Method for optimization radiotherapy particle beams

• US 8,492,735 B2
• Filed: 05/27/2010
• Issued: 07/23/2013
• Est. Priority Date: 05/27/2010
• Status: Active Grant

• Current Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Inventors: Brand, Matthew
• Primary Examiner(s): Souw, Bernard E
• Application Number:
  US12/788,437
• Publication Number:
  US 20110291028A1
• Time in Patent Office: 1,153 Days
• Field of Search: 250/492.1, 250/492.21, 250/492.22, 250/492.23, 250/492.3, 250/526, 378/1, 378/2, 378/65, 378/92, 378/97, 378/98, 378/210, 378/64, 378/901
• US Class Current: 250/492.22
• CPC Class Codes: A61N 2005/1087 Ions; Protons
• CPC Class Codes: A61N 5/103 Treatment planning systems
• CPC Class Codes: A61N 5/1031 using a specific method of dose optimization

Abstract

Radiation doses are optimized by providing a model of the set of beams and a target dose in normalized forms. A Gram matrix is determined from the model. The target dose is subsampled to determine initial intensity values for the set of beams. Then, the following steps are iterated until convergence. A very small positive value, 0<ε<<1, is added to each intensity value to ensure the intensity value is greater than zero. Each intensity value is multiplied by the Gram matrix to determine a product, which is divided element-wise into the normalized target dose to determine corresponding ratios. If the ratios are all close to 1, within a numerical error tolerance, the intensity values of the set of beam are output. Otherwise, the intensity values are multiplied by the ratios before a next iteration.

Claims

1. A method for optimizing radiation doses delivered by a set of beams, wherein each beam is a radiotherapy particle beam, comprising the steps of:

providing a dose matrix A indicating a dose delivered to m target voxels by n beams;

providing a target dosage pattern vector b required for a radiotherapy; and

determining, using a processor, a non-negative beam weights vector x that specifies individual intensities of the beams of radiation for radiating a target according to the target dosage pattern, such that underdoses and overdoses of the radiation are minimized, wherein the determining comprises;

determining the weights vector x according to

x←

diag(└

h+┌

Q┐

x┘

)diag(└

Q┘

x)<sup>−

1</sup>x;

wherein Q is a matrix whose elements are the inner products of columns of the dose matrix A, Q{dot over (=)}A^TAε

<sup>m×

n</sup>, T is a transpose operator, R is a space of real numbers, h is a vector, h{dot over (=)}A^Tbε

^m, diag( ) indicates a diagonal matrix, ┌

Q┐

is a matrix whose elements are positive elements of the matrix Q, ┌

Q┐

is a matrix whose elements are absolute values of negative elements of the matrix Q.

2. The method of claim 1, wherein the determining the weights vector x comprises:

multiplying the weights vector x by the matrix ┌

Q┐

to produce a product ┌

Q┐

X;

multiplying the weights vector x by the matrix ┌

Q┐

to produce a product ┌

Q┐

X;

forming the vector h of inner products of columns of the matrix A with the target dosage pattern vector b;

determining a sum of the vector h and the product ┌

Q┐

X;

dividing the sum element-by-element by the product ┌

Q┐

X to produce a vector of ratios; and

multiplying the weights vector x by the vector of ratios to adjust the weights vector x.

3. The method of claim 2, further comprising:

determining the vector ratios iteratively for the adjusted weights vector x until elements of the vector of ratios are close to one.

4. The method of claim 2, further comprising:

determining the vector ratios iteratively for the adjusted weights vector x until changes of elements of weights vector x are close to zero.

5. The method of claim 1, wherein the underdoses and overdoses of the radiation are minimized according to

6. The method of claim 1, wherein the underdoses of radiation are eliminated and overdoses of the radiation are minimized according to a least distance problem (LDP)

7. The method of claim 1, wherein the underdoses of radiation are eliminated and overdoses of the radiation are minimized according to a leas distance problem in a non-negative least squares (NNLS) form

8. A method for optimizing radiation doses delivered by a set of beams, wherein each beam is a radiotherapy particle beam, comprising the steps of:

determining a non-negative beam weights vector x for a dose matrix A indicating a dose delivered to in target voxels by n beams for radiating a target according to a target dosage pattern vector b, such that underdoses and overdoses of the radiotherapy are minimized, wherein the determining comprises;

multiplying the weights vector x by a matrix ┌

Q┐

whose elements are positive inner products of columns of the dose matrix A to produce a product ┌

Q┐

X;

multiplying the weights vector x by a matrix ┌

Q┐

whose elements are negated negative inner products of the columns of the dose matrix A to produce a product ┌

Q┐

X;

forming a vector h of inner products of a matrix Q with the target dosage pattern vector b, wherein Q{dot over (=)}A^TAε

<sup>m×

m</sup>, T is a transpose operator, R represents a space of real numbers, and h{dot over (=)}A^Tbε

^m;

determining a sum of the vector h and the product ┌

Q┐

X;

dividing the sum by the product ┌

Q┐

X to produce a vector of ratios; and

multiplying, the weights vector x by the vector of ratios to adjust the weights vector x, wherein steps of the method are performed by a processor.

9. The method of claim 8, further comprising;

determining the vector ratios iteratively for the adjusted weights vector x until elements of the vector of ratios are close to one.