It should be noted that this linear relationship exists only for stable electrode systems. When electrodes are pulsed at very high applied voltages or in certain combinations, dielectric breakdown (arcing) has been observed, indicating a destabilization of the electric field. This tendency is especially noticeable in electrodes of small diameter ( < 0.4mm) and can be corrected by increasing electrode diameter until the system is again stable.

Example 5: Field Strengths in the Electrode Region

Since damage to tissue undergoing electroporation can be correlated to excessively high field strengths near the electrodes, it is important to understand how field distribution can improve the safety of electroporation. Evaluations are performed using the apparatus described in Example 1 to analyze the effect of electrode diameter on field strengths near the electrode surface. The testing should be comprised of electrodes spaced 2.0cm apart with diameters of 0.3mm, 1.13mm, 1.57mm, 2.38mm, and 3.18mm.

Testing of field strengths near the electrode is performed by connecting one probe to the pulse electrode and placing the other in the stereotaxic apparatus. The probe can then be placed in various locations relative to the pulse electrode in order to measure the electric field strengths near the electrode.

In the first test the probe is placed exactly 2.0mm from the edge of the electrode being tested. Figure 10 demonstrates that as the electrode diameter is increased there is a significant decrease in the electric field across the 2.0mm near the electrode. This result supports the use of larger diameter electrodes in tissue to mitigate the risk of electric field induced cell damage.

Example 6: Large Diameter Electrodes Incorporated into Complex Arrays

The system described in Example 1 is employed to determine the effect of larger diameter electrodes in the generation of electric fields by more complex arrays.

Four electrodes of diameter 0.3mm and four electrodes of diameter 1.13mm are placed in a square orientations with "L" equal to 0.65cm (inside edge to inside edge). Four electrodes of diameter 0.3mm and four electrodes of diameter 1.13mm are placed into a rectangular orientation with the a major axis dimension of 1.0cm. This shape corresponds to a single configuration of a hexagonal electrode array. Each array is pulsed in a parallel bipolar format. This type of parallel pulsing causes a compression of the electric fields in the region between the bipolar pairs and results in a better overall field distribution. Voltage readings are taken throughout the array area to determine the field profile as well as the region of weakest field strength. Figure 11 A, 11B and 11C show a comparison between the two complex arrays and the original bipolar array for each electrode diameter. As can be seen, an improvement in field distribution is obtained by the use of more complex arrays as well as increased electrode diameter.

Example 7: Use of conductive solutions to improve propagation of electric fields.

Evaluating the feasibility of using conductive solutions to improve electric field distribution can be obtained using the test system described in Example 2.

After measuring the voltage levels at 1.0mm increments between the bipolar electrode system (utilizing 0.3mm stainless steel needle electrodes), to obtain a baseline reading, approximately 2mL of a saline solution roughly three times the ionic strength

(conductivity) of the gel is injected around each electrode. Care is taken to distribute the injection equally across the full 2cm depth of the electrodes. After the high conductivity saline is injected, voltage measurements can be taken between the electrodes according to the procedure outlined in Example 2. Figure 12 illustrates the results of this evaluation. It is apparent that a significant improvement in field distribution is provided by the injection of higher conductivity saline in the electrode regions. This improvement is comparable in nature to those obtained through the use of improved electrode arrays, as well as the use of larger diameter electrodes. It is also noted that the effect is temporary as the saline diffuses away from the injection site. After one hour, there appears to be a significant reduction in the distribution benefits.

Example 8 - Electrochemical reactions in physiological salt solution

The behavior of an electroporation system in physiological saline can be evaluated as disclosed above, where bipolar electrodes (0.35mm diameter, stainless steel) are placed 1.0cm apart in physiological saline (0.9% NaCl), connected to a Cytopulse PA-2000 pulse generator and pulsed repeatedly at lOOOV/cm.

Observations from the tests indicate that a layer of bubbles forms around the cathodic (electron delivering) electrode. Analysis indicates that the gas being formed is hydrogen, which is a product of the reduction of water. As the diameter of the electrodes is increased from 0.3mm to 1.5mm, the density of the gaseous hydrogen layer around the electrode appears to be reduced. An increase in the voltage or duration of the applied pulses leads to more significant production of the hydrogen, indicating that hydrogen formation is proportional to the current flow in the medium. It should also be noted that a dark substance begins to form on the anodic (electron accepting) electrode. It is especially prevalent on the side facing the cathodic electrode. The substance is dark gray to black in color and continues to darken as more pulses are applied. The rate of color change seems to increase as the voltage or duration of the pulses is increased.

Tests on other electrode materials reveals several differences in behavior. When testing electrodes composed of more inert metals such as gold and platinum it is observed that while hydrogen gas continues to form at the cathodic electrode, gas also forms around the anodic electrode. Anodic electrodes composed of these metals do not exhibit any of the corrosive substance formed on the stainless electrodes. Analysis reveals that the gas produced at the anodic electrode is chlorine, which is a product of the oxidation of the chloride ion. These observations are confirmed in the chemical equations which describe the electrolysis of an aqueous sodium chloride solution:

Cathode 2H₂O (1) + 2e^" → H₂ (g) + 2OH^" (reduction)

Anode (inert) 2C1" + 2e^" → Cl₂ (g) (oxidation)

Anode (active) M^x+ + xCl^" + xe^" → MC1_X (oxidation) where M is a metal such as Fe, Ag, or Cu. Example 9 - Arcing in physiological saline

The test system described in Example 8 is also useful for the evaluation of electrical arcing at the distal tip of the electrodes. It has been observed that when a threshold voltage is exceeded a spark is produced at the cathodic electrode tip, leading to unstable current flow. The threshold voltage for arcing is affected by the radius of curvature of the electrode tip. Sharp points have a lower threshold for arcing, and smaller diameter electrodes exhibit more pronounced sparks. Based on these observations, it appears that the arcing is caused by excessive current densities at the electrodes, and can be alleviated by using electrodes of larger diameter with smooth, rounded tips.

Further testing demonstrates the importance of balanced electrode surface area when applying high voltage pulses. If the effective electrode length (length of the electrically conductive portion) of the cathode is reduced by insulation, electrical arcing will be more pronounced and occur at a lower threshold voltage. If sufficient insulation is applied to the anode then the arcing will be observed at the anodic electrode.

This phenomena is important for the use of multiple electrode systems. The total surface area of the anodic and cathodic electrodes should be balanced to reduce the potential for electrical arcing. Effective electrode length and electrode number should both be considered to insure that a cathodic and anodic balance exists.

All patents and patent applications cited in this specification are hereby incorporated by reference as if they had been specifically and individually indicated to be incorporated by reference.

Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity and understanding, it will be apparent to those of ordinary skill in the art in light of the disclosure that certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims.

Claims

What Is Claimed Is:

1. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes located within a predetermined three-dimensional space in a patient, each of said electrodes independently having a cross sectional surface dimension of E_s wherein the ratio of the cross-sectional surface dimension of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula

X = (E_S+ + E_S.)²/L wherein X is a value greater than approximately 2mm²/mm and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

2. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes located within a predetermined three-dimensional space in a patient, each of said electrodes independently having a substantially curvilinear cross section with a cross sectional radius of E_r wherein the ratio of the cross-sectional area of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula X = ╧Ç(E_r+ ² + E_r.²)/L wherein X is a value greater than approximately 0.08mm²/mm; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

3. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes adapted to be located within a predetermined three-dimensional space in a patient, each of said electrodes having a cross-sectional diameter of at least approximately 0.5 millimeters; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

4. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes adapted to be located within a predetermined three-dimensional space in a patient, each of said electrodes having a cross-sectional circumference of at least approximately 1.5 millimeters; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

5. An electrode system as recited in claim 1 wherein the cross section of each individually-addressable electrode is substantially curvilinear.

6. An electrode system as recited in claim 5 wherein the cross section of each individually-addressable electrode is approximately circular.

7. An electrode system as recited in claim 1 wherein the electrodes are hollow.

8. An electrode system as recited in claim 1 wherein each of said electrodes comprises an electrically conductive region and an electrically nonconductive region.

9. An electrode system as recited in claim 1 comprising at least three individually addressable electrodes disposed so as to form a triangle in a plane intersecting said electrodes.

10. An electrode system as recited in claim 9 wherein the elongate electrodes are oriented in approximately parallel directions.

11. An electrode system as recited in claim 9 wherein the triangle is of approximately equilateral geometry.

12. An electrode system as recited in claim 9 wherein said array comprises at least four electrodes disposed so as to form two interconnected triangles in a plane intersecting said electrodes.

13. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes located within a predetermined three-dimensional space in a patient, said electrodes arranged to provide at least one reference electrode in electrically-conductive communication with a plurality of geometrically-oriented satellite electrodes; each of said electrodes independently having a cross sectional surface dimension of E_s wherein the ratio of the cross-sectional surface dimension of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula

X = (E_S+ + E_S.)²/L wherein X is a value greater than approximately 0.75mm²/mm; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

14. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes located within a predetermined three-dimensional space in a patient, said electrodes arranged to provide at least one reference electrode in electrically-conductive communication with a plurality of geometrically-oriented satellite electrodes, each of said electrodes independently having a substantially curvilinear cross section with a cross sectional radius of E_r wherein the ratio of the cross- sectional area of any selected pair of adjacent electrodes having opposite polarity to the distance (L) separating said adjacent electrodes is expressed by the formula

X = ╧Ç(E_r+ ² + E,²)/L wherein X is a value greater than approximately 0.03mm²/mm; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

15. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes adapted to be located within a predetermined three-dimensional space in a patient, said electrodes arranged to provide at least one reference electrode in electrically- conductive communication with a plurality of geometrically-oriented satellite electrodes; each of said electrodes having a cross-sectional diameter of greater than approximately 0.35 millimeters; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

16. An electrode system for the delivery of electroporation-inducing electrical waveforms to a patient comprising: a plurality of individually-addressable elongate electrodes adapted to be located within a predetermined three-dimensional space in a patient, said electrodes arranged to provide at least one reference electrode in electrically- conductive communication with a plurality of geometrically-oriented satellite electrodes; each of said electrodes having a cross-sectional circumference of at least approximately 1.1 millimeters; and electrical impulse generating means operatively connected to said individually-addressable electrodes for generating electroporation-inducing electrical fields between said electrodes.

17. An electrode system as recited in claim 13 wherein the cross section of each individually -addressable electrode is substantially curvilinear.

18. An electrode system as recited in claim 17 wherein the cross section of each individually-addressable electrode is approximately circular.

19. An electrode system as recited in claim 13 wherein the electrodes are hollow.

20. An electrode system as recited in claim 13 wherein each of said electrodes comprises an electrically conductive region and an electrically nonconductive region.

21. An electrode system as recited in claim 13 comprising at least three individually addressable electrodes disposed so as to form a triangle in a plane intersecting said electrodes.

22. An electrode system as recited in claim 21 wherein the elongate electrodes are oriented in approximately parallel directions.

23. An electrode system as recited in claim 21 wherein the triangle is of approximately equilateral geometry.

24. An electrode system as recited in claim 21 wherein said array comprises at least four electrodes disposed so as to form two interconnected triangles in a plane intersecting said electrodes.