idref="DRAWINGS">FIG. 3G: zero order interpolation; for FIG. 3H: SciPy nearest interpolation; and for FIG. 3I: SciPy linear interpolation.

FIG. 4A depicts an example method 400 for computing an initial estimate (e.g., initial vector φ′) for each transducer location based on an initial model of the subject that is missing at least one type of material compared to the model of the subject. This example method 400 may be used to accomplish step S104 in the method 100A/100B of FIG. 1A/1B. While an order of operations is indicated in FIG. 4A for 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 herein.

At step S402, the method 400 may include generating an initial model of the subject that is missing at least one type of material compared to the model of the subject. That is, the initial model may be generated by taking the model of the subject's body and changing the values in voxels associated with the at least one type of material to be removed to zero (or another values that signifies a lack of material at the voxel locations). As such, generating the initial model may include removing all instances of the at least one type of material from the voxels of the model of the subject's body. The initial model of the subject may be missing, for example, brain tissue compared to the model of the subject. Other, or additional, types of tissue or other material(s) may also be missing from the initial model in other embodiments. The initial model may be generated based on an assumption of a uniform medium (e.g., air) and/or a lack of material located throughout the voxels representative of the missing material(s).

At step S404, the method 400 may include computing an initial matrix A′ and an initial vector b′ to be used in computing the initial vector φ′ for the plurality of transducer locations, wherein A′φ′=b′, and wherein each initial vector b′ is based on the boundary conditions for each respective transducer location. The initial matrix A′ and initial vector b′ may be computed based on the initial model of the subject generated in step S402. This results in an initial matrix A′ that is easier to solve for than matrix A (e.g., takes less computational time).

By first solving for the initial vector φ′ using the initial matrix A′, the method 400 provides a closer initial estimate for input to the optimization algorithm, thereby reducing the total amount of time to solve for $ and select one or more transducer locations.

FIG. 4B depicts an example method 450 for computing an initial estimate (e.g., initial vector φ′) for each transducer location based on an initial model of the subject that is missing all types of material (e.g., tissue, gel, ceramic, polymer, other parts of the transducer, etc.) that are not perfect conductors compared to the model of the subject. This represents an exemplary implementation of the method 400 described in FIG. 4A. The example method 450 may be used to accomplish steps S104 and S106 in the method 100A/100B of FIG. 1A/1B. While an order of operations is indicated in FIG. 4B for 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 herein.

At step S452, the method 450 may include generating an initial model of the subject that is missing all types of material compared to the model of the subject, except for the electrode elements located in three-dimensional space. That is, the initial model may be generated by taking the model of the subject's body and changing the values in the voxels associated with all tissues, ceramic, polymer, gel, and other materials located between the oppositely positioned electrode elements to zero. As such, generating the initial model includes removing everything that is not a perfect (or near-perfect) conductor to obtain a set of perfect conductors suspended in mid-air. In this medium (e.g., air), the solution to A′φ′=b′ can be determined by a simple formula for each voxel.

At step S454, the method 450 may include computing an initial estimate (φ′) of electrical potentials in each voxel based on the sign of the voltage that each electrode element is charged with and the distance of the voxel from each electrode element. This provides an approximation (φ′) of the solution in an air-only medium.

By first solving for the initial vector φ′ using distances and charges of the electrode elements compared to each voxel, the method 450 may provide a closer initial estimate for input to the optimization algorithm, thereby reducing the total amount of time to solve for $ and select one or more transducer locations.

FIGS. 5A and 5B depict results of different simulations showing the electrical potentials at a transducer location of a subject's head. FIG. 5A depicts a simulation of the electrical potentials (φ) computed by solving Equation (2), using the model of the subject without any tissue removed. This represents the results, for example, of step S110 of FIG. 1A but with an initial estimate for the initial vector φ′ using a previous technique. FIG. 5B depicts a simulation of the electrical potentials (φ′) computed by solving Equation (1), using an initial vector φ′ that was computed from initial models having all types of materials removed excepted for electrode elements. FIG. 5B represents the results, for example, of step S454 of FIG. 4B. As such, the simulation results shown in FIG. 5B represent an initial vector φ′ (initial estimate) to be used to solve Equation (2) and reach the results of FIG. 5A more quickly.

Table 1 provides results of computing the electrical potentials (φ) associated with a transducer location using step S110 of FIG. 1A based on an initial estimate (φ′) computed using various methods described above. Table 1 also includes results of a previous method for solving equation (2) without first computing an initial estimate (φ′) as a “warm start” for the optimization.

TABLE 1

Using
Using method
Using method

method
of FIG. 2 using
of FIG. 2

Previous
of
nearest neighbor
using linear

method
FIG. 4B
interpolation
interpolation

Total
100.17
58.438
42.067
40.293

computation

time

(seconds)

As shown in Table 1, computing the electrical potentials (φ) associated with a transducer location takes approximately 100.17 seconds according to the previous method. Computing the initial estimate (φ′) according to the method of FIG. 4B (removing all material that is not a perfect conductor) and then computing the electrical potentials (φ) using the computed initial estimate takes a total of approximately 58.438 seconds. This is less than 60% of the time for the previous method, indicating good computational time savings. Computing the initial estimate (φ′) according to the method of FIG. 2 (using n=2 for down-sampling and a nearest neighbor interpolation scheme for up-sampling) and then computing the electrical potentials (φ) using the computed initial estimate takes a total of approximately 42.067 seconds. Computing the initial estimate (φ′) according to the method of FIG. 2 (using n=2 for down-sampling and a linear interpolation scheme for up-sampling) and then computing the electrical potentials (φ) using the computed initial estimate takes a total of approximately 40.293 seconds. As such computing the electrical potentials (φ) using the initial estimate computed via the method 200 of FIG. 2 was shown to take only approximately 40% of the time as the previous method, indicating good computational time savings.

FIG. 6 depicts an example method 600 for computing an initial estimate (e.g., initial vector φ′) based on a generic model. Steps S608 and S610 of this example method 600 may be used to accomplish step S106 in the method 100A/100B of FIG. 1A/1B. Steps S602-S606 may be performed once for a given generic model, and the solution to step S606 may be saved in memory for use in performing the method 100A/100B of FIG. 1A/1B for any given subject. While an order of operations is indicated in FIG. 6 for 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 herein.

At step S602, the method 600 may include obtaining a generic model that represents a same region of a body as the model of the subject. As an example, the generic model and the model of the subject may both represent a head or brain. The generic model of the head or brain may include, for example, the Colin-27 Average Brain, Stereotaxic Registration Model. As another example, the generic model and the model of the subject may both represent a torso.

At step S604, the method 600 may include computing a matrix A″ and a vector b″ for the generic model to be used in computing a vector φ″. The matrix A″ may represent one or more types of tissue, estimated tissue conductivity, and/or other features located in the voxels of the generic model. The b″ vector may be computed based on the boundary conditions for each respective transducer location, at locations within the generic model.

At step S606, the method 600 may include computing the vector φ″ for each respective transducer location. Specifically, the vector φ″ for each transducer location may be computed by computationally solving Equation (3) above. It should be noted that the vector φ″ may be determined in other ways than computationally solving a system of equations. The vector φ″ for each transducer location may be saved in memory as representing the solution for electrical potentials taken with respect to the generic model. Steps S602-S606 may be performed only one time as the “true solution” for the generic model (e.g., an average brain or torso). Then, the solution (φ″) for the generic model may be used to determine φ′ for various different subjects using steps S608 and S610 described below. For example, after the solution for the generic model is calculated, this solution may be received or accessed as the first step in the method 600, and the method proceeds to step S608.

At step S608, the method 600 may include determining an affine mapping between the generic model and the model of the subject. This may involve determining an affine transformation from the generic model to the model of the subject based on landmarks, etc., detected from the image data used to obtain the model of the subject.

At step S610, the method 600 may include computing an initial vector φ′ for each respective transducer location by calculating a distortion of the vector φ″ based on the mapping between the generic model and the model of the subject determined in step S608. That is, step S610 involves using an inverse of the affine mapping known from the generic model to map the solution φ″ of the generic model backwards to an approximate solution φ′ for the given subject.

By first solving for the initial vector φ′ using the generic model and affine mapping, the method 600 provides a closer initial estimate for input to the optimization algorithm, thereby reducing the total amount of time to solve for the vector φ and select one or more transducer locations.

Exemplary Apparatuses

FIG. 7 depicts an example apparatus 700 to apply alternating electric fields (e.g., TTFields) to a subject's body. The system may be used for treating a target region of a subject's body with an alternating electric field (e.g., TTFields). As an 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 (such as, for example, in FIG. 8, which has four transducers 800). As another 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. Other transducer array placements on the subject's body may be possible.

The example apparatus 700 depicts an example having four transducers (or “transducer arrays”) 700A-D. Each transducer 700A-D may include substantially flat electrode elements 702A-D positioned on a substrate 704A-D and electrically and physically connected (e.g., through conductive wiring 706A-D). The substrates 704A-D may include, for example, cloth, foam, flexible plastic, and/or conductive medical gel. Two transducers (e.g., 700A and 700D) 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 and 700C) may be a second pair of transducers configured to similarly apply an alternating electric field to the target region.

The transducers 700A-D may be coupled to a voltage generator, such as AC voltage generator 708, and the system may further include a controller 710 communicatively coupled to the AC voltage generator 708. The controller 710 may include a computer having one or more processors 712 and memory 714 accessible by the one or more processors. The memory 714 may store instructions that when executed by the one or more processors control the AC voltage generator 708 to induce alternating electric fields between pairs of the transducers 700A-D according to one or more voltage waveforms and/or cause the computer to perform one or more methods disclosed herein. The controller 710 may monitor operations performed by the AC voltage generator 708 (e.g., via the processor(s) 712). One or more sensor(s) 716 may be coupled to the controller 710 for providing measurement values or other information to the controller 710.

The electrode elements 702A-D may be capacitively coupled. In one example, the electrode elements 702A-D are ceramic electrode elements coupled to each other via conductive wiring 706A-D. When viewed in a direction perpendicular to its face, the ceramic electrode elements may be circular shaped or non-circular shaped. In other embodiments, the array of electrode elements are not capacitively coupled, and there is no dielectric material (such as ceramic, or high dielectric polymer layer) associated with the electrode elements.

The structure of the transducers 700A-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 be conductive or non-conductive.

The transducer may include any desired number of 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. In certain 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 non-limiting 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.

FIG. 9 depicts an example computer apparatus for use with the embodiments herein. As an example, the apparatus 900 may be a computer to implement certain inventive techniques disclosed herein, such as selecting transducer locations for delivering TTFields to a subject. For example, the steps f FIG. 1A/1B, FIG. 2, FIG. 4, and/or FIG. 6 may be performed by a computer, such as the apparatus 900. As an example, the apparatus 900 may be used as the controller 710 of FIG. 7, or as a separate computer apparatus located remote from the controller 710. The apparatus 900 may include one or more processors 902, memory 904, one or more input devices, and one or more output devices 906.

As one example, based on input 908, the one or more processors 902 generate control signals to control the voltage generator. As an example, the input 908 may be user input. As an example, the input 908 may be from another computer in communication with the apparatus 900. The input 908 may be received in conjunction with one or more input devices (not shown) of the apparatus 900.

The memory 904 may be accessible by the one or more processors 902 (e.g., via a link 903) so that the one or more processors 902 may read information from and write information to the memory 904. The memory 904 may store instructions that when executed by the one or more processors 902 implement one or more methods of the present disclosure.

The one or more output devices 906 may provide the status of the operation of the invention, such as transducer location selection, voltages being generated, and other operational information. The output device(s) 906 may provide visualization data according to certain embodiments of the invention.

The apparatus 900 may be an apparatus for selecting transducer locations for delivering tumor treating fields to a subject, the apparatus including: one or more processors (such as one or more processors 902); and memory (such as memory 904) accessible by the one or more processors, the memory storing instructions that when executed by the one or more processors, cause the apparatus to perform one or more methods described herein.

The memory 904 may be a non-transitory processor readable medium containing a set of instructions thereon for selecting transducer locations for delivering tumor treating fields to a subject, wherein when executed by a processor (such as processor 902), the instructions cause the processor to perform one or more methods described herein.

ILLUSTRATIVE EMBODIMENTS

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

Embodiment 1: A computer-implemented method for selecting at least one transducer location for delivering tumor treating fields to a subject, the method comprising: obtaining a three-dimensional model of the subject, the model comprising voxels; computing an initial vector φ′ for each of a plurality of transducer locations, wherein each initial vector φ′ represents an initial estimate of electrical potentials for the model for each respective transducer location; computing a matrix A and a vector b, wherein the matrix A is based on the model, wherein the vector b is based on boundary conditions for each respective transducer location; computing a vector φ using the matrix A, the vector b, and the initial vector φ′ for each transducer location, wherein Aφ=b, wherein each vector φ represents electrical potentials for the model for each respective transducer location; and selecting one or more transducer locations for delivering tumor treating fields to the subject based on the vectors φ.

Embodiment 2: The method of Embodiment 1, wherein computing the vector φ for each transducer location comprises using an iterative optimizer with the initial vector φ′ for each transducer location.