Optimal Treatment Planning in Radiotherapy based on Boltzmann Transport Equations

基于玻尔兹曼传输方程的放射治疗最优治疗规划

• 批准号: 130542091
• 负责人: Professor Dr. Martin Frank
• 金额: --
• 依托单位: Scientific Computing Center (SCC)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/130542091?language=en
• 关键词: Optimal; Treatment; Planning; Radiotherapy; based

We plan to investigate optimal control problems used in clinical external beam radiotherapy. The starting point is the formulation of the treatment planning problem as an optimal control problem for the Boltzmann Continuous Slowing Down model. Mathematically, the model consists of an integro–partial differential equation in energy, spatial and angular variables. Besides analytical investigations on existence and regularity of solutions and optimal controls we study moment approximations to the high–dimensional phase space in order to devise efficient numerical schemes. The relation between optimization and moment approximation will also be investigated. We use the analytical and numerical results on real CT−patient data and compare the optimal treatment plans obtain by solving the control problem with standard Monte–Carlo methods.

我们计划研究临床外照射放射治疗中的最优控制问题。出发点是制定的治疗计划问题作为玻尔兹曼连续减慢模型的最优控制问题。在数学上，该模型由能量、空间和角度变量的积分-偏微分方程组成。除了分析调查的存在性和规律性的解决方案和最优控制，我们研究的时刻近似的高维相空间，以制定有效的数值方案。最佳化和矩近似之间的关系也将被研究。我们使用的分析和数值计算结果对真实的CT患者数据和比较的最佳治疗计划，通过解决控制问题与标准的蒙特-卡罗方法。