调强放疗中的数学规划问题研究
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摘要
调强放疗技术能够保证在杀死癌症细胞的同时最大程度地保护正常组织,避免并发症的出现,被认为是恶性肿瘤治疗的主要技术手段之一。调强放疗逆向计划系统是调强放疗软件部分的核心,主要建立在数学规划问题的精确建模与快速求解的基础之上。其中,强度图强度优化、强度图平滑优化和两步整合优化等优化问题是目前研究的热点。在解决这几个问题时尽可能使用凸规划数学建模,不仅避免了非凸规划求解过程的不确定性和不准确性,且让小规模规划整合为大规模或超大规模规划有迹可循。
重点研究了调强放疗逆向计划系统中的几个关键技术问题,主要包括以下几个方面。
首先,强度图强度优化问题要求依据临床医生的剂量需求逆向求解各射野所需调制的射线强度。带有剂量体积约束的强度优化以及基于等效生物剂量模型的强度优化是该类问题建模求解的难点。对于前者,指出了传统的剂量排序技术的不足,以线性约束二次规划模型作为基础,给出了更为科学的基于几何距离排序技术的迭代求解策略；对于后者,改变了传统生物剂量模型与现有医学评价系统脱节的不足,给出了基于体积剂量函数的等效均匀剂量的定义及相应的能够转化为一般的剂量体积约束问题的数学模型。利用公开的四个临床测试病例对几何距离排序技术和剂量排序技术进行了实验比较,结果显示前者能够在满足剂量体积约束时让靶区获取更高的剂量适形度。
其次,由于抑制强度图噪音将大大降低射线调制时所需的总机器跳数,强度图平滑优化要求解决强度图过多起伏的问题。针对传统的目标项平滑策略难以解决的五大问题,首次提出了约束条件平滑策略。该策略能够进行智能平滑,将强度求解与子野分解这两个环节有机地结合。针对几种典型的叶片单向滑动子野分解模式进行了数学建模。除了部分同步/严格同步型以外,其他所有的子野分解模式都成功地转化为线性约束二次规划模型。两个临床测试病例的实验比较结果表明,在相同剂量分布的基础上,约束条件平滑策略能够使用更低的总机器跳数实现整个放疗。
再次,两步整合优化希望解决强度图优化和子野分解优化两者脱节的问题。针对传统单步整合优化求解困难的特点,采用了带有反馈信息的两步整合优化策略来控制总机器跳数和总子野个数。在该思路的指导下,对叶片双向滑动的两种子野分解模式给出了新的整合优化算法。并在两个临床测试病例上分别对全变差整合优化算法和新整合优化算法进行了实验。结果表明,新算法在等同总机器跳数和总子野个数的条件下,能够产生更优的剂量分布。
Intensity-modulated radiation therapy technology has been considered as one of the main technical means in cancer treatment, because IMRT can guarantee killing cancer cells while protecting normal tissue from complications as much as possible. Inverse planning system is the core part of the whole IMRT software, which is mainly based on accurate mathematical modeling and fast solving methods. Where, fluence map optimization, map smoothing optimization, and two step integration optimization are research focuses currently. In solving these problems, we always adhere to create the mathematical models under the framework of convex programming, which avoids uncertainty and inaccuracy occurred in non-convex programming solving process and enables to integrate small-scale programming to large scale or enormous scale.
We studied several key technical issues of the inverse planning system in intensity modulated radiation therapy, which included the following aspects.
Firstly, fluence map optimization wants to inverse solve the ray intensity of each radiation field according to dose requirements from doctors. Fluence map optimization problems with dose-volume constraints as well as which based on equivalent uniform dose model are difficult to be solved. For the former, we pointed out the shortcomings of the traditional dose sorting technology, used the linear constrained quadratic programming model as a foundation, and gived the iterative solution strategy based on more scientific geometric distance sorting technique. For the latter, we changed the existing deficiencies of discrepancy in the traditional biological model and medical evaluation system, and gived the definition of equivalent uniform dose based on volume dose function as well as the corresponding mathematical model which can be transformed into a general dose-volume constraints fluence map optimization problem. The experiments of four opened clinical test cases showed that our method was able to obtain a higher degree of dose conformity while meeting the dose volume constraints.
Secondly, ss the noise suppression could significantly reduce the total number of monitor units in intensity modulation, map smoothing optimization wants to reduce the map fluctuation. According to the five intractable issues from the traditional objective smoothing strategy, we proposed constrained smoothing strategy for the first time. The strategy could carry out intelligent smoothing and well linked the fluence map solving process and leaf sequence process. We created mathematical models for several typical unidirectional sweeping leaf sequencing patterns. Except for the partial synchronized/ strictly synchronized type, all other types have been successfully transformed into linear constrained quadratic programming models. The experimental results on two clinical testing cases showed that the new method can guarantee to use less total number of monitor units to achieve the radiotherapy under the same dose distribution.
Thirdly, two step integration optimization hopes to reduce the gap between fluence map optimization and leaf sequencing optimization. For the reason that it was hard to solve the integration optimization model created by the traditional single-step style, we adopted the two-step integration strategy with feedback information to control the total number of monitor units and the total number of segments. With this idea, we have gived new integration optimization algorithms for two bidirectional sweeping leaf sequencing patterns. We tested the new algorithms and the total variation smoothing integration algorithms on two clinical testing cases respectively. The results showed that under the same condition of total number of monitor units and total number of segments, the new algorithm can produce better dose distribution.
重点研究了调强放疗逆向计划系统中的几个关键技术问题,主要包括以下几个方面。
首先,强度图强度优化问题要求依据临床医生的剂量需求逆向求解各射野所需调制的射线强度。带有剂量体积约束的强度优化以及基于等效生物剂量模型的强度优化是该类问题建模求解的难点。对于前者,指出了传统的剂量排序技术的不足,以线性约束二次规划模型作为基础,给出了更为科学的基于几何距离排序技术的迭代求解策略；对于后者,改变了传统生物剂量模型与现有医学评价系统脱节的不足,给出了基于体积剂量函数的等效均匀剂量的定义及相应的能够转化为一般的剂量体积约束问题的数学模型。利用公开的四个临床测试病例对几何距离排序技术和剂量排序技术进行了实验比较,结果显示前者能够在满足剂量体积约束时让靶区获取更高的剂量适形度。
其次,由于抑制强度图噪音将大大降低射线调制时所需的总机器跳数,强度图平滑优化要求解决强度图过多起伏的问题。针对传统的目标项平滑策略难以解决的五大问题,首次提出了约束条件平滑策略。该策略能够进行智能平滑,将强度求解与子野分解这两个环节有机地结合。针对几种典型的叶片单向滑动子野分解模式进行了数学建模。除了部分同步/严格同步型以外,其他所有的子野分解模式都成功地转化为线性约束二次规划模型。两个临床测试病例的实验比较结果表明,在相同剂量分布的基础上,约束条件平滑策略能够使用更低的总机器跳数实现整个放疗。
再次,两步整合优化希望解决强度图优化和子野分解优化两者脱节的问题。针对传统单步整合优化求解困难的特点,采用了带有反馈信息的两步整合优化策略来控制总机器跳数和总子野个数。在该思路的指导下,对叶片双向滑动的两种子野分解模式给出了新的整合优化算法。并在两个临床测试病例上分别对全变差整合优化算法和新整合优化算法进行了实验。结果表明,新算法在等同总机器跳数和总子野个数的条件下,能够产生更优的剂量分布。
Intensity-modulated radiation therapy technology has been considered as one of the main technical means in cancer treatment, because IMRT can guarantee killing cancer cells while protecting normal tissue from complications as much as possible. Inverse planning system is the core part of the whole IMRT software, which is mainly based on accurate mathematical modeling and fast solving methods. Where, fluence map optimization, map smoothing optimization, and two step integration optimization are research focuses currently. In solving these problems, we always adhere to create the mathematical models under the framework of convex programming, which avoids uncertainty and inaccuracy occurred in non-convex programming solving process and enables to integrate small-scale programming to large scale or enormous scale.
We studied several key technical issues of the inverse planning system in intensity modulated radiation therapy, which included the following aspects.
Firstly, fluence map optimization wants to inverse solve the ray intensity of each radiation field according to dose requirements from doctors. Fluence map optimization problems with dose-volume constraints as well as which based on equivalent uniform dose model are difficult to be solved. For the former, we pointed out the shortcomings of the traditional dose sorting technology, used the linear constrained quadratic programming model as a foundation, and gived the iterative solution strategy based on more scientific geometric distance sorting technique. For the latter, we changed the existing deficiencies of discrepancy in the traditional biological model and medical evaluation system, and gived the definition of equivalent uniform dose based on volume dose function as well as the corresponding mathematical model which can be transformed into a general dose-volume constraints fluence map optimization problem. The experiments of four opened clinical test cases showed that our method was able to obtain a higher degree of dose conformity while meeting the dose volume constraints.
Secondly, ss the noise suppression could significantly reduce the total number of monitor units in intensity modulation, map smoothing optimization wants to reduce the map fluctuation. According to the five intractable issues from the traditional objective smoothing strategy, we proposed constrained smoothing strategy for the first time. The strategy could carry out intelligent smoothing and well linked the fluence map solving process and leaf sequence process. We created mathematical models for several typical unidirectional sweeping leaf sequencing patterns. Except for the partial synchronized/ strictly synchronized type, all other types have been successfully transformed into linear constrained quadratic programming models. The experimental results on two clinical testing cases showed that the new method can guarantee to use less total number of monitor units to achieve the radiotherapy under the same dose distribution.
Thirdly, two step integration optimization hopes to reduce the gap between fluence map optimization and leaf sequencing optimization. For the reason that it was hard to solve the integration optimization model created by the traditional single-step style, we adopted the two-step integration strategy with feedback information to control the total number of monitor units and the total number of segments. With this idea, we have gived new integration optimization algorithms for two bidirectional sweeping leaf sequencing patterns. We tested the new algorithms and the total variation smoothing integration algorithms on two clinical testing cases respectively. The results showed that under the same condition of total number of monitor units and total number of segments, the new algorithm can produce better dose distribution.
引文
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