Systems and methods for determining transducer locations for delivering tumor treating fields using a discretized model of a subject
A computer-implemented method for selecting at least one transducer location for delivering tumor treating fields to a subject, the method including: obtaining a three-dimensional model which includes voxels associated with image data of the subject; computing a discretization of the model to obtain a discretized model; computing boundary conditions for the discretized model; computing a matrix A is based on the discretized model and a vector b based on the boundary conditions for each respective transducer location; computing a vector φ using the matrix A and the vector b for each transducer location, wherein the vector φ is computed by computationally solving an equation Aφ=b, wherein each vector φ represents electrical potentials for the discretized 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.
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 associated with image data of the subject;
computing a discretization of the model to obtain a discretized model;
computing boundary conditions for the discretized model, wherein the boundary conditions represent at least transducer locations on the subject;
computing a matrix A and a vector b, wherein the matrix A is based on the discretized model, wherein the vector b is based on the boundary conditions for each respective transducer location;
computing a vector φ using the matrix A and the vector b for each transducer location, wherein the vector φ is computed by computationally solving an equation Aφ=b, wherein each vector φ represents electrical potentials for the discretized 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.
2 . The method of claim 1 , wherein the discretized model comprises a uniform grid of the voxels in the three-dimensional model of the subject.
3 . The method of claim 1 , wherein the discretized model comprises an octree grid of the voxels in the three-dimensional model of the subject.
4 . The method of claim 1 , wherein the boundary conditions represent the transducer locations as voltage sources on the subject.
5 . The method of claim 1 , wherein the boundary conditions represent the transducer locations as current sources on the subject.
6 . The method of claim 1 , wherein the equation Aφ=b is computationally solved based on a Cholesky-based direct matrix inversion of the matrix A.
7 . The method of claim 1 , wherein the equation Aφ=b is computationally solved using an algebraic multigrid (AMG) method or a conjugate gradient (CG) method.
8 . The method of claim 1 , further comprising computing a tumor treating fields dosage of the discretized model of the subject using the vectors φ for each transducer location,
wherein the one or more transducer locations are selected based on the computed tumor treating fields dosages.
9 . The method of claim 1 , wherein computing the vector φ is not based on air cells in the discretized model.
10 . The method of claim 1 , wherein computing the vector φ is based on cover-loop cells in the discretized model.
11 . The method of claim 1 , further comprising displaying a representation of a selected transducer location on a representation of the subject.
12 . The method of claim 1 , wherein the model of the subject represents a head of the subject.
13 . The method of claim 1 , wherein the model of the subject represents a torso of the subject.
14 . The method of claim 1 , wherein each transducer location comprises locations for at least two transducer arrays, wherein each transducer array comprises a plurality of electrode elements.
15 . An apparatus for selecting transducer locations for delivering tumor treating fields to a subject, the apparatus 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 apparatus to:
obtain a three-dimensional model of the subject, the model comprising voxels;
compute a cell discretization of the model to obtain a discretized model;
compute a vector φ by solving Aφ=b for each of a plurality of transducer locations, A being a matrix based on the discretized model, b being a vector based on the discretized model;
compute at least one of electric power loss density, current density, or electric field intensity at locations of the discretized model of the subject using the vectors φ for each transducer location; and
select one or more transducer locations based on the computed electric power loss density, computed current density, or computed electric field intensity.
16 . The apparatus of claim 15 , wherein the discretized model comprises a uniform grid of the voxels in the three-dimensional model of the subject.
17 . The apparatus of claim 15 , wherein the discretized model comprises an octree grid of the voxels in the three-dimensional model of the subject.
18 . The apparatus of claim 15 , wherein the vector φ is computed for each transducer location based on boundary conditions for each respective transducer location.
19 . The apparatus of claim 15 , wherein a first vector φ and a second vector φ are computed simultaneously.
20 . A computer-implemented method for computing a dosage of tumor treating fields delivered to a subject, the method comprising:
obtaining a three-dimensional model of the subject, the model comprising voxels;
computing a discretization of the model to obtain a discretized model;
determining a location on the discretized model of the subject to place a pair of transducers for delivering tumor treating fields;
computing boundary conditions for the discretized model, wherein the boundary conditions represent the location of the transducers on the subject;
computing a vector φ by solving Aφ=b for the boundary conditions, A being a matrix based on the discretized model, b being a vector based on the discretized model, the vector φ representing electrical potentials for the discretized model;
computing at least one of electric power loss density, current density, or electric field intensity at locations of the discretized model of the subject using the vector φ; and
computing a dosage of tumor treating fields delivered to the subject based on at least one of the computed electric power loss density, computed current density, or computed electric field intensity.