A gradient-based direct aperture optimization_Journal of Biomedical Engineering

Authors：

YANG Jie ^1,2 , ZHANG Pengcheng ¹ , ZHANG Liyuan ¹ ,  GUI Zhiguo ^1,3

1. National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, P.R.China;
2. School of Medicine Management, Shanxi University of TCM, Taiyuan 030619, P.R.China;
3. Key Laboratory of Instrumentation Science & Dynamic Measurement, North University of China, Taiyuan 030051, P.R.China;

Corresponding author：

GUI Zhiguo, Email: gzgtg@163.com

Keywords：

direct aperture optimization; simulated annealing; limited-memory BFGS for bound-constrained; intensity-modulated radiotherapy

DOI：

10.7507/1001-5515.201609041

Video：

Export PDF Favorites Scan Get Citation

Abstract Full text Figures/Tables Video References Cited by

Aiming at the disadvantages of traditional direct aperture optimization (DAO) method, such as slow convergence rate, prone to stagnation and weak global searching ability, a gradient-based direct aperture optimization (GDAO) is proposed. In this work, two different optimization methods are used to optimize the shapes and the weights of the apertures. Firstly, in order to improve the validity of the aperture shapes optimization of each search, the traditional simulated annealing (SA) algorithm is improved, the gradient is introduced to the algorithm. The shapes of the apertures are optimized by the gradient based SA method. At the same time, the constraints between the leaves of multileaf collimator (MLC) have been fully considered, the optimized aperture shapes are meeting the requirements of clinical radiation therapy. After that, the weights of the apertures are optimized by the limited-memory BFGS for bound-constrained (L-BFGS-B) algorithm, which is simple in calculation, fast in convergence rate, and suitable for solving large scale constrained optimization. Compared with the traditional SA algorithm, the time cost of this program decreased by 15.90%; the minimum dose for the planning target volume was improved by 0.29%, the highest dose for the planning target volume was reduced by 0.45%; the highest dose for the bladder and rectum, which are the organs at risk, decreased by 0.25% and 0.09%, respectively. The results of experiment show that the new algorithm can produce highly efficient treatment planning a short time and can be used in clinical practice.

Citation： YANG Jie, ZHANG Pengcheng, ZHANG Liyuan, GUI Zhiguo. A gradient-based direct aperture optimization. Journal of Biomedical Engineering, 2018, 35(3): 358-367. doi: 10.7507/1001-5515.201609041 Copy

1.	Bjarngard B, Kijewski P, Pashby C. Description of a computer controlled therapy machine. Int J Radiat Oncol Biol Phys, 1977, 2(77): 142-143.
2.	Seco J, Evans P M, Webb S. An optimization algorithm that incorporates IMRT delivery constraints. Phys Med Biol, 2002, 47(6): 899-915.
3.	Shepard D M, Earl M A, Li X A, et al. Direct aperture optimization: a turnkey solution for step-and-shoot IMRT. Med Phys, 2002, 29(6): 1007-1018.
4.	Earl M A, Afghan M K, Yu C X, et al. Jaws-only IMRT using direct aperture optimization. Med Phys, 2007, 34(1): 307-314.
5.	Li Y, Yao J, Yao D. Genetic algorithm based deliverable segments optimization for static intensity-modulated radiotherapy. Phys Med Biol, 2003, 48(20): 3353-3374.
6.	Cotrutz C, Xing L. Segment-based dose optimization using a genetic algorithm. Phys Med Biol, 2003, 48(18): 2987-2998.
7.	Preciado-Walters F, Langer M P, Rardin R L, et al. Column generation for IMRT cancer therapy optimization with implementable segments. Ann Oper Res, 2006, 148(1): 65-79.
8.	Romeijn H E, Ahuja R K, Dempsey J F, et al. A column generation approach to radiation therapy treatment planning using aperture modulation. SIAM J Optim, 2005, 15(3): 838-862.
9.	Men C, Romeijn H E, Taşkin Z C, et al. An exact approach to direct aperture optimization in IMRT treatment planning. Phys Med Biol, 2007, 52(24): 7333-7352.
10.	Salari E, Men C, Romeijn H E. Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach. Med Phys, 2011, 38(3): 1266-1279.
11.	Bednarz G, Michalski D, Houser C, et al. The use of mixed-integer programming for inverse treatment planning with pre-defined field segments. Phys Med Biol, 2002, 47(13): 2235-2245.
12.	Salari E, Unkelbach J. A column-generation-based method for multi-criteria direct aperture optimization. Phys Med Biol, 2013, 58(3): 621-639.
13.	Cassioli A, Unkelbach J. Aperture shape optimization for IMRT treatment planning. Phys Med Biol, 2013, 58(2): 301-318.
14.	王捷, 裴曦, 曹瑞芬, 等. 一种快速调强放射治疗直接子野优化方法. 中国医学物理学杂志, 2015, 32(1): 4-7.
15.	Byrd R H, Lu P, Nocedal J, et al. A limited memory algorithm for bound constrained optimization[J]. SIAM Journal on Scientific Computing, 1995, 16(5): 1190-1208.
16.	Wu Q, Mohan R, Niemierko A, et al. Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose. Int J Radiat Oncol Biol Phys, 2002, 52(1): 224-235.
17.	Romeijn H E, Dempsey J F, Li J G. A unifying framework for multi-criteria fluence map optimization models. Phys Med Biol, 2004, 49(10): 1991-2013.
18.	张鹏程. 精确放射治疗剂量计算及方案优化方法研究. 南京: 东南大学, 2014: 46-47.
19.	Hoffmann A L, den Hertog D, Siem A Y, et al. Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects. Phys Med Biol, 2008, 53(22): 6345-6362.
20.	Kirkpatrick S, Gelatt C D Jr., Vecchi M P. Optimization by simulated annealing. Science, 1983, 220(4598): 671-680.
21.	Kirkpatrick S, Toulouse G. Configuration space analysis of traveling salesman problem. J Phys, 1985, 46(8): 1277-1292.
22.	Powell M J D. How bad are the BFGS and DFP methods when the objective function is quadratic?. Mathematical Programming , 1985, 34(1): 34-47.
23.	Liu D C, Nocedal J. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 1989, 45(1-3): 503-528.
24.	张丽媛, 张鹏程, 桂志国, 等. 一种基于生物准则的 IMRT 方案优化方法. 计算机应用研究, 2017, 34(5): 1303-1307.
25.	Deasy J O, Blanco A I, Clark V H. CERR: a computational environment for radiotherapy research. Med Phys, 2003, 30(5): 979-985.
26.	Ahnesjö A, Saxner M, Trepp A. A pencil beam model for photon dose calculation. Med Phys, 1992, 19(2): 263-273.
27.	Dale E, Hellebust T P, Skjønsberg A, et al. Modeling normal tissue complication probability from repetitive computed tomography scans during fractionated high-dose-rate brachytherapy and external beam radiotherapy of the uterine cervix. Int J Radiat Oncol Biol Phys, 2000, 47(4): 963-971.
28.	Marks L B, Yorke E D, Jackson A, et al. Use of normal tissue complication probability models in the clinic. Int J Radiat Oncol Biol Phys, 2010, 76(3 Suppl): S10-S19.

1. Bjarngard B, Kijewski P, Pashby C. Description of a computer controlled therapy machine. Int J Radiat Oncol Biol Phys, 1977, 2(77): 142-143.
2. Seco J, Evans P M, Webb S. An optimization algorithm that incorporates IMRT delivery constraints. Phys Med Biol, 2002, 47(6): 899-915.
3. Shepard D M, Earl M A, Li X A, et al. Direct aperture optimization: a turnkey solution for step-and-shoot IMRT. Med Phys, 2002, 29(6): 1007-1018.
4. Earl M A, Afghan M K, Yu C X, et al. Jaws-only IMRT using direct aperture optimization. Med Phys, 2007, 34(1): 307-314.
5. Li Y, Yao J, Yao D. Genetic algorithm based deliverable segments optimization for static intensity-modulated radiotherapy. Phys Med Biol, 2003, 48(20): 3353-3374.
6. Cotrutz C, Xing L. Segment-based dose optimization using a genetic algorithm. Phys Med Biol, 2003, 48(18): 2987-2998.
7. Preciado-Walters F, Langer M P, Rardin R L, et al. Column generation for IMRT cancer therapy optimization with implementable segments. Ann Oper Res, 2006, 148(1): 65-79.
8. Romeijn H E, Ahuja R K, Dempsey J F, et al. A column generation approach to radiation therapy treatment planning using aperture modulation. SIAM J Optim, 2005, 15(3): 838-862.
9. Men C, Romeijn H E, Taşkin Z C, et al. An exact approach to direct aperture optimization in IMRT treatment planning. Phys Med Biol, 2007, 52(24): 7333-7352.
10. Salari E, Men C, Romeijn H E. Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach. Med Phys, 2011, 38(3): 1266-1279.
11. Bednarz G, Michalski D, Houser C, et al. The use of mixed-integer programming for inverse treatment planning with pre-defined field segments. Phys Med Biol, 2002, 47(13): 2235-2245.
12. Salari E, Unkelbach J. A column-generation-based method for multi-criteria direct aperture optimization. Phys Med Biol, 2013, 58(3): 621-639.
13. Cassioli A, Unkelbach J. Aperture shape optimization for IMRT treatment planning. Phys Med Biol, 2013, 58(2): 301-318.
14. 王捷, 裴曦, 曹瑞芬, 等. 一种快速调强放射治疗直接子野优化方法. 中国医学物理学杂志, 2015, 32(1): 4-7.
15. Byrd R H, Lu P, Nocedal J, et al. A limited memory algorithm for bound constrained optimization[J]. SIAM Journal on Scientific Computing, 1995, 16(5): 1190-1208.
16. Wu Q, Mohan R, Niemierko A, et al. Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose. Int J Radiat Oncol Biol Phys, 2002, 52(1): 224-235.
17. Romeijn H E, Dempsey J F, Li J G. A unifying framework for multi-criteria fluence map optimization models. Phys Med Biol, 2004, 49(10): 1991-2013.
18. 张鹏程. 精确放射治疗剂量计算及方案优化方法研究. 南京: 东南大学, 2014: 46-47.
19. Hoffmann A L, den Hertog D, Siem A Y, et al. Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects. Phys Med Biol, 2008, 53(22): 6345-6362.
20. Kirkpatrick S, Gelatt C D Jr., Vecchi M P. Optimization by simulated annealing. Science, 1983, 220(4598): 671-680.
21. Kirkpatrick S, Toulouse G. Configuration space analysis of traveling salesman problem. J Phys, 1985, 46(8): 1277-1292.
22. Powell M J D. How bad are the BFGS and DFP methods when the objective function is quadratic?. Mathematical Programming , 1985, 34(1): 34-47.
23. Liu D C, Nocedal J. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 1989, 45(1-3): 503-528.
24. 张丽媛, 张鹏程, 桂志国, 等. 一种基于生物准则的 IMRT 方案优化方法. 计算机应用研究, 2017, 34(5): 1303-1307.
25. Deasy J O, Blanco A I, Clark V H. CERR: a computational environment for radiotherapy research. Med Phys, 2003, 30(5): 979-985.
26. Ahnesjö A, Saxner M, Trepp A. A pencil beam model for photon dose calculation. Med Phys, 1992, 19(2): 263-273.
27. Dale E, Hellebust T P, Skjønsberg A, et al. Modeling normal tissue complication probability from repetitive computed tomography scans during fractionated high-dose-rate brachytherapy and external beam radiotherapy of the uterine cervix. Int J Radiat Oncol Biol Phys, 2000, 47(4): 963-971.
28. Marks L B, Yorke E D, Jackson A, et al. Use of normal tissue complication probability models in the clinic. Int J Radiat Oncol Biol Phys, 2010, 76(3 Suppl): S10-S19.

Previous Article
Research on the correlation of brain function based on improved phase locking value
Next Article
Medical computer-aided detection method based on deep learning

Journal of Biomedical Engineering

A gradient-based direct aperture optimization

Abstract Full text Figures/Tables Video References Cited by

Previous Article

Next Article

Format

Content