The feasibility of a volumetric modulated arc therapy (VMAT) based coronal arc (cARC) technique for treating a single brain metastasis or lesion proximal to the brainstem or optic chiasm was evaluated. Coplanar (CP) a...The feasibility of a volumetric modulated arc therapy (VMAT) based coronal arc (cARC) technique for treating a single brain metastasis or lesion proximal to the brainstem or optic chiasm was evaluated. Coplanar (CP) and non-coplanar (NCP) treatment plans to an anthropomorphic head/neck phantom scanned head-first supine were compared to a cARC plan with the phantom rotated vertically. A set of planning target volumes (PTVs) were contoured centrally between the brainstem and optic chiasm (“Ant PTVs”) and posterior to brainstem (“Post PTVs”). Dosimetric indices such as conformity index (C.I.), gradient measure (G.M.), and dose volume histograms (DVHs) were compared for CP, NCP and cARC techniques. The TG101 guidelines for organs-at-risk (OARs), and 95% of PTV receiving at least 100% of the prescription dose (D95 = 100%) were used as plan objectives. Reductions in D50 and D30 to the brainstem of 85.1% ± 3.9% and 87.6% ± 3.2%, respectively were seen for “Post PTVs”, and 51.1% ± 17.8% and 85.6% ± 6.0% respectively for “Ant PTVs” using cARC versus CP (p ≤ 0.01). For chiasm, reductions of D50 and D30 were 61.7% ± 3.2% and 44.2% ± 8.9% for “Ant PTVs”, by 69.3% ± 8.0% and 74.3% ± 8.2% for “Post PTVs” (p ≤ 0.01). Comparing cARC to NCP led to similar dosimetric improvements. The conformity index (C.I.) was measured to be 1.101 ± 0.038, 1.088 ± 0.054, and 1.060 ± 0.040 for cARC, CP and NCP respectively (p ≤ 0.01). The overall GM in cm was 0.581 ± 0.097, 0.708 ± 0.064, and 0.476 ± 0.050 for cARC, CP and NCP respectively (p ≤ 0.01). The mean distance gradient fall-off (in cm) was 0.249 ± 0.038 (cARC), 0.749 ± 0.107 (CP), and 0.621 ± 0.068 (NCP) at the center slice in anterior-posterior direction of the target volume (p ≤ 0.01). The objective of this study is to compare the dosimetric indices of cARC with CP and NCP techniques. In conclusion, cARC can provide improved dosimetry as compared to CP and NCP for lesion proximal to the brainstem or optic chiasm.展开更多
In this paper, we introduce the concept of a strongly regular (α,β)-family. It gener- alizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular (α,β)-geometries from ...In this paper, we introduce the concept of a strongly regular (α,β)-family. It gener- alizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular (α,β)-geometries from strongly regular (α,β)-families. Furthermore, we prove that each strongly regular (α,β)-geometry constructed from a strongly regular (α,β)-regulus translation is isomorphic to a translation strongly regular (α,β)-geometry; while t - r > β, the converse is also true.展开更多
In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine...In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston＇s picture.展开更多
文摘The feasibility of a volumetric modulated arc therapy (VMAT) based coronal arc (cARC) technique for treating a single brain metastasis or lesion proximal to the brainstem or optic chiasm was evaluated. Coplanar (CP) and non-coplanar (NCP) treatment plans to an anthropomorphic head/neck phantom scanned head-first supine were compared to a cARC plan with the phantom rotated vertically. A set of planning target volumes (PTVs) were contoured centrally between the brainstem and optic chiasm (“Ant PTVs”) and posterior to brainstem (“Post PTVs”). Dosimetric indices such as conformity index (C.I.), gradient measure (G.M.), and dose volume histograms (DVHs) were compared for CP, NCP and cARC techniques. The TG101 guidelines for organs-at-risk (OARs), and 95% of PTV receiving at least 100% of the prescription dose (D95 = 100%) were used as plan objectives. Reductions in D50 and D30 to the brainstem of 85.1% ± 3.9% and 87.6% ± 3.2%, respectively were seen for “Post PTVs”, and 51.1% ± 17.8% and 85.6% ± 6.0% respectively for “Ant PTVs” using cARC versus CP (p ≤ 0.01). For chiasm, reductions of D50 and D30 were 61.7% ± 3.2% and 44.2% ± 8.9% for “Ant PTVs”, by 69.3% ± 8.0% and 74.3% ± 8.2% for “Post PTVs” (p ≤ 0.01). Comparing cARC to NCP led to similar dosimetric improvements. The conformity index (C.I.) was measured to be 1.101 ± 0.038, 1.088 ± 0.054, and 1.060 ± 0.040 for cARC, CP and NCP respectively (p ≤ 0.01). The overall GM in cm was 0.581 ± 0.097, 0.708 ± 0.064, and 0.476 ± 0.050 for cARC, CP and NCP respectively (p ≤ 0.01). The mean distance gradient fall-off (in cm) was 0.249 ± 0.038 (cARC), 0.749 ± 0.107 (CP), and 0.621 ± 0.068 (NCP) at the center slice in anterior-posterior direction of the target volume (p ≤ 0.01). The objective of this study is to compare the dosimetric indices of cARC with CP and NCP techniques. In conclusion, cARC can provide improved dosimetry as compared to CP and NCP for lesion proximal to the brainstem or optic chiasm.
基金the Scientific Research Start-Up Foundation of Qingdao University of Science and Technology in China. (No.0022327)
文摘In this paper, we introduce the concept of a strongly regular (α,β)-family. It gener- alizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular (α,β)-geometries from strongly regular (α,β)-families. Furthermore, we prove that each strongly regular (α,β)-geometry constructed from a strongly regular (α,β)-regulus translation is isomorphic to a translation strongly regular (α,β)-geometry; while t - r > β, the converse is also true.
基金Supported by National Natural Science Foundation of China (Grant No. 10631060)Doctoral Fund of the Ministry of Education of China (Grant No. 5171042-055)
文摘In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston＇s picture.
