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首页> 外文会议>International Conference on Computational Science and Its Applications(ICCSA 2006) pt.5; 20060508-11; Glasgow(GB) >A Fast Integration Method and Its Application in a Medical Physics Problem
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A Fast Integration Method and Its Application in a Medical Physics Problem

机译：快速积分方法及其在医学物理问题中的应用

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摘要

A numerical integration method is proposed to evaluate a very computationally expensive integration encountered in the analysis of the optimal dose grid size for the intensity modulated proton therapy (IMPT) fluence map optimization (FMO). The resolution analysis consists of obtaining the Fourier transform of the 3-dimensional (3D) dose function and then performing the inverse transform numerically. When the proton beam is at an angle with the dose grid, the Fourier transform of the 3D dose function contains integrals involving oscillatory sine and cosine functions and oscillates in all of its three dimensions. Because of the oscillatory behavior, it takes about 300 hours to compute the integration of the inverse Fourier transform to achieve a relative accuracy of 0.1 percent with a 2 GHz Intel PC and using an iterative division algorithm. The proposed method (subsequently referred to as table method) solves integration problems with a partially separated integrand by integrating the inner integral for a number of points of the outer integrand and finding the values of other evaluation points by interpolation. The table method reduces the computational time to less than one percent for the integration of the inverse Fourier transform. This method can also be used for other integration problems that fit the method application conditions.
机译：提出了一种数值积分方法来评估在强度调制质子治疗（IMPT）能量通量图优化（FMO）的最佳剂量网格大小的分析中遇到的计算量很大的积分。分辨率分析包括获得3维（3D）剂量函数的傅立叶变换，然后进行数值逆变换。当质子束与剂量网格成一定角度时，3D剂量函数的傅立叶变换包含涉及振荡正弦和余弦函数的积分，并在其所有三个维度上都进行振荡。由于存在振荡行为，因此使用2 GHz Intel PC并使用迭代除法算法计算傅里叶逆变换的积分需要大约300个小时，以实现0.1％的相对精度。所提出的方法（以下称为表格方法）通过对外部被积分体的多个点积分内部积分并通过插值找到其他评估点的值来解决部分分离的被积分体的积分问题。表格方法将逆傅立叶变换的积分计算时间减少到百分之一以下。该方法还可用于其他适合方法应用条件的积分问题。

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