Influence of Position and Radiation Technique on Organs at Risk in Radiotherapy of Rectal Cancer

The influence of the position and radiation technique on the organs at risk（OARs） in radiotherapy of rectal cancer was evaluated. The relationship between the volume of irradiated small bowel（VSB） and acute bowel toxicity was determined. A total of 97 cases of rectal cancer were retrospectively randomized to receive radiotherapy with the designated treatment positions and radiation plans. Among 64 patients in the supine position, 32 patients were given three-dimensional conformal radiotherapy（3DCR） and 32 patients were subjected to intensity-modulated radiation therapy（IMRT） respectively. The rest 33 patients were treated with 3DCRT in the prone position with a belly board. The VSB was calculated for doses from 5 to 45 Gy at an interval of 5 Gy. With prescription dose in planned target volume（PTV） of 50 Gy, the dose distribution, conformal index for PTV（CIPTV）, dose-volume histogram（DVH） of OARs, the correlation of VSB and the acute toxicity were compared. The results were shown as follows：（1） Among the 3 methods, there were no differences in PTV＇s converge including V95 and D95;（2） For IMRT under a supine position, CIPTV was closest to 1, the mean dose of small bowel decreased（P〈0.05）, and the mean VSB from V30 to V45 significantly decreased（P〈0.05）.（3） For 3DCRT with a belly board under a prone position, the mean dose and the mean VSB from 40 to 45 Gy were less than those for 3DCRT under a supine position（P〈0.05）;（4） Mean proportion of VSB was significantly greater in the patients experiencing diarrhea grade 2-4 than in those with diarrhea grade 0-1 at dose levels from V30 to V45（P〈0.05）. It was concluded that for the radiotherapy of rectal cancer, IMRT technique might decrease the high-dose VSB to reduce the risk of acute injury. 3DCRT with a belly board under a prone position is superior to 3DCRT under a supine position, which could be a second choice for radiation of rectal cancer.

W（a, b） Lie Conformal Algebra and Its Conformal Module of Rank One

For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.

The Lie Conformal Algebra of a Block Type Lie Algebra

Let L be a Lie algebra of Block type over C with basis {Lα,i ｜ a,i ∈ Z} and brackets [Lα,i, Lβ,j] = （β（i ＋ 1） - α（j ＋ 1））Lα＋β,i＋j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with C[δ]- basis { Lα（w） ｜ α ∈ Z} and λ-brackets [Lα（w）λLβ（w）] = （αδ ＋ （α ＋β）A）Lα＋β（w）. Finally, we give a classification of free intermediate series B-modules.

Structure of a Class of Rank Two Lie Conformal Algebras

Letβbe a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras L(β)are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivations and conformal biderivations of L(β)are studied.Besides,central extensions and conformal modules of rank one of L(β)are determined.

Cohomology of Lie Conformal Algebra Vir× Cur g

In this article,we compute cohomology groups of the semisimple Lie conformal algebra S=Vir × Cur g with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra g.