本文以蒙地卡羅法進行物質的幾何圖形建構以及粒子穿透物質的模擬，分別以水以及去氧核醣核酸分子來觀察質子射線在這兩項物質中的劑量散佈情形。由於粒子在物質中並不會以直線前進，而會因為碰撞而產生行進路線偏移，所以十分難預測其能量轉移的狀況，尤其類似本文以一億個質子來進行模擬的狀況，因此必須以蒙地卡羅法來進行亂數分布來模擬每個質子的行徑路線，然後再推算出劑量的散布；而本文利用的模擬工具為Geant4(for Geometry and Tracking)。根據前人所做的模擬數據，還有實驗所得到的數據，可以比對出利用此系統所做出的模擬成果是否據有高度的可信度。在得知該模擬擁有高可信度後，便可以利用量子化學Gaussian建立出細部的DNA模型，以觀察出該DNA在所施放的射線當中受到的影響以及雙股、單股的斷鍵的情形。Gaussian是一套利用第一原理密度泛函理論來進行多電子系統分子軌道計算的模擬工具。DNA的斷裂是會影響到一個細胞中蛋白質的轉譯，所以有可能會造成小核醣核酸(Si-RNA)、接受器蛋白(receptor protein)、通道蛋白(channel protein)等等的不正常，進而造成各式各樣的疾病。本次模擬的主要目的在於確切計算出質子入射的初始能量在進入人體時所留下的劑量是否會高過腦瘤DNA的鍵結能，並且藉此模擬DNA的斷鍵結果，以確認在劑量之布拉格峰(Bragg Peak)處及低劑量之處是否會造成細胞的破損。如果在布拉格峰處有造成細胞損害，而低劑量處無造成細胞損害，則表示該入射能量所產生的射線只會對目標腫瘤細胞產生傷害，並不會對所經過的細胞造成毀滅性的傷害，達成質子治療非接觸式破壞癌症細胞之目的。

Brain cancer is a lethal disease which is quite difficult to cure by traditional therapy such as surgery since human brain consists of very complicated nervous system. It is very likely to make undesirable mistakes during an operation. Proton therapy is a very effective method to destroy brain cancer cells because it has a special characteristic: the Bragg Peak. This special feature allows the dose deposit in the premier part of the incident path to remain at a very low value and then suddenly soar to the climax. With this magnificent phenomenon, it is possible to kill the tumor cells without damaging other normal cells, thus avoiding unwanted side effects after the cure.
In this paper, we use Monte-Carlo method and quantum chemistry to simulate the behavior of protons traveling through substrates such as water and calculate the dose distribution and other properties. To build a DNA model and calculate its bonding energy through quantum chemistry methods, Gaussian is a tool required. As to obtain the dose distribution and proton range by using Monte-Carlo method, Geant4 would be an adequate computer program for the task.
According to our research, the dose deposit in the front part of the model actually seems to be too low to break the bonding of DNA. Only the dose near the Bragg Peak is capable of breaking the backbone of the DNA structure. Therefore, proton therapy is proved to be a safe way to remedy brain cancer by now.

目錄
摘要 I
符號表 IV
第一章 緒論 4
1.1放射線治療的起源 4
1.2傳統癌症治療回顧 5
1.3質子治療文獻回顧 7
1.4癌細胞與去氧核醣核酸 8
1.5人腦介紹 11
1.6研究動機與目標 11
第二章 計算量子力學與粒子碰撞理論 13
2.1 密度泛函理論 15
2.1.1 Kohn-Sham定理 16
2.1.2交換─相關泛函理論 17
2.1.3 B3LYP交換─相關泛函理論 18
2.1.4 自洽場計算 18
2.2 基底函數理論 20
2.2.1基底函數6-31G簡介 22
2.3分子碰撞理論 23
2.3.1 線性能量轉換 23
2.3.2 古典波爾阻擋能力 24
2.3.3 近代物理修正的分子碰撞理論 26
2.3.4 莫特散射 27
2.3.5 貝特公式 31
2.4射線行進距離與劑量吸收 34
2.4.1 吸收劑量之量值 35
2.4.2 劑量對生物體的影響 36
第三章 模擬方法與模型建構 37
3.1模擬方法與計算流程 37
3.2 Gaussian的模擬模型建立 38
3.3 Gaussian的模擬設定 39
3.3.1 原子軌域與能隙 39
3.3.2吉布斯自由能 40
3.3.3紅外線與拉曼光譜 41
3.4 Geant4模擬設定 43
第四章 結果與討論 45
4.1以水為材料之模擬結果 45
4.2去氧核醣核酸的幾何最佳化 47
4.3染色質去氧核醣核酸之斷裂模擬 49
4.3.1 距離入射點一公分處的DNA分析 50
4.3.2 距離入射點兩公分處的DNA分析 52
4.3.3 距離入射點2.8公分處的DNA分析 54
第五章 結論與未來工作建議 56
5.1結論 56
5.2未來工作建議 57
參考文獻 58

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