TRANSDUCER ARRAYS CAPABLE OF ASSUMING A SUBSTANTIALLY CONICAL SHAPE

A transducer apparatus for delivering tumor treating fields to a subject's body, the transducer apparatus comprising: a substrate; and an array of at least one electrode disposed on the substrate, the array configured to be positioned over the subject's body with a face of the array facing the subject's body; wherein the transducer apparatus is substantially non-planar, wherein the transducer apparatus is substantially shaped as a truncated elliptical paraboloid, truncated oblique cone, or truncated cone, and a substantially circular opening is formed by an opening at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone.

BACKGROUND

Tumor treating fields (TTFields) are low intensity alternating electric fields within the intermediate frequency range (for example, 50 kHz to 1 MHz), which may be used to treat tumors as described in U.S. Pat. No. 7,565,205. In current commercial systems, TTFields are induced non-invasively into the region of interest by electrode assemblies (e.g., arrays of capacitively coupled electrodes, also called electrode arrays, transducer arrays or simply “transducers”) placed on the patient's body and applying alternating current (AC) voltages between the transducers. Conventionally, a first pair of transducers and a second pair of transducers are placed on the subject's body. AC voltage is applied between the first pair of transducers for a first interval of time to generate an electric field with field lines generally running in the front-back direction. Then, AC voltage is applied at the same frequency between the second pair of transducers for a second interval of time to generate an electric field with field lines generally running in the right-left direction. The system then repeats this two-step sequence throughout the treatment.

DESCRIPTION OF EMBODIMENTS

This application describes exemplary transducers (or transducer apparatuses) used to apply TTFields to a subject's body for treating one or more cancers.

Transducers used to apply TTFields to a subject's body often include multiple electrode elements electrically coupled together on a substrate and attached to the subject's body at a desired location, for example, via an adhesive backing of the substrate or a separately applied adhesive. Transducers may have large, rectangular surfaces so as to maximize a number of electrode elements that are located on the transducer for applying TTFields to the subject's body. As recognized by the inventors, such transducers may not desirably attach to portions of a subject having a non-planar surface, such as a breast.

The inventors have now recognized that a need exists for transducers that can conform to three-dimensional structures of a subject's body. For example, transducers may be structured to surround, conform, adapt to, or be positioned on or around a breast of a subject and/or a chemotherapy port of a subject. In some embodiments described herein, transducers may be capable of being deformed from being substantially planar to being substantially conical, such as a substantially truncated elliptical paraboloid, a substantially truncated oblique cone, or a substantially truncated cone, or the like. When situated around a breast site, for example, a substantially circular opening may be formed by an opening at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone, for example, to avoid coverage of a subject's nipple. When situated around a chemotherapy port, for example, the chemotherapy port may be located within an opening of the transducer, where the transducer may have a single part or a plurality of parts to form the opening.

The system described herein further provides a practical method to determine a shape and placement of transducers on a subject's body for applying tumor treating fields. For example, a computer-based system may select a first location on the subject's body for placement of a first transducer and a second location on the subject's body for placement of a second transducer, based on one or more simulations of an electric field distribution through a target region in the subject's body. The computer-based system may select a transducer such as described herein as one of the selected transducers.

Different types of transducers are described herein. Each of the embodiments disclosed herein may be used for one or more of the transducer types described herein.

FIGS.1A and1Bdepict an example of transducers positioned at locations on a subject's body for delivery of TTFields.FIG.1Adepicts a first transducer100located on the front of the subject's right breast and a second transducer102located on the front of the subject's left thigh.FIG.1Bdepicts a third transducer104located on the left side of the subject's upper back and a fourth transducer106located on the back of the subject's right thigh. Each of the transducers100,102,104, and106may include one or more electrode elements located on a surface that is flexible for contouring the transducer to the subject's body. The transducers100,102,104, and106may be capable of delivering TTFields to the subject's body.

Similarly,FIGS.2A and2Bdepict another example of transducers positioned at locations on a subject's body for delivery of TTFields.FIG.2Adepicts a first transducer200located on the front of the subject's right thorax and a second transducer202located on the front of the subject's left thigh.FIG.2Bdepicts a third transducer204located on the left side of the subject's upper back and a fourth transducer206located on the back of the subject's right thigh. Each of the200,202,204, and206may include one or more electrode elements located on a surface that is flexible for contouring the transducer to the subject's body.

Transducers arranged on a subject's torso (as shown inFIGS.1A-2B) are capable of applying TTFields to a tumor in the subject's thorax or abdomen. The transducers may be located at various other combinations of locations on the subject's torso than those ofFIGS.1A-2B.

FIGS.1A and1BandFIGS.2A and2Billustrate an assembly for applying TTFields to a subject's body while avoiding at least one area with an anatomic feature or device. For example, inFIG.1A, the surface of the transducer100is shaped and adapted for contouring over a breast of the subject's body while avoiding a nipple108of the subject's body. In some embodiments, once placed on the subject's body, a substantially circular opening110coincides with the nipple108of the subject's body, such that no electrodes of the transducer are located over the nipple108.

As another example, inFIG.2A, the surface of the transducer200is shaped and adapted for contouring to avoid a chemotherapy port208on the subject's body. In particular, the surface of the transducer200is adapted to be positioned on the subject's body such that a substantially circular opening210of the transducer200coincides with a location on the subject's body having the chemotherapy port208. In another example, the surface of the transducer200may be positioned on the subject's body with two opposing portions of the transducer surface spaced apart to straddle a location on the subject's body having the chemotherapy port208. No electrodes of the transducer200may be located over the chemotherapy port208. Chemotherapy ports208are often inserted into a subject's body prior to the subject receiving TTFields treatment. The transducers disclosed herein may enable the application of TTFields to a region of interest in the subject's thorax or abdomen without interfering with or being affected by the subject's chemotherapy port208.

Turning back toFIGS.1A and1B, one or more other transducers102,104, and106may have a different shape than the transducer100. As illustrated, for example, each of the second, third, and fourth transducers102,104, and106of the assembly has a different shape than the first transducer100. In some embodiments, each of the second, third, and fourth transducers102,104, and106may have the same or a substantially similar shape to each other. As illustrated, the surface of at least one of the transducers102,104, and106may have a substantially convex shape. More particularly, the surface of at least one of the transducers102,104, and106may have a rectangular, substantially rectangular with rounded corners (as illustrated), circular, oval, ovaloid, ovoid, or elliptical shape. Similar situations may apply to the transducers200,202,204, and206. In particular, the transducer200illustrated inFIG.2Amay have a similar shape as the transducer100illustrated inFIG.1A, and the transducers202,204, and206illustrated inFIGS.2A and2Bmay have similar shapes as the transducers102,104, and106shown inFIGS.1A and1B.

In other embodiments, one or more of the other transducers102,104, and106may have a surface having the same shape or a mirror image shape of the transducer100ofFIGS.1A and1B. Similarly, one or more of the other transducers202,204, and206may have a surface having the same shape or a mirror image shape compared to the transducer200ofFIGS.2A and2B.

FIG.3Adepicts a top view of two example transducers300A and300B. The transducer300A,300B (and any other transducers disclosed or discussed herein) may be capable of delivering TTFields to a subject's body. The transducers300A and300B have the same shape and the same features. The transducer300A,300B may include a substrate302(having a first side to face the subject and a second side opposite the first side) and an array of at least one electrode (not shown) disposed on the first side of the substrate302. In some embodiments, the transducer300A,300B (and any other transducers disclosed or discussed herein) may include a layer of anisotropic material, as discussed further herein below. For example, the layer of anisotropic material may overlay the at least one electrode on the skin-facing side of the array of the at least one electrode (such that the layer of anisotropic material may be facing the first side of the substrate302). In some embodiments, the layer of anisotropic material may be present as, or may compromise, a laminate having a layer of conductive adhesive, a layer of anisotropic material, and a layer of conductive adhesive. In some embodiments, the anisotropic material is a sheet of graphite. In some embodiments, the layer of anisotropic material is a sheet of pyrolytic graphite, graphitized polymer film, or graphite foil made from compressed high purity exfoliated mineral graphite. In some embodiments, the layer of anisotropic material may take the same or similar shape as that of the substrate302, and may be of a similar size or slightly smaller than that of the substrate. Moreover, in some embodiments, a layer of adhesive may be present between the substrate and the layer of anisotropic material. For simplicity,FIGS.1-5do not show both the substrate and the layer of anisotropic material, although both may be present in one or more (or all) of these embodiments. For embodiments without a layer of anisotropic material, the shape of the main body of the transducer may (or may not) reflect the shape of the substrate (e.g.,302,402,502,702inFIGS.3-5and7).FIG.6Ashows the layer of anisotropic material as603, the exterior edge642of which may (as inFIG.6A), or may not, contour the shape of the main body of the transducer. Similarly, in describing the process of deforming the planar transducer to produce the non-planar transducer, it is to be understood that the substrate and the layer of anisotropic material may have the same or similar shape (overlapping one on the other) and may be adhered to one another. Accordingly, in some embodiments, folding a first portion of the substrate over a second portion of the substrate may include folding both layers (the substrate and the layer of anisotropic material) simultaneously.

The transducer300A,300B (and any other transducers disclosed or discussed herein) may include any of the features discussed herein and may include any desired number of electrode elements (e.g., one or more electrode elements). The transducer300A,300B may be configured to be positioned over a subject's body with a face of the array facing the subject's body. In some embodiments, the transducer300A,300B may be substantially planar. In some embodiments, the transducer300A,300B may be substantially planar prior to being located, applied, or affixed to a subject. In some embodiments, when viewed from a direction perpendicular to a face of the array, the transducer300A,300B may have a substantially pear-shaped or rounded triangular-shaped surface. In some embodiments, when viewed from a direction perpendicular to the face of the array, the substrate302(or layer of anisotropic material303) may have a substantially pear-shaped or rounded triangular-shaped surface.

In some embodiments, when viewed from a direction perpendicular to the face of the array and when the transducer300A,300B is substantially planar, the substrate302(or layer of anisotropic material303) may have an opening304located towards a wider portion316than a narrower portion318of the substrate302(or layer of anisotropic material303). In some embodiments, no electrodes are in the opening304. The opening304may have at least one concave edge305defining the opening304between two opposing portions, namely a first portion330and a second portion332, of the substrate302(or layer of anisotropic material303). The concave edge305may include a substantially C-shaped concave surface. The first portion330and the second portion332may be mirror images of each other and may have reflectional symmetry. The reflectional symmetry of the first portion330and the second portion332may be about a centerline325. In other embodiments, the first portion330and the second portion332may not be mirror images of each other and may not have reflectional symmetry.

In some embodiments, when viewed from a direction perpendicular to the face of the array and when the transducer300A,300B is substantially planar, the transducer300A,300B may include a first end portion306separated from a second end portion308by a gap310. The gap310may be located closer to the wider portion316than the narrower portion318of the substrate302(or layer of anisotropic material303). The centerline325may run through a longest dimension of the substrate302(or layer of anisotropic material303) and through a center of the gap310. The substrate302(or layer of anisotropic material303) may have reflectional symmetry, and the reflectional symmetry of the substrate302(or layer of anisotropic material303) may be about the centerline325.

The substrate302(or layer of anisotropic material303) may have two opposing ends (or opposing sides), namely a first end312and a second end314. The gap310may be defined as being between the two opposing ends312,314of the substrate302(or layer of anisotropic material303). The first end312may include a convex edge, and the second end314may include a convex edge.

The first end portion306may have a first edge320and a second edge322. The first edge320may define a portion of an exterior edge340of the substrate302(or layer of anisotropic material303) and may be convex shaped. The second edge322may define a portion of the concave edge305of the opening304and may be concave shaped. The second end portion308may have a first edge324and a second edge326. The first edge324may define a portion of the exterior edge340of the substrate302(or layer of anisotropic material303) and may be convex shaped. The second edge326may define a portion of the concave edge305of the opening304and may be concave shaped. The opening304may have a partially circular, nearly circular, substantially partially circular, or substantially nearly circular edge defined by the first edge322and the second edge326.

In some embodiments, the first portion330and the second portion332may be used to define the opening304. In some embodiments, the first end portion306and the second end portion308may be used to define the opening304. In some embodiments, the first end portion306and the second end portion308may be used to define the gap310. In some embodiments, the first portion330and the second portion332may be closer to the narrower portion318, and the first end portion306and the second end portion308may be closer to the wider portion316. In some embodiments, the first portion330and the first end portion306may at least partially overlap, and in some embodiments, the second portion332and the second end portion308may at least partially overlap.

In some embodiments, the first end portion306and the second end portion308may each include a portion of the array of at least one electrode. In other embodiments, only one of the first end portion306or the second end portion308includes a portion of the array of at least one electrode. In some embodiments, the first end portion306and the second end portion308are part of a single continuous substrate302(or layer of anisotropic material303). In other embodiments, the first end portion306and the second end portion308are located on two separate discontinuous sections of substrate302(or layer of anisotropic material303).

The transducer300A,300B may be capable of being deformed from being substantially planar to being substantially non-planar, such as being deformed to be shaped as a substantially truncated elliptical paraboloid or substantially truncated oblique cone, or the like. As a non-planar shape, the transducer300A,300B may be substantially conical, such as substantially truncated elliptical paraboloid or substantially truncated oblique cone.

FIG.3Bdepicts the transducer300B applied to an example breast site. For ease in explanation, the transducer300B is depicted on a mannequin. When the transducer300B is deformed and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening350may be formed by the opening304at a truncated portion352of the truncated elliptical paraboloid or truncated oblique cone. In some embodiments, when the transducer300B is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the substantially circular opening350may be formed at the truncated portion352of the truncated elliptical paraboloid or truncated oblique cone by removing the gap310between two opposing ends, namely between the first end312and the second end314of the substrate302(or layer of anisotropic material303). In some embodiments, when the transducer300B is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the first end portion306abuts, touches, or overlaps the second end portion308, and/or the second end portion308abuts, touches, or overlaps the first end portion306. As shown inFIG.3B, the second end314of the second end portion308overlaps the first end312of the first end portion306. As shown inFIG.3B, the abutting, touching, or overlapping of the first end portion306and the second end portion308is situated at a lower portion of the breast of the subject. A similar description may apply for the transducer300A (with the same labelling notations, shown inFIG.3A/3B) when the transducer300A is deformed and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone. Transducer300A may similarly be applied to a breast site.

In some embodiments, the transducer300A,300B may be substantially non-planar. In such embodiments, the transducer300A,300B may be substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, and a substantially circular opening350may be formed by an opening304at a truncated portion352of the truncated elliptical paraboloid or truncated oblique cone. In such embodiments, the transducer300A,300B may be adapted to be positioned on or around an anatomical feature of a subject, for example a breast (FIG.3B). The substantially circular opening350may coincide with a first location on a subject, for example a nipple, and no electrodes of the transducer array may be located over the nipple.

FIG.4Adepicts a top view of two example transducers400A and400B. The transducers400A and400B are mirror images of each other, but otherwise have the same shape and the same features. Although, inFIG.4Athe two example transducers400A and400B are shown as mirror images of each other, they need not be, and, accordingly, the labelling system inFIG.4Afollows a left-side/right-side convention as opposed to a mirror image convention. The transducers400A and400B are similar to the transducer300A,300B (and follow a similar description and labeling notation) but differ in that each of the transducers400A and400B do not have reflectional symmetry. The substrates402A,402B (or layer of anisotropic material403A,403B) have openings404A,404B and gaps410A,410B respectively. In some embodiments, the gaps410A,410B may be situated on one side of the substrate402A,402B (or layer of anisotropic material403A,403B). When viewed from a direction perpendicular to the face of the array and when the transducer400A is substantially planar, the gap410A is on the left side of the substrate402A (or layer of anisotropic material403A). The first portion430A is smaller than the second portion432A. When viewed from a direction perpendicular to the face of the array and when the transducer400B is substantially planar, the gap410B is on the right side of the substrate402B (or layer of anisotropic material403B). The first portion430B is larger than the second portion432B.

The transducer400A,400B may be capable of being deformed from being substantially planar to being substantially non-planar, such as being deformed to be shaped as a truncated elliptical paraboloid or truncated oblique cone.FIG.4Bdepicts the transducer400B applied to an example breast site. For ease in explanation, the transducer400B is depicted on a mannequin. When the transducer400B is deformed and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening450B may be formed by the opening404B at a truncated portion452B of the truncated elliptical paraboloid or truncated oblique cone. In some embodiments, when the transducer400B is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the substantially circular opening450B may be formed at the truncated portion452B of the truncated elliptical paraboloid or truncated oblique cone by removing the gap410B between two opposing ends, namely between the first end412B and the second end414B of the substrate402B (or layer of anisotropic material403B). In some embodiments, when the transducer400B is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the first end portion406B abuts, touches, or overlaps the second end portion408B, and/or the second end portion408B abuts, touches, or overlaps the first end portion406B. As shown inFIG.4B, the second end414B of the second end portion408B overlaps the first end412B of the first end portion406B. As shown inFIG.4B, the abutting, touching, or overlapping of the first end portion406B, and the second end portion408B is situated at a lower portion of the breast of the subject (although other positions of the abutting, touching, or overlapping may be present in other embodiments). A similar description may apply for the transducer400A (with similar labelling notations shown inFIG.4A, except that for transducer400A, the first end portion is408A and the second end portion is406A; and the second end is412A and the first end is414A) when the transducer400A is deformed and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone. Transducer400A may similarly be applied to a breast site.

FIGS.5A and5Bdepict a top view of an example transducer500A. The transducer500A is similar to the transducer400B but includes a second substrate (and/or layer of anisotropic material)570A. In some embodiments, the transducer500A may include a second substrate (and/or layer of anisotropic material)570A separate from the substrate502A (or layer of anisotropic material503A) (FIG.5A). A second array of at least one electrode may be disposed on the second substrate (and/or layer of anisotropic material)570A, and the second array may be configured to be positioned over the subject's body with a face of the second array facing the subject's body. In some embodiments, the second substrate (and/or layer of anisotropic material)570A is substantially C-shaped. In some embodiments, the transducer500A may include the second substrate (and/or layer of anisotropic material)570A which may abut, touch or overlap the first substrate502A (or layer of anisotropic material503A) (FIG.5B). In some embodiments, when the transducer500A (which may include abutting, touching or overlapping second substrate (and/or layer of anisotropic material)570A) is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening550A is defined by the former opening504A (within the former gap510A,FIG.5A) and the substantially C-shaped second substrate (and/or layer of anisotropic material)570A. In some embodiments, when the transducer500A is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a first end portion576A of the substantially C-shaped second substrate (and/or layer of anisotropic material)570A may overlap the first end portion506A of the substrate502A (or layer of anisotropic material503A) in an overlap area580(shaded area inFIG.5B), and a second end portion578A of the substantially C-shaped second substrate (and/or layer of anisotropic material)570A may overlap the second end portion508A of the substrate502A (or layer of anisotropic material503A) in an overlap area582(shaded area inFIG.5B). InFIG.5Bthe overlap area580and the overlap area582have a different size and/or a different shape. However, in some embodiments, the overlap area580and the overlap area582may have a same size and/or a same shape. In some embodiments, the array disposed on substrate502A and the second array disposed on the substrate570A are electrically connected when one overlaps (and contacts) the other. Prior to locating the transducer500A on a subject, the substrate502A (or layer of anisotropic material503A) and the second substrate (and/or layer of anisotropic material)570A may be separate from each other (and not electrically connected), as shown inFIG.5A. Once the transducer500A is located on a subject, the substrate502A (or layer of anisotropic material503A) and the second substrate (and/or layer of anisotropic material)570A may be abutting, touching, or overlapping each other, as shown inFIG.5B. In alternative embodiments, the substrate502A (or layer of anisotropic material503A) and the second substrate (and/or layer of anisotropic material)570A may be abutting, touching, or overlapping each other prior to positioning the transducer500A on the subject.

FIGS.5C and5Ddepict a top view of an example transducer500B. The transducer500B is similar to the transducer300A,300B but, in addition to the substrate502B (or layer of anisotropic material503B) (analogous to the substrate302/layer of anisotropic material303), the transducer500B includes a second substrate (and/or layer of anisotropic material)570B. Similar to the second substrate (and/or layer of anisotropic material)570A, the second substrate (and/or layer of anisotropic material)570B may also be substantially C-shaped. The substrate502B (or layer of anisotropic material503B) of the transducer500B may be substantially similar in structure to the substrate502A (or layer of anisotropic material503A) of the transducer500A except that the gap510B of the opening504B may be situated in a different exemplary position (FIG.5C) as compared to the gap510A of opening504A (FIG.5A). In some embodiments, when the transducer500B is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a first end portion576B of the substantially C-shaped second substrate (and/or layer of anisotropic material)570B may overlap a first end portion506B of the substrate502B (or layer of anisotropic material503B) in an overlap area584(shaded area inFIG.5D), and a second end portion578B of the substantially C-shaped second substrate (and/or layer of anisotropic material)570B may overlap a second end portion508B of the substrate502B (or layer of anisotropic material503B) in an overlap area586(shaded area inFIG.5D). InFIG.5Dthe overlap area584and the overlap area586have a same size and/or a same shape (although they need not be; in some embodiments, the overlap area584and the overlap area586may have a different size and/or a different shape). In other respects, the formation and operation of the transducer500B (including formation of a substantially circular opening550B) may be similar to the transducer500A (including formation of a substantially circular opening550A) and may be similarly shaped as a truncated elliptical paraboloid or truncated oblique cone. In some embodiments, the array disposed on substrate502B and the second array disposed on the substrate570B are electrically connected when one overlaps (and contacts) the other. Prior to locating the transducer500B on a subject, the substrate502B (or layer of anisotropic material503B) and the second substrate (and/or layer of anisotropic material)570B may be separate from each other (and not electrically connected), as shown inFIG.5C. Once the transducer500B is located on a subject, the substrate502B (or layer of anisotropic material503B) and the second substrate (and/or layer of anisotropic material)570B may be abutting, touching, or overlapping each other, as shown inFIG.5D. In alternative embodiments, the substrate502B (or layer of anisotropic material503B) and the second substrate (and/or layer of anisotropic material)570B may be abutting, touching, or overlapping each other prior to positioning the transducer500B on the subject.

When applied to an anatomical feature of a subject, such as a breast or a chemotherapy port, a transducer may be difficult to fit in the correct position. For example, the transducer may be too small to cover a correct location on a breast; or, as another example, it may not be possible or practical to place the transducer on the chemotherapy port. In such situations, for example, transducers500A,500B may be used by first positioning the substrate502A,502B (or layer of anisotropic material503A,503B) on the subject, and then positioning the second substrate (and/or layer of anisotropic material)570A,570B on the subject to form a truncated elliptical paraboloid or truncated oblique cone having a substantially circular opening550A,550B. In some embodiments, the second substrate (and/or layer of anisotropic material)570A and570B may have the same shape and size, or very similar shape and/or size, and may be capable of being used with different shaped substrates, such as the substrate502A and the substrate502B (or layer of anisotropic material503A,503B).

FIG.6Adepicts a top view of an example transducer600. The transducer600is similar to the example transducer300A,300B inFIG.3and with similar feature labeling, but instead of having a gap310, the transducer600includes a slit660. The top view inFIG.6Aadditionally depicts a layer of anisotropic material603which may overlay (and partially obscure) a substrate602. The substrate602may be, or may comprise, an adhesive bandage to affix the transducer600to the subject. When viewed from a direction perpendicular to the face of the transducer600and when the transducer600is substantially planar, the slit660may be located between an exterior edge640of the substrate602and a concave edge605of the opening604. The slit660may separate a first end portion606of the transducer600from a second end portion608of the transducer600. The slit660may be defined by a first edge662of the first end portion606and a second edge664of the second end portion608. As an example, the slit660may be a visible gap between the first edge662and the second edge664. As an example, the slit660may be formed by scoring the transducer600. The first edge662and the second edge664may both be straight lines between the exterior edge640of the substrate602and the concave edge605. The slit660may be through the layer of anisotropic material603having a peripheral edge642. The slit660may be through the substrate602having the exterior edge640. The slit660may be through both the substrate602and the layer of anisotropic material603(as shown inFIG.6A). Similar embodiments may exist for transducers having a substrate but no layer of anisotropic material, or having a layer of anisotropic material but no substrate.

FIG.6Bdepicts the transducer600applied to an example breast site. For ease in explanation, the transducer600is depicted on a mannequin. In some embodiments, when the transducer600is deformed and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening650may be formed by the opening604at a truncated portion652of the truncated elliptical paraboloid or truncated oblique cone. To form the substantially circular opening650, the first end portion606may overlap the second end portion608(or vice-versa). Referring toFIG.6A, an overlap portion668(the shaded section) of the second end portion608may be designated to overlap the first end portion606. InFIG.6B, the second end portion608overlaps at least a part of the first end portion606. In other embodiments, the first end portion606may overlap at least a part of the second end portion608. Referring back toFIG.6B, the edge664at least partially overlaps (or extends onto) the first end portion606, and the edge662is at least partially behind the second end portion608. Due to the overlapping, the substantially circular opening650may or may not be perfectly circular (the latter is illustrated inFIG.6B).

FIG.6Cdepicts a top view of an example transducer610. The transducer610is similar to the example transducer600inFIG.6Aand with similar feature labeling, but instead of having a substantially pear-shaped or rounded triangular-shaped surface, the transducer610has a circular shaped surface. With a circular shaped surface, the transducer610may be better adapted than a substantially pear-shaped or rounded triangular-shaped surface to be placed on or around a breast of a subject or a chemotherapy port of a subject. The top view inFIG.6Cadditionally depicts a layer of anisotropic material613which may overlay (and partially obscure) a substrate612. The substrate612may be, or may comprise, an adhesive bandage to affix the transducer610to the subject. When viewed from a direction perpendicular to the face of the array and when the transducer610is substantially planar, a slit670may be located between an exterior edge621of the substrate612and a concave edge615of the opening614. The slit670may separate a first end portion616of the transducer610from a second end portion618of the transducer610. The slit670may be defined by a first edge672of the first end portion616and a second edge674of the second end portion618. As an example, the slit670may be a visible gap between the first edge672and the second edge674. As an example, the slit670may be formed by scoring the transducer610. The first edge672and the second edge674may both be straight lines between the exterior edge621of the substrate612and the concave edge615. The slit670may be through the layer of anisotropic material613having peripheral edge619. The slit670may be through the substrate612having exterior edge621. The slit670may be through both the substrate612and the layer of anisotropic material613(as shown inFIG.6C). Similar embodiments may exist for transducers having a substrate but no layer of anisotropic material, or having a layer of anisotropic material but no substrate.

FIG.6Ddepicts the transducer610applied to an example breast site. For ease in explanation, the transducer610is depicted on a mannequin. In some embodiments, when the transducer610is deformed and substantially shaped as a truncated cone, a substantially circular opening680may be formed by the opening614at a truncated portion682of the truncated cone. To form the substantially circular opening680, the first end portion616may overlap the second end portion618(or vice-versa). Referring toFIG.6C, an overlap portion678(the shaded section) of the second end portion618may be designated to overlap the first end portion616. InFIG.6D, the second end portion618overlaps at least a part of the first end portion616(by an amount equivalent to the overlap portion678). In other embodiments, the first end portion616may overlap at least a part of the second end portion618. Referring back toFIG.6D, the edge674at least partially overlaps (or extends onto) the first end portion616, and the edge672is at least partially behind the second end portion618. Due to the overlapping, the substantially circular opening680may (should be) perfectly circular or may not be perfectly circular (the latter is illustrated inFIG.6D, primarily to illustrate the first end portion616and the first edge672, both of which would be obscured if the overlap were perfect).

FIG.7depicts an example apparatus700to apply alternating electric fields (e.g., TTFields) to the subject's body. The system may be used for treating a target region of a subject's body with an alternating electric field. In an example, the target region may be in the subject's torso, and an alternating electric field may be delivered to the subject's body via two pairs of transducer arrays positioned on at least one of a thorax, an abdomen, or one or both thighs of the subject's body (such as, for example, inFIGS.1A and1B, which has four transducers100,102,104, and106, and inFIGS.2A and2B, which has four transducers200,202,204, and206). In another example, the target region may be in the subject's brain, and an alternating electric field may be delivered to the subject's body via two pairs of transducer arrays positioned on a head of the subject's body. Other transducer array placements on the subject's body may be possible.

The example apparatus700depicts an example system having four transducers (or “transducer arrays”)700A-D. Each transducer700A-D may include substantially flat electrode elements704A-D positioned on a substrate702A-D and electrically and physically connected (e.g., through conductive wiring707A-D). The substrates702A-D may include, for example, cloth, foam, flexible plastic, and/or conductive medical gel or adhesive. As described herein, the transducers700A-D may be substantially planar (flat), but one or more of the transducers700A-D may be configured such that the transducer is capable of being deformed from being substantially planar to being substantially non-planar (e.g., being substantially shaped as a truncated elliptical paraboloid, a truncated oblique cone, a truncated cone, or the like). Two transducers (e.g.,700A and700D) may be a first pair of transducers configured to apply an alternating electric field to a target region of the subject's body. The other two transducers (e.g.,700B and700C) may be a second pair of transducers configured to similarly apply an alternating electric field to the target region.

The transducers700A-D may be coupled to an AC voltage generator720, and the system may further include a controller710communicatively coupled to the AC voltage generator720. The controller710may include a computer having one or more processors724and memory726accessible by the one or more processors. The memory726may store instructions that when executed by the one or more processors control the AC voltage generator720to induce alternating electric fields between pairs of the transducers700A-D according to one or more voltage waveforms and/or cause the computer to perform one or more methods disclosed herein. The controller710may monitor operations performed by the AC voltage generator720(e.g., via the processor(s)724). One or more sensor(s)728may be coupled to the controller710for providing measurement values or other information to the controller710(e.g., thermistors providing temperature measurements).

The voltage generator720may provide one or more voltages to the different pairs of transducers (e.g.,700A/D,700B/C) for applying alternating electric fields to the subject's body. The controller710may instruct the voltage generator720to generate the one or more voltages according to one or more waveforms. For example, the method described below with reference toFIG.7may be implemented using the voltage generator720and controller710.

The structure of the transducers700A-D may take many forms. The transducers may be affixed to the subject's body or attached to or incorporated in clothing covering the subject's body. The transducer may include suitable materials for attaching the transducer to the subject's body. For example, the suitable materials may include cloth, foam, flexible plastic, and/or a conductive medical gel.

The transducer may include any desired number of electrode elements (e.g., one or more electrode elements). For example, the transducer may include one, two, three, four, five, six, seven, eight, nine, ten, or more electrode elements (e.g., twenty electrode elements). Various shapes, sizes, and materials may be used for the electrode elements. Any constructions for implementing the transducer (or electric field generating device) for use with embodiments of the invention may be used as long as they are capable of (a) delivering TTFields to the subject's body and (b) being positioned at the locations specified herein. The transducer may be conductive or non-conductive. In some embodiments, an AC signal may be capacitively coupled into the subject's body. In some embodiments, at least one electrode element of the first, the second, the third, or the fourth transducer can include at least one ceramic disk that is adapted to generate an alternating electric field. In some embodiments, at least one electrode element of the first, the second, the third, or the fourth transducer includes a polymer film that is adapted to generate an alternating field. For example, at least one electrode element may include polymer films disposed over pads on a printed circuit board or over substantially planar pieces of metal. In an embodiment, such polymer films have a high dielectric constant, such as, for example, a dielectric constant greater than 10.

The disclosed transducers may also include a layer of anisotropic material located on a side of the array of electrode elements facing the subject's body, as disclosed, for example, in United States Patent Application Publication No. 2023/0037806 A1. The layer of anisotropic material may have anisotropic thermal properties and/or anisotropic electrical properties. If the layer of anisotropic material has anisotropic thermal properties (for example, greater thermal conductivity in the plane of the layer than through the plane of the layer), then the layer spreads heat out more evenly over a larger surface area. If the layer of anisotropic material has anisotropic electrical properties (for example, greater electrical conductivity in the plane of the layer than through the plane of the layer), then the layer spreads the current out more evenly over a larger surface area. In each case, this lowers the temperature of any hot spots and raises the temperature of the cooler regions when a given AC voltage is applied to the array of electrode elements. Accordingly, the current can be increased (thereby increasing the therapeutic effect) without exceeding the safety temperature threshold at any point on the subject's skin.

In some embodiments, the layer of anisotropic material is anisotropic with respect to electrical conductivity properties. In some embodiments, the layer of anisotropic material is anisotropic with respect to thermal conductivity properties. In some preferred embodiments, the layer of anisotropic material is anisotropic with respect to both electrical conductivity properties and thermal conductivity properties.

The anisotropic thermal properties include directional thermal properties. Specifically, the layer of anisotropic material may have a first thermal conductivity in a direction that is perpendicular to its front face (skin-facing surface) that is different from a thermal conductivity of the layer of anisotropic material in directions that are parallel to the front face. For example, the thermal conductivity of the layer of anisotropic material in directions parallel to the front face is more than two times higher than the first thermal conductivity. In some preferred embodiments, the thermal conductivity in the parallel directions is more than ten times higher than the first thermal conductivity. For example, the thermal conductivity of the sheet in directions that are parallel to the front face may be more than: 1.5 times, 2 times, 3 times, 5 times, 10 times, 20 times, 100 times, 200 times, or even more than 1,000 times higher than the first thermal conductivity.

The anisotropic electrical properties include directional electrical properties. Specifically, the layer of anisotropic material may have a first electrical conductivity (or, conversely, resistance) in a direction that is perpendicular to its front face that is different from an electrical conductivity (or resistance) of the layer of anisotropic material in directions that are parallel to the front face. For example, the resistance of the layer of anisotropic material in directions parallel to the front face may be less than the first resistance. In some preferred embodiments, the resistance in the parallel directions is less than half of the first resistance or less than 10% of the first resistance. For example, the resistance of the layer of anisotropic material in directions that are parallel to the front face may be less than: 75%, 50%, 40%, 30%, 20%, 10%, 5%, 1%, 0.5%, or even less than 0.1% of the first resistance.

In some embodiments (e.g., when the layer of anisotropic material is a sheet of pyrolytic graphite), the layer of anisotropic material has both anisotropic electrical properties and anisotropic thermal properties.

FIG.8depicts an example computer apparatus for use with the embodiments herein. As an example, the apparatus800may be a computer to implement certain techniques disclosed herein, such as selecting transducer locations for delivering TTFields to a subject as discussed with respect toFIG.9below. As an example, the apparatus800may be a controller apparatus to apply alternating electric fields for the embodiments herein. For example, the apparatus800may be used as the controller710ofFIG.7. The apparatus800may include one or more processors802, memory804, one or more input devices (not shown, but depicted as input808), and one or more output devices806.

The memory804is accessible by the one or more processors802so that the one or more processors802can read information from and write information to the memory804. The memory804may store instructions that when executed by the one or more processors802implement one or more embodiments of the present disclosure. For example, the apparatus800may include one or more processors and memory accessible by the one or more processors, where the memory stores instructions that when executed by the one or more processors, cause the apparatus800to perform operations to implement one or more embodiments of the present disclosure.

In one example, based on input808, the one or more processors802may generate control signals to control the voltage generator to implement an embodiment of the invention. The input808may be user input, sensor input, or input from another computer in communication with the apparatus800. The input808may be received in conjunction with one or more input devices (not shown) of the apparatus800. The output devices806may provide the status of the operation of the invention, such as transducer selection, voltages being generated, and other operational information. The output devices806may provide visualization data.

FIG.9is a flowchart depicting an example method900of determining the shape and placement of transducers on a subject's body for applying TTFields. As illustrated, the method900may begin at step S902with determining a target region in the subject's body. This may be accomplished by, for example, analyzing one or more sets of image data (e.g., magnetic resonance imaging (MRI) data, computer tomographic (CT) data, etc.) to determine an approximate location and/or 3D volume of the target (e.g., tumor) and/or target region in the subject's body.

At step S904, the method900includes selecting a location on the subject's body for placement of transducers based on one or more simulations of an electric field distribution through the target region in the subject's body. This may involve, for example, performing one or more simulations (using a simulation algorithm) of the expected electric field distribution through the target region of the subject's body based on image data associated with the subject's body. More particularly, the determination may be made by comparing simulations for different possible transducer location pairs, ranking the results, and recommending a pair of transducer locations based on expected electric field distributions through the target region.

At step S906, the method900includes determining if the location intersects a designated area of the subject's body. The designated area may be, for example, a breast or a chemotherapy port. The breast area may be identified, for example, via an image processing module identifying landmarks (e.g., anatomical features and/or devices) depicted in one or more images included with image data of the subject's body. The image processing module may use one or more object identification and/or tracking algorithms to determine/detect the locations of one or more landmarks. In another example, the breast area may be identified based on user inputs including, for example, an indication of the presence and/or approximate location of a chemotherapy port in the area, body measurements (e.g., breast size measurements), an indication of the presence and/or approximate location of a nipple, and others. An area around a chemotherapy port may similarly be designated.

At step S908, the method900includes selecting a transducer shape for the transducer based on the designated area on the subject's body. Selecting the transducer shape may involve, for example, determining at step S906whether the location overlaps at least a nipple of the breast area or the location overlaps a chemotherapy port. The selected shape may include a shape as described above. In some embodiments, the method900may include selecting the particular shape based on factors such as, for example, the relative size and position of the overlapping portion of a breast, a nipple, or a chemotherapy port. The selected transducer shape may be a shape other than a default shape. The selected transducer shape may be a shape as described herein such that the transducer is capable of being deformed from being substantially planar to being substantially non-planar (e.g., being substantially shaped as a truncated elliptical paraboloid, a truncated oblique cone, a truncated cone, or the like).

In an example, at step S910the method900may optionally further include determining an orientation of the transducer at the location of the subject's body to prevent the transducer from covering at least a portion of the designated area (e.g., a nipple or a chemotherapy port in the designated area).

At step S912, upon determining that the location does not overlap a designated area, another transducer shape (e.g., a default transducer shape) may be selected at step S912for the transducer. As an example, a default transducer shape may be a rectangular, substantially rectangular with rounded corners, circular, oval, ovaloid, ovoid, or an elliptical shape.

At step S924, the method900includes outputting the recommended transducer shape and location to a user (e.g., via an output on a user interface). Step S924may also include outputting a recommended orientation of the transducer to the user. The outputs may be in the form of visual notifications for transducer array placement. That is, the one or more recommended placement positions for the transducer array and a breast, a nipple, and/or a chemotherapy port may be displayed to the user. The notification may visually instruct the user where to place a transducer array to 1) avoid a nipple or a chemotherapy port on the subject's body, and 2) receive an optimized electric field applied to the target region.

While an order of operations is indicated inFIG.9for illustrative purposes, the timing and ordering of such operations may vary where appropriate without negating the purpose and advantages of the examples set forth in detail throughout the remainder of this disclosure.

ILLUSTRATIVE EMBODIMENTS

The invention includes other illustrative embodiments (“Embodiments”) as follows.

Embodiment 1. A transducer apparatus for delivering tumor treating fields to a subject's body, the transducer apparatus comprising a substrate; and an array of at least one electrode disposed on the substrate, the array configured to be positioned over the subject's body with a face of the array facing the subject's body; wherein, when viewed from a direction perpendicular to the face of the array, the substrate has a substantially pear-shaped or rounded triangular-shaped surface having an opening located towards a wider portion of the substantially pear-shaped or rounded triangular-shaped surface, and no electrodes are in the opening, wherein the transducer apparatus is substantially planar, wherein the transducer apparatus is capable of being deformed from being substantially planar to being non-planar and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening is formed by the opening at a truncated portion of the truncated elliptical paraboloid or truncated oblique cone.

Embodiment 2: The transducer apparatus of Embodiment 1, wherein when viewed from a direction perpendicular to the face of the array and when the transducer apparatus is substantially planar, the transducer apparatus comprises a first end portion separated from a second end portion by a gap, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the first end portion abuts, touches, or overlaps the second end portion.

Embodiment 2A: The transducer apparatus of Embodiment 2, wherein the first end portion has a first edge and a second edge, the first edge defining a portion of an exterior edge of the substantially pear-shaped or rounded triangular-shaped surface, the second edge defining a portion of the opening; and wherein the second end portion has a first edge and a second edge, the first edge defining a portion of the exterior edge of the substantially pear-shaped or rounded triangular-shaped surface, the second edge defining a portion of the opening.

Embodiment 2B: The transducer apparatus of Embodiment 2, wherein the first end portion and the second end portion each include a portion of the array of at least one electrode.

Embodiment 2C: The transducer apparatus of Embodiment 2, wherein only one of the first end portion or the second end portion includes a portion of the array of at least one electrode.

Embodiment 5D: The transducer apparatus of Embodiment 2, wherein the first end portion and the second end portion are part of a single continuous substrate.

Embodiment 5E: The transducer apparatus of Embodiment 2, wherein the first end portion and the second end portion are located on two separate discontinuous sections of substrate.

Embodiment 3: The transducer apparatus of Embodiment 1, wherein when viewed from a direction perpendicular to the face of the array and when the transducer apparatus is substantially planar, the substrate includes a slit between an exterior edge of the substrate and an edge of the opening, wherein the slit separates a first end portion of the transducer apparatus from a second end portion of the transducer apparatus, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the first end portion overlaps the second end portion.

Embodiment 4: The transducer apparatus of Embodiment 1, wherein, when viewed from a direction perpendicular to the face of the array and when the transducer apparatus is substantially planar, the substrate has at least one concave edge defining the opening between two opposing sides of the substrate, and the opening defines a substantially C-shaped surface at the wider portion of the substantially pear-shaped or rounded triangular-shaped surface.

Embodiment 5: The transducer apparatus of Embodiment 4, wherein the substrate has reflectional symmetry.

Embodiment 6: The transducer apparatus of Embodiment 4, wherein a gap defined by the substantially C-shaped surface is situated on one side of the substrate and is defined by a centerline running through a longest dimension of the substrate and through a center of the gap.

Embodiment 7: The transducer apparatus of Embodiment 1, further comprising a second substrate separate from the substrate; wherein the second substrate is substantially C-shaped, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, the substantially circular opening is defined by the opening and the substantially C-shaped second substrate; and, optionally, wherein a second array of at least one electrode is disposed on the second substrate, the second array configured to be positioned over the subject's body with a face of the second array facing the subject's body.

Embodiment 8: The transducer apparatus of Embodiment 7, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, each end portion of the substantially C-shaped second substrate overlaps separate portions of the substrate.

Embodiment 9: The transducer apparatus of Embodiment 7, wherein the array and the second array are electrically connected.

Embodiment 10: The transducer apparatus of Embodiment 1, wherein the substrate is adapted to be positioned on or around an anatomical feature of a subject.

Embodiment 11: The transducer apparatus of Embodiment 10, wherein the anatomical feature is a breast.

Embodiment 12: The transducer apparatus of Embodiment 1, wherein the substantially circular opening coincides with a first location on a subject, and wherein the first location comprises a nipple, and no electrodes of the transducer array are located over the nipple.

Embodiment 13: The transducer apparatus of Embodiment 1, further comprising a layer of anisotropic material on a skin-facing side of the array.

Embodiment 14: The transducer apparatus of Embodiment 13, wherein the anisotropic material is a sheet of graphite.

Embodiment 14A: The transducer apparatus of Embodiment 13, wherein the layer of anisotropic material is a sheet of pyrolytic graphite, graphitized polymer film, or graphite foil made from compressed high purity exfoliated mineral graphite.

Embodiment 14B: A method of using the apparatus of Embodiment 1, comprising applying the substrate on or around an anatomical feature of a subject's body such that the substantially circular opening coincides with a first location on the subject's body; and generating an electric field from the array of electrodes.

Embodiment 14C: The method of Embodiment 14B, wherein the first location comprises a nipple, and no electrodes of the array are located over the nipple.

Embodiment 14D: A transducer apparatus for delivering tumor treating fields to a subject's body, the transducer apparatus comprising: a substrate; and an array of at least one electrode disposed on the substrate, the array configured to be positioned over the subject's body with a face of the array facing the subject's body; wherein, when viewed from a direction perpendicular to the face of the array, the substrate has a substantially pear-shaped or rounded triangular-shaped surface, the substrate has two ends defining a gap between two opposing sides of the substrate, the gap located closer to a wider portion than a narrower portion of the substantially pear-shaped or rounded triangular-shaped surface, and no electrodes are in the gap, wherein the transducer apparatus is substantially planar, wherein the transducer apparatus is capable of being deformed from being substantially planar to being non-planar and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening is formed at a truncated portion of the truncated elliptical paraboloid or truncated oblique cone by removing the gap between two opposing sides of the substrate.

Embodiment 14E: A computer-implemented method to determine a shape and placement of transducers on a subject's body for applying tumor treating fields, the computer comprising one or more processors and memory accessible by the one or more processors, the memory storing instructions that when executed by the one or more processors cause the computer to perform the method, the method comprising: determining a target region in the subject's body to apply tumor treating fields; selecting a first location on the subject's body for placement of a first transducer apparatus and a second location on the subject's body for placement of a second transducer apparatus, based on one or more simulations of an electric field distribution through the target region in the subject's body; selecting a first transducer apparatus based on the first location intersecting a breast area of the subject's body; selecting a second transducer apparatus for the second location; and outputting the first transducer apparatus, the first location, the second transducer apparatus, and the second location to a user, wherein, when viewed from a direction perpendicular to the face of the first transducer apparatus, the first transducer apparatus has a substantially pear-shaped or rounded triangular-shaped surface having an opening located towards a wider portion of the substantially pear-shaped or rounded triangular-shaped surface, wherein the first transducer apparatus is capable of being deformed from being substantially planar to being non-planar and substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, wherein when the first transducer apparatus is substantially shaped as a truncated elliptical paraboloid or truncated oblique cone, a substantially circular opening is formed at a truncated portion of the truncated elliptical paraboloid or truncated oblique cone.

Embodiment 15: A transducer apparatus for delivering tumor treating fields to a subject's body, the transducer apparatus comprising a substrate; and an array of at least one electrode disposed on the substrate, the array configured to be positioned over the subject's body with a face of the array facing the subject's body; wherein the transducer apparatus is substantially non-planar, wherein the transducer apparatus is substantially shaped as a truncated elliptical paraboloid, truncated oblique cone, or truncated cone, and a substantially circular opening is formed by an opening at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone.

Embodiment 16: The transducer apparatus of Embodiment 15, wherein the substrate is adapted to be positioned on or around an anatomical feature of a subject.

Embodiment 16A: The transducer apparatus of Embodiment 16, wherein the anatomical feature is a breast.

Embodiment 17: The transducer apparatus of Embodiment 15, wherein the substantially circular opening coincides with a first location on a subject, wherein the first location comprises a nipple, and no electrodes of the transducer array are located over the nipple.

Embodiment 18: The transducer apparatus of Embodiment 15, further comprising a layer of anisotropic material on a skin-facing side of the array.

Embodiment 19: The transducer apparatus of Embodiment 18, wherein the anisotropic material is a sheet of graphite.

Embodiment 19A: The transducer apparatus of Embodiment 18, wherein the layer of anisotropic material is a sheet of pyrolytic graphite, graphitized polymer film, or graphite foil made from compressed high purity exfoliated mineral graphite.

Embodiment 20: A computer-implemented method to determine a shape and placement of transducers on a subject's body for applying tumor treating fields, the computer comprising one or more processors and memory accessible by the one or more processors, the memory storing instructions that when executed by the one or more processors cause the computer to perform the method, the method comprising: determining a target region in the subject's body to apply tumor treating fields; selecting a first location on the subject's body for placement of a first transducer apparatus and a second location on the subject's body for placement of a second transducer apparatus, based on one or more simulations of an electric field distribution through the target region in the subject's body; selecting a first transducer apparatus based on the first location intersecting a breast area of the subject's body; selecting a second transducer apparatus for the second location; and outputting the first transducer apparatus, the first location, the second transducer apparatus, and the second location to a user, wherein the first transducer apparatus is substantially non-planar, wherein the first transducer apparatus is substantially shaped as a truncated elliptical paraboloid, truncated oblique cone, or truncated cone, and a substantially circular opening is formed at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone.

Embodiment 21: A method of administering tumor treating fields (TTFields) to a subject, the method comprising: determining a target region in the subject's body to apply tumor treating fields; selecting a location on the subject's body for placement of a transducer apparatus based on one or more simulations of an electric field distribution through the target region in the subject's body; selecting a transducer apparatus based on the location intersecting a breast area of the subject's body, the transducer apparatus comprising a first end portion separated from a second end portion by a gap, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid, truncated oblique cone, or truncated cone, the first end portion abuts, touches, or overlaps the second end portion; applying the transducer apparatus to the location on the subject's body intersecting the breast area of the subject's body; and overlapping the first end portion and the second end portion to obtain a 3-D structure or a non-planar transducer structure, wherein a substantially circular opening is formed at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone.

Embodiment 21A: The method of Embodiment 21, further comprising: delivering alternating electric fields to the subject via at least one pair of transducer apparatuses, wherein the at least one pair of transducer apparatuses comprises the transducer apparatus on the location intersecting the breast area of the subject's body.

Embodiment 22: A method of positioning a transducer array over a contoured surface of a subject, the method comprising: determining a target region in the subject's body to apply tumor treating fields; selecting a location on the subject's body for placement of a transducer apparatus based on one or more simulations of an electric field distribution through the target region in the subject's body; selecting a transducer apparatus based on the location intersecting a breast area of the subject's body, the transducer apparatus comprising a first end portion separated from a second end portion by a gap, wherein when the transducer apparatus is substantially shaped as a truncated elliptical paraboloid, truncated oblique cone, or truncated cone, the first end portion abuts, touches, or overlaps the second end portion; applying the transducer apparatus to the location on the subject's body intersecting the breast area of the subject's body; and overlapping the first end portion and the second end portion to obtain a 3-D structure or a non-planar transducer structure, wherein a substantially circular opening is formed at a truncated portion of the truncated elliptical paraboloid, truncated oblique cone, or truncated cone.

Embodiment 22A: The method of Embodiment 22, further comprising: delivering alternating electric fields to the subject via at least one pair of transducer apparatuses, wherein the at least one pair of transducer apparatuses comprises the transducer apparatus on the location intersecting the breast area of the subject's body.

Optionally, for each embodiment described herein, the voltage generation components supply the transducers with an electrical signal having an alternating current waveform at frequencies in a range from about 50 kHz to about 1 MHz, or from about 100 kHz to about 500 kHz, and appropriate to deliver TTFields treatment to the subject's body.

Embodiments illustrated under any heading or in any portion of the disclosure may be combined with embodiments illustrated under the same or any other heading or other portion of the disclosure unless otherwise indicated herein or otherwise clearly contradicted by context. For example, and without limitation, embodiments described in dependent claim format for a given embodiment (e.g., the given embodiment described in independent claim format) may be combined with other embodiments (described in independent claim format or dependent claim format).

Numerous modifications, alterations, and changes to the described embodiments are possible without departing from the scope of the present invention defined in the claims. It is intended that the present invention not be limited to the described embodiments, but that it has the full scope defined by the language of the following claims, and equivalents thereof.