In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con...In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.展开更多
Introduction: Radiation therapy after breast surgery is an integral part of the treatment of early breast cancer. The goal of radiation therapy is to achieve the best possible coverage of the planning target volume (P...Introduction: Radiation therapy after breast surgery is an integral part of the treatment of early breast cancer. The goal of radiation therapy is to achieve the best possible coverage of the planning target volume (PTV), while reducing the dose to organs at risk (OARs) which are normal tissues whose sensitivity to irradiation could cause damage that can lead to modification of the treatment plan. In the last decade, radiation oncologist started to use the Intensity Modulated Radiotherapy (IMRT) and Volumetric Modulated Arc Therapy (VMAT) for irradiating the breast, in order to achieve better dose distribution and target dose to the PTV and OAR. The aim of this study is to compare 2 external radiotherapy techniques (VMAT vs 3D) for patients with node-positive left breast cancer. Patients and Methods: We randomly selected 10 cases of postoperative radiotherapy for breast cancer in our hospital. The patients are all female, the average age was 45.4 years old, and the primary lesions are left breast. The ANOVA test was used to compare the mean difference between subgroups, and the p value Results: Dose volume histogram (DVH) was used to analyze each evaluation dose of clinical target volume (CTV) and organs at risk (OARs). Compared to 3DCRT plans, VMAT provided more uniform coverage to the breast and regional lymph nodes. The max point dose for tVMAT was lower on average (106.4% for VMAT versus 109% for 3DCRT). OAR sparing was improved with tVMAT, with a lower average V17Gy for the left lung (27.91% for VMAT versus 30.04% for 3DCRT, p and lower for V28Gy (13.75% for VMAT versus 22.34% for 3DCRT, p = 0.01). We also found a lower V35Gy for the heart on VMAT plan (p = 0.02). On the contrary, dose of contralateral breast was lower in 3DCRT than VMAT (0.59 Gy vs 3.65 Gy, p = 0.00). Conclusion: The both types of plans can meet the clinical dosimetry demands of postoperative radiotherapy for left breast cancer. The VMAT plan has a better conformity, but 3CDRT can provide a lower dose to the contralateral organs (breast and lung) to avoid the risk of secondary cancers.展开更多
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between ...A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between a matrix and any of its full row rank submatrices.Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple.Two examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.展开更多
目的探索左心室(left ventricle,LV)作为新的危及器官(organ at risk,OAR)在左乳腺癌保乳术后放疗中心脏保护的作用。方法随机选取13例左乳腺癌接受保乳术及术后辅助放疗患者的计划CT图像。由同一个放疗医师勾画靶区和OAR,OAR包括心脏...目的探索左心室(left ventricle,LV)作为新的危及器官(organ at risk,OAR)在左乳腺癌保乳术后放疗中心脏保护的作用。方法随机选取13例左乳腺癌接受保乳术及术后辅助放疗患者的计划CT图像。由同一个放疗医师勾画靶区和OAR,OAR包括心脏、LV、左右肺和右侧乳腺。每个患者由物理师制定4个治疗计划。所有治疗计划的处方剂量均为50 Gy,25次。比较PTV、心脏、左右肺和右侧乳腺的剂量体积参数。结果与TF计划相比,在IMRT计划中PTV的最大剂量[除了IMRT(H)计划外]和最小剂量有不同程度增加。与IMRT(H)计划相比,在IMRT(H+LV)和IMRT(LV)计划中PTV内的最大剂量分别增加,大于V110高剂量体积增加。与TF计划相比,在IMRT计划中心脏的平均剂量、中位剂量、V5、V10分别增加0.9%～22.3%(P>0.05)、78.3%～110.6%(P<0.05)、179.3%～209.2%(P<0.05)、24.7%～97.7%。心脏最大剂量、V15、V20分别降低18.6%～36.7%(P<0.05)、7.2%～52.6%、48.3%～79.5%(P<0.05)。左肺在IMRT计划中高剂量体积(大于V17)明显降低,而低剂量体积(小于V12)明显升高。结论左乳腺癌保乳术后IMRT中增加左心室作为OAR可降低心脏照射剂量。展开更多
基金Supported by the National Natural Science Foundation of China (61175055)the Innovation Term of Higher Education of Hubei Province,China (T201109)+1 种基金the Natural Science Foundation of Hubei Province (2012FFB01101)the Natural Science Foundation of Education Committee of Hubei Province (D20131903)
文摘In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
文摘Introduction: Radiation therapy after breast surgery is an integral part of the treatment of early breast cancer. The goal of radiation therapy is to achieve the best possible coverage of the planning target volume (PTV), while reducing the dose to organs at risk (OARs) which are normal tissues whose sensitivity to irradiation could cause damage that can lead to modification of the treatment plan. In the last decade, radiation oncologist started to use the Intensity Modulated Radiotherapy (IMRT) and Volumetric Modulated Arc Therapy (VMAT) for irradiating the breast, in order to achieve better dose distribution and target dose to the PTV and OAR. The aim of this study is to compare 2 external radiotherapy techniques (VMAT vs 3D) for patients with node-positive left breast cancer. Patients and Methods: We randomly selected 10 cases of postoperative radiotherapy for breast cancer in our hospital. The patients are all female, the average age was 45.4 years old, and the primary lesions are left breast. The ANOVA test was used to compare the mean difference between subgroups, and the p value Results: Dose volume histogram (DVH) was used to analyze each evaluation dose of clinical target volume (CTV) and organs at risk (OARs). Compared to 3DCRT plans, VMAT provided more uniform coverage to the breast and regional lymph nodes. The max point dose for tVMAT was lower on average (106.4% for VMAT versus 109% for 3DCRT). OAR sparing was improved with tVMAT, with a lower average V17Gy for the left lung (27.91% for VMAT versus 30.04% for 3DCRT, p and lower for V28Gy (13.75% for VMAT versus 22.34% for 3DCRT, p = 0.01). We also found a lower V35Gy for the heart on VMAT plan (p = 0.02). On the contrary, dose of contralateral breast was lower in 3DCRT than VMAT (0.59 Gy vs 3.65 Gy, p = 0.00). Conclusion: The both types of plans can meet the clinical dosimetry demands of postoperative radiotherapy for left breast cancer. The VMAT plan has a better conformity, but 3CDRT can provide a lower dose to the contralateral organs (breast and lung) to avoid the risk of secondary cancers.
基金supported by the National Natural Science Foundation of China under Grant Nos.12171469,12001030 and 12201210the National Key Research and Development Program under Grant No.2020YFA0712300the Fundamental Research Funds for the Central Universities under Grant No.2682022CX048。
文摘A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented.The key idea is to establish a relationship between a matrix and any of its full row rank submatrices.Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple.Two examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.
文摘目的探索左心室(left ventricle,LV)作为新的危及器官(organ at risk,OAR)在左乳腺癌保乳术后放疗中心脏保护的作用。方法随机选取13例左乳腺癌接受保乳术及术后辅助放疗患者的计划CT图像。由同一个放疗医师勾画靶区和OAR,OAR包括心脏、LV、左右肺和右侧乳腺。每个患者由物理师制定4个治疗计划。所有治疗计划的处方剂量均为50 Gy,25次。比较PTV、心脏、左右肺和右侧乳腺的剂量体积参数。结果与TF计划相比,在IMRT计划中PTV的最大剂量[除了IMRT(H)计划外]和最小剂量有不同程度增加。与IMRT(H)计划相比,在IMRT(H+LV)和IMRT(LV)计划中PTV内的最大剂量分别增加,大于V110高剂量体积增加。与TF计划相比,在IMRT计划中心脏的平均剂量、中位剂量、V5、V10分别增加0.9%～22.3%(P>0.05)、78.3%～110.6%(P<0.05)、179.3%～209.2%(P<0.05)、24.7%～97.7%。心脏最大剂量、V15、V20分别降低18.6%～36.7%(P<0.05)、7.2%～52.6%、48.3%～79.5%(P<0.05)。左肺在IMRT计划中高剂量体积(大于V17)明显降低,而低剂量体积(小于V12)明显升高。结论左乳腺癌保乳术后IMRT中增加左心室作为OAR可降低心脏照射剂量。
