OBJECTIVE To analyze the therapeutic effects and side effects of intensity-modulated radiotherapy (IMRT) with different fractionated doses in treating astrocytoma.METHODS During a period from October 2001 to Decemb...OBJECTIVE To analyze the therapeutic effects and side effects of intensity-modulated radiotherapy (IMRT) with different fractionated doses in treating astrocytoma.METHODS During a period from October 2001 to December 2006, 58 patients with astrocytoma were treated using IMRT. Based on the World Health Organization (WHO) classification, 32 of the 58 cases were grade-Ⅱ, 20 grade-Ⅲ and 6 grade-IV (glioblastoma multiforme, GBM). Thirty-two of the 58 patients (3 with grade IV, 11 with grade Ⅲ, and the other 18 with grade II who were over 40 years) were treated with hyperfractionated IMRT (Hyper Fr IMRT), and the other 26 patients were treated with standard fractionated IMRT (St Fr IMRT).RESULTS The 1-, 3- and 5-year overall survival (OS) rates were respectively 86%, 52%, and 45%, and the 1-, 3- and 5-year progression-free survival (PFS) rates were respectively 77%, 38%, and 25%. Using an analytical hierarchy process it was shown that concerning the patients with grade II astrocytoma classified based on WHO grading, the therapeutic effect was much better in the group of Hyper Fr IMRT than in the St Fr IMRT group. There was no statistical significance of the differences in the OS and PFS rates between the 2 groups (P = 0.049 and P = 0.006). The OS and PFS rates of the patients with grade-III astrocytoma were both higher in the group with Hyper Fr IMRT than in the St Fr IMRT group. However, there was no statistical significance of the differences between the 2 groups. Advanced RTOG grade-Ⅲ(radiation therapy oncology group, RTOG) neurotoxicity occurred only in 1 of the cases.CONCLUSION Compared with the St Fr IMRT, the Hyper Fr IMRT may help to prolong the survival of patients with astrocytoma.展开更多
This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no smal...This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no small parameter is assumed.The harmonic residue of balance equation is separated in two parts at each step.The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement.The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again.Three kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples respectively.Highly accurate limited cycle frequency and amplitude are captured.The results match well with the exact solutions or numerical solutions for a wide range of control parameters.Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems.Moreover,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.展开更多
文摘OBJECTIVE To analyze the therapeutic effects and side effects of intensity-modulated radiotherapy (IMRT) with different fractionated doses in treating astrocytoma.METHODS During a period from October 2001 to December 2006, 58 patients with astrocytoma were treated using IMRT. Based on the World Health Organization (WHO) classification, 32 of the 58 cases were grade-Ⅱ, 20 grade-Ⅲ and 6 grade-IV (glioblastoma multiforme, GBM). Thirty-two of the 58 patients (3 with grade IV, 11 with grade Ⅲ, and the other 18 with grade II who were over 40 years) were treated with hyperfractionated IMRT (Hyper Fr IMRT), and the other 26 patients were treated with standard fractionated IMRT (St Fr IMRT).RESULTS The 1-, 3- and 5-year overall survival (OS) rates were respectively 86%, 52%, and 45%, and the 1-, 3- and 5-year progression-free survival (PFS) rates were respectively 77%, 38%, and 25%. Using an analytical hierarchy process it was shown that concerning the patients with grade II astrocytoma classified based on WHO grading, the therapeutic effect was much better in the group of Hyper Fr IMRT than in the St Fr IMRT group. There was no statistical significance of the differences in the OS and PFS rates between the 2 groups (P = 0.049 and P = 0.006). The OS and PFS rates of the patients with grade-III astrocytoma were both higher in the group with Hyper Fr IMRT than in the St Fr IMRT group. However, there was no statistical significance of the differences between the 2 groups. Advanced RTOG grade-Ⅲ(radiation therapy oncology group, RTOG) neurotoxicity occurred only in 1 of the cases.CONCLUSION Compared with the St Fr IMRT, the Hyper Fr IMRT may help to prolong the survival of patients with astrocytoma.
基金supported by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2011AQ022 and ZR2012AL03)
文摘This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no small parameter is assumed.The harmonic residue of balance equation is separated in two parts at each step.The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement.The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again.Three kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples respectively.Highly accurate limited cycle frequency and amplitude are captured.The results match well with the exact solutions or numerical solutions for a wide range of control parameters.Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems.Moreover,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.