Method for optimizing multiple electrode positions and creating a 3D model

Abstract

A 3D model of the AC conductivity (at a given frequency) of an anatomical volume can be created by obtaining two MRI images of the anatomical volume, where the two images have different repetition times. Then, for each voxel in the anatomical volume, the ratio IR of the intensities of the corresponding voxels in the two MRI images is calculated. Then, this calculated IR is mapped into the corresponding voxel of the 3D model of the AC conductivity at the given frequency. The given frequency is below 1 MHz (e.g., 200 kHz). In some embodiments, the 3D model of the AC conductivity at the given frequency is used to determine the position of the electrodes in TTField (Tumor Treating Fields) therapy.

Description

[0001] Cross - reference to related applications

[0002] This application claims the benefit of U.S. Provisional Application 62 / 655,670, filed on April 10, 2018, which is hereby incorporated by reference in its entirety. Background of the Invention

[0003] Tumor treating fields or TTFields are low - intensity (e.g., 1 - 3 V / cm) alternating electric fields in the intermediate frequency range (100 - 300 kHz). This non - invasive treatment targets solid tumors and is described in U.S. Patent 7,565,205, which is hereby incorporated by reference in its entirety. TTFields are approved for the treatment of glioblastoma multiforme and can be delivered, for example, by means of the Optune TM system, which includes a transducer array placed on the shaved head of a patient. TTFields are typically delivered by two pairs of transducer arrays that generate perpendicular fields within the treated tumor. More specifically, for the Optune system, one pair of electrodes is located on the left and right (LR) of the tumor, while the other pair of electrodes is located on the front and back (AP) of the tumor.

[0004] In - vivo and in - vitro studies have shown that the efficacy of TTField therapy increases with increasing electric field strength. Thus, optimizing the placement of the array on the patient's scalp to increase the strength in the brain lesion area is standard practice for the Optune system. To improve treatment, the position of the transducers can be adapted according to the patient - specific head anatomy and tumor location. The position of the transducers and the electrical properties (EP) of the brain tissue can be used to determine how TTFields are distributed within the head. Multiple conventional methods can be used to accomplish array placement optimization, such as using the NovoTal TM system or using the method described in U.S. Patent 10,188,851 to place the array on the scalp as close as possible to the tumor, U.S. Patent 10,188,851 is hereby incorporated by reference in its entirety.

[0005] U.S. Patent 10,188,851 explains that the position of the electrodes can be optimized by obtaining conductivity measurements in the anatomical volume based on MRI using diffusion - weighted imaging (DWI) or diffusion - tensor imaging (DTI), and then directly generating a 3D map of the electrical conductivity of the brain from the obtained conductivity or resistivity measurements without segmenting the anatomical volume into tissue types. Although this method has many advantages, it is relatively slow and typically provides a relatively small number of slices for the image. Summary of the Invention

[0006] One aspect of the present invention relates to a first method for creating a 3D model of the AC conductivity or resistivity of an anatomical volume at a given frequency below 1 MHz. The first method includes obtaining first and second MRI images of the anatomical volume having associated first and second repetition times, respectively. The first and second repetition times are different. For each voxel in the anatomical volume, a ratio IR of the intensity of the corresponding voxel in the first MRI image to the intensity of the corresponding voxel in the second MRI image is calculated. Then, the IR calculated for each voxel in the anatomical volume is mapped into the corresponding voxel of a 3D model of AC conductivity or resistivity at the given frequency.

[0007] In some instances of the first method, the given frequency is between 100 and 300 kHz. In some instances of the first method, the given frequency is between 180 and 220 kHz. In some instances of the first method, the first MRI image is a T1 image and the second MRI image is a T1 image. In some instances of the first method, the first MRI image is a T1 image and the second MRI image is a proton density image. In some instances of the first method, the first repetition time is between 400 and 800 ms and the second repetition time is between 2 and 5 seconds.

[0008] In some instances of the first method, the anatomical volume includes white and gray matter of the brain. In some instances of the first method, the 3D model of AC conductivity or resistivity is a 3D model of AC conductivity.

[0009] Another aspect of the present invention relates to a second method for optimizing the positions of a plurality of electrodes placed on a subject's body, wherein the electrodes are used to apply an electric field in a target tissue within an anatomical volume at a given frequency below 1 MHz. The second method includes obtaining first and second MRI images of the anatomical volume having associated first and second repetition times, respectively. The first and second repetition times are different. For each voxel in the anatomical volume, a ratio IR of the intensity of the corresponding voxel in the first MRI image to the intensity of the corresponding voxel in the second MRI image is calculated. Then, the IR calculated for each voxel in the anatomical volume is mapped into the corresponding voxel of a 3D model of AC conductivity or resistivity at the given frequency. The second method further includes identifying the position of the target tissue within the anatomical volume; and determining the positions for the electrodes based on the 3D model of conductivity or resistivity and the position of the target tissue.

[0010] In some instances of the second method, the given frequency is between 100 and 300 kHz. In some instances of the second method, the given frequency is between 180 and 220 kHz. In some instances of the second method, the first MRI image is a T1 image and the second MRI image is a T1 image. In some instances of the second method, the first MRI image is a T1 image and the second MRI image is a proton density image. In some instances of the second method, the first repetition time is between 400 and 800 ms and the second repetition time is between 2 and 5 seconds.

[0011] Some instances of the second method further include attaching electrodes to the subject's body at determined locations and applying an electrical signal between the attached electrodes to apply an electric field in the target tissue.

[0012] In some instances of the second method, the anatomical volume includes the white and gray matter of the brain. In some instances of the second method, the anatomical volume is the brain and the determination of the positions of the electrodes is based on a composite model in which the 3D model of the conductivity or resistivity of the brain is surrounded by a model of at least one shell with a constant conductivity.

[0013] In some instances of the second method, the anatomical volume is the brain surrounded by cerebrospinal fluid and the determination of the positions of the electrodes is based on a composite model in which the 3D model of the conductivity or resistivity of the brain is surrounded by a model of at least one shell with a constant conductivity.

[0014] In some instances of the second method, the 3D model of conductivity or resistivity is a 3D model of conductivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flow chart of an example for creating a model of the head and using the model to optimize the electric field.

[0016] Figure 2A and 2B are in vivo conductivity estimation diagrams at frequencies of 200 kHz and 1 MHz, respectively. DETAILED DESCRIPTION

[0017] This application describes a method for creating a realistic head model for simulating TTFields that is more computationally efficient and provides higher resolution than the prior art methods described in U.S. Patent 10,188,851. More specifically, instead of determining the conductivity for each voxel in an anatomical volume based on DWI or DTI, the conductivity for each voxel is determined based on two MRI images with different repetition times. (For example, a first set of T1 MRI images captured with a repetition time of 700 ms and a second set of T1 MRI images captured with a repetition time of 4 seconds.)

[0018] Using the image ratio between two MRI images instead of DWI or DTI images (as in the '851 patent) provides improved results because the number of frames required to form a single DTI image slice is much higher than the number of frames required to form a single T1 image slice. As a result, the DTI image will include many fewer slices than the T1 image (assuming the patient spends the same amount of time in the MRI machine).

[0019] This description is divided into two parts: Part 1 provides a detailed description of a method for creating a realistic head model for TTField simulation from MRI data with minimal user intervention. Part 2 provides a detailed description of how to use the model created in Part 1 to optimize the TTField array position.

[0020] Figure 1 is a flowchart of an example for creating a model (in steps S11 - S14) and using the model to optimize the electric field (steps S21 - S24).

[0021] Part 1: Creating a realistic computational human model (phantom) from MRI data.

[0022] Creating an accurate computational human model involves precisely mapping electrical properties (e.g., conductivity, resistivity) at each point within the computational human model.

[0023] Directly using an MRI sequence to map electrical properties reduces the need for precise tissue segmentation (which is a time - consuming and labor - intensive task) because the electrical properties of each point are defined directly from the MRI rather than from the tissue types assigned to them during segmentation. Thus, the segmentation process can be simplified or even eliminated without compromising the accuracy of the computational human model. Note that although the embodiments described herein discuss mapping conductivity, alternative embodiments can provide similar results by mapping different electrical properties such as resistivity.

[0024] Figure 1Steps S11 - S14 therein depict an example of a set of steps that can be used to generate a computational human model representative of a patient based on MRI conductivity measurements.

[0025] Step S11 is an image acquisition step. In this step, both structural data and data from which a conductivity map can be calculated from the structural data are acquired. For example, the structural data can be obtained from standard T1 and T2 MRI sequences. As explained below, the conductivity map is generated from two MRI sequences with different repetition times. Thus, the image acquisition step S11 must include acquiring first and second MRI images of the anatomical volume in question at different repetition times. In one example, the first MRI image of the anatomical volume can be a T1 image with a repetition time of 700 ms, and the second MRI image of the anatomical volume can be a T1 image with a repetition time of 4 seconds. In another example, the first MRI image of the anatomical volume can be a T1 image with a repetition time of 700 ms, and the second MRI image of the anatomical volume can be a standard proton density (PD) image with a repetition time between 2 and 3 seconds.

[0026] To create a good computational human model, high - resolution images should be acquired. For both structural and conductivity - related images, a resolution of at least 1 mm×1 mm×1 mm is preferred. Lower - resolution images can be used for one or both of these types of images, but the lower resolution will result in a less accurate human model.

[0027] Optionally, the data set can be inspected and images affected by large artifacts can be removed. Scanner - specific pre - processing can be applied. For example, images can be converted from DICOM format to NIFTI. Different steps of pre - processing may be registering all images to a standard space (e.g., Montreal Neurological Institute, MNI, space). This can be done using readily available software packages including but not limited to FSLFLIRT and SPM.

[0028] Step S12 is a step of processing the structural image. As mentioned above, the workflow presented herein uses MRI - based conductivity measurements to create a computational human model. However, the structural image can still be used to identify the boundaries of the head, and to identify regions belonging to specific tissues within the brain where it may be advantageous to assign typical conductivity values not derived from MRI measurements. For example, since the water content in the skull and scalp is relatively low, the methods described herein are not precise for determining the conductivity within those regions. To avoid this shortcoming, it may be advantageous to manually or automatically identify and segment the skull and scalp within the image and assign typical conductivity values to the regions corresponding to these layers (but still relying on MRI - based measurements for regions corresponding to the brain, as described below).

[0029] For example, the outer tissue shell or convex hull can be used as a model of the skull and scalp. If a rough segmentation of the outer layer is feasible, creating the corresponding convex hull is routine and can be performed using standard algorithms and software. Another option for the user is to measure the thickness of the outer layer at the representative region (where the transducer array may be placed) by validating the structural image. These measurements can be used to create concentric shells or layers representative of the skull and scalp. These layers can be obtained by deforming a default elliptical structure, which can be the default convex hull of the scalp segmentation.

[0030] Water content-based electrical property tomography (wEPT) is a method that uses the ratio of two T1-weighted images with different repetition times (TR) to map electrical properties (EP) based on an empirically derived relationship between T1 relaxation values (T1), water content (WC), and EP. Using typical WC and EP values for healthy tissues reported in the literature to derive an empirical model, wEPT has been applied to map the EP of a healthy brain at 128 MHz. See E. Michel, D. Hernandez, and S.Y Lee, “Electrical conductivity and permittivity maps of brain tissues derived from water content based on T1-weighted acquisition” Magn. Reson. Med., vol. 77, pp. 1094-1103, 2016, which is incorporated herein by reference in its entirety. Michel explains that as one moves “closer to the ultra-high frequency (UHF) range, [tissue] EP is almost entirely determined by water content”; and at these frequencies (e.g., at the 128 MHz frequency tested by Michel), the following equation:

[0031]

[0032] can be used to determine the water content from the image ratio (IR) of two T1-weighted MRI images with different TR; and the following equation

[0033]

[0034] can be used to determine the conductivity from the water content.

[0035] Surprisingly, the inventors have experimentally determined that even at a frequency of 200 kHz, which is more than 500 times lower than the 128 MHz frequency disclosed in Michel, Equation 2 still provides a viable approximation of the conductivity sufficient for subsequent use in simulating the intensity of TTFields in brain tissue. Two of the inventors' experiments are described immediately below.

[0036] In one experiment, 32 tissue samples from three different healthy calf brains and cerebrospinal fluid (CSF) samples from two pigs were analyzed. By connecting the Ag / AgCl electrodes of an impedance meter to each sample and measuring the dielectric properties of the samples using the parallel plate method, the image ratio of two T1-weighted MRI images with different TRs was calculated, and the EP of the samples was measured. The water content of the samples was estimated by measuring the difference between the dry weight and the wet weight of the samples.

[0037] Performing curve fitting using these measurements yields an empirical model that, for 200 kHz and 1 MHz, connects the IR to the WC (the coefficient of Equation "1") and connects the WC to the estimation of conductivity (the coefficient of Equation "2"). The optimal choice for the combination of TRs of the two T1-weighted images was estimated to be TRshort = 700 ms and TRlong = 4000 ms.

[0038] In another experiment, 4 mouse brain tumor models were used to study the applicability of Equation 2 at 200 kHz. Imaging was performed in a Bruker 1T icon scanner. For each mouse, 3D in vivo images (including a T1 MRI sequence with a short repetition time, a T1 MRI sequence with a long repetition time, and a T2 MRI sequence for sample segmentation) were acquired together with a total of 20 slices before euthanizing the animal. Then, curve fitting was used to map the WC and conductivity at 200 kHz and 1 MHz. Available maps of the conductivity approximation at 200 kHz and the conductivity approximation at 1 MHz were obtained.

[0039] Subsequently, a total of 35 excised samples were studied by measuring the water content in the electrical properties of each sample. For each sample, the measured values were compared with the median WC and EP in the corresponding voxels of the conductivity map generated from the MRI, based on the segmentation performed on the T2 image. To compare these in vivo MRI-based conductivity estimations, the model coefficients were adapted to account for the difference in the T1 and EP values measured at a lower ex vivo temperature.

[0040] Experimental measurements revealed an average error of 3.1% for MRI-based water content estimation in both models. The experimental measurements also revealed an average error of 22.8% and 24.3% for MRI-based conductivity estimation at 200 kHz (for two different models respectively), while at 1 MHz (for two different models respectively) it was 26.4% and 23.9%. For WC, the measurement error was estimated to be ~1%, while for MRI-based conductivity estimation, the measurement error was ~10%. Also, this level of accuracy of conductivity estimation is sufficient to run the TTField simulations described in Part 2 below.

[0041] In the resulting conductivity estimation maps, anatomical structures and tumors are clearly visible. See, for example, the in-vivo 200 kHz conductivity estimation map and the 1 MHz conductivity estimation map depicted respectively in Figure 2A and Figure 2B respectively.

[0042] Given these experimental results of 3D maps of conductivity at low frequencies (e.g., 200 kHz) indicating the anatomical volume that can be directly generated from MRI data, it becomes possible to generate a 3D map of the conductivity of a person's head from MRI data without segmenting the MRI into tissue types, and then use this 3D map of conductivity to optimize the position of the electrodes for applying 200 kHz TTField to a person's head (by running simulations using the 3D map as described in Part 2 below).

[0043] Return Figure 1 , steps S13 and S14 jointly create a 3D conductivity map from the MRI images with short and long repetition times previously obtained in step S11. More specifically, in step S13, the ratio IR of the intensity of each voxel in the first MRI image to the intensity of the corresponding voxel in the second MRI image was calculated for each voxel in the anatomical volume. Then, in step S14, the calculated IR for each voxel in the anatomical volume was mapped to the corresponding voxel of the 3D map of conductivity at a given frequency without segmenting the anatomical volume into tissue types.

[0044] For any given set of settings of a given MRI machine, a set of coefficients w1 and w2 of the above Equation 1 that provide the best fit between the image ratio IR and water content can be determined. Additionally, for any given frequency at which TTField will ultimately be used, a set of coefficients c1, c2, and c3 of the above Equation 2 that provide the best fit between water content and conductivity estimation can be determined.

[0045] Because the above Equation 1 is used to calculate WC from IR, and the above Equation 2 is used to calculate the conductivity estimate from WC, and because all coefficients w1, w2, c1, c2, and c3 can be predetermined based on the known settings of the MRI machine and the known frequency under which TTField will be applied, it becomes possible to generate a look-up table that maps the IR at any given pixel to the conductivity estimate for that pixel. When using such a look-up table, step S14 can be achieved by simply obtaining the image ratio calculated in S13, inserting the image ratio into the look-up table, and obtaining the conductivity estimate from the look-up table. Alternatively, step S14's mapping can be achieved mathematically by using curve fitting of the above Equations 1 and 2. Alternatively, a different set of curve fitting equations (e.g., fitting a polynomial function instead of the exponential function that appears in Equation 1) can be used to achieve the mapping in step S14 mathematically.

[0046] After the conductivity map of the anatomical volume is generated in step S14, the resulting conductivity map can be merged with the conductivity of the shell surrounding the anatomical volume (connected to step S12 as described above). For example, in the context of the brain, the initial conductivity maps of the gray matter, white matter, and any tumors contained therein will be generated in step S14. And to finalize the model of the head, a constant conductivity shell representing the CSF, skull, and scalp is added to the initial conductivity map. Alternatively, because the water content of the CSF is high enough, the initial conductivity map generated in step S14 can cover the gray matter, white matter, any tumors contained therein, and the CSF. In this case, to finalize the model of the head, a constant conductivity shell representing the skull and scalp is added to the initial conductivity map of the brain and CSF.

[0047] Optionally, when fractional anisotropy (or any other measurement that can be derived from conductivity data) is found, it is preferred to examine adjacent elements to avoid outliers (e.g., to eliminate GM points identified within WM).

[0048] Part 2: Optimizing the TTField array position using an actual head model

[0049] The optimization of the array layout refers to finding the array layout that optimizes the electric field within the diseased area (tumor) of the patient's brain. This optimization can be achieved by performing the following four steps: (S21) identifying the volume targeted for treatment (target volume) within the actual head model; (S22) automatically placing the transducer array on the actual head model and setting the boundary conditions; (S23) once the array is placed on the actual head model and the boundary conditions are applied, calculating the electric field developed within the actual head model; and (S24) running an optimization algorithm to find the layout that produces the best electric field distribution within the target volume. Detailed examples of implementing these four steps are provided below.

[0050] Step S21 involves locating the target volume (i.e., defining the region of interest) within the actual head model. The first step in finding the layout that produces the best electric field distribution within the patient's body is to correctly identify the location and target volume in which the electric field should be optimized.

[0051] In some embodiments, the target volume will be the gross tumor volume (GTV) or the clinical target volume (CTV). The GTV is the grossly verifiable extent and location of the tumor, while the CTV includes the verified tumor (if present) and any other tissue with suspected tumor. In many cases, the CTV is found by defining a volume that encloses the GTV and adding a margin of a predefined width around the GTV.

[0052] To identify the GTV or CTV, it is necessary to identify the volume of the tumor within the MRI image. This can be performed manually by the user, automatically, or using a semi - automatic method in which a user - assisted algorithm is used. When performing this task manually, the MRI data can be presented to the user, and the user may be asked to sketch the volume of the CTV based on the data. The data presented to the user can be structural MRI data (e.g., T1, T2 data). Different MRI modalities can be registered with each other, and the user can be presented with the option to view any dataset and sketch the CTV. The user can be asked to sketch the CTV on a 3D volumetric representation of the MRI, or the user can be given the option to view the individual 2D slices of the data and mark the CTV boundaries on each slice. Once the boundaries are marked on each slice, the CTV can be found within the anatomical volume (and thus within the actual model). In this case, the volume marked by the user will correspond to the GTV. In some embodiments, the CTV can then be found by adding a margin of a predefined width to the GTV. Similarly, in other embodiments, the user can be asked to mark the CTV using a similar process.

[0053] An alternative to the manual method is to use an automatic segmentation algorithm to find the CTV. These algorithms perform an automatic segmentation algorithm to identify the CTV using the structural MRI data.

[0054] Optionally, a semi - automatic segmentation method of the MRI data can be implemented. In an example of these methods, the user iteratively provides input to the algorithm (e.g., the location of the tumor on the image, roughly marking the boundaries of the tumor, delineating the region of interest in which the tumor is located). Then it is used by the segmentation algorithm. Then, the user can be given the option to refine the segmentation to obtain a better estimate of the location and volume of the CTV within the head.

[0055] Regardless of whether an automatic or semi-automatic method is used, the identified tumor volume will correspond to the GTV, and then the CTV can be automatically found by expanding the GTV volume by a predetermined amount (e.g., defining the CTV as the volume of a 20 mm-wide margin surrounding the tumor).

[0056] Note that in some cases, it may be sufficient for the user to define the region of interest in which they want to optimize the electric field. This region of interest can be, for example, a volume of any shape within a box-shaped volume, a spherical volume, or an anatomical volume surrounding the tumor. When using such a method, a complex algorithm for precisely identifying the tumor may not be required.

[0057] Step S22 involves automatically calculating the position and orientation of the array on the actual head model for a given iteration. In the Optune TM device, each transducer array used to deliver TTFields includes a set of ceramic disk electrodes that are coupled to the patient's head through a layer of medical gel. When the array is placed on an actual patient, the disks align naturally parallel to the skin, and good electrical contact occurs between the array and the skin because the medical gel deforms to match the body's contour. However, the virtual model is composed of strictly defined geometries. Therefore, placing the array on the model requires an exact method to find the orientation and contour of the model surface at the location where the array is to be placed, and to find the thickness / geometry of the gel required for the model array to ensure good contact with the actual patient model. To achieve fully automatic optimization of the field distribution, these calculations must be performed automatically.

[0058] Multiple algorithms can be used to perform this task, and one such algorithm is described in U.S. Patent 10,188,851, which is incorporated herein by reference in its entirety.

[0059] Step S23 involves calculating the electric field distribution within the head model for a given iteration. Once the head human model is constructed and the transducer array (i.e., the electrode array) for applying the field is placed on the actual head model, a volume mesh suitable for finite element (FE) method analysis can be created. The next boundary conditions can be applied to the model. Examples of boundary conditions that may be used include Dirichlet boundary (constant voltage) conditions on the transducer array, Neumann boundary conditions (constant current) on the transducer array, or floating potential boundary conditions, which set the potential at that boundary such that the integral of the normal component of the current density equals a specified magnitude. Then a suitable finite element solver (e.g., a low-frequency quasi-static electromagnetic solver) or an alternative finite difference (FD) algorithm can be used to solve the model. Existing software packages such as Sim4Life, Comsol Multiphysics, Ansys, or Matlab can be used to perform meshing, apply boundary conditions, and solve the model. Alternatively, custom computer code implementing the FE (or FD) algorithm can be written. This code can utilize existing open-source software resources such as C-Gal (for creating meshes) or FREEFEM++ (software written in C++ for rapid testing and finite element simulation). The final solution of the model will be a dataset that describes the electric field distribution or related quantities such as the electric potential within the calculated human model for a given iteration.

[0060] Step S24 is an optimization step. An optimization algorithm is used to find the array layout that optimizes the delivery of the electric field to the diseased region (tumor) of the patient's brain for two application directions (LR and AP, as described above). The optimization algorithm will utilize methods for automatic array placement and methods for solving the electric field within the head model in a well-defined sequence in order to find the optimal array layout. Considering the two directions in which the electric field is applied, the optimal layout will be the layout that maximizes or minimizes a certain objective function of the electric field in the diseased region of the brain. This objective function can be, for example, the maximum intensity within the diseased region or the average intensity within the diseased region. It is also possible to define other objective functions.

[0061] There are multiple methods that can be used to find the optimal array layout for a patient, and three of these methods are described below. One optimization method is an exhaustive search. In this method, the optimizer will include a library with a finite number of array layouts that should be tested. The optimizer performs simulations for all the array layouts in the library (e.g., by repeating steps S22 and S23 for each layout) and picks the array layout that produces the best field intensity in the tumor (the best layout is the layout in the library that produces the highest (or lowest) value for the optimization objective function, e.g., the electric field intensity delivered to the tumor).

[0062] Another optimization method is iterative search. This method encompasses the use of algorithms such as the minimum descent optimization method and the simplex search method. Using this method, the algorithm can iteratively test different array layouts on the head and calculate the objective function for the electric field in the tumor for each layout. Therefore, this method also involves repeating steps S22 and S23 for each layout. At each iteration, the algorithm automatically picks the configuration to be tested based on the results of the previous iteration. The algorithm is designed to converge such that the objective function defined for the field in the tumor is maximized (or minimized).

[0063] However, there is yet another optimization method that is based on placing a dipole at the center of the tumor in the model. This method is different from the other two methods because it does not rely on solving for the field intensity for different array layouts. Instead, the optimal position for the array is found by placing a dipole aligned with the direction of the expected field at the center of the tumor in the model and solving for the electromagnetic potential. The region on the scalp where the electric potential (or possibly the electric field) is maximum will be the location where the array is placed. The logic of this method is that the dipole will generate the maximum electric field at the tumor center. By reciprocity, if we can generate the computed field / voltage on the scalp, then we expect to obtain the maximum field distribution at the tumor center (the location where the dipole is placed). With our current system, the closest we can actually get to this is to place the array in the region where the potential induced by the dipole on the scalp is maximum.

[0064] Note that alternative optimization schemes can be used to find the array layout that optimizes the electric field in the diseased region of the brain. For example, an algorithm that combines various of the above methods. As an example of how to combine these methods, an algorithm that combines the above third method (i.e., placing a dipole at the center of the tumor in the model) with the second method (i.e., iterative search) is considered. By this combination, using the method of placing a dipole at the tumor center, the array layout is initially found. This array layout is used as the input for an iterative search to find the optimal layout.

[0065] Once the layout that optimizes the electric field in the diseased region of the patient's brain has been determined (e.g., using any of the methods explained herein), the electrodes are placed at the determined locations. Then an AC voltage is applied to the electrodes (e.g., as described in U.S. Patent 7,565,205, which is incorporated herein by reference) to treat the disease.

[0066] Also note that the concepts described herein are not limited to representing the outer layers (scalp, skull, CSF) as a convex hull, and other methods can be used to roughly estimate the MRI data. Examples include simple geometric forms such as ellipsoids, spheres, elliptical structures, or other methods for creating tissue envelopes. Additionally, the concepts described herein are not limited to approximations of the outer layers, i.e., the scalp, skull, and CSF layers can also be obtained by conventional segmentation of the MRI.

[0067] Also note that instead of using segmentations of the scalp, skull, and CSF, approximations of these outer layers can be used. For example, the user can be asked to measure the thicknesses of the scalp, skull, and CSF in representative regions. These tissues can then be approximated as concentric geometric entities having the user-measured thicknesses around the brain (similar to the default convex hulls of the scalp, sphere, ellipsoid, etc.). This approximation models the head as an (almost) elliptical structure, which ignores features such as the ears, nose, mouth, and chin. However, since the array and treatment are only delivered to the supratentorial region of the head, this approximation seems justified. In some embodiments, it may also be possible to combine two or more of the three tissue types into one layer and assign a single conductivity value to that layer. For example, the scalp and skull can be introduced as one layer with a single conductivity (and optionally with a uniform thickness).

[0068] The computational human model constructed in this way can also be used in other applications where it may be useful to calculate the electric field and / or current distribution within the head. These applications include, but are not limited to: direct and alternating current transcranial stimulation; simulation of implantable stimulation electrode field maps: planning the placement of implantable stimulation electrodes; and source localization in EEG.

[0069] Finally, although this application describes a method for optimizing the array layout on the head, the method can potentially be extended to optimize the array layout for treating other body regions, such as the chest or abdomen.

[0070] Although the invention has been disclosed with reference to some embodiments, many modifications, variations, and changes can be made to the described embodiments without departing from the scope and scope of the invention as defined by the appended claims. Therefore, it is intended that the invention not be limited to the described embodiments, but rather have the full scope defined by the language of the appended claims and their equivalents.

Claims

1. A method for optimizing the positions of a plurality of electrodes that can be placed on a subject's body, the electrodes being used to apply an electric field in a target tissue within an anatomical volume at a given frequency, the method comprising the following steps: Obtaining a first MRI image of the anatomical volume, the first MRI image having an associated first frequency and an associated first repetition time; Obtaining a second MRI image of the anatomical volume, the second MRI image having an associated second frequency and an associated second repetition time different from the first repetition time; For each voxel in the anatomical volume, calculating a ratio IR of the intensity of the corresponding voxel in the first MRI image to the intensity of the corresponding voxel in the second MRI image; and Mapping the IR calculated for each voxel in the anatomical volume into the corresponding voxel of a 3D model of conductivity or resistivity at the given frequency, wherein the given frequency is less than 1 MHz, wherein the given frequency is different from the first frequency, and wherein the given frequency is different from the second frequency; Identifying the location of the target tissue within the anatomical volume; And Based on the 3D model of conductivity or resistivity at the given frequency generated in the mapping step and the location of the target tissue identified in the identifying step, determining the positions of the electrodes.

2. The method according to claim 1, wherein the given frequency is between 100 and 300 kHz.

3. The method according to claim 1, wherein the given frequency is between 180 and 220 kHz.

4. The method according to claim 1, wherein the first MRI image is a T1 image and the second MRI image is a T1 image.

5. The method according to claim 1, wherein the first MRI image is a T1 image and the second MRI image is a proton density image.

6. The method according to claim 1, wherein the first repetition time is between 400 and 800 ms and the second repetition time is between 2 and 5 seconds.

7. The method according to claim 1, wherein the anatomical volume includes white and gray matter of the brain.

8. The method according to claim 1, wherein the anatomical volume is the brain, and wherein the determination of the positions of the electrodes is based on a composite model in which the 3D model of conductivity or resistivity of the brain is surrounded by a model of at least one shell having a constant conductivity.

9. The method according to claim 1, wherein the anatomical volume is the brain surrounded by cerebrospinal fluid, and wherein the determination of the positions of the electrodes is based on a composite model in which the 3D model of conductivity or resistivity of the brain is surrounded by a model of at least one shell having a constant conductivity.

10. The method according to claim 1, wherein the 3D model of conductivity or resistivity is a 3D model of conductivity.

11. A method for creating a 3D model of AC conductivity or resistivity of an anatomical volume at a given frequency, the method comprising the following steps: Obtain a first MRI image of the anatomical volume, the first MRI image having an associated first frequency and an associated first repetition time; Obtain a second MRI image of the anatomical volume, the second MRI image having an associated second frequency and an associated second repetition time different from the first repetition time; For each voxel in the anatomical volume, calculate a ratio IR of the intensity of the corresponding voxel in the first MRI image to the intensity of the corresponding voxel in the second MRI image; and Map the IR calculated for each voxel in the anatomical volume to the corresponding voxel of a 3D model of AC conductivity or resistivity at the given frequency, where the given frequency is below 1 MHz, where the given frequency is different from the first frequency, and where the given frequency is different from the second frequency.

12. The method according to claim 11, wherein the given frequency is between 100 and 300 kHz.

13. The method according to claim 11, wherein the given frequency is between 180 and 220 kHz.

14. The method according to claim 11, wherein the first MRI image is a T1 image and the second MRI image is a T1 image.

15. The method according to claim 11, wherein the first MRI image is a T1 image and the second MRI image is a proton density image.

16. The method according to claim 11, wherein the first repetition time is between 400 and 800 ms and the second repetition time is between 2 and 5 seconds.

17. The method according to claim 11, wherein the anatomical volume includes white and gray matter of the brain.

18. The method according to claim 11, wherein the 3D model of AC conductivity or resistivity is a 3D model of AC conductivity.

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