Fluence map generation methods for radiotherapy
Described herein are methods for fluence map generation or fluence map optimization (FMO) for radiation therapy. One variation of a method for generating a fluence map comprises smoothing out nondifferentiable penalty functions and using an accelerated proximal gradient method (e.g., FISTA) to compute a fluence map that may be used by a radiotherapy system to apply a selected dose of radiation to one or more regions of interest (ROI) or volumes of interest (VOI).
1. A method for calculating a fluence map for radiation therapy, the method comprising:
selecting a volume of interest;
selecting a plurality of voxels within the volume of interest, wherein each of the voxels has an acceptable dose range;
selecting a set of candidate beamlets b={b i } having initial beamlet intensity weights x 0 ={x i 0 };
calculating a dose matrix A for the volume of interest based on the set of candidate beamlets b, wherein the dose matrix A contains per-voxel dose values delivered to each of the plurality of voxels by each of the candidate beamlets b; and
calculating a fluence map having a final set of beamlet intensity weights x k by adjusting the initial beamlet intensity weights according to a proximal gradient method (x k−1 →x k ) with a penalty function containing one or more linear penalties that iterates on the initial beamlet intensity weights until the adjusted beamlet intensity weights converge on a final set of beamlet intensity weights such that changes between iterations of the beamlet intensity weights are less than a predetermined residual criterion.
2. The method of claim 1 , wherein the proximal gradient method is an accelerated proximal gradient method.
3. The method of claim 2 , wherein the proximal gradient method is a fast iterative shrinkage-thresholding algorithm (FISTA).
4. The method of claim 1 , wherein the one or more linear penalties comprises one or more L 1 penalties.
5. The method of claim 1 , wherein the penalty function has been smoothed such that the penalty function is differentiable.
6. The method of claim 5 , wherein the penalty function has been smoothed using Moreau-Yosida regularization.
7. The method of claim 1 , wherein the initial set of beamlet intensity weights {x 0 } is an all-zero vector.
8. The method of claim 1 , wherein the beamlets in the set of candidate beamlets b are divided between a smaller set of firing angles {f i }.
9. The method of claim 8 , wherein the set of firing angles {f i } comprises a plurality of angles around a patient area of a radiation treatment device.
10. The method of claim 9 , wherein the plurality of firing angles are evenly distributed 360 degrees around the patient area.
11. The method of claim 1 , wherein the proximal gradient method penalty function comprises one or more quadratic penalties.
12. The method of claim 11 , wherein the one or more quadratic penalties comprises one or more L 2 penalties.
13. The method of claim 1 , wherein the penalty function penalizes voxel dose excursions outside of the acceptable dose range.
14. The method of claim 13 , wherein the penalty function is a single-value penalty function that aggregates the voxel dose excursions outside of the acceptable dose range of all of the voxels in the volume of interest.
15. The method of claim 1 , wherein the acceptable dose range of each of the plurality of voxels is determined at least in part by a treatment plan.
16. The method of claim 1 , wherein the volume of interest is a first volume of interest and the method further comprises:
selecting a second volume of interest;
selecting a second plurality of voxels within the second volume of interest, wherein each of the voxels has an acceptable dose range; and
wherein calculating the dose matrix A further comprises calculating the dose matrix A for the first and second volumes of interest based on the set of candidate beamlets b, wherein the dose matrix A contains per-voxel dose values delivered to each of the first and second plurality of voxels by each of the candidate beamlets b.
17. The method of claim 1 , further comprising segmenting the fluence map into a set of multi-leaf collimator and radiation source positioning instructions.
18. The method of claim 1 , wherein the proximal gradient method penalty function comprises one or more indicator functions, the one or more indicator functions comprising an indicator function for an L∞-norm ball.
19. A system for calculating a fluence map for radiation therapy, the system comprising:
a processor configured to:
select a volume of interest;
select a plurality of voxels within the volume of interest, wherein each of the voxels has an acceptable dose range;
select a set of candidate beamlets b={b i } having initial beamlet intensity weights x 0 ={x i 0 };
calculate a dose matrix A for the volume of interest based on the set of candidate beamlets b, wherein the dose matrix A contains per voxel dose values delivered to each of the plurality of voxels by each of the candidate beamlets b;
calculate a fluence map comprising a final set of beamlet intensity weights x k by adjusting the initial beamlet intensity weights according to a proximal gradient method update (x k−1 →x k ) with a penalty function containing one or more linear penalties that iterates on the initial beamlet intensity weights until the adjusted beamlet intensity weights converge on a final set of beamlet intensity weights such that changes between iterations of the beamlet intensity weights are less than a predetermined residual criterion; and
store the fluence map in a processor memory.
20. The system of claim 19 , wherein the proximal gradient method is an accelerated proximal gradient method.
21. The system of claim 20 , wherein the accelerated proximal gradient method is a fast iterative shrinkage-thresholding algorithm (FISTA).
22. The system of claim 19 , wherein the one or more linear penalties comprises one or more L 1 penalties.
23. The system of claim 19 , wherein the penalty function has been smoothed such that the penalty function is differentiable.
24. The system of claim 23 , wherein the penalty function has been smoothed using Moreau-Yosida regularization.
25. The system of claim 19 , wherein the penalty function penalizes voxel dose excursions outside of the acceptable dose range.
26. The system of claim 25 , wherein the penalty function is a single-value penalty function that aggregates the voxel dose excursions outside of the acceptable dose range of all of the voxels in the volume of interest.
27. The system of claim 19 , wherein the acceptable dose range of each of the plurality of voxels is determined at least in part by a treatment plan.
28. The system of claim 19 , wherein the processor is further configured to:
select a second volume of interest;
select a second plurality of voxels within the second volume of interest, wherein each of the voxels has an acceptable dose range; and
wherein calculating the dose matrix A further comprises calculating the dose matrix A for the first and second volumes of interest based on the set of candidate beamlets b, wherein the dose matrix A contains per-voxel dose values delivered to each of the first and second plurality of voxels by each of the candidate beamlets b.
29. The system of claim 19 , further comprising a radiation therapy system comprising a therapeutic radiation source movable about a patient area and configured to apply radiation beamlets to the patient area according to the fluence map.
30. The system of claim 29 , wherein a set of firing angles{f i } comprises a plurality of angles around the patient area of a radiation treatment device.
31. The system of claim 30 , wherein the plurality of firing angles are evenly distributed 360 degrees around the patient area.
32. The system of claim 29 , wherein the radiation therapy system further comprises a multi-leaf collimator disposed in a beam path of the therapeutic radiation source, and wherein the processor is configured to segment the fluence map into a set of multi-leaf collimator instructions and to transmit the instructions to the radiation therapy system.
33. The system of claim 29 , wherein the radiation therapy system further comprises one or more PET detectors.
34. The system of claim 29 , wherein the therapeutic radiation source is movable about the patient area at a speed of at least about 40 RPM.
35. The system of claim 19 , wherein the proximal gradient method penalty function comprises one or more indicator functions, the one or more indicator functions comprising an indicator function for an L∞-norm ball.