Wu Xingen, Brezovich Ivan A, Fiveash John B
Department of Radiation Oncology, University of Alabama at Birmingham, 35249, USA.
Brachytherapy. 2009 Oct-Dec;8(4):361-6. doi: 10.1016/j.brachy.2008.11.005. Epub 2009 Feb 20.
To find the coefficients for bi- and tri-exponential fitting functions to represent the radial dose functions of 16 commercially available brachytherapy sources.
The search for the coefficients was done using a genetic algorithm. Coefficients were encoded into chromosomes, which were subjected to crossover and mutation. After each operation, chromosomes were evaluated according to their fitness and the better ones were chosen with higher probability for the next generation. The best chromosomes obtained after 2000 operations were used for the coefficients.
For all brachytherapy sources, tri-exponential dose functions agreed with the respective input data within 1.4%. The mean deviation, obtained by averaging absolute deviations of all sources and input data, was <1.0%. For 8 of the 16 sources, the fit offered by bi-exponential functions was virtually identical to that of tri-exponential ones.
Tri-exponential functions can accurately represent the radial dose functions of all commercially available brachytherapy sources. For the eight sources where bi-exponential functions provide nearly equally accurate fits, their continued usage is recommended.
寻找双指数和三指数拟合函数的系数，以表示16种市售近距离放射治疗源的径向剂量函数。
使用遗传算法寻找系数。系数被编码到染色体中，染色体进行交叉和变异操作。每次操作后，根据染色体的适应度对其进行评估，并以更高的概率选择较好的染色体进入下一代。经过2000次操作后获得的最佳染色体用于确定系数。
对于所有近距离放射治疗源，三指数剂量函数与各自的输入数据的符合度在1.4%以内。通过对所有源和输入数据的绝对偏差进行平均得到的平均偏差<1.0%。对于16种源中的8种，双指数函数提供的拟合与三指数函数几乎相同。
三指数函数可以准确地表示所有市售近距离放射治疗源的径向剂量函数。对于双指数函数能提供几乎同样准确拟合的8种源，建议继续使用它们。
