基于等效均匀剂量的目标函数及蒙特卡罗法卷积核的实现
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摘要
放射治疗是治疗癌症的三大主要手段之一,约有60%-70%的肿瘤病人需要进行放射治疗。从经典的三维适形放射治疗技术发展到现在的调强放射治疗技术是放射肿瘤学史上的一次重大变革。调强放疗计划不同于传统的放疗计划,它是逆向计划过程。即:首先由临床医生提出数字化的临床目标,然后由计划系统优化参数,使治疗计划的结果最接近期望的临床目标。鉴于实际问题的复杂性,调强放射治疗的优势还远没有在临床应用中完全发挥出来,尚有许多急需解决的问题。目标函数的构建和蒙特卡罗方法卷积核的获取,是调强放疗计划系统中的关键技术。
目标函数是优化和评价一个治疗计划的重要目标,它不仅是输出剂量与输入射线参数之间的纽带,它更能反映出一个治疗计划的优劣。物理目标函数是目前应用最广泛的,但它不能反映出剂量不均匀性对实际照射效果的影响;等效均匀剂量目标函数的出现,在一定程度上弥补了这个缺陷。
本文从等效均匀剂量提出的背景入手,介绍等效均匀剂量发展和推演的过程,并从数理角度对等效均匀剂量进行浅析。为了说明它的应用效果,在其他条件不变的情况下,用等效均匀剂量目标函数和剂量目标函数优化同样的治疗计划。结果表明等效均匀剂量的目标函数可以取得更均匀的剂量分布,更有效地保护危险器官和正常组织,且算法收敛速度更快。等效均匀剂量中参数的取值是它在应用过程中的一个难点,本文运用实例分析了参数取值对优化结果的影响。等效均匀剂量具有严格的生物学背景,它在一定程度上可以模拟出人体组织器官的剂量效应、反映出肿瘤控制率的大小,因此它可以看作是物理目标函数到生物目标函数的过渡。
剂量计算是放疗计划中的核心和灵魂。调强放疗的发展使得不规则野剂量的准确计算成为迫切的需要,目前不规则野剂量计算的经典方法是三维卷积法,即:剂量由比释总能函数和能量沉积核卷积得到。
获取能量沉积核的方法有直接实验测量法、高斯函数逼近法、解卷积法和蒙特卡罗方法。其中蒙特卡罗法是获取能量沉积核最为精确的方法。本文的另一个主要研究工作是基于EGS的蒙特卡罗法卷积核的获取。本文的第四至五章阐述了卷积核的含义及其常见获取方法,概述了蒙特卡罗方法思想。目前蒙特卡罗法由于巨大的时间消耗还不能应用于临床的剂量计算,但是用蒙特卡罗法获取卷积核等同于在均匀媒质中、微小的单元面积下,用蒙特卡罗法进行剂量计算,这无疑是可行的。在简单介绍EGS开发包的基础上,本文用它获取了能量沉积核,并将这个核与解卷积法得到的笔射束核应用于同样的病例,分析二者差异,结果发现,采用蒙特卡罗法的卷积核,靶区内剂量分布的不均匀性远远超过用解卷积法获取的笔射束核。
本文的最后对工作中的遗留问题进行了总结,并对今后的工作进行了展望。
Together with surgery and chemotherapy, radiotherapy plays an important role in oncology, both in the definitive and palliative aspects of treatment. It treats with about 60%-70% patients suffering from cancer and cures 40% of them. It is a historic advancement that the classical three-dimensional (3D) conformal radiotherapy (3DCRT) evolved into the intensity modulated radiotherapy (IMRT). IMRT is an inverse treatment planning, that is, the planner defines certain constrains for the desired dose distribution, and the optimization process the computer trying to find the treatment setup that matches the constraints as closely as possible. However, the advantages of IMRT have not been fully utilized yet, due to the complicated clinical conditions.
This paper mainly concerns two critical issues of IMRT: the objective function and the convolution kernels based on Monte Carlo method. Objective function is an important designation to optimize and evaluate the treatment plan. It doesn't only connect the practical dose-output and expected goals, but indicates the extent of the treatment plan to be accepted. Physical function is the most widely used nowadays, but it fails to imply the influence of the dose inhomogeneity to the treatment planning while the function based on equivalent uniform dose(EUD) works better in this aspect.
This paper proposes the application of the objective function based on EUD in IMRT. EUD is defined as "that dose which, when distributed uniformly across the target volume, causes the survival of the same number of colognes as the delivered non-uniform dose distribution". The background of EUD, the mathematical analysis of EUD is given in chapter3. Both EUD-based and dose-based objective functions are applied to optimize the same IMRT plans. It is found that EUD-based criteria provides better target coverage and is capable of improving the spring of critical structure beyond the specified requirements. Equivalent uniform dose based objective function needs only a small number of parameters and allows exploration of a much larger universe of solutions. It has nice derivability and convexity. It also can be a surrogate of biologic index such as tumor control probability and normal tissue complication probability. It dose have a bright future in IMRT.
Dose calculation is the kernel and the soul of the treatment planning system. Accurate dose calculation for irregular field has always been an essential topic in IMRT. Convolution is nowadays a popular dose calculation method by which dose is calculated by convolving the released photon energy with an energy deposition kernel.
Monte Carlo is the most perfect method in theory to implement the energy deposition kernel. Chapter 4 and Chapter 5 illustrate the Monte Carlo method, the EGS Monte Carlo Code and finally apply the EGS codes to achieve an energy deposition kernel. The EGS Monte Carlo energy deposition kernel and the pencil beam kernel extracted by deconvolution method are used to compute the dose distribution for same plans. It is found that there is remarkable dose inhomogeneity in target region when employing the EGS Monte Carlo kernel.
The end part of the paper gives an overview and puts forward the issues to do in the future.
目标函数是优化和评价一个治疗计划的重要目标,它不仅是输出剂量与输入射线参数之间的纽带,它更能反映出一个治疗计划的优劣。物理目标函数是目前应用最广泛的,但它不能反映出剂量不均匀性对实际照射效果的影响;等效均匀剂量目标函数的出现,在一定程度上弥补了这个缺陷。
本文从等效均匀剂量提出的背景入手,介绍等效均匀剂量发展和推演的过程,并从数理角度对等效均匀剂量进行浅析。为了说明它的应用效果,在其他条件不变的情况下,用等效均匀剂量目标函数和剂量目标函数优化同样的治疗计划。结果表明等效均匀剂量的目标函数可以取得更均匀的剂量分布,更有效地保护危险器官和正常组织,且算法收敛速度更快。等效均匀剂量中参数的取值是它在应用过程中的一个难点,本文运用实例分析了参数取值对优化结果的影响。等效均匀剂量具有严格的生物学背景,它在一定程度上可以模拟出人体组织器官的剂量效应、反映出肿瘤控制率的大小,因此它可以看作是物理目标函数到生物目标函数的过渡。
剂量计算是放疗计划中的核心和灵魂。调强放疗的发展使得不规则野剂量的准确计算成为迫切的需要,目前不规则野剂量计算的经典方法是三维卷积法,即:剂量由比释总能函数和能量沉积核卷积得到。
获取能量沉积核的方法有直接实验测量法、高斯函数逼近法、解卷积法和蒙特卡罗方法。其中蒙特卡罗法是获取能量沉积核最为精确的方法。本文的另一个主要研究工作是基于EGS的蒙特卡罗法卷积核的获取。本文的第四至五章阐述了卷积核的含义及其常见获取方法,概述了蒙特卡罗方法思想。目前蒙特卡罗法由于巨大的时间消耗还不能应用于临床的剂量计算,但是用蒙特卡罗法获取卷积核等同于在均匀媒质中、微小的单元面积下,用蒙特卡罗法进行剂量计算,这无疑是可行的。在简单介绍EGS开发包的基础上,本文用它获取了能量沉积核,并将这个核与解卷积法得到的笔射束核应用于同样的病例,分析二者差异,结果发现,采用蒙特卡罗法的卷积核,靶区内剂量分布的不均匀性远远超过用解卷积法获取的笔射束核。
本文的最后对工作中的遗留问题进行了总结,并对今后的工作进行了展望。
Together with surgery and chemotherapy, radiotherapy plays an important role in oncology, both in the definitive and palliative aspects of treatment. It treats with about 60%-70% patients suffering from cancer and cures 40% of them. It is a historic advancement that the classical three-dimensional (3D) conformal radiotherapy (3DCRT) evolved into the intensity modulated radiotherapy (IMRT). IMRT is an inverse treatment planning, that is, the planner defines certain constrains for the desired dose distribution, and the optimization process the computer trying to find the treatment setup that matches the constraints as closely as possible. However, the advantages of IMRT have not been fully utilized yet, due to the complicated clinical conditions.
This paper mainly concerns two critical issues of IMRT: the objective function and the convolution kernels based on Monte Carlo method. Objective function is an important designation to optimize and evaluate the treatment plan. It doesn't only connect the practical dose-output and expected goals, but indicates the extent of the treatment plan to be accepted. Physical function is the most widely used nowadays, but it fails to imply the influence of the dose inhomogeneity to the treatment planning while the function based on equivalent uniform dose(EUD) works better in this aspect.
This paper proposes the application of the objective function based on EUD in IMRT. EUD is defined as "that dose which, when distributed uniformly across the target volume, causes the survival of the same number of colognes as the delivered non-uniform dose distribution". The background of EUD, the mathematical analysis of EUD is given in chapter3. Both EUD-based and dose-based objective functions are applied to optimize the same IMRT plans. It is found that EUD-based criteria provides better target coverage and is capable of improving the spring of critical structure beyond the specified requirements. Equivalent uniform dose based objective function needs only a small number of parameters and allows exploration of a much larger universe of solutions. It has nice derivability and convexity. It also can be a surrogate of biologic index such as tumor control probability and normal tissue complication probability. It dose have a bright future in IMRT.
Dose calculation is the kernel and the soul of the treatment planning system. Accurate dose calculation for irregular field has always been an essential topic in IMRT. Convolution is nowadays a popular dose calculation method by which dose is calculated by convolving the released photon energy with an energy deposition kernel.
Monte Carlo is the most perfect method in theory to implement the energy deposition kernel. Chapter 4 and Chapter 5 illustrate the Monte Carlo method, the EGS Monte Carlo Code and finally apply the EGS codes to achieve an energy deposition kernel. The EGS Monte Carlo energy deposition kernel and the pencil beam kernel extracted by deconvolution method are used to compute the dose distribution for same plans. It is found that there is remarkable dose inhomogeneity in target region when employing the EGS Monte Carlo kernel.
The end part of the paper gives an overview and puts forward the issues to do in the future.
引文
[1]胡逸民,肿瘤放射物理学.北京:原子能出版社,1999,538.
[2]L.Jones,P.Hoban.A comparison of physically and radiobiologically based optimization for IMRT[J].Med.Phys.2002,29(7):1447-55.
[3]C.Thieke,T.Bortfeld,A.Niemierko,et al.From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning[J].Med.Phys.2003,30(9):2332-39.
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[5]Qiuwen Wu,Radhe Mohan.Algorithms and functionality of an intensity modulated radiotherapy optimization system[J].Med.Phys.2000,27(4):701-10.
[6]马金利,蒋国梁.调强适形放射治疗计划的优化目标与临床评价.中华放射肿瘤生物学杂志[J].2004,13(3):204-7.
[7]李宝生,于金明,王立英,等.调强放射治疗计划[J],中国肿瘤,2001,10(8):461-63.
[8]Wu QW,Mohan R,Niemierko A,et al.Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose[J].Int J Radiat Oncol Biol Phys.,2002,52(1):224-35.
[9]A.Brahme.Dosimetric precision requirements in radiation therapy[J].Acta Radiol.Oncol.,1984,23(1):379-91.
[10]A.Niemierko.Reporting and analyzing dose distributions:A concept of equivalent uniform dose[J].Med.Phys.1997,24(8):103-10.
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[12]C.S.Park,Y.Kim and N.Lee et al.,Method to account for dose fraction in analysis of IMRT plans:modified equivalent uniform dose[J].Int.J.Radiat.Oncol.,Biol.,Phys.2005, 62(3):925-32.
[13]卢险峰主编.最优化方法应用基础.上海:同济大学出版社,2003.
[14]Q Wu,D Djajaputra,HH Liu,et al.Dose sculpting with generalized equivalent uniform dose[J].Med.Phys.2005,32(5):1387-96.
[15]Jian Z.Wang and X.Allen Li.Evaluation of external beam radiotherapy and brachytherapy for localized prostate cancer using equivalent uniform dose[J].Med.Phys.2003,30(1):33-40.
[16]S.L.Paul et al.Conformal radiotherapy computation by the method of alternating projections onto convex sets[J].Phys.Med.Biol.1997,42(6):1065-86.
[17]Panayiotis Mawoidis,Bengt K Lind and Anders Brahme.Biologically effective uniform dose(D) for specification,report and comparison of dose response relations and treatment plans[J].Phys.Med.Biol.2001,46(10):2607-30.
[18]Choi B,Deasy JO.The generalized equivalent uniform dose function as a basis for intensity-modulated treatment planning[J].Phys Med Biol.,2002,47(20):579-89.
[19]金浩宇,吕庆文,周凌宏.用解卷积方法提取笔射束核的实现.中国生物医学工程学报[J].2004,23(4):382-5.
[20]乐文友,戴建荣,高黎.鼻咽癌调强放疗等效均匀剂量优化方法对腮腺的保护作用[J].中华放射肿瘤学杂志,2006,15(6):484-8.
[21]王鑫,何少琴.精确放疗所面对的生物学问题[J].中华肿瘤防治杂志,2006,13(10):10-3.
[22]Martin A Ebert.Viability of the EUD and TCP concepts as reliable dose indicators[J].Phys Med Biol.,2000,45(2):441-8.
[23]Liu HH,Verhaegen F.An investigation of energy spectrum and lineal energy variations in mega-voltage photon beams used for radiotherapy.Radiat.Prot.Dosim.,2002,99(2):425-7.
[24]Zhang XD,Wu QW and Mohan R.Speed and convergence properties of gradient algorithms of optimization of IMRT[J].Med Phys,2004,31(5):1141-52.
[25]朱琳,周凌宏,王卓宇.调强放疗优化中目标函数的研究进展[J].国际生物医学工程杂志,2007,30(4):227-9.
[26]周凌宏,唐木涛,王卓宇等.基于遗传算法的剂量优化技术研究[J].南方医科大学学报,2006,26(4):46-8.
[27]朱琳,周凌宏,王卓宇.基于等效均匀剂量的目标函数在调强放疗计划优化中的应用[J].中华放射肿瘤学杂志,2007,16(5):386-9。
[28]Zhu Lin,Zhou Ling-hong,Wang Zhuo-yu.The Two Kinds of Objective Function in IMRT.Proceedings of the 2007 IEEE,the 1~(st) International Conference on Bioinformatics and Biomedical Engineering,Wuhan,China,July6-8,2007.
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[2]L.Jones,P.Hoban.A comparison of physically and radiobiologically based optimization for IMRT[J].Med.Phys.2002,29(7):1447-55.
[3]C.Thieke,T.Bortfeld,A.Niemierko,et al.From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning[J].Med.Phys.2003,30(9):2332-39.
[4]T.Bortfeld.Physical vs biological objectives for treatment plan optimization[J].Radiother.Oncol.,1996,40(2):185.
[5]Qiuwen Wu,Radhe Mohan.Algorithms and functionality of an intensity modulated radiotherapy optimization system[J].Med.Phys.2000,27(4):701-10.
[6]马金利,蒋国梁.调强适形放射治疗计划的优化目标与临床评价.中华放射肿瘤生物学杂志[J].2004,13(3):204-7.
[7]李宝生,于金明,王立英,等.调强放射治疗计划[J],中国肿瘤,2001,10(8):461-63.
[8]Wu QW,Mohan R,Niemierko A,et al.Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose[J].Int J Radiat Oncol Biol Phys.,2002,52(1):224-35.
[9]A.Brahme.Dosimetric precision requirements in radiation therapy[J].Acta Radiol.Oncol.,1984,23(1):379-91.
[10]A.Niemierko.Reporting and analyzing dose distributions:A concept of equivalent uniform dose[J].Med.Phys.1997,24(8):103-10.
[11]Niemierko A.A generalized concept of equivalent uniform dose(EUD)[J].Med.Phys,1999,26:1100.
[12]C.S.Park,Y.Kim and N.Lee et al.,Method to account for dose fraction in analysis of IMRT plans:modified equivalent uniform dose[J].Int.J.Radiat.Oncol.,Biol.,Phys.2005, 62(3):925-32.
[13]卢险峰主编.最优化方法应用基础.上海:同济大学出版社,2003.
[14]Q Wu,D Djajaputra,HH Liu,et al.Dose sculpting with generalized equivalent uniform dose[J].Med.Phys.2005,32(5):1387-96.
[15]Jian Z.Wang and X.Allen Li.Evaluation of external beam radiotherapy and brachytherapy for localized prostate cancer using equivalent uniform dose[J].Med.Phys.2003,30(1):33-40.
[16]S.L.Paul et al.Conformal radiotherapy computation by the method of alternating projections onto convex sets[J].Phys.Med.Biol.1997,42(6):1065-86.
[17]Panayiotis Mawoidis,Bengt K Lind and Anders Brahme.Biologically effective uniform dose(D) for specification,report and comparison of dose response relations and treatment plans[J].Phys.Med.Biol.2001,46(10):2607-30.
[18]Choi B,Deasy JO.The generalized equivalent uniform dose function as a basis for intensity-modulated treatment planning[J].Phys Med Biol.,2002,47(20):579-89.
[19]金浩宇,吕庆文,周凌宏.用解卷积方法提取笔射束核的实现.中国生物医学工程学报[J].2004,23(4):382-5.
[20]乐文友,戴建荣,高黎.鼻咽癌调强放疗等效均匀剂量优化方法对腮腺的保护作用[J].中华放射肿瘤学杂志,2006,15(6):484-8.
[21]王鑫,何少琴.精确放疗所面对的生物学问题[J].中华肿瘤防治杂志,2006,13(10):10-3.
[22]Martin A Ebert.Viability of the EUD and TCP concepts as reliable dose indicators[J].Phys Med Biol.,2000,45(2):441-8.
[23]Liu HH,Verhaegen F.An investigation of energy spectrum and lineal energy variations in mega-voltage photon beams used for radiotherapy.Radiat.Prot.Dosim.,2002,99(2):425-7.
[24]Zhang XD,Wu QW and Mohan R.Speed and convergence properties of gradient algorithms of optimization of IMRT[J].Med Phys,2004,31(5):1141-52.
[25]朱琳,周凌宏,王卓宇.调强放疗优化中目标函数的研究进展[J].国际生物医学工程杂志,2007,30(4):227-9.
[26]周凌宏,唐木涛,王卓宇等.基于遗传算法的剂量优化技术研究[J].南方医科大学学报,2006,26(4):46-8.
[27]朱琳,周凌宏,王卓宇.基于等效均匀剂量的目标函数在调强放疗计划优化中的应用[J].中华放射肿瘤学杂志,2007,16(5):386-9。
[28]Zhu Lin,Zhou Ling-hong,Wang Zhuo-yu.The Two Kinds of Objective Function in IMRT.Proceedings of the 2007 IEEE,the 1~(st) International Conference on Bioinformatics and Biomedical Engineering,Wuhan,China,July6-8,2007.
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