現今腫瘤治療有許多方法，除了傳統的手術治療以及化學治療外，重離子腫瘤治療也越來越普及。相對於傳統治療，重離子治療為非侵入性治療且副作用較小，主要利用高能離子束在特定位置下釋放能量的特性來治療腫瘤。重離子治療腫瘤中，主要為重離子束的深度劑量曲線前低後面急遽上升且急遽下降的優點，利用控制重離子能量將劑量準確的放射在腫瘤位置上，而降低對於正常細胞的傷害，達到最有效率的腫瘤治療。
重離子治療的物理層面上，精確的計算能量損失是一重點，本研究目的為建立一套模型，探討重離子在進入介質中的能量損失，可以準確的描述重離子束在介質中的深度劑量變化情形。我們利用Runge-Kutta數值方法來計算高能重離子束隨深度變化能量釋放情形，預測重離子束能量釋放位置以及釋放劑量，並將我們的結果與Stopping and Range of Ions in Matter (SRIM)模擬套件相互比較。最後再將此數值模擬應用於計算高能重離子束進入人體內的情形。

In recent years, Heavy-Ion Tumor Therapy (HITT) has received a lot of atten-tion as it offers significant advantages for the treatment of deep-seated local tumors with an enhanced biological effectiveness in comparison to conventional megavolt photon therapy or those using protons. The physical depth-dose distribution in tissue is characterized by a small entrance dose and a distinct maximum or the Bragg peak near the end of range with a sharp fall-off at the distal edge. While tumor therapy with protons is a well-established treatment modality, the application of heavy ions is so far restricted to only a few facilities in the world.
On the physical aspects of HITT, accurate determination of specific energy loss (SEL) or stopping power is very important to the improvement of modeling the relative biological effectiveness and developing powerful computer algorithms for treatment planning. In this work, the relativistic version of the Bethe-Bloch formula is revisited and SEL of heavy ions in water is calculated. The SEL for a fast charged particle moving through water is calculated by numerical method. The Bragg curve of the stopping power for various charged particles has been evaluated by the first-order approximation and Runge-Kutta method. Numerical simulations have been employed to predict the total stopping power and compared with those calculated using the Stopping and Range of Ions in Matter (SRIM) code. Detailed analysis and simulation results are given and discussed here.

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