Patent Description:
Each of the <FIG> examples also includes a second pair of electrode arrays including one electrode array at a right-side position <NUM>/<NUM> and a second electrode array at a left-side position <NUM>/<NUM>. When an AC voltage is applied between the right-side array and the left-side array, the field lines of the resulting electric field will run generally between the left and right sides of the subject. AC voltages are applied in an alternating sequence between (i) the anterior/posterior (A/P) electrode arrays and (ii) the right/left (R/L) electrode arrays so that the direction of the field will switch repeatedly (e.g., every <NUM> sec. ) between the two directions described above.

While the A/P and R/L electrode arrays are well suited for applying electric fields in two roughly perpendicular directions into many portions of a subject's body, a number of situations can be envisioned in which A/P and R/L electrodes may be difficult or impossible to use. Examples include situations in which a subject has a sore or ulcer at one of the commonly-used sites for positioning an electrode array, as well as treating tumors at locations where using both AlP and R/L electrodes would be uncomfortable and/or impractical (e.g., in a subject's neck, elbow, knee, etc.).

<CIT> discloses an exemplary apparatus for applying electric fields.

The invention is directed to an apparatus for treating a target region in a subject's body with TTFields according to claim <NUM>.

The embodiments described below overcome the aforementioned limitations of using AlP and R/L electrodes by including at least one pair of electrode arrays configured to generate a longitudinal field in the target region. Note that as used herein: (<NUM>) in the context of the head and main portion of the body, the longitudinal axis is perpendicular to both the anterior-posterior axis and the lateral axis; (<NUM>) in the context of a leg or arm, the longitudinal axis is the proximal-distal axis; (<NUM>) the term "longitudinal field" refers to a field which runs in the same general direction as the longitudinal axis, and is not limited to fields that are exactly parallel to the longitudinal axis; (<NUM>) electrode arrays designed to generate longitudinal fields are referred to as "longitudinal arrays"; and (<NUM>) conventional electrode arrays designed to generate fields that run generally between either the left and right sides of the subject or the front and back of the subject are referred to as "latitudinal arrays.

To generate a longitudinal field, a pair of ring-shaped or arc-shaped electrode arrays that fit around the subject's body may be used, with one array positioned above the other. In some embodiments, the arrays are designed as rings that completely surround the body part on which they are placed. In other embodiments, the arrays are designed as arcs (e.g., semicircles) that partially surround the body part on which they are placed. When a voltage is applied between the upper and lower electrode arrays, the electric field that develops between them will be longitudinally oriented.

<FIG> is a schematic illustration depicting a first order estimate of how longitudinal fields can be generated in the body. In this example, we consider the electric field in a solid conducting cylindrical body <NUM> when an AC voltage <NUM> is applied between thin ring-shaped electrode rings <NUM>, <NUM> on either end of the cylinder <NUM>. It turns out that the resulting electric field in the cylinder <NUM> will be almost uniformly directed longitudinally along the cylinder, as indicated by field lines <NUM>, and will also penetrate into the interior of the cylinder <NUM>. In some embodiments, the pair of electrode arrays for the delivery of TTFields may be designed as two ring-shaped arrays that fit around the subject's body, with one array placed above the other.

Using longitudinal fields can provide significant advantages because TTFields are more effective when they are parallel to the axis of cell division. As a result, increasing the number of directions at which the fields are applied can increase the effectiveness against the tumor that is being treated (in which the orientation of the cells during division can vary). Notably, the use of longitudinal arrays opens up new options for array layouts on the body that can optimize both field distribution and subject comfort.

<FIG> depict four examples of longitudinal pairs of electrode arrays designed to deliver TTFields to different parts of a person's body. In all of these embodiments, each of the electrode arrays includes one or more electrode elements mounted on a substrate that is configured to hold the electrode elements against the subject's body so that the electrode elements completely surround the respective body part. In some preferred embodiments, the substrate is flexible in order to promote conformance with the subject's body. An example of a suitable approach for mounting individual electrode elements on a flexible substrate is described below in connection with <FIG>.

In the <FIG> embodiment, which is intended, e.g., for delivering fields to the thorax or abdomen, the first electrode array is placed at a position <NUM> around the torso (e.g., just above the subject's waist), and the second electrode array is placed at a position <NUM> around the subject's neck. In the <FIG> embodiment, which is intended, e.g., for delivering fields to the abdomen, the first electrode array is placed at a position <NUM> around the torso (e.g., just above the subject's waist), and the second electrode array is placed at a position <NUM> around the torso (e.g., at the top of the subject abdomen). In alternative embodiments (not shown), e.g., for delivering fields to the lungs, the first electrode array is placed below the chest (similar to position <NUM> in <FIG>) and the second electrode array is placed around the subject's neck (similar to position <NUM> in <FIG>.

In the <FIG> embodiment, which is intended, e.g., for delivering fields to a portion of the arm, the first electrode array is placed at a position <NUM> on the arm that is proximal to the target region, and the second electrode array is placed at a position <NUM> on the arm that is distal to the target region. Target regions within the elbow can be accommodated by adjusting the location of these positions <NUM>, <NUM>. Similarly, in the <FIG> embodiment, which is intended, e.g., for delivering fields to a portion of the leg, the first electrode array is placed at a position <NUM> on the leg that is proximal to the target region, and the second electrode array is placed at a position <NUM> on the leg that is distal to the target region. Target regions within the knee can be accommodated by adjusting the location of these positions <NUM>, <NUM>.

In the <FIG> embodiment, which is intended, e.g., for delivering TTFields to the infratentorial brain, the brain stem, and to the neck, the first electrode array is placed at a position <NUM> around the subject's neck, and the second electrode array is placed at a position <NUM> that is close to the crown of the subject's head. In the <FIG> embodiment, which is an alternative embodiment intended for delivering fields to these same anatomic locations, the first electrode array is placed at a position <NUM> around the subject's neck, and the second electrode array is placed at a position <NUM> on top of the subject's head.

Each of the embodiments depicted in <FIG> may be used for implementing a method of treating a target region in a subject's body with TTFields by (<NUM>) affixing a first set of one or more electrodes to the subject's body so as to surround a first part of the subject's body at a position that is longitudinally prior to the target region; (<NUM>) affixing a second set of one or more electrodes to the subject's body so as to surround a second part of the subject's body at a position that is longitudinally subsequent to the target region; and (<NUM>) applying a first AC voltage with a frequency of <NUM>-<NUM> between the first set of one or more electrodes and the second set of one or more electrodes so as to impose a first AC electric field with field lines that run through the target region longitudinally, the first AC electric field having a field strength of at least <NUM> V/cm in at least a portion of the target region. In some preferred embodiments, the first and second sets of one or more electrodes our capacitively coupled to the subject body.

Depending on the anatomic location at which they are used, longitudinal arrays may provide one or more of the following advantages. First, longitudinal arrays may enable coverage of certain target regions with higher field intensities than latitudinal arrays. For instance, when treating lung tumors using only conventional latitudinal arrays, the arrays on the sides of the subject have to be positioned below the armpits. As a result, the field intensity in the upper lobes of the lungs is relatively low. In contrast, longitudinal arrays positioned around the waist and around the neck (as depicted in <FIG>) can provide a more uniform high field intensity throughout the lungs (as described below in connection with <FIG>).

Second, longitudinal arrays may adhere better to body contours than latitudinal arrays in certain anatomic locations. For example, when treating the thorax, latitudinal arrays placed on the chest may not adhere well to body contours (e.g., in the case of female breasts), leading to sub-optimal electric contact of the arrays and the body, reducing field intensity in the tumor. In these situations, the electric coupling of the field to the body through longitudinal arrays may provide better coverage than the electric coupling of the field to the body through latitudinal arrays.

Third, large latitudinal arrays placed on the subject's body can limit motion or cause discomfort to the subject in certain anatomic locations. For example, when treating the thorax, large latitudinal arrays placed on the subject's chest (e.g., as depicted in <FIG>) may cause discomfort or even limit motion. In these cases, using a pair of properly designed longitudinal arrays (e.g., as depicted in <FIG>) to deliver the field can help to improve comfort, because a longitudinal pair of arrays, with one array circumventing the neck and one circumventing the upper abdomen or waist, can be more comfortable for the subject to use.

A fourth significant advantage is that the electric fields that are generated using longitudinal arrays are roughly perpendicular to the electric fields that are generated by latitudinal arrays (i.e., anterior-posterior or laterally-positioned sets of electrode arrays). Arrays designed to create longitudinal fields (e.g., as depicted in <FIG>) can therefore be combined with conventional arrays designed to create latitudinal fields in order to treat the target region with fields at a plurality of different directions, which can increase the efficacy of the treatment. The availability of longitudinal arrays also provides additional degrees of freedom for finding layouts for the electrodes that optimize field distribution and subject comfort.

<FIG> depict examples in which a pair of longitudinal arrays (e.g., similar to those described above in connection with <FIG>) are combined with a pair of latitudinal arrays. In each of these situations, after the electrodes are affixed at their respective positions, (a) an AC voltage is applied between the first and second sets of electrodes that are arranged longitudinally in order to impose a longitudinal field in the target region, and (b) an AC voltage is applied between the third and fourth sets of electrodes that are arranged latitudinally in order to impose a latitudinal field in the target region. These steps (a) and (b) are repeated in an alternating sequence for the duration of the treatment, in order to repeatedly switch the direction of the field that is being imposed in the target region. In some embodiments, the switching rate is between <NUM> and <NUM> seconds. Because treatment preferably proceeds for many hours at a time, each of these steps (a) and (b) is preferably repeated at least <NUM>,<NUM> times. Preferably, the frequency of the AC voltages is between <NUM> and <NUM>, and in some preferred embodiments, the frequency is between <NUM> and <NUM>. In some preferred embodiments (e.g., for treating pancreatic cancer and certain types of lung cancer), the frequency is between <NUM> and <NUM>. In some preferred embodiments (e.g., for treating ovarian cancer), the frequency is between <NUM> and <NUM>. Preferably, each of the electric fields that is imposed in the target region has a field strength of at least <NUM> V/cm.

In the <FIG>/B embodiment, which is intended, e.g., for delivering fields to the thorax, the longitudinal array is implemented with the first electrode array placed at a position <NUM> just above the subject's waist, and the second electrode array placed at a position <NUM> around the subject's neck. And in addition, a latitudinal array is provided with a third electrode array placed at a position <NUM> on the subject's chest, and a fourth electrode array placed at a position <NUM> on the subject's back. In this embodiment, the direction of the field lines of the latitudinal field will run from front to back.

In the <FIG> embodiment, which is also intended, e.g., for delivering fields to the thorax, the longitudinal array is implemented in the same way as in <FIG>, but the latitudinal array is implemented with the third electrode array placed at a position <NUM> on the subject's right side, and the fourth electrode array placed at position <NUM> on the subject's left side. In this embodiment, the direction of the field lines of the latitudinal field will run from side to side.

In the <FIG>/F embodiment, which is also intended, e.g., for delivering fields to the thorax, the longitudinal array is implemented in the same way as <FIG>, but the latitudinal array is implemented with the third electrode array placed at a position <NUM> on the left side of the subject's chest, and a fourth electrode array placed at position <NUM> on the right side of the subject's back. In this embodiment, the direction of the field lines of the latitudinal field will run diagonally through the subject's chest from front to back.

In the <FIG> embodiment, which is intended, e.g., for delivering TTFields to the infratentorial brain, the longitudinal array is implemented with the first electrode array placed at a position <NUM> around the subject's neck, and the second electrode array placed at a position <NUM> that is close to the crown of the subject's head. And in addition, a latitudinal array is provided with a third electrode array placed at a position <NUM> on the left side of the subject's head, and a fourth electrode array placed at position <NUM> on the right side of the subject's head. In this embodiment, the direction of the field lines of the latitudinal field will run from side to side. Alternatively, the latitudinal array may be provided using third and fourth electrodes (not shown) placed at positions on the front and back of the subject's head.

The <FIG> embodiment is similar to the <FIG> embodiment, except that the longitudinal array is implemented with the first electrode array placed at a position <NUM> around the subject's neck, and the second electrode array placed at a position <NUM> on top of the subject's head.

Note that in addition to the embodiments described above in connection with <FIG>, a wide variety of alternative configurations that combine a pair of longitudinally positioned arrays with a pair of latitudinally positioned arrays can be readily envisioned for use at a wide range of anatomic locations, as will be apparent to persons skilled in the relevant arts.

<FIG> depict examples in which a pair of longitudinal arrays (e.g., similar to those described above in connection with <FIG>) are combined with two pairs of latitudinal arrays. In each of these situations, (a) an AC voltage is applied between the first and second set of electrodes that are arranged longitudinally in order to impose a longitudinal field in the target region, (b) an AC voltage is applied between the third and fourth set of electrodes that are arranged latitudinally in order to impose a first latitudinal field in the target region; and (c) an AC voltage is applied between the fifth and sixth set of electrodes that are arranged latitudinally in order to impose a second latitudinal field in the target region. The angle between the first latitudinal field and the second latitudinal field is preferably between <NUM>° and <NUM>°, and most preferably as close as possible to <NUM>°. These steps (a), (b), and (c) are repeated in an alternating sequence for the duration of the treatment, in order to repeatedly switch the direction of the field that is being imposed in the target region between each of the three directions. In some embodiments, the switching rate is between <NUM> and <NUM> seconds. Because treatment preferably proceeds for many hours at a time, each of these steps (a), (b), and (c) is preferably repeated at least <NUM>,<NUM> times.

In the <FIG>/B embodiment, which is intended, e.g., for delivering fields to the thorax, the longitudinal array is implemented with the first electrode array placed at a position <NUM> just above the subject's waist, and the second electrode array placed at a position <NUM> around the subject's neck. In addition, a first latitudinal array is provided with a third electrode array placed at a position <NUM> on the subject's chest, and a fourth electrode array placed at a position <NUM> on the subject's back, in order to generate a first latitudinal field with field lines that run from front to back. Finally, a third latitudinal array is provided with a fifth electrode array placed at position <NUM> on the right side of the subject's body, and a sixth electrode array placed at position <NUM> on the left side of the subject body, in order to generate a second latitudinal field with field lines that run from side to side.

SCiD embodiment is similar to the <FIG>/B embodiment, except that the third and fourth electrode arrays are placed at positions <NUM> and <NUM> on the subject's front and back, respectively; and the fifth and sixth electrode arrays are placed at positions <NUM> and <NUM> on the subject's front and back, respectively. In this embodiment, the first latitudinal field will have field lines that run from the front right to the back left; and the second latitudinal field will have field lines that run from the front left to the back right. The angle between the first latitudinal field and the second latitudinal field is preferably between <NUM>° and <NUM>°, and most preferably as close as possible to <NUM>°.

Here again, in addition to the two embodiments described above in connection with <FIG>, a wide variety of alternative configurations that combine a pair of longitudinally positioned arrays with two pairs of latitudinally positioned arrays can be readily envisioned for use at a wide range of anatomic locations, as will be apparent to persons skilled in the relevant arts.

The discussion of <FIG> above explains the positions at which the various sets of electrodes are placed on the subject's body, but do not describe the construction of those sets of electrodes. A wide variety of construction for implementing those sets of electrodes may be used, including but not limited to the configurations depicted in <FIG>.

<FIG> depicts a first configuration that is suitable for affixing a set of electrodes <NUM> to a subject's body. In this embodiment, each set of electrodes <NUM> includes a plurality of individual electrode elements <NUM> mounted on a band-shaped substrate <NUM>. The band -shaped substrate <NUM> is shaped and dimensioned to fit on the particular body part where it will be used. For example, for the longitudinal array depicted at position <NUM> in <FIG>, the substrate <NUM> will be a flexible substrate that resembles a belt; for the longitudinal array depicted at position <NUM> in <FIG>, the substrate <NUM> would be a flexible substrate that resembles a choker; and for the longitudinal array depicted at position <NUM> in <FIG>, the substrate <NUM> would be a flexible substrate that resembles a headband; etc. The job of the substrate <NUM> is to hold the individual electrode elements <NUM> against the subject's skin so that those elements make good contact the skin. Optionally, conductive gel may be applied between the electrode elements <NUM> and the subject's skin.

In some embodiments, each of the individual electrode elements <NUM> is a disk-shaped capacitively coupled electrode with a high dielectric constant, such as the electrode elements used in the conventional Novocure TTF-<NUM> transducer arrays. In alternative embodiments, instead of using a plurality of individual electrode elements <NUM>, a single electrode element (not shown) may be used, in which case the single electrode element is preferably either flexible or contoured to conform with the particular portion of the subject's body where it will be used.

The individual electrode elements <NUM> within each set of electrodes <NUM> are wired together using appropriate wiring <NUM>. For example, the individual electrode elements <NUM> may be wired in parallel, in series, or in a parallel/series combination. Optionally, this wiring <NUM> may terminate at a connector 64_ This connector <NUM> may be used to connect the set of electrodes <NUM> with the AC signal generator <NUM>, so that the AC signal generator <NUM> can apply a voltage between two sets of electrodes.

<FIG> depicts a second configuration that is suitable for affixing a panel-shaped set of electrodes <NUM>' to a subject's body. This configuration includes a plurality of individual electrode elements <NUM> mounted on a panel-shaped substrate <NUM>'. The wiring <NUM> and connector <NUM> in this <FIG> embodiment is similar to the corresponding elements in <FIG>. This <FIG> embodiment is best suited for placement at locations <NUM>-<NUM> (depicted in <FIG>) and for generating the lateral fields described above in connection with those embodiments.

A wide variety of alternative substrate configurations for mounting a plurality of individual electrode elements will be apparent to persons skilled in the relevant arts, based on the anatomical position at which the electrode elements are positioned. <FIG> depict the positioning of the electrode elements in three such configurations. The substrate that supports the electrode elements for the longitudinal sets of electrodes <NUM>, <NUM> shown in <FIG>/B (which depict front and back views, respectively) will be similar to the band-shaped configuration shown in <FIG>, scaled to the appropriate size for the relevant anatomy. The substrate that supports the electrode elements for the anterior/posterior latitudinal sets of electrodes <NUM>/<NUM> depicted in <FIG>/D (which depict front and back views, respectively) and for the right/left latitudinal sets of electrodes <NUM>/<NUM> depicted in <FIG>/F (which depict front and back views, respectively), will be similar to the panel-shaped configurations shown in <FIG>, scaled and shaped to the appropriate size for the relevant anatomy. Combining all three of the electrode configurations <FIG>/B, 7C/D, and 7E/F and cycling the field between those three pairs of electrodes to provide three different field directions can provide excellent field coverage of the upper lobes of the lungs while maintaining patient comfort.

Finite element method calculations reveal that longitudinal arrays can provide effective penetration of relevant anatomical structures. In one example, a plurality of ceramic disk-shaped electrode elements is distributed at a first position <NUM> that corresponds to the waist and a second position <NUM> that corresponds to the neck of a realistic computational phantom as depicted in <FIG>/B.

<FIG> depicts the strength of the electric field for this example, as calculated using a finite element simulation, for axial slices <NUM>-<NUM> spaced at regular vertical intervals through the lungs. This simulation reveals that it is possible to obtain field intensities between <NUM>-<NUM> V/cm field intensities throughout most of the lungs using longitudinal arrays. <FIG>/B depict the directions <NUM> of the field lines of the longitudinal field through the body and the lungs, respectively, for this simulation. These figures show the longitudinal nature of those field lines.

In some cases, using at least one pair of longitudinal arrays may be the only practical way to treat a tumor using TTFields. For instance, if a tumor is located in a joint such as the knee or elbow, using only lateral sets of electrodes could significantly hamper the subject's mobility.

<FIG> depict inner and outer views, respectively, of an embodiment intended for delivering fields to a knee using two pairs of longitudinal arrays, which overcomes this mobility problem. In this embodiment, a first substrate holds a first set of one or more electrodes against the leg so that it partially surrounds the front side of the leg at a position <NUM> that is proximal to the knee, a second substrate holds a second set of one or more electrodes against the leg so that it partially surrounds the back side of the leg at a position <NUM> that is distal to the knee, a third substrate holds a third set of one or more electrodes against the leg so that it partially surrounds the back side of the leg at a position <NUM> that is proximal to the knee, and a fourth substrate holds a fourth set of one or more electrodes against the leg so it partially surrounds the front side of the leg at a position <NUM> that is distal to the knee.

Each set of electrodes at positions <NUM>-<NUM> is preferably shaped like an open arc that conform with the contours of the leg. This arc shape may be achieved using flexible substrates upon which a plurality of individual electrode elements are mounted, as described above in connection with <FIG>. Alternatively, the arc shape may be achieved using a rigid substrate upon which one or more electrode elements are mounted. When the open arc configuration is used for the electrode arrays, it is important to place the arrays in any given pair on opposite aspects of the body part being used to ensure that the field penetrates the body, because if both arcs in a given electrode pair are placed on the same aspect on the body, then a significant electric field may only develop in the superficial regions of the body.

In this embodiment, a first AC voltage is applied between the set of electrodes affixed at position <NUM> and the set of electrodes affixed at position <NUM>, resulting in an electric field with field lines that run in the general direction of the dashed line <NUM>. Subsequently, a second AC voltage is applied between the set of electrodes affixed at position <NUM> and the set of electrodes affixed at position <NUM>, resulting in an electric field with field lines that run in the general direction of the dotted line <NUM>. This configuration would result in two electric fields that form an X-shape through the joint. Although the directions of these two fields (<NUM>, <NUM>) may not be perpendicular, the angle between those fields will be sufficiently large to provide improved results with respect to a single-direction field. Preferably, the frequency of the first and second AC voltages is between <NUM> and <NUM>. In some preferred embodiments, this frequency is between <NUM> and <NUM>. Preferably, the strength of the two electric fields is at least <NUM> V/cm in at least a portion of the target region.

In alternative embodiments, a knee may be treated by combining one pair of longitudinal arrays positioned above and below the joint with one pair of latitudinal arrays placed on the lateral sides of the joint. In these embodiments, the longitudinal arrays may completely surround the leg (e.g., as seen in <FIG>) or may partially surround the leg (e.g., as described above in connection with <FIG>).

Note that the same concepts described above in connection with <FIG> in the context of a knee can also be applied in the context of an elbow or to other joints if appropriate changes to the relevant dimensions are made.

Note that in some cases (e.g., the <FIG> embodiments), the arrays are designed to completely circumvent the body part on which they are placed, and in other cases (e.g., the <FIG> embodiments), the arrays are designed as open arcs that do not completely circumvent the body part on which they are is placed. But in both of those array configurations, each of the arrays must be positioned at a different position along the longitudinal axis.

TTFields may be delivered through electrode arrays that capacitively couple the electric field generated by a field generating device into the body. For instance, the array design structure described in <CIT>, could be incorporated into the design of longitudinal arrays. The electrode arrays could also be designed as a composite electrode comprising a plurality of ceramic elements that are designed to be positioned against the subject's skin as described in <CIT>.

In some embodiments, the arrays are designed as a set of ceramic disks with a high dielectric constant which are connected to the body via a thin conductive gel. The disks in each array are electrically inter-connected via a flex wire, and an adhesive tape is placed above the disks so that the array adheres firmly to the subject's body. The components for creating the longitudinal arrays may be similar to those that are currently used to deliver TTFields to the head using Optune™, as well as to deliver TTFields to the torso using the NovoTTF-<NUM>. The ceramic elements can be wired in parallel, in series, or in any combination of parallel and series (e.g., <NUM> groups wired in parallel, where each group includes <NUM> disks wired in series.

Optionally, the design of the array layout could be performed with the assistance of finite element simulations, which could be used to calculate the expected field distribution that any specific design of longitudinal arrays will yield. Such designs may be optimized to deliver a maximal field intensity to a target region.

Optionally, the disks in each array may be connected in a manner that enables them to be fitted to subjects of different sizes (e.g., each array may comprise several connected patches with a small number of disks, or the disks may be connected with flexible connectors).

While the above embodiments are described in the context of a human subject, they may also be used for other animals (e.g., dogs, horses, etc.) by making appropriate modifications, which will be apparent to persons skilled in the relevant arts.

Claim 1:
An apparatus for treating a target region in a subject's body with TTFields, the apparatus comprising:
a first pair of ring-shaped electrode arrays (<NUM>, <NUM>; <NUM>) configured completely to surround a respective body part longitudinally prior to the target region and
longitudinally subsequent to the target region, the first pair of electrode arrays (<NUM>, <NUM>; <NUM>) each comprising a plurality of individual electrode elements (<NUM>) wired together using wiring (<NUM>) and mounted on a band-shaped substrate (<NUM>), the band-shaped substrate (<NUM>) being shaped and dimensioned to fit on the body part and configured to hold the individual electrode elements (<NUM>) against the subject's body; and
an AC voltage generator (<NUM>) configured to generate an AC voltage with a frequency of <NUM>-<NUM> between the individual electrode elements (<NUM>) of the first pair of electrode arrays (<NUM>, <NUM>; <NUM>) to impose a first electric field with field lines that run longitudinally through the target region, wherein the first electric field has a field strength of at least <NUM> V/cm.