第4回国際

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ISSN 0441-2540

第 52 巻第7号

2 0 0 9. 0 7

Vol. 52

特集

第4回国際

「細胞分子及軽影響」

4th NIRS International Open Laboratory Workshop

on Cellular and Molecular Eﬀ ects of Light Ions

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第52巻第7号

2 0 0 9 . 0 7

Vol. 52

特集

第4回放医研国際 ｢細胞 分子及軽 影響｣

主催：国際オープンラボラトリー重粒子線治療モデル研究ユニット

4th NIRS International Open Laboratory Workshop on Cellular

and Molecular Effects of Light Ions, planned by Particle Therapy Model Research Unit

編集後記

2）Particle transport approaches for biological optimized inverse treatment planning

生物学的最適化逆方向治療計画粒子輸送試

Johanna Kempe Medical Radiation Physics, Department of Oncology-Pathology, Sweden

研究所腫瘍・病理学部医療放射線物理研究

16

31

_4）Development of biologically optimized radiation therapy:

Maximizing the apoptotic cell kill

生物学的最適化放射線療法開発：細胞死最大化

Patrick Vreede and Anders Brahme

Division of Medical Radiation Physics, Department of Oncology-Pathology, Sweden.

研究所腫瘍・病理学部医療放射線物理研究

、

24

3） Apoptosis and Molecular Responses Induced in Tumour and Normal Cells in vitro Exposed to Accelerated Ions

培養腫瘍正常細胞加速誘発分子応答

Annelie E. Meijer Medical Radiation Physics, Department of Oncology-Pathology, Sweden

研究所腫瘍・病理学部医療放射線物理研究 / 大学

E.

59

1） Development of the X tal Cube : The Next Generation PET Detector Using Semiconductor Photo-detectors

半導体受光素子用 次世代PET検出器 X tal Cube 開発

Naoko Inadama^1）, Yujiro Yazaki^2,1）, Hideo Murayama^1）, Fumihiko Nishikido^1）, Taiga Yamaya^1）, Eiji Yoshida^1）, Hiroto Osada^2,1）, Kengo Shibuya^3,1）, Mikio Suga^2,1）, and Takaji Yamashita^4）

1）Molecular Imaging Center, NIRS, 2）Chiba University, 3）University of Tokyo, 4）Hamamatsu Photonics K. K.

放射線医学総合研究所分子 研究

稲玉直子、矢崎祐次郎、村山秀雄、錦戸文彦、山谷泰賀、吉田英治、長田拓人、澁谷憲悟、菅幹夫

千葉大学矢崎祐次郎、長田拓人、菅幹夫東京大学澁谷憲悟浜松 株式会社山下貴司

08

Designed by S. Ban

：伴貞幸

Commentary

解説

Hirohiko Tsujii Executive Director and Director of International Open Laboratory Sadayuki Ban Head, Planning Office, International Open Laboratory

Head, Planning and Promotion Office, Research Center for Charged Particle Therapy

理事・国際 辻井博彦

国際 運営室長・重粒子医科学 運営企画室長伴貞幸

53

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4th NIRS International

Open Laboratory Workshop on Cellular and Molecular Effects of Light Ions,

planned by Particle Therapy Model Research Unit

4 放射線科学 Vol.52 No.7 2009 放射線科学 Vol.52 No.7 2009 5

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7 放射線科学 Vol.52 No.7 2009 6 放射線科学 Vol.52 No.7 2009

Editor-in-Chief Hirohiko Tsujii*, M.D.,Ph.D.

編集長辻井博彦

Associate Editors Sadayuki Ban*, Ph.D.

編集員伴貞幸

Naruhiro Matsufuji*, Ph.D.

松藤成弘

Takeshi Murakami*, Ph.D.

村上健

Masanori Okamoto*, Ph.D.

岡本正則

*National Institute of Radiological Science, Chiba, Japan 放射線医学総合研究所

Editorial Board

Radiological Sciences

放射線科学

Volume 52, Special Issue : July 2009

第52巻特集号、第7号 2009年

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9 放射線科学 Vol.52 No.7 2009

Feature :4th NIRS International Open Laboratory Workshop on Cellular and Molecular Effects of Light Ions

1）Development of the X tal Cube :The Next Generation PET Detector Using Semiconductor Photo-detectors

半導体受光素子用次世代PET検出器 X tal Cube 開発

Naoko Inadama^1）, Yujiro Yazaki^2,1）, Hideo Murayama^1）, Fumihiko Nishikido^1）, Taiga Yamaya^1）, Eiji Yoshida^1）, Hiroto Osada^2,1）, Kengo Shibuya^3,1）, Mikio Suga^2,1）, and Takaji Yamashita^4）

1）Molecular Imaging Center, NIRS, 2）Chiba University, 3）University of Tokyo, 4）Hamamatsu Photonics K. K.

[email protected]

稲玉直子^1）、矢崎祐次郎^2,1）、村山秀雄^1）、錦戸文彦^1）、山谷泰賀^1）、吉田英治^1）、 長田拓人^2,1）、澁谷憲悟^3,1）、菅幹夫^2,1）、山下貴司^4）

1）放射線医学総合研究所分子 研究 、 2）千葉大学、 3）東京大学、

4）浜松 株式会社

ABSTRACT

We are engaged in the development of an X tal cube which is a three-dimensional (3D) block detector for the next-generation PET system. It consists of a 3D array of cubic crystal segments (a crystal block) and semiconductor photo-detectors such as Avalanche photodiodes (APD) or Multi-Pixel Photon Counters (MPPC). By identifying the light-emitted crystal segments, it is possible to obtain 3D position information of gamma-rays absorbed in the crystal block. In the crystal block, there are no reﬂ ectors inserted between the crystal segments, and the photo-detectors are located on the surface area of the crystal block. This detector arrangement minimizes light attenuation in the crystal block as the path length from the scintillation points to the photo-detectors is minimum so as to achieve favorable detector performance.

By sparsely arranging the photo-detectors on the surface of the crystal block, it is possible to reduce the number of photo-detectors. The area not coupled to the photo-detectors is covered with reflectors. We have investigated crystal identification performance as a function of the photo-detector arrangement as a preliminary study to the development of an X tal cube.

INTRODUCTION

A depth of interaction (DOI) detector provides three-dimensional (3D) position information of gamma- ray absorption in the detector. A PET scanner having high sensitivity requires the use of long slender scintillation crystals and large axial view, which causes

要約

我々研究現在、次世代 PET 検出器期待 X tal cube（）開発取組。X tal cube 、立方体結晶素子 3 次元配列（結晶） Avalanche photodiodes

（APD） Multi-Pixel Photon Counters （MPPC）半導

体受光素子構成、光発生結晶

素子特定結晶内 γ線吸収位置 3 次元得検出器。受光素子結晶配

列表面配置、間光

逃反射材覆。受光素子配置、常受

光素子光発生点近位

置、光受光光

路長短分減衰少済。、結

果得光量多、X tal cube 検出器良好性能期待。

本実験、X tal cube 開発基礎研究、受光素子配置配置得検出器結晶識別能関係調。

序論

Depth of interaction （DOI）検出器、検出器内 γ線吸収位置深方向含 3 次元得検出器

。PET 装置高感度、結

晶十分検出効率得長、装置視野

立体角大体軸長長望

稲玉直子（Naoko Inadama）

degradation of spatial resolution because of oblique incidence of gamma-rays to the detector ( Fig. 1 a) ).

Because the spatial resolution is recovered by the DOI information as shown in Fig. 1 b), the DOI encoding technique is an important factor to realize a PET scanner with both a high sensitivity and a high spatial resolution.

Various DOI encoding methods have been reported, which include pulse shape discrimination of different scintillation crystals [1, 2], the DOI crystal layer arrangement in which each crystal layer was shifted half of the crystal element pitch to cause different responses between the crystal layers [3, 4].

There are other methods such as the use of a DOI detector with specified wavelength interference filters [5] and the use of a detector consisting of a 3D crystal array in which some parts of the reﬂ ectors are removed to control the scintillation light path in the array so as to obtain DOI information [6]. Most of the schemes above use position-sensitive photomultiplier tubes (PS-PMT).

Recently, there have been many proposals to replace the PS -PMT with semiconductor photo- detectors, e.g., avalanche photodiodes (APD) or Geiger- mode APDs (Si-PM or MPPC: (Multi-Pixel Photon Counter)), both chosen in light of their remarkable advancement in recent years [7, 8]. These compact and thin photo-detectors have a potential for overcoming the limitations of detector design; a promising feature due to the fact that, for instance, they do not obstruct in gamma-ray detection in the detector ring arrangement for PET even when placed in front of the detector. We have initiated a project to develop a new DOI detector

、同時斜方向入射 γ線視差位置分解能劣化引起（Fig. 1 a））。劣化 Fig.

1 b）示 DOI 情報回復

、DOI 情報得技術 PET 装置高感度・高分解能

両立欠要素。

現在様々 DOI 検出手法提案。波

形異結晶素子 DOI 方向並波

形違結晶種類特定 DOI 情報得波形弁別法

［1, 2］、結晶配列 DOI 方向結晶半個分配置 DOI 方向結晶応答位置

配列内結晶特定 DOI 情

報得方法［3, 4］、特定波長対干渉

DOI 方向結晶配列間挿入 DOI 情報得方法［5］、3 次元結晶配列内特定結晶素子間反射材

挿入光広制御

DOI 方向結晶応答位置 DOI 情報得方法

［6］。含、今提案 DOI

検出器位置弁別型光電子増倍管（PS-PMT）

用。

近年、（APD）

APD（Si-PM、 MPPC（Multi-Pixel Photon Counter））

半導体受光素子急速発展遂、受 PS-PMT 半導体受光素子置換 DOI 検出法提案

出［7, 8］。小型薄半導体受光素子新検出器可能性持、例、今

PET 装置組込時被検者側検出器上面受光素子置 γ線検出際散乱体

考、体積小

半導体受光素子可能。背景中、

半導体受光素子用 DOI 検出器「

（X tal cube）」提案、開発立上。今回我々、初期実験 X tal cube 検出器性能調。

Fig.1：Comparison of spatial resolution in the PET scanner a) without and b) with depth of interaction (DOI) information.

図1：PET装置 Depth of interaction（DOI）情報 a）場合 b）場合位置分解能比較。

特集／第4回放医研国際 ｢細胞 分子及 軽 影響｣

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4回放医研

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10 放射線科学 Vol.52 No.7 2009 特集第

4回放医研

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scheme using semiconductor photo-detectors. We call the DOI detector as X tal cubes . In this study, preliminary experiments have been conducted to assess detector performance of the X tal cube.

MATERIALS AND METHODS

A. X tal cube design

Fig. 2 shows the sample design of our X tal cube, in which small cubic crystal segments are arranged to form a long cubic crystal block. A number of semiconductor photo -detectors are partially coupled to the six surfaces of the crystal block. Unlike the conventional PET detectors, no refl ector material is inserted in the crystal block, which may have caused light attenuation due to the long light path to the photo-detector and the refl ection loss. Since no refl ector is inserted in the crystal block in the X tal cube, the scintillation light propagates symmetrically into the x, y, z directions. 3D information can be obtained for light output in the X tal cube by placing photo-detectors on the six surfaces of the cube. Whereas light spreads isotropically in the detectors constituting a monolithic scintillation crystal block, scintillation light propagation in the X tal cube is subject to constraints imposed by the boundaries of the crystal segments.

Position calculation based on all photo-detector signals permits identiﬁ cation of the scintillated crystal segment in the crystal block. While it is clear that covering the crystal block with closely packed photo-detectors over all surfaces can provide optimum performance, our goal was to achieve a reasonable level of detector performance with a limited number of photo-detectors. The surface area not coupled to photo-detectors is covered with reﬂ ectors to reduce light loss.

It is logical to assume that an X tal cube will have a high eﬃ ciency in collecting scintillation light because its crystal block contains no reﬂ ectors that might cause light attenuation as mentioned above, and also because the photo-detectors are always located near scintillation

crystals so that light can be detected before it is possible for attenuation to occur. The photo-detector arrangement allows smaller segmentation of crystals in the depth direction compared to the conventional DOI detectors and the use of cubic-like crystals that provides isotropic spatial resolution for the gamma-rays from any directions.

In addition, the X tal cube has a compact structure and thus facilitates flexible PET system design. The solid- state photo-detectors are less influenced by a magnetic ﬁ eld so that it can be used in MR-PET systems.

B. Experiments

We evaluated crystal identifi cation performance in some photo-detector arrangements as a basic study to fi nd the most appropriate arrangement for the X tal cube. The experimental setup is shown in Fig. 3. The arrangements were fi rst applied on one surface of the crystal block. In this study, a position-sensitive PMT (PS-PMT) was used instead of semiconductor photo-detectors which were not available to us, to detect scintillation light. The surface coupled to the PS-PMT was covered with a reflector with vacancies (holes) at the positions where are to set semiconductor photo-detectors in future work. Detecting scintillation light with the PS-PMT through the vacancies (holes) must show the similar result to the one obtained with using semiconductor photo-detectors set at the vacancy positions. Other fi ve surfaces of the crystal block were covered with refl ectors. Multilayer polymer mirrors 材料方法

A.

Fig. 2 、X tal cube 1 例。X tal

cube 、小立方体結晶素子 3

次元配列全体立方体結晶形成、 6

面半導体受光素子間隔結合

。結晶内部反射材入、結晶内部発生光 x, y, z 方向対称的広、広先半導体受光素子検出。

、X tal cube 、結晶 6 面配置半

導体受光素子光 3 次元的受光

。通常検出器結

晶配列 1 面受光素子結合結晶配列内部反

射材入光受光素子方向誘導

必要、、受光光路長

長反射自体光減衰促進

。X tal cube 結晶内部反射材用光減衰抑制期待。一方、結晶

一塊結晶構成検出器当然

結晶内反射材存在。検出

器光発生点放射状均一広

対 X tal cube 結晶素子間境界光広

制御傾向。結晶内 γ線検出

結晶素子特定 X tal cube 結合受光

素子信号用位置演算。結晶

表面全体受光素子隙間結合位置演

算細結晶特定精度上

明、我々目的限数受光

素子妥当検出器性能達成。受光

素子結合表面部分、多

光受光反射材覆。

X tal cube 、前述結晶内部反射材

光減衰加

光発生点近常受光素子位置

光収率高思。他

、受光素子数調整他方法 DOI 方

向分割数多、結晶素子立方体

γ線入射方向寄均一検出器分解能

得、作様々 PET 装置

対応、利点挙。、

半導体受光素子磁場影響受、MR-PET

装置検出器活用重要要素。

B. 実験

X tal cube 受光素子配置基礎研究、数通受光素子配置結晶識別能評価。Fig. 3 実験

示。準備関係、実験半導体受光素子代位置弁別型光電子増倍管（PS-PMT）

用。半導体受光素子受光面積同大穴開反射材 PS-PMT 入射窓覆有感領域穴限、半導体受光素子穴位置配置場

合性能見積。、結晶一面

評価行。他 5 面反射材覆。用反射材、反射率 98 %、厚 0.065 mm multilayer polymer mirrors（MPM、住友 3M 社製）。結晶 2.9 mm × 2.9 mm × 3.75 mm Gd2SiO5結晶（GSO、日立化成社製）6 × 6 配列 6 層分積層構成、配列内

結晶間空気、反射材光学接着剤用

。結晶層結晶応答測定結晶側面各層 2 mm 幅絞 662 keV γ線照

Fig.2：Design of the X tal cube. A number of semiconductor photo-detectors are set on all surfaces of a 3-dimensional (3D) crystal array and detect scintillation light 3-dimensionaly.

図2：X tal cube検出器一例。X tal cube 、結晶素子 3次

元配列（結晶）表面半導体受光素子配置、結晶内発生

光 3次元的受光。受光素子結合部以外表面反射材覆

。

Fig.3：Experimental setup Detection of scintillation light with a PS- PMT through the holes of the reflector is equivalent to the detection with semiconductor photo-detectors set at the holes positions

図3：実験。PS-PMT 用、半導体受光素子配置場所

半導体受光素子同穴開反射材 PS-PMT表面敷感度

有効制限、半導体受光素子位置受光場合

同等性能得。

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(MPMs) of 98 % refractivity and 0.065 mm thickness were used as reflectors (Sumitomo 3M, Ltd., Japan). A six-layer 6×6 crystal array consisting of Gd₂SiO₅ (GSO) crystals in each dimension of 2.9 mm×2.9 mm×3.75 mm (Hitachi Chemical Co., Ltd., Japan) was used. No reﬂ ectors were inserted, and neither were optical compounds used.

To investigate the performance of each crystal layer, 662 keV gamma-rays were collimated to a 2 mm wide fan- beam and irradiated onto the side face of anyone crystal layer. A 256-channel, ﬂ at panel PS-PMT (256ch FP-PMT;

H9500, Hamamatsu Photonics K.K., Japan) was used for the experiments. Its anode interval was 3.04 mm and the normally required 256 anodes were reduced to only four by using a resistor chain provided by the manufacturer.

Anode signals were collected by NIM modules and a CAMAC ADC.

Fig. 4 shows the photo-detector arrangement patterns examined in this experiment. Pattern (a) is an arrangement in which 3×3 photo-detectors were used and distributed on the surface uniformly. In pattern (b), the number of photo-detectors was increased. Pattern (c) is an arrangement in which 16 photo-detectors were used and four of them covers each corner crystal. Pattern (d) represents an arrangement in which photo-detectors weighted in the peripheral positions were used. Crystal identification performance was evaluated on the 2D position histogram at some layers in the depth direction.

The 2D position histogram is a scatter plot of the Anger- type calculation results for the photo-detector signals and plots the form response of each crystal element in the crystal block. Scintillation crystals can be identiﬁ ed, provided that the different crystal responses are distinguishable in the histogram.

射、結晶応答測定。用 256-channel ﬂ at panel PS-PMT（256ch FP-PMT；H9500、浜松社製）

16 × 16 、間隔

3.04 mm 。信号処理負担減 256 個

出力付属品抵抗用 4 隅

4 出力、NIM 、CAMAC

用収集。

Fig. 4 今回試受光素子配列示。最初試

（a）、結晶一部受光素子光学結合 3 × 3 受光素子均等配列

。（b）、受光素子数増

、（c）、16 個受光素子用隅結晶

光反射受光目的

。（d）、端列結晶光対

受光部多配列。結晶識別能受光素子信

号計算結果 2 次元

上評価。同結晶素子検出場合、受光面光分布似

上同位置演算結果、

結果、結晶内結晶素子応答形

成。結晶応答他結晶重区別

可能、結晶識別可能。

Fig.4：Photo-detector arrangement patterns considered in this study. The Upper figures show the photo-detector positions on the surface of the crystal block and the lower ones, the shape of the reflectors for measurement using a PS-PMT. Each reflector reflects corresponding photo-detector arrangement patterns.

図4：実験試半導体受光素子配列。上図結晶表面半導体受光素子配列、下図実験 PS-PMT表面敷

各半導体受光素子配列対応反射材。

Fig.5：2D position histograms of the Layer-4 and Layer-6 crystals with photo-detector arrangement patterns (a) to (d).

図5： (a) (d) 半導体受光素子配列考慮得 4層目 6層目結晶素子 2次元。

Fig.6：Comparison of the 2D position histograms before (same histograms as those shown in Fig. 5, pattern (d)) and after replacing reflectors to have the photo-detector arrangement cover all surfaces of the crystal block in the case of pattern (d).

図6：半導体受光素子配列 (d) 対応反射材側面、上面用場合 2次元変化。図5 側面、上面反射材覆

場合（左）比、半導体受光素子結合部反射材今回光漏結晶識別能改善（右）。

Pattern(a) Pattern(b) Pattern(c) Pattern(d)

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RESULTS

Fig. 5 shows the 2D position histograms obtained for each detector arrangement. In the arrangement pattern (a), the responses of the four crystal elements, coupled directly to the same photo-detector, overlap, and the crystal elements cannot be identified for Layer-6.

The histogram for Layer- 4 shows the same poor identiﬁ cation tendency. This suggests that scintillation light is scarcely detected by nearby photo-detectors that are not directly coupled to the scintillation crystal element. The 2D position histogram for pattern (b) shows the effect of adding one more directly coupled photo-detector for some central crystal elements.

The responses of the central part can be clearly discriminated. The trials conducted to achieve discrete responses for outer crystal elements have demonstrated the effectiveness of adding a photo-detector to cover peripheral area in the case of patterns (c) and (d), with optimum performance results having been obtained for all trials with pattern (d) although only one photo- detector had been directly coupled for some central crystals.

Fig. 6 shows the changes in the 2D position histogram associated with the replacement of reﬂ ectors needed in order to have the photo-detector arrangement cover all surfaces of the crystal block. The histograms were obtained by using only the PS-PMT signals below for calculating the histograms shown in Fig. 5. These results indicate that a reduction of the crystal block surface area covered with reflectors improves crystal identiﬁ cation performance. It is therefore reasonable to expect that the use of additional photo-detector signals on the top and side surfaces is effective in improving performance still further.

DISCUSSION AND CONCLUSION

We introduced an X tal cube as a next-generation DOI PET detector, in which the scintillation light is detected 3 -dimensionaly by coupled semiconductor photo-detectors provided on all surfaces of the 3D scintillation crystal array. In this design, the scintillation light is detected by the photo-detectors near the light- emitting position before any considerable attenuation can occur in the crystal block so that the X tal cube has a potential for use as a DOI detector capable of achieving high performance in terms of sensitivity and spatial and time resolution.

結果

Fig. 5 受光素子配列得 4 層目 6 層

目結晶 2 次元示。

層上数、X tal cube 全表面受光素子結合場合受光素子最離層 4 層目直接結合 6 層目評価行。（a）、同受光素子結合 4 結晶応答重

結晶識別不可能。光

受光面十分広、計算際

4 結晶近受光素子信号影響結晶応

答現位置差出。従、得

結果光広示。特徴結晶

結晶素子 3 次元配列構成

考、結晶大一塊結晶形成場

合異点。（b）、直接結合

受光素子増効果中央結晶応答分離良

。（c）、（d）、端列結晶対

応答分離良目的受光素子配列

、受光素子数 16 個、中央結晶素子

直接結合受光素子減関端結

晶受光部多（d）最良

結果得。

PS-PMT 結合面以外表面全体覆反射材最結晶識別能良（d）反射材変

得 2 次元 Fig. 6 示。

側面、上面光漏関、結晶識別能

改善見。PS-PMT 結合面状態 Fig. 5 条件全同、側面、上面反射材面積減底面受光結晶識別能良

。、側面、上面反射材光量損失防性能劣化防、同時結晶識別能悪

化。側面、上面受光部設

X tal cube 構造、光量損失反射部減 2 重

効果。

考察結論

我々開発行次世代 DOI PET 検出器 X tal cube 、結晶素子 3 次元的配列結晶

内 γ線検出結晶素子発光

結晶全表面配置半導体受光素子 3 次元的検出。従来検出器、反射材結

晶間挟、光受光素子結合

一面導工夫光路長長光減衰

招、X tal cube 光反射材

反射光多近受光素子受光

光減衰伴考。

光収率高 X tal cube 高感度、分解能、

特性 DOI 検出器期待。

The basic study was carried out to throw light on the dependence of crystal identiﬁ cation performance on the photo-detector arrangement and helped us find an arrangement with a favorable level of performance (Fig. 5). It was also found that covering all crystal block surfaces with reflectors in the photo-detector arrangement (pattern (d)) much improved the crystal identification performance as a result of reducing the reﬂ ector area (Fig. 6). It is thus legitimate to anticipate further improvement in detector performance through the use of scintillation light signals detected on all surfaces of the crystal block.

ACKNOWLEDGEMENT

This study was conducted as a part of the Grant- in-Aid for Scientific Research (No. 19300188) from the Japan Society for the Promotion of Science.

X tal cube 特性知基礎実験、結晶表面受光素子配置結晶識別能変化 1 表面調。結果、16 個受光素子配列（

（d））十分結晶識別能得、

配置結晶全表面対行、側面、上面

反射部減、1 表面読出性能

改善見（Fig. 6）。今回基礎実験受光 1

表面行、全表面信号受光位置演

算用、結晶識別能向上

期待。

謝辞

本研究一部、科学研究費補助金若手研究 B「高感度全身用 PET 検出器開発」（No. 19300188）一環

実施。

REFERENCES

[ 1 ] J. Seidel, J. J. Vaquero, S. Siegel, W. R. Gandler, and M. V. Green, Depth identiﬁ cation accuracy of a three layer phoswich PET detector module, IEEE Trans. on Nucl. Sci., vol. 46, No. 3, pp.485 ‒ 490, June 1999.

[ 2 ] S. Yamamoto and H. Ishibashi, A GSO depth of interaction detector for PET, IEEE Trans. on Nucl. Sci., vol.

45, No. 3, pp.1078 ‒ 1082, June 1998.

[ 3 ] H. Liu, T. Omura, M. Watanabe, and T. Yamashita, Development of a depth of interaction detector for γ -rays, Nucl. Inst. Meth., A 459, pp. 182-190,2001.

[ 4 ] N. Zhang, C. J. Thompson, D. Togane, F. Cayouette, K. Q. Nguyen, M. L. Camborde, Anode position and last dynode timing circuits for dual-layer BGO scintillator with PS-PMT based modular PET detectors, IEEE Trans. Nucl. Sci., Vol. 49, No. 5, pp. 2203-2207, October 2002.

[ 5 ] T. Hasegawa, M. Ishikawa, K. Maruyama, N. Inadama, E. Yoshida, and H. Murayama, Depth-of-interaction recognition using optical ﬁ lters for nuclear medicine imaging, IEEE Trans. Nucl. Sci., vol.52, , No. 1, pp. 4 -7, February 2005.

[ 6 ] T. Tsuda, H. Murayama, K. Kitamura, T. Yamaya, E. Yoshida, T. Omura, H. Kawai, N. Inadama, and N. Orita, A four layer depth of interaction detector block for small animal PET, IEEE Trans. Nucl. Sci., vol.51, No. 5, pp.

2537-2542, October 2004.

[ 7 ] Y. Shao, R. W. Silverman, R. Farrell, L. Cirignano, R. Grazioso, K. S. Shah, G. Visser, M. Clajus, T. O. Tumer, and S. R. Cherry, Design strudies of a high resolution PET detector using APD array, IEEE Trans. Nucl. Sci., Vol.

47, No. 3, pp. 1051-1057, June 2000.

[ 8 ] C. S. Levin, Design of a high-resolution and high-sensitivity scintillation crystal array for PET with nearly complete light collection, IEEE Trans. Nucl. Sci., Vol. 49, No. 5, pp. 2236-2243, October 2000.

(9)

transport into two components; loss of particles and lateral spread. The lateral distribution function is based on a two fold Fokker-Planck expansion of the continuous slowing down approximation (CSDA) of the Boltzmann equation, within the small energy loss and deﬂ ection angle approximation. Physical quantizes distributions such as the absorbed dose and radiation quality distribution of the light ion can be determined in the media of interest in use of the light ion pencil beam transport, in combination with developed analytical expressions [7-8] .

A quite simple expression of the mean energy depth dependency for light ions in therpeutic energies, can be written according to ;

❶

where the dimensionless transport parameter , S0R0/ 0, express the ratio between the mean stopping power over whole range to the initial stopping power, and can be determined directly when is known for the initial energy

0 and the corresponding initial stopping power S0 for the material of interest, [7].

In relation to the solution of the pencil beam transport, taking small angle approximation into account, where the diff erences between the planar fl uence to the total fluence is almost neglible, i.e Φ^Ρ(z)≈Φ^Ρ,^p(z), the absorbed dose of the primary particles in a broad beam can be given by direct integration of the exponentially decreasing pr ima r y f luence, Φ₀exp(‒µ z) a nd the associated fl uence weighted mean stopping power, ^Φ^Ρ;

❷

In Eq. ❷ the fluence weighted mean stopping power is here based on the depth dependence of a the mean energy (z), cf. Eq.❶,, within the approximation (z)≈S( (z)). Eq. ❷ is valid approximately up to the particle practical range,R_p, where the ﬂ uence is rapidly reduced to zero, cf [7-8].

Transport of fragments in therapeutic light ion beams

The transport of the generated fragments can be based on the known transport of the primary particles,

E(z)=E0(1‒ )^S⁰^R⁰^/E⁰ R₀

z

、微小損失微小角近似下、連続減速近似（CSDA）下 Boltzmann 輸送方程式 Fokker- Planck 方程式二重展開得。重粒子線吸収線量線質等物理量分布、重粒子

輸送任意物質中、開発解析的

表式求 [7-8]。

治療領域重粒子線平均

深度依存性、以下極簡単式表。

❶

式、輸送程度示無次元量S0R0/ 0 初期阻止能飛程全体平均阻止能比表、初期

0 R0 既知、対象物質対応

初期阻止能S0 既知場合、直接求。

輸送解関、面全

間差無視、 Φ^Ρ(z)≈Φ^Ρ,p(z) 小角近似考慮、指数関数的減少一次

Φ0exp(‒µz) 関連重付平均阻止能 ^{Φ Ρ} 直接積分、広

一次粒子吸収線量。

❷

式 ❷ 、重付平均阻止能、近似 (z)≈S( (z)) 範囲内平均 (z) 深度依存性基。式 ❶ 参照。式 ❷ 、

急速減少粒子実用飛程Rp 有効

。［7-8］参照。

治療用重粒子線 粒子輸送

核反応生粒子輸送一次粒子輸

送基考。、

E(z)=E0(1‒ )^S⁰^R⁰^/E⁰ R0

z

D(z)=∬

ρ S^Φ(z)

Φ^Ρ(z)=

ρ

S(E)ΦΕ,Ω^Ρ (z)dEdΩ=

ρ S^Φ(z)

cosΘ^Φ≈ Φ^Ρ^,Ρ(z)

ρ S^Φ(z)

Φ^Ρ,p.(z)≈

ρ S E (z)

Φ^Ρ0exp(‒µz) INTRODUCTION

Improvements in target delineation, such as molecular and functional imaging contribute to more accurate determination of doses for tumour eradication in the biological optimized radiation treatment [1-3].

The improved dose conformity and radiation quality distribution of the light ions in comparison to the convectional beams increases the possibility to deliver prescribed tumour suicidal doses almost without normal tissue injury, not least in cases where the target is unresectable, radio resistant and located near organs at risk [4-5]. An essential prerequisite for the success in the application of such beams is the correct knowledge of their absorbed dose, radiation quality and biological effect distribution in the patient and their accurate integration in the treatment planning system.

Speciﬁ ed transport quantizes can be calculated by the Monte Carlo or analytical methods. However, Monte Carlo simulations of particle transport are often quite time-consuming for routine biological optimized inverse treatment planning. Analytical transport calculations are therefore often more useful for fast determination of the absorbed dose and for other physical quantities within the patient. In this context, results from recently developed analytical transport theories which relates to this issues are brieﬂ y discussed below.

SOME THEORIES

Transport of projectiles in therapeutic light ion beams The analytical primary light ion transport is a solution of the Boltzmann equation from the practically important generalized case of Gaussian incident primary light ion beams of arbitrary mean square radius, mean square angular spread, and covariance [6]. This solution is based upon the idea of separating the primary particles

緒言

生物学的最適化放射線療法、分子機

能等標的描出技術進歩腫瘍根治

必要線量正確決定［1-3］。従来放射線比較重粒子線線量局所集中性線質分布優、標的切除不能症例、放射線抵抗性示症例、標的危険臓器近接

症例、正常組織障害

与必要腫瘍制御線量輸送可能性

高［4-5］。重粒子線治療成功、患者体内吸収線量、線質、生物学的影響分布正確知識持、要因治療計画

正確統合必須。

特殊化輸送定量化法分析法

計算。、生物学的最適

化逆方向治療計画（inverse treatment planning）

用、粒子線輸送

時非常煩雑。、患者体内物理量生物学的影響分布迅速求、時解析的表式極有用得。本稿、目的近年開発解析的輸送理論、及得結果

簡単紹介。

理論

治療用重粒子線 入射粒子輸送

一次粒子輸送、実用上重要任意平均二乗半径、平均二乗角度分散、共分散

分布一次粒子、Boltzmann 輸送方程式解解析的得 [6]。解、一次粒子

輸送粒子損失側方広 2

成分分考方基。側方分布関数

生物学的最適化逆方向治療計画粒子輸送試

2） Particle transport approaches for biological optimized inverse treatment planning

Johanna Kempe

Medical Radiation Physics, Department of Oncology-Pathology, Karolinska Institutet, Box 260, SE 171 76 Stockholm, Sweden

研究所

腫瘍・病理学部医療放射線物理研究

（Johannna Kempe）

D(z)=∬

ρ S^Φ(z)

Φ^Ρ(z)= ρ

S(E)ΦΕ,Ω^Ρ (z)dEdΩ=

ρ S^Φ(z)

cosΘ^Φ≈ Φ^Ρ^,Ρ(z)

ρ S^Φ(z)

Φ^Ρ,p.(z)≈ ρ S E (z)

Φ^Ρ₀exp(‒µz)

特集／第4回放医研国際 ｢細胞 分子及 軽 影響｣

特集第

4回放医研

国

際

第4回国際

第 52 巻 第7号

2 0 0 9. 0 7

Vol. 52

特 集

第4回国際

「細胞 分子 及 軽 影響」

4th NIRS International Open Laboratory Workshop

on Cellular and Molecular Eﬀ ects of Light Ions

2 0 0 9 . 0 7

Vol. 52

16

31

24

08

53

4th NIRS International

Open Laboratory Workshop on Cellular and Molecular Effects of Light Ions,

Radiological Sciences

放射線科学

Volume 52, Special Issue : July 2009

1）Development of the X tal Cube :The Next Generation PET Detector Using Semiconductor Photo-detectors

2） Particle transport approaches for biological optimized inverse treatment planning

第 52 巻第7号

特集

「細胞分子及軽影響」