放射治疗方案的优化方法研究
|
摘要
优化是放射治疗计划系统的重要组成部分之一。针对放射治疗方案的优化问题,本文提出了一系列解决方案,主要包括以下几个方面:
1)较全面地介绍了现代最优化理论及方法,对NSGA-II多目标优化遗传算法进行了较深入的研究,提出了在该方法中加入局部搜索算子及外部精英收集池的改进算法-NSGA-II多目标混合遗传算法。
2)针对伽玛刀立体定向放射治疗计划系统中的优化问题提出了一个两步优化的方案。首先采用一种改进的基于距离变换的几何优化方法,优化靶点的数目、位置及相应准直器直径;然后根据几何优化获得的靶点参数,研究了基于混合遗传算法GA-BFGS方法优化靶点权重的方法,以避免梯度法可能会陷入局部极小的问题。
3)针对全身伽玛刀治疗体部肿瘤的靶点设计优化问题,提出了一种新颖的靶点设计及优化解决方案,建立了基于包围盒的优化模型,然后采用遗传算法进行求解,使治疗过程更为简便快捷,并有利于减少治疗过程中的定位误差,填补了全身伽玛刀靶点设计优化研究的空白。
4)针对全身伽玛刀治疗体部肿瘤的治疗路径优化问题,在靶点优化的基础上,提出了采用遗传算法进行治疗路径优化的解决方案,使治疗过程更为简便快捷,有利于减少治疗过程中医生的劳动强度。当靶点数过多时,我们给出了一种分层优化的解决方案,以减少优化时间,满足临床的实际要求。
5)实现了一种基于NSGA-Ⅱ多目标混合遗传算法的调强放射治疗逆向计划的优化方法,其中局部搜索采用L-BFGS算法。该方法得到的非劣解在目标空间分布均匀,计算速度快,鲁棒性好。
6)在Windows平台上开发了一套用于周围血管内放射治疗计划优化的主动漫游虚拟现实系统,用于提取血管的几何结构;建立血管内放射治疗计划的优化模型,采用适宜的优化方法进行优化,该方法综合运用了混合遗传算法GA-BFGS方法和快速模拟退火算法优化相关的参数,其中GA-BFGS算法用于优化连续参数即放射源的照射时间,快速模拟退火算法用于优化离散参数即放射源的位置。这一策略综合考虑了目标函数的形式,BFGS的快速收敛性,遗传算法的全局收敛性,以及模拟退火算法的全局收敛性。
Optimization plays an important role in the radiation treatment planning. In this thesis, a collection of optimization solutions is presented for the radiation treatment planning problems.
Firstly, modern optimization theory and methods are reviewed, and a hybrid multiobjective optimization algorithm, which combines state-of-the-art multiobjective optimization algorithm-NSGA-II with local search methods and external elitist pool, is developed. The experimental results show that hybridization with local search can efficiently improve the search ability of the multiobjective optimization algorithms, and well distributed Pareto set could be got.
Secondly, a two-step automated treatment planning algorithm is developed for the Leksell Gamma Knife, a specialized unit for radiation treatment of brain tumour. In the first step, an improved distance transform based method is used to find the best number of shots, shot locations and collimator sizes for treatment planning. In the second step, in order to avoid trapping into local minimum, a hybrid genetic algorithm combined with BFGS algorithm is employed to find the optimal radiation exposure time by fixing the values of the discrete variables generated in the first step.
Thirdly, a novel shot design and optimization method is proposed for the whole body Gamma Knife treatment planning system which is used to treat large tumor, a boundary box based optimization model is proposed and solved by genetic algorithm. The method makes the treatment procedure more convenient and fast, and reduces the shot location error during the treatment procedure.
Fourthly, on the basis of shots optimization arrangement for the whole body Gamma Knife treatment planning system, genetic algorithm is applied to find the best treatment path to make the treatment procedure more convenient and reduce the doctor’s work intensity. In case of a large amount of shots are needed, a layer by layer treatment path optimization scheme is proposed to reduce computation time and meet the clinical need, but with a little performance decrease. Fifthly, NSGA-Ⅱhybrid multiobjective optimization algorithm,using L-BFGS algorithm as local search method, is applied to the optimization of inverse planning in intensity modulated radiation therapy(IMRT). The non-dominated solutions obtained by hybrid multiobjective optimization algorithm are distributed uniformly and this algorithm is more robust than those of the weighted method. The last non-dominated solutions allow the doctors to select the solution which best fits the clinical needs according to the corresponding decision tools such as dose-volume histograms, isodose lines, and the distribution of the solutions.
Finally, a method combined the active navigation with optimization algorithm for the planning of peripheral intravascular brachytherapy is proposed. A virtual reality system based on active navigation is developed on Windows platform for the peripheral intravascular brachytherapy, and an optimization model is proposed for the peripheral intravascular brachytherapy. According to the characteristics of the vessel obtained by active navigation, a method combined GA-BFGS hybrid genetic algorithm with simulated annealing algorithm is applied to optimize the related parameters,GA-BFGS hybrid genetic algorithm is used to optimize the continuous parameters, i.e., the dwell time; simulated annealing is used to optimize discrete parameter, i.e., the dwell positions located at the centreline of the vascular. This strategy takes into consideration the formula of the objective function, the fast convergence of BFGS algorithm and the global convergence of both genetic algorithm and simulated annealing algorithm.
1)较全面地介绍了现代最优化理论及方法,对NSGA-II多目标优化遗传算法进行了较深入的研究,提出了在该方法中加入局部搜索算子及外部精英收集池的改进算法-NSGA-II多目标混合遗传算法。
2)针对伽玛刀立体定向放射治疗计划系统中的优化问题提出了一个两步优化的方案。首先采用一种改进的基于距离变换的几何优化方法,优化靶点的数目、位置及相应准直器直径;然后根据几何优化获得的靶点参数,研究了基于混合遗传算法GA-BFGS方法优化靶点权重的方法,以避免梯度法可能会陷入局部极小的问题。
3)针对全身伽玛刀治疗体部肿瘤的靶点设计优化问题,提出了一种新颖的靶点设计及优化解决方案,建立了基于包围盒的优化模型,然后采用遗传算法进行求解,使治疗过程更为简便快捷,并有利于减少治疗过程中的定位误差,填补了全身伽玛刀靶点设计优化研究的空白。
4)针对全身伽玛刀治疗体部肿瘤的治疗路径优化问题,在靶点优化的基础上,提出了采用遗传算法进行治疗路径优化的解决方案,使治疗过程更为简便快捷,有利于减少治疗过程中医生的劳动强度。当靶点数过多时,我们给出了一种分层优化的解决方案,以减少优化时间,满足临床的实际要求。
5)实现了一种基于NSGA-Ⅱ多目标混合遗传算法的调强放射治疗逆向计划的优化方法,其中局部搜索采用L-BFGS算法。该方法得到的非劣解在目标空间分布均匀,计算速度快,鲁棒性好。
6)在Windows平台上开发了一套用于周围血管内放射治疗计划优化的主动漫游虚拟现实系统,用于提取血管的几何结构;建立血管内放射治疗计划的优化模型,采用适宜的优化方法进行优化,该方法综合运用了混合遗传算法GA-BFGS方法和快速模拟退火算法优化相关的参数,其中GA-BFGS算法用于优化连续参数即放射源的照射时间,快速模拟退火算法用于优化离散参数即放射源的位置。这一策略综合考虑了目标函数的形式,BFGS的快速收敛性,遗传算法的全局收敛性,以及模拟退火算法的全局收敛性。
Optimization plays an important role in the radiation treatment planning. In this thesis, a collection of optimization solutions is presented for the radiation treatment planning problems.
Firstly, modern optimization theory and methods are reviewed, and a hybrid multiobjective optimization algorithm, which combines state-of-the-art multiobjective optimization algorithm-NSGA-II with local search methods and external elitist pool, is developed. The experimental results show that hybridization with local search can efficiently improve the search ability of the multiobjective optimization algorithms, and well distributed Pareto set could be got.
Secondly, a two-step automated treatment planning algorithm is developed for the Leksell Gamma Knife, a specialized unit for radiation treatment of brain tumour. In the first step, an improved distance transform based method is used to find the best number of shots, shot locations and collimator sizes for treatment planning. In the second step, in order to avoid trapping into local minimum, a hybrid genetic algorithm combined with BFGS algorithm is employed to find the optimal radiation exposure time by fixing the values of the discrete variables generated in the first step.
Thirdly, a novel shot design and optimization method is proposed for the whole body Gamma Knife treatment planning system which is used to treat large tumor, a boundary box based optimization model is proposed and solved by genetic algorithm. The method makes the treatment procedure more convenient and fast, and reduces the shot location error during the treatment procedure.
Fourthly, on the basis of shots optimization arrangement for the whole body Gamma Knife treatment planning system, genetic algorithm is applied to find the best treatment path to make the treatment procedure more convenient and reduce the doctor’s work intensity. In case of a large amount of shots are needed, a layer by layer treatment path optimization scheme is proposed to reduce computation time and meet the clinical need, but with a little performance decrease. Fifthly, NSGA-Ⅱhybrid multiobjective optimization algorithm,using L-BFGS algorithm as local search method, is applied to the optimization of inverse planning in intensity modulated radiation therapy(IMRT). The non-dominated solutions obtained by hybrid multiobjective optimization algorithm are distributed uniformly and this algorithm is more robust than those of the weighted method. The last non-dominated solutions allow the doctors to select the solution which best fits the clinical needs according to the corresponding decision tools such as dose-volume histograms, isodose lines, and the distribution of the solutions.
Finally, a method combined the active navigation with optimization algorithm for the planning of peripheral intravascular brachytherapy is proposed. A virtual reality system based on active navigation is developed on Windows platform for the peripheral intravascular brachytherapy, and an optimization model is proposed for the peripheral intravascular brachytherapy. According to the characteristics of the vessel obtained by active navigation, a method combined GA-BFGS hybrid genetic algorithm with simulated annealing algorithm is applied to optimize the related parameters,GA-BFGS hybrid genetic algorithm is used to optimize the continuous parameters, i.e., the dwell time; simulated annealing is used to optimize discrete parameter, i.e., the dwell positions located at the centreline of the vascular. This strategy takes into consideration the formula of the objective function, the fast convergence of BFGS algorithm and the global convergence of both genetic algorithm and simulated annealing algorithm.
引文
[1] http://www.iarc.fr/pageroot/PRELEASES/pr145a.html
[2] 谷铣之,殷蔚伯,刘泰福,潘国英主编,肿瘤放射治疗学[M],北京医科大学、中国协和医科大学联合出版社,1993.
[3] 严玉龙,立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D],东南大学博士论文,1997.
[4] 于金明,殷蔚伯,李宝生主编,肿瘤精确放射治疗学[M],山东科学技术出版社,2004.
[5] http://www.brachytherapy.com/index.html
[6] 於文雪, 李松毅, Haigron P, 罗立民, 等. γ -射线血管内照射治疗计划系统的研制[J]. 东南大学学报(自然科学版),2002. 32(4): 586~589
[7] Pascal H, Lucas A, Moisan C, Yu WX, et al. Planning of Intravascular Brachytherapy Based on Virtual Exploratory Navigation in X-ray CT Images[A]. Proceeding of SPIE, 2001. 4681: 148~158.
[8] Shu H Z, Yan Y L, Bao X D, et al. Treatment planning optimization by quasi Newton and simulated annealing methods for gamma unit treatment system[J]. Phys Med Biol, 1998. 43: 2795~2805.
[9] Shu H Z, Yan Y L, Luo L M, et al. Three dimensional optimization of treatment planning for gamma unit treatment system[J]. Med Phys, 1998. 25: 2352~2357.
[10] 舒华忠, 严玉龙, 鲍旭东等,立体定向放射外科中的旋转式伽玛刀治疗计划的优化[J]. 齐鲁肿瘤杂志, 1997. 4(3 ): 212~214.
[11] 舒华忠, 严玉龙, 鲍旭东等,立体定向放射外科中的γ -刀治疗规划的优化[J].东南大学学报,1997. 27(4): 19~25.
[12] Pla C, Podgorsak E B, Pla M, Souhami L, Clark B G, Caron J L. Considerations on the use of multiple isocenters in stereotactic radiosurgery[J]. Med. Phys., 1995. 22:676.
[13] Gibon D, Rousseau J, Castelain B, et al. Treatment planning optimization by conjugate gradients and simulated annealing methods in stereotatic radiosurgery[J]. Int. J. Radiat. Oncol. Biol. Phys., 1995. 33: 201~210.
[14] 李乃弘, 周非亚, 於文雪, 于金明, 尹勇, 基于肿瘤形状的几何优化靶点方法[J]. 齐鲁肿瘤杂志, 1999. 6(4 ): 212~214.
[15] Wu Q J, Bourland J D. Three-dimensional skeletonization for computer-assisted treatment planning in radiosurgery[J]. Computerized Medical Imaging and Graphics, 2000. 24: 243~251.
[16] Luo L M, Shu H Z, Yu W X, Yan Y L, Bao X D, Fu Y. Optimizing computerized treatment planning for the gamma knife by source culling. Int. J. Radiat. Oncol. Biol. Phys., 1999. 45(5): 1339~1346.
[17] Wu X G, Zhu Y P, Luo L M. Linear programming based on neural networks for radiotherapy treatment planning[J]. Phys. Med. Biol., 2000. 45: 719~728.
[18] Rosen I I, et al. Treatment plan optimization using linear programming[J]. Med. Phys., 1991. 18: 141~152.
[19] Langer M, et al. Comparison of mixed integer programming and fast simulated annealing for optimizing beam weights in radiation therapy[J]. Med. Phys., 1996. 23: 957~964.
[20] Lee E K, Fox T, Crocker I. Optimization of radiosurgery treatment planning via mixed integer programming[J]. Med. Phys., 2000. 27: 995~1004.
[21] Bortfeld T, et al. Methods of image-reconstruction from projections applied to conformation radiotherapy[J]. Phys. Med. Biol., 1990. 35: 1423~1434.
[22] Bortfeld T. Optimized planning using physical objectives and constraints[J]. Semin Radiat. Oncol. 1999. 9(1): 20~34.
[23] Cho P S et al. Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets[J]. Med. Phys., 1998. 25: 435~443.
[24] Holmes T, et al. A unified approach to the optimization of brachytherapyand external beam dosimetry[J]. Int. J. Radiat. Oncol. Biol. Phys., 1991. 20: 859~873.
[25] Hristov D, et al. On the implementation of dose-volume objectives in gradient algorithms for inverse treatment planning[J]. Med. Phys. 2002. 29: 848~856.
[26] Starkschall G, Pollack A, Stevens C W. Treatment planning using a dose-volume feasibility search algorithm[J]. Int. J. Radiat. Oncol. Biol. Phys., 2001. 49: 1419~1427 .
[27] Wu Q W, Mohan R. Algorithms and functionality of an intensity modulated radiotherapy optimization system[J]. Med. Phys., 2000. 27: 701–711.
[28] Hou Q, Wang Y G. Molecular dynamics used in radiation therapy[J]. Phys. Rev. Lett., 2001.87: 168101-1~168101-4.
[29] Hou Q, et al. An optimization algorithm for intensity modulated radiotherapy—The simulated dynamics with dose-volume constraints[J]. Med. Phys., 2003. 30: 61~68.
[30] Morrill S M, et al. Treatment planning optimization using constrained simulated annealing[J]. Phys. Med. Biol., 1991. 36: 1341~1361.
[31] Rosen I I, et al. Comparison of simulated annealing algorithms for conformal therapy treatment planning[J]. Int. J. Radiat. Oncol. Biol. Phys., 1995. 33: 1091~1099.
[32] Webb S. Optimization of conformal radiotherapy dose distributions by simulated annealing[J]. Phys. Med. Biol., 1991. 36: 1227~1237.
[33] Wu X G, et al. Selection and determination of beam weights based on genetic algorithms for conformal radiotherapy treatment planning[J]. Phys. Med. Biol., 2000. 45: 2547~2558.
[34] Bortfeld T, et al. Physical vs biological objectives for treatment plan optimization[J], Radiother. Oncol., 1996. 40: 185~187.
[35] Langer M, et al. Large-scale optimization of beam weights under dosevolume restrictions[J]. Int. J. Radiat. Oncol. Biol. Phys., 1990. 18: 887–893.
[36] Wu Q W, et al. Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose[J]. Int. J. Radiat. Oncol. Biol. Phys., 2002. 52: 224~235.
[37] Cotrutz C, Lahanas M, Kappas K, Baltas D. A multiobjective gradient based dose optimization algorithm for external beam conformal radiotherapy[J]. Phys. Med. Biol.. 2001. 46(8): 2161~2175
[38] Lahanas M, Schreibmann E, Baltas D. Multiobjective inverse planning in intensity modulated radiotherapy with constrained-free gradient-based optimization algorithms[J]. Phys. Med. Biol., 2003. 48(17): 2843~2871
[39] Lahanas M, Baltas D, Zamboglou N. Anatomy-based three-dimensional dose optimization in brachytherapy using multiobjective genetic algorithms[J]. Med. Phys., 1999. 26: 1904~1918.
[40] Kawrakow I, Fippel M. Investigation of variance reduction techniques for Monte Carlo photon dose calculation using XVMC[J]. Phys. Med. Biol., 2000. 45:2163~2183
[41] Kawrakow I and Fippel M. VMC++, a MC algorithm optimized for electron and photon beam dose calculations for RTP.[C] Proceedings of the 22th annual EMBS international conference, 2000. 1490~1493
[42] James H V, Atherton S, Budgell G J, Kirby M C, Williams P C, Verification of dynamic multileaf collimation using an electronic portal imaging device[J]. Phys. Med. Biol., 2000. 45(2): 495~509.
[43] Vieira S C, Dirkx M L P, Pasma K L, Heijmen B J M. Dosimetric verification of x-ray fields with steep dose gradients using an electronic portal imaging device[J]. Phys. Med. Biol., 2003. 48(2): 157~166.
[44] Ling C C, Humm J, Larson S, et al. Towards multidimensional diotherapy (MD-CRT) : biological imaging and biological conformality[J]. Int. J. Radiat Oncol Biol Phys., 2000. 47 (3): 551~560.
[45] Alber M and N¨usslin F, An objective function for radiation treatment optimization based on local biological measures[J]. Phys. Med. Biol., 1999. 44: 479~93.
[1] 袁亚湘,孙文瑜著. 最优化理论与方法[M].科学出版社,2001
[2] 施光燕,董加礼. 最优化方法[M].高等教育出版社,1999
[3] 吴祈宗. 运筹学与最优化方法[M].机械工业出版社,2003
[4] 王小平,曹立民. 遗传算法-理论、应用与软件实现[M]. 西安交通大学出版社,2002
[5] 王凌. 智能优化算法及其应用[M] 北京:清华大学出版社,2001
[6] Liu DC, Nocedal J. On the limited memory BFGS method for the large scale optimization[J]. Math. Program. 1989. 45: 503-528.
[7] Michalewicz Z. Genetic Algorithm + Data Structure = Evolution Programs[M], 2nd ed., Springer-Verlag, New York, 1994.
[8] Goldberg DE, Richardson J. Genetic algorithms with sharing for multimodal function optimization [C]. Proc 2nd Int Conf Genetic Algorithms and Their Applications [C]. NJ: L awrence Erlbaum, 1987. 41~49.
[9] Cedeno W. The multi-niche crowding genetic algorithm: Analysis and applications [D]. Univ of California, 1995.
[10] Mahfoud S W. Crowding and preselection revisited [C]. Proc 2nd Conf Parallel Problem Solving from Nature[C]. Amsterdam, 1992. 27~36.
[11] Mahfoud S W. Crossover interactions among niches [C]. Proc 1st IEEE Conf Evolutionary Computation[C ]. NJ: IEEE Press, 1994. 188-193.
[12] De Jong K A. Analysis of the behavior of a class of genetic adaptive systems[D]. Univ. of Michigan, 1975.
[13] Harik G. Finding multimodal solutions using restricted tournament selection [C]. Proc 6th Int Conf Genetic Algorithms. CA: Morgan Kaufmann, 1995. 24~31.
[14] Horn J. Multicriteria decision making. In Thomas B?ck, D. B. Fogel, and Z. Michalewicz, editors, Handbook of Evolutionary Computation. Institute of Physics Publishing, Bristol (UK), 1997. F1.9:1-F1.9:15.
[15] Schaffer J D. Multiple objective optimization with vector evaluate genetic algorithms[D]. Ph.D.Thesis, Vanderbilt University, 1984.
[16] Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms[C]. Proceedings of the 1st International Conference on Genetic Algorithms, July 1, 1985. 93~100.
[17] Fourman M P. Compaction of symbolic layout using genetic algorithms[C]. In: John J. Grefenstette, eds. Proceedings of an International Conference on Genetic Algorithms and Their Applications, Pittsburgh, PA, July 24-26 1985, 141~153,
[18] Deb K, Goldberg D E. An investigation of niche and species formation in genetic functionoptimization [C]. Proc 3rd Int Conf Genetic Algorithms, CA: Morgan Kaufmann, 1989. 42~50.
[19] Fonseca C M, Fleming P J. An overview of evolutionary algorithms in multiobjective optimization [J]. Evolutionary Computation, 1995. 3(1): 1~16.
[20] Srinivas N, Deb K. Multiobjective function optimization using non-dominated sorting genetic algorithms[J]. Evolutionary Computation, 1995. 2(3): 221~248.
[21] Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput., 2000. 8(2): 173~195.
[22] Deb K., Agrawal S., Pratap A., and Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002. 6(2): 182~197.
[23] 玄光男,程润伟著,于音杰,周根贵译.遗传算法与工程优化[M].清华大学出版社,2004.
[24] Ishibuchi H, Murata T. Multi-objective genetic local search algorithm[C]. Proc. of 3rd IEEE International Conference on Evolutionary Computation, 1996. 119~124.
[25] Jaszkiewicz A. Genetic local search for multi-objective combinatorial optimization[J]. European Journal of Operational Research, 2002. 137(1), 50~71,.
[26] Ishibuchi H, Yoshida T, Murata T. Selection of initial solutions for local search in multiobjective evolutionary algorithms[C]. Proc. of 2002 Congress on Evolutionary Computation, 2002, 950~955.
[27] Knowles J D, Corne D W. M-PAES: A memetic algorithm for multiobjective optimization[C]. Proc. of 2000 Congress on Evolutionary Computation, 2000. 325~332.
[28] Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithm[C]. Proceedings of the 1st International Conference on Genetic Algorithms, San Mateo, 1985. 93~100.
[29] Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems[J]. Evolutionary Computation, 1999. 7(3): 205-230.
[1] 陈炳桓.立体定向放射[M].北京出版社,1994.
[2] 严玉龙,立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D]. 东南大学博士论文,1997.
[3] Shu H Z, Yan Y L, Bao X D, et al. Treatment planning optimization by quasi Newton and simulated annealing methods for gamma unit treatment system[J]. Phys Med Biol, 1998. 43(10): 2795~2805.
[4] Shu H Z, Yan Y L, Luo L M, et al. Three dimensional optimization of treatment planning for gamma unit treatment system[J]. Med. Phys, 1998. 25(12): 2352~2357.
[5] 舒华忠, 严玉龙, 鲍旭东, 等. 立体定向放射外科中的旋转式伽玛刀治疗计划的优化[J]. 齐鲁肿瘤杂志, 1997. 4(3 ): 212~214.
[6] 舒华忠, 严玉龙, 鲍旭东, 等. 立体定向放射外科中的γ -刀治疗规划的优化[J].东南大学学报,1997. 27(4): 19~25.
[7] Pla C, Podgorsak E B, Pla M, et al. Considerations on the use of multiple isocenters in stereotatic radiosurgery[J]. Med. Phys, 1995. 22(5): 676.
[8] Gibon D, Rousseau J, Castelain B, et al. Treatment planning optimization by conjugate gradients and simulated annealing methods in stereotatic radiosurgery[J]. Int. J. Radiat. Oncol.Biol. Phys., 1995. 33(1): 201~210.
[9] 李乃弘, 周非亚, 於文雪, 于金明, 尹勇. 基于肿瘤形状的几何优化靶点方法[J]. 齐鲁肿瘤杂志, 1999. 6(4): 212~214.
[10] Wu Q J, Bourland J D. Three-dimensional skeletonization for computer-assisted treatment planning in radiosurgery[J]. Computerized Medical Imaging and Graphics, 2000. 24(4): 243~251.
[11] Thomas H W, Taeil Y, Sanford L M, et al. A geometrically based method for automated radiosurgery planning[J]. Int. J. Radiat. Oncol. Biol. Phys., 2000. 48(5): 1599~1611.
[12] Zhou Y, Arie K, Arthur W T. Three dimensional skeleton and centerline generation based on an approximate minimum distance field[J]. The Visual Computer, 1998. 14(7): 303~314.
[13] Palagyi K. 3D Thinning algorithms (skeletonization) and its medical applications. http://www.inf.u-szeged.hu/~palagyi/skel/skel.html#Introduction
[14] Gunilla B. On digital distance transforms in three dimensions[J]. Computer Vision and Image Understanding, 1996. 64(3): 368~376.
[15] Hristov D H, Fallone B G.. An active set algorithm for treatment planning optimization[J]. Med. Phys., 1997. 24(9): 1455~1464.
[1] 李小平, 李培根.立体定向伽玛射线全身治疗系统[J],中国医疗器械杂志,2003. 27(1):15~18.
[2] http://www.our.com.cn/production/cpgy.htm.
[3] 玄光男,程润伟著,汪定伟,唐加福,黄敏译. 遗传算法与工程设计[M]. 科学出版社,2000.
[4] 燕忠. 蚁群优化算法的研究与应用[D]. 东南大学硕士论文,2002
[5] Goldberg D E, Lingle JR. Alleles loci and the traveling salesman problem[C]. In Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Eribaum Associates, Mahwah, NJ, 1985. 154~159.
[6] Grefenstette J, Gopal R, Rosmaita R, Gucht D. Genetic algorithms for the traveling salesman problem[C]. In Proceedings of the Second International Conference on Genetic Algorithms. Lawrence Eribaum Associates, Mahwah, NJ, 1985. 160~168.
[7] Michalewicz Z. Genetic Algorithm + Data Structure = Evolution Programs[M], 2nd ed., Springer-Verlag, New York, 1994.
[8] Davis L. Applying adaptive algorithms to domains[C]. In Proceedings of the International Joint Conference on Artifical Intelligence. 1985. 162~164.
[9] Oliver l, Smith D, Holland J. A study of permutation crossover operators on the traveling salesman problem[C]. Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application, 1987. 224~230.
[10] Bean J. Genetic algorithms and random keys keys for sequencing and optimization[J]. ORSA Journal on Computing, 1994. 6(2): 154~160.
1 于金明,殷蔚伯,李宝生主编.肿瘤精确放射治疗学[M].山东科学技术出版社,2004
2 Brahame A. Treatment optimization using physical and radiobiological objective functions. In: Smith A. eds. Radiation Therapy Physics, Berlin: Springer. 1995. 210~246.
3 舒华忠, 鲍旭东, 於文雪, 罗立民. 立体定向放射外科治疗的方案优化[J]. 世界医疗器械,2000. 16(12): 20~25.
4 吴新根, 吕维雪, 罗立民. 有约束模拟退火法优化 3D 立体定向放射治疗计划[J]. 生物医学工程学杂志,1998. 15(3): 250~255.
5 吴新根, 吕维雪, 罗立民. 分阶段多准则立体定向放射治疗计划研究[J]. 中国医疗器械杂志,1998. 22(6): 320~322.
6 吴新根,罗立民,鲍旭东,吕维雪. 放射治疗计划的神经网络优化算法[J].中国生物医学工程学报,2002. 21(4):320~324
7 Xing L, Li J G, Donaldson S, Le Q T, Boyer A L. Optimization of importance factors in inverse Planning[J]. Phys. Med. Biol., 1999. 44(10): 2525~2536
8 Bednarz G., Michalski D, Anne R P, Valicenti K R. Inverse treatment planning using volume-based objective functions[J]. Phys. Med. Biol., 2004. 49(12): 2503~2514
9 Cotrutz C, Lahanas M, Kappas K, Baltas D. A multiobjective gradient based dose optimization algorithm for external beam conformal radiotherapy[J]. Phys. Med. Biol., 2001. 46(8): 2161~2175
10 Lahanas M, Schreibmann E, Baltas D. Multiobjective inverse planning in intensity modulated radiotherapy with constrained-free gradient-based optimization algorithms[J]. Phys. Med. Biol., 2003. 48(17): 2843~2871
11 Deb K, Agrawal S, Pratap A, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002. 6(2): 182~197.
12 谷铣之,殷蔚伯,刘泰福,潘国英主编.肿瘤放射治疗学[M].北京医科大学、中国协和医科大学联合出版社,1993.
13 严玉龙.立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论 与技术研究[D].东南大学博士论文,1997.
14 王凌. 智能优化算法及其应用[M].清华大学出版社,2001.
[1] Califf R M, Fortin D F, Frid DJ, et al. Restenosis after coronary angioplasty: an overview[J]. J Am Coll Cardiol, 1991. 17 Supple B:2B~13B.
[2] Leimgruber P P, Roubin G S, Hollman J, et al. Restenosis after successful coronary angioplasty in patients with single vessel disease. Circulation 1986. 73:710~717.
[3] Holmas D R J, Vliestra R E, Smith H L, et al. Restenosis after percutaneous transluminal coronary angioplasty(PTCA): A report from the PTCA registry of the National Heart,lung,and Blood Institute[J]. Am J Cardiol, 1984. 53:77c~81c.
[4] Nath R, Amols H, Coffey C, Duggan D, et al. Intravascular brachytherapy physics: Report of the AAPM Radiation Therapy Committee Task Group No 60[J]. Med. Phys., 1999. 26 (2): 119~152.
[5] Roelandt J R T C, Di Mario C, et al. Three-dimensional reconstruction of intracoronary ultrasound images: rationale, approaches, problems and directions[J]. Cirulation., 1994. 90(2): 1044～1055.
[6] Wahle A, Lopez J J, Pennington E C, Meeks S L, et al. Effects of vessel geometry and catheter position on dose delivery in intracoronary brachytherapy[J]. IEEE Trans Biomed Eng., 2003. 50(11): 1286~1295.
[7] 於文雪, 李松毅, Haigron P, 罗立民等. γ -射线血管内照射治疗计划系统的研制[J]. 东南大学学报(自然科学版),2002. 32(4): 586~589.
[8] Haigron P, Lucas A, Moisan C, Yu WX, et al., Planning of Intravascular Brachytherapy Based on Virtual Exploratory Navigation in X-ray CT Images[C]. Proceeding of SPIE, 2001. 4681: 148~158.
[9] 张惠,傅瑶,Haigron P,罗立民, 基于场景分析的交互式漫游[J]. 东南大学学报,2001. 31(2): 18-22.
[10]Kong T Y, Rosenfeld A., Digital topology: Introduction and survey[J]. Computer Vision, Graphics, and Image Processing, 1989. 48(3): 357~393.
[11]罗立民,Coatrieux Jean-Louis. 医学图象中体数据的光线跟踪法显示。 东南大学学报, 1992. 22(6): 7-12.
[12]罗立民,鲍旭东. 多功能光线跟踪方法. 东南大学学报,1994. 24(5):14~19
[13]Bellemare Marc-Emmanuel, Haigron P, Lucas Antoine, Coatrieux Jean-Louis. Depth Map Based Scene Analysis for Active Navigation[C]. In: Clough A and Chen CT, eds.The SPIE Conference on Physiology and Function from Multidimensional Images, SPIE Proceedings, Feb. 1999. 3660: 202~213.
[14]Hong L, Muraki S, Bartz D, Kaufman A. Virtual Voyage: Interactive Navigation in the Human Colon[C]. Proc. ACM SIGGRAPH, August 1997. 27~34.
[15]谷铣之,殷蔚伯,刘泰福,潘国英主编,肿瘤放射治疗学[M]. 北京医科大学、中国协和医科大学联合出版社,1993.
[16]Nath R, Anderson L L, Luxton G, Weaver K A, Williamson J F, et al. Dosimetry of interstitial brachytherapy sources: Recommandations of the AAPM Radiation Therapy Committee Task Group No. 43[J]. Med. Phys., 1995. 22(2): 209~234.
[17]Lu Y, Li S, Spellbring D, Song P, et al., Dose-surface histogram as treatment planning tool for prostate conformal therapy[J]. Med. Phys., 1995. 22(3), 279~284.
[18]严玉龙. 立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D]. 东南大学博士论文,1997.
[2] 谷铣之,殷蔚伯,刘泰福,潘国英主编,肿瘤放射治疗学[M],北京医科大学、中国协和医科大学联合出版社,1993.
[3] 严玉龙,立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D],东南大学博士论文,1997.
[4] 于金明,殷蔚伯,李宝生主编,肿瘤精确放射治疗学[M],山东科学技术出版社,2004.
[5] http://www.brachytherapy.com/index.html
[6] 於文雪, 李松毅, Haigron P, 罗立民, 等. γ -射线血管内照射治疗计划系统的研制[J]. 东南大学学报(自然科学版),2002. 32(4): 586~589
[7] Pascal H, Lucas A, Moisan C, Yu WX, et al. Planning of Intravascular Brachytherapy Based on Virtual Exploratory Navigation in X-ray CT Images[A]. Proceeding of SPIE, 2001. 4681: 148~158.
[8] Shu H Z, Yan Y L, Bao X D, et al. Treatment planning optimization by quasi Newton and simulated annealing methods for gamma unit treatment system[J]. Phys Med Biol, 1998. 43: 2795~2805.
[9] Shu H Z, Yan Y L, Luo L M, et al. Three dimensional optimization of treatment planning for gamma unit treatment system[J]. Med Phys, 1998. 25: 2352~2357.
[10] 舒华忠, 严玉龙, 鲍旭东等,立体定向放射外科中的旋转式伽玛刀治疗计划的优化[J]. 齐鲁肿瘤杂志, 1997. 4(3 ): 212~214.
[11] 舒华忠, 严玉龙, 鲍旭东等,立体定向放射外科中的γ -刀治疗规划的优化[J].东南大学学报,1997. 27(4): 19~25.
[12] Pla C, Podgorsak E B, Pla M, Souhami L, Clark B G, Caron J L. Considerations on the use of multiple isocenters in stereotactic radiosurgery[J]. Med. Phys., 1995. 22:676.
[13] Gibon D, Rousseau J, Castelain B, et al. Treatment planning optimization by conjugate gradients and simulated annealing methods in stereotatic radiosurgery[J]. Int. J. Radiat. Oncol. Biol. Phys., 1995. 33: 201~210.
[14] 李乃弘, 周非亚, 於文雪, 于金明, 尹勇, 基于肿瘤形状的几何优化靶点方法[J]. 齐鲁肿瘤杂志, 1999. 6(4 ): 212~214.
[15] Wu Q J, Bourland J D. Three-dimensional skeletonization for computer-assisted treatment planning in radiosurgery[J]. Computerized Medical Imaging and Graphics, 2000. 24: 243~251.
[16] Luo L M, Shu H Z, Yu W X, Yan Y L, Bao X D, Fu Y. Optimizing computerized treatment planning for the gamma knife by source culling. Int. J. Radiat. Oncol. Biol. Phys., 1999. 45(5): 1339~1346.
[17] Wu X G, Zhu Y P, Luo L M. Linear programming based on neural networks for radiotherapy treatment planning[J]. Phys. Med. Biol., 2000. 45: 719~728.
[18] Rosen I I, et al. Treatment plan optimization using linear programming[J]. Med. Phys., 1991. 18: 141~152.
[19] Langer M, et al. Comparison of mixed integer programming and fast simulated annealing for optimizing beam weights in radiation therapy[J]. Med. Phys., 1996. 23: 957~964.
[20] Lee E K, Fox T, Crocker I. Optimization of radiosurgery treatment planning via mixed integer programming[J]. Med. Phys., 2000. 27: 995~1004.
[21] Bortfeld T, et al. Methods of image-reconstruction from projections applied to conformation radiotherapy[J]. Phys. Med. Biol., 1990. 35: 1423~1434.
[22] Bortfeld T. Optimized planning using physical objectives and constraints[J]. Semin Radiat. Oncol. 1999. 9(1): 20~34.
[23] Cho P S et al. Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets[J]. Med. Phys., 1998. 25: 435~443.
[24] Holmes T, et al. A unified approach to the optimization of brachytherapyand external beam dosimetry[J]. Int. J. Radiat. Oncol. Biol. Phys., 1991. 20: 859~873.
[25] Hristov D, et al. On the implementation of dose-volume objectives in gradient algorithms for inverse treatment planning[J]. Med. Phys. 2002. 29: 848~856.
[26] Starkschall G, Pollack A, Stevens C W. Treatment planning using a dose-volume feasibility search algorithm[J]. Int. J. Radiat. Oncol. Biol. Phys., 2001. 49: 1419~1427 .
[27] Wu Q W, Mohan R. Algorithms and functionality of an intensity modulated radiotherapy optimization system[J]. Med. Phys., 2000. 27: 701–711.
[28] Hou Q, Wang Y G. Molecular dynamics used in radiation therapy[J]. Phys. Rev. Lett., 2001.87: 168101-1~168101-4.
[29] Hou Q, et al. An optimization algorithm for intensity modulated radiotherapy—The simulated dynamics with dose-volume constraints[J]. Med. Phys., 2003. 30: 61~68.
[30] Morrill S M, et al. Treatment planning optimization using constrained simulated annealing[J]. Phys. Med. Biol., 1991. 36: 1341~1361.
[31] Rosen I I, et al. Comparison of simulated annealing algorithms for conformal therapy treatment planning[J]. Int. J. Radiat. Oncol. Biol. Phys., 1995. 33: 1091~1099.
[32] Webb S. Optimization of conformal radiotherapy dose distributions by simulated annealing[J]. Phys. Med. Biol., 1991. 36: 1227~1237.
[33] Wu X G, et al. Selection and determination of beam weights based on genetic algorithms for conformal radiotherapy treatment planning[J]. Phys. Med. Biol., 2000. 45: 2547~2558.
[34] Bortfeld T, et al. Physical vs biological objectives for treatment plan optimization[J], Radiother. Oncol., 1996. 40: 185~187.
[35] Langer M, et al. Large-scale optimization of beam weights under dosevolume restrictions[J]. Int. J. Radiat. Oncol. Biol. Phys., 1990. 18: 887–893.
[36] Wu Q W, et al. Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose[J]. Int. J. Radiat. Oncol. Biol. Phys., 2002. 52: 224~235.
[37] Cotrutz C, Lahanas M, Kappas K, Baltas D. A multiobjective gradient based dose optimization algorithm for external beam conformal radiotherapy[J]. Phys. Med. Biol.. 2001. 46(8): 2161~2175
[38] Lahanas M, Schreibmann E, Baltas D. Multiobjective inverse planning in intensity modulated radiotherapy with constrained-free gradient-based optimization algorithms[J]. Phys. Med. Biol., 2003. 48(17): 2843~2871
[39] Lahanas M, Baltas D, Zamboglou N. Anatomy-based three-dimensional dose optimization in brachytherapy using multiobjective genetic algorithms[J]. Med. Phys., 1999. 26: 1904~1918.
[40] Kawrakow I, Fippel M. Investigation of variance reduction techniques for Monte Carlo photon dose calculation using XVMC[J]. Phys. Med. Biol., 2000. 45:2163~2183
[41] Kawrakow I and Fippel M. VMC++, a MC algorithm optimized for electron and photon beam dose calculations for RTP.[C] Proceedings of the 22th annual EMBS international conference, 2000. 1490~1493
[42] James H V, Atherton S, Budgell G J, Kirby M C, Williams P C, Verification of dynamic multileaf collimation using an electronic portal imaging device[J]. Phys. Med. Biol., 2000. 45(2): 495~509.
[43] Vieira S C, Dirkx M L P, Pasma K L, Heijmen B J M. Dosimetric verification of x-ray fields with steep dose gradients using an electronic portal imaging device[J]. Phys. Med. Biol., 2003. 48(2): 157~166.
[44] Ling C C, Humm J, Larson S, et al. Towards multidimensional diotherapy (MD-CRT) : biological imaging and biological conformality[J]. Int. J. Radiat Oncol Biol Phys., 2000. 47 (3): 551~560.
[45] Alber M and N¨usslin F, An objective function for radiation treatment optimization based on local biological measures[J]. Phys. Med. Biol., 1999. 44: 479~93.
[1] 袁亚湘,孙文瑜著. 最优化理论与方法[M].科学出版社,2001
[2] 施光燕,董加礼. 最优化方法[M].高等教育出版社,1999
[3] 吴祈宗. 运筹学与最优化方法[M].机械工业出版社,2003
[4] 王小平,曹立民. 遗传算法-理论、应用与软件实现[M]. 西安交通大学出版社,2002
[5] 王凌. 智能优化算法及其应用[M] 北京:清华大学出版社,2001
[6] Liu DC, Nocedal J. On the limited memory BFGS method for the large scale optimization[J]. Math. Program. 1989. 45: 503-528.
[7] Michalewicz Z. Genetic Algorithm + Data Structure = Evolution Programs[M], 2nd ed., Springer-Verlag, New York, 1994.
[8] Goldberg DE, Richardson J. Genetic algorithms with sharing for multimodal function optimization [C]. Proc 2nd Int Conf Genetic Algorithms and Their Applications [C]. NJ: L awrence Erlbaum, 1987. 41~49.
[9] Cedeno W. The multi-niche crowding genetic algorithm: Analysis and applications [D]. Univ of California, 1995.
[10] Mahfoud S W. Crowding and preselection revisited [C]. Proc 2nd Conf Parallel Problem Solving from Nature[C]. Amsterdam, 1992. 27~36.
[11] Mahfoud S W. Crossover interactions among niches [C]. Proc 1st IEEE Conf Evolutionary Computation[C ]. NJ: IEEE Press, 1994. 188-193.
[12] De Jong K A. Analysis of the behavior of a class of genetic adaptive systems[D]. Univ. of Michigan, 1975.
[13] Harik G. Finding multimodal solutions using restricted tournament selection [C]. Proc 6th Int Conf Genetic Algorithms. CA: Morgan Kaufmann, 1995. 24~31.
[14] Horn J. Multicriteria decision making. In Thomas B?ck, D. B. Fogel, and Z. Michalewicz, editors, Handbook of Evolutionary Computation. Institute of Physics Publishing, Bristol (UK), 1997. F1.9:1-F1.9:15.
[15] Schaffer J D. Multiple objective optimization with vector evaluate genetic algorithms[D]. Ph.D.Thesis, Vanderbilt University, 1984.
[16] Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms[C]. Proceedings of the 1st International Conference on Genetic Algorithms, July 1, 1985. 93~100.
[17] Fourman M P. Compaction of symbolic layout using genetic algorithms[C]. In: John J. Grefenstette, eds. Proceedings of an International Conference on Genetic Algorithms and Their Applications, Pittsburgh, PA, July 24-26 1985, 141~153,
[18] Deb K, Goldberg D E. An investigation of niche and species formation in genetic functionoptimization [C]. Proc 3rd Int Conf Genetic Algorithms, CA: Morgan Kaufmann, 1989. 42~50.
[19] Fonseca C M, Fleming P J. An overview of evolutionary algorithms in multiobjective optimization [J]. Evolutionary Computation, 1995. 3(1): 1~16.
[20] Srinivas N, Deb K. Multiobjective function optimization using non-dominated sorting genetic algorithms[J]. Evolutionary Computation, 1995. 2(3): 221~248.
[21] Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput., 2000. 8(2): 173~195.
[22] Deb K., Agrawal S., Pratap A., and Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002. 6(2): 182~197.
[23] 玄光男,程润伟著,于音杰,周根贵译.遗传算法与工程优化[M].清华大学出版社,2004.
[24] Ishibuchi H, Murata T. Multi-objective genetic local search algorithm[C]. Proc. of 3rd IEEE International Conference on Evolutionary Computation, 1996. 119~124.
[25] Jaszkiewicz A. Genetic local search for multi-objective combinatorial optimization[J]. European Journal of Operational Research, 2002. 137(1), 50~71,.
[26] Ishibuchi H, Yoshida T, Murata T. Selection of initial solutions for local search in multiobjective evolutionary algorithms[C]. Proc. of 2002 Congress on Evolutionary Computation, 2002, 950~955.
[27] Knowles J D, Corne D W. M-PAES: A memetic algorithm for multiobjective optimization[C]. Proc. of 2000 Congress on Evolutionary Computation, 2000. 325~332.
[28] Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithm[C]. Proceedings of the 1st International Conference on Genetic Algorithms, San Mateo, 1985. 93~100.
[29] Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems[J]. Evolutionary Computation, 1999. 7(3): 205-230.
[1] 陈炳桓.立体定向放射[M].北京出版社,1994.
[2] 严玉龙,立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D]. 东南大学博士论文,1997.
[3] Shu H Z, Yan Y L, Bao X D, et al. Treatment planning optimization by quasi Newton and simulated annealing methods for gamma unit treatment system[J]. Phys Med Biol, 1998. 43(10): 2795~2805.
[4] Shu H Z, Yan Y L, Luo L M, et al. Three dimensional optimization of treatment planning for gamma unit treatment system[J]. Med. Phys, 1998. 25(12): 2352~2357.
[5] 舒华忠, 严玉龙, 鲍旭东, 等. 立体定向放射外科中的旋转式伽玛刀治疗计划的优化[J]. 齐鲁肿瘤杂志, 1997. 4(3 ): 212~214.
[6] 舒华忠, 严玉龙, 鲍旭东, 等. 立体定向放射外科中的γ -刀治疗规划的优化[J].东南大学学报,1997. 27(4): 19~25.
[7] Pla C, Podgorsak E B, Pla M, et al. Considerations on the use of multiple isocenters in stereotatic radiosurgery[J]. Med. Phys, 1995. 22(5): 676.
[8] Gibon D, Rousseau J, Castelain B, et al. Treatment planning optimization by conjugate gradients and simulated annealing methods in stereotatic radiosurgery[J]. Int. J. Radiat. Oncol.Biol. Phys., 1995. 33(1): 201~210.
[9] 李乃弘, 周非亚, 於文雪, 于金明, 尹勇. 基于肿瘤形状的几何优化靶点方法[J]. 齐鲁肿瘤杂志, 1999. 6(4): 212~214.
[10] Wu Q J, Bourland J D. Three-dimensional skeletonization for computer-assisted treatment planning in radiosurgery[J]. Computerized Medical Imaging and Graphics, 2000. 24(4): 243~251.
[11] Thomas H W, Taeil Y, Sanford L M, et al. A geometrically based method for automated radiosurgery planning[J]. Int. J. Radiat. Oncol. Biol. Phys., 2000. 48(5): 1599~1611.
[12] Zhou Y, Arie K, Arthur W T. Three dimensional skeleton and centerline generation based on an approximate minimum distance field[J]. The Visual Computer, 1998. 14(7): 303~314.
[13] Palagyi K. 3D Thinning algorithms (skeletonization) and its medical applications. http://www.inf.u-szeged.hu/~palagyi/skel/skel.html#Introduction
[14] Gunilla B. On digital distance transforms in three dimensions[J]. Computer Vision and Image Understanding, 1996. 64(3): 368~376.
[15] Hristov D H, Fallone B G.. An active set algorithm for treatment planning optimization[J]. Med. Phys., 1997. 24(9): 1455~1464.
[1] 李小平, 李培根.立体定向伽玛射线全身治疗系统[J],中国医疗器械杂志,2003. 27(1):15~18.
[2] http://www.our.com.cn/production/cpgy.htm.
[3] 玄光男,程润伟著,汪定伟,唐加福,黄敏译. 遗传算法与工程设计[M]. 科学出版社,2000.
[4] 燕忠. 蚁群优化算法的研究与应用[D]. 东南大学硕士论文,2002
[5] Goldberg D E, Lingle JR. Alleles loci and the traveling salesman problem[C]. In Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Eribaum Associates, Mahwah, NJ, 1985. 154~159.
[6] Grefenstette J, Gopal R, Rosmaita R, Gucht D. Genetic algorithms for the traveling salesman problem[C]. In Proceedings of the Second International Conference on Genetic Algorithms. Lawrence Eribaum Associates, Mahwah, NJ, 1985. 160~168.
[7] Michalewicz Z. Genetic Algorithm + Data Structure = Evolution Programs[M], 2nd ed., Springer-Verlag, New York, 1994.
[8] Davis L. Applying adaptive algorithms to domains[C]. In Proceedings of the International Joint Conference on Artifical Intelligence. 1985. 162~164.
[9] Oliver l, Smith D, Holland J. A study of permutation crossover operators on the traveling salesman problem[C]. Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application, 1987. 224~230.
[10] Bean J. Genetic algorithms and random keys keys for sequencing and optimization[J]. ORSA Journal on Computing, 1994. 6(2): 154~160.
1 于金明,殷蔚伯,李宝生主编.肿瘤精确放射治疗学[M].山东科学技术出版社,2004
2 Brahame A. Treatment optimization using physical and radiobiological objective functions. In: Smith A. eds. Radiation Therapy Physics, Berlin: Springer. 1995. 210~246.
3 舒华忠, 鲍旭东, 於文雪, 罗立民. 立体定向放射外科治疗的方案优化[J]. 世界医疗器械,2000. 16(12): 20~25.
4 吴新根, 吕维雪, 罗立民. 有约束模拟退火法优化 3D 立体定向放射治疗计划[J]. 生物医学工程学杂志,1998. 15(3): 250~255.
5 吴新根, 吕维雪, 罗立民. 分阶段多准则立体定向放射治疗计划研究[J]. 中国医疗器械杂志,1998. 22(6): 320~322.
6 吴新根,罗立民,鲍旭东,吕维雪. 放射治疗计划的神经网络优化算法[J].中国生物医学工程学报,2002. 21(4):320~324
7 Xing L, Li J G, Donaldson S, Le Q T, Boyer A L. Optimization of importance factors in inverse Planning[J]. Phys. Med. Biol., 1999. 44(10): 2525~2536
8 Bednarz G., Michalski D, Anne R P, Valicenti K R. Inverse treatment planning using volume-based objective functions[J]. Phys. Med. Biol., 2004. 49(12): 2503~2514
9 Cotrutz C, Lahanas M, Kappas K, Baltas D. A multiobjective gradient based dose optimization algorithm for external beam conformal radiotherapy[J]. Phys. Med. Biol., 2001. 46(8): 2161~2175
10 Lahanas M, Schreibmann E, Baltas D. Multiobjective inverse planning in intensity modulated radiotherapy with constrained-free gradient-based optimization algorithms[J]. Phys. Med. Biol., 2003. 48(17): 2843~2871
11 Deb K, Agrawal S, Pratap A, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002. 6(2): 182~197.
12 谷铣之,殷蔚伯,刘泰福,潘国英主编.肿瘤放射治疗学[M].北京医科大学、中国协和医科大学联合出版社,1993.
13 严玉龙.立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论 与技术研究[D].东南大学博士论文,1997.
14 王凌. 智能优化算法及其应用[M].清华大学出版社,2001.
[1] Califf R M, Fortin D F, Frid DJ, et al. Restenosis after coronary angioplasty: an overview[J]. J Am Coll Cardiol, 1991. 17 Supple B:2B~13B.
[2] Leimgruber P P, Roubin G S, Hollman J, et al. Restenosis after successful coronary angioplasty in patients with single vessel disease. Circulation 1986. 73:710~717.
[3] Holmas D R J, Vliestra R E, Smith H L, et al. Restenosis after percutaneous transluminal coronary angioplasty(PTCA): A report from the PTCA registry of the National Heart,lung,and Blood Institute[J]. Am J Cardiol, 1984. 53:77c~81c.
[4] Nath R, Amols H, Coffey C, Duggan D, et al. Intravascular brachytherapy physics: Report of the AAPM Radiation Therapy Committee Task Group No 60[J]. Med. Phys., 1999. 26 (2): 119~152.
[5] Roelandt J R T C, Di Mario C, et al. Three-dimensional reconstruction of intracoronary ultrasound images: rationale, approaches, problems and directions[J]. Cirulation., 1994. 90(2): 1044～1055.
[6] Wahle A, Lopez J J, Pennington E C, Meeks S L, et al. Effects of vessel geometry and catheter position on dose delivery in intracoronary brachytherapy[J]. IEEE Trans Biomed Eng., 2003. 50(11): 1286~1295.
[7] 於文雪, 李松毅, Haigron P, 罗立民等. γ -射线血管内照射治疗计划系统的研制[J]. 东南大学学报(自然科学版),2002. 32(4): 586~589.
[8] Haigron P, Lucas A, Moisan C, Yu WX, et al., Planning of Intravascular Brachytherapy Based on Virtual Exploratory Navigation in X-ray CT Images[C]. Proceeding of SPIE, 2001. 4681: 148~158.
[9] 张惠,傅瑶,Haigron P,罗立民, 基于场景分析的交互式漫游[J]. 东南大学学报,2001. 31(2): 18-22.
[10]Kong T Y, Rosenfeld A., Digital topology: Introduction and survey[J]. Computer Vision, Graphics, and Image Processing, 1989. 48(3): 357~393.
[11]罗立民,Coatrieux Jean-Louis. 医学图象中体数据的光线跟踪法显示。 东南大学学报, 1992. 22(6): 7-12.
[12]罗立民,鲍旭东. 多功能光线跟踪方法. 东南大学学报,1994. 24(5):14~19
[13]Bellemare Marc-Emmanuel, Haigron P, Lucas Antoine, Coatrieux Jean-Louis. Depth Map Based Scene Analysis for Active Navigation[C]. In: Clough A and Chen CT, eds.The SPIE Conference on Physiology and Function from Multidimensional Images, SPIE Proceedings, Feb. 1999. 3660: 202~213.
[14]Hong L, Muraki S, Bartz D, Kaufman A. Virtual Voyage: Interactive Navigation in the Human Colon[C]. Proc. ACM SIGGRAPH, August 1997. 27~34.
[15]谷铣之,殷蔚伯,刘泰福,潘国英主编,肿瘤放射治疗学[M]. 北京医科大学、中国协和医科大学联合出版社,1993.
[16]Nath R, Anderson L L, Luxton G, Weaver K A, Williamson J F, et al. Dosimetry of interstitial brachytherapy sources: Recommandations of the AAPM Radiation Therapy Committee Task Group No. 43[J]. Med. Phys., 1995. 22(2): 209~234.
[17]Lu Y, Li S, Spellbring D, Song P, et al., Dose-surface histogram as treatment planning tool for prostate conformal therapy[J]. Med. Phys., 1995. 22(3), 279~284.
[18]严玉龙. 立体定向放射疗法的治疗规划— 适形放疗与立体定向放射外科治疗规划的理论与技术研究[D]. 东南大学博士论文,1997.