System and method for planning a radiation therapy treatment
View Patent ↗A method for planning a radiation therapy treatment of a body represented by a volume of voxels determines a radiation dose matrix representing a spatial distribution of a radiation dose of beams of radiation irradiating the volume with homogeneous stopping power. The beams are collimated and are shifted copies of each other at each depth of the volume, and the spatial distribution is determined by calculating cumulative beam-axial doses in a single matrix-matrix multiplication and redistributing the cumulative beam-axial doses to all voxels in the volume using a convolution. Next, a set of correcting operations is applied to the radiation dose matrix to produce a cumulative voxel radiation dose of the volume. Each correcting operation is linear, independent from another correcting operation and has a transform.
1. A method for planning a radiation therapy treatment of a body represented by a volume of voxels, comprising:
determining a radiation dose matrix representing a spatial distribution of a radiation dose of beams of radiation irradiating the volume with homogeneous stopping power, wherein the beams are collimated and are shifted copies of each other at each depth of the volume, wherein the spatial distribution is determined by calculating cumulative beam-axial doses in a single matrix-matrix multiplication and redistributing the cumulative beam-axial doses to all voxels in the volume using a convolution; and
applying a set of correcting operations to the radiation dose matrix to produce a cumulative voxel radiation dose of the volume, wherein each correcting operation is linear, independent from another correcting operation and has a transform, wherein steps of the method are performed by at least one processor.
2. The method of claim 1 , wherein the determining comprises:
multiplying a vector representing weights of the beams by a matrix representing energy profiles of the beams to estimate values of a total radiation at each depth of each beam;
substituting values in an zeroed 3D array representing the voxels in the volume with corresponding values of the total radiation; and
convolving each depth plane in the volume with a spreading kernel.
3. The method of claim 1 , wherein the determining comprises:
determining the radiation dose matrix as a matrix-vector products Aw of a fluence matrix A representing relative intensity of radiation delivered to each voxel in the volume by each beam and a vector of nonnegative beam weights w representing time of radiation of each beam of radiation according to
Aw =vec( B T mat( w )( N N )),
wherein N be a matrix in which each column is a spatially shifted copy of values of lateral distribution, B is a matrix of spatially shifted energy profiles, such that each column in the matrix B includes an energy profile for the beams in the same depth, wherein is a Kronecker product of matrices, a function vec(•) vectorizes its argument, and a function mat(•) reshapes its argument into a matrix that conforms with its left and right multiplicands, and wherein T is a transpose operator.
4. The method of claim 1 , wherein the set of correcting operations includes an operation for correcting a uniformity of a lateral distribution of energy of each beam at each depth, comprising:
convolving each row of the radiation dose matrix to determine the multiplication (N N), wherein the convolving includes a first convolution with a first vector in a first lateral direction, followed by a second convolution with a second vector in a second lateral direction orthogonal to the first lateral direction.
5. The method of claim 4 , wherein the convolving is according to
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wherein w i is the weight on the ith beam, B i (z) is an integral of an energy profile at a depth z, and N((x, y),σ 2 i (z)) is a 2D Gaussian field of variance σ 2 i (z) centered at an axis (x, y), an v j is a spreading kernel in a set J predetermined for the depth z.
6. The method of claim 1 , wherein the set of correcting operations includes an operation for correcting an assumption of the homogeneous stopping power, further comprising:
stretching each voxel in proportion to the stopping power of corresponding tissue of the volume to produce a stretched grid;
determining a redistribution matrix R that linearly maps irradiation values deposited into a regular grid to values deposited into the stretched grid; and
multiplying the redistribution matrix R with the radiation dose matrix.
7. The method of claim 1 , wherein the set of correcting operations includes an operation for correcting an assumption of a parallel distribution of the collimated beams, further comprising:
counter-warping a Euclidean space of tissue density data of the volume before determining the radiation dose; and
reversing the counter-warping after determining the radiation dose.
8. The method of claim 1 , wherein the set of correcting operations includes an operation for correcting multi-port propagation of the beams of radiation using a rotation of the volume with respect to, further comprising:
counter-rotating the volume to align a grid of the volume with a port to produce a counter-rotated volume;
determining a rotation matrix to redistribute the radiation dose in each voxel of the volume to corresponding voxels in the counter-rotated volume; and
summing the radiation dose of the corresponding voxels of the volume and the counter-rotated volume.
9. The method of claim 1 , further comprising:
adding to the volume a proximal layer of voxels with a stopping power equivalent to a cumulative stopping power of media between a source of the beams and the body.
10. The method of claim 1 , further comprising:
performing transform operations to the cumulative voxel radiation dose of the volume in an order reversed from an order of operations determining the cumulative voxel radiation dose.
11. A method for planning a radiation therapy treatment of a body represented by a volume of voxels, comprising:
determining a radiation dose matrix representing a spatial distribution of a radiation dose of a regular 3D grid of beams irradiating the volume with homogeneous stopping power; and
applying a set of correcting operations to the radiation dose matrix to produce a cumulative voxel radiation dose of the volume, wherein the set of correcting operation includes one or combination of
an operation for correcting an assumption of uniformity of lateral distribution of energy of each collimated beam,
an operation for correcting an assumption of the homogeneous stopping power of the volume,
an operation for correcting an assumption of a parallel distribution of the collimated beams,
an operation for correcting an assumption of a multi-port propagation of the collimated beams, and
an operation for correcting an assumption for a cumulative stopping power of media between a beam source and the patient, wherein each correcting operation is linear, independent from another correcting operation and has a transform, and wherein steps of the method are performed by a parallel processor.
12. A radiation therapy system comprising a parallel processor for determining an approximation of a radiation dose matrix representing a spatial distribution of a radiation dose of beams of radiation irradiating a body represented by a volume of voxels, wherein the spatial distribution is determined by calculating cumulative beam-axial doses in a single matrix-matrix multiplication and redistributing the cumulative beam-axial doses to all voxels in the volume using a convolution, and for correcting the approximation using a set of linear correcting operations.