目的：McLellan 於1992年發表了電子劑量計算的數值演算方法，在數值模擬方法上採用等空間取樣法（equal spacing）做機率分佈的取樣，其缺點是在計算時非常耗時。本研究中在數值方法上採用一個稱做等機率分佈（equal probability）的方法，期望能減少取樣數目並維持同樣的計算準確度。在這篇報告中，我們將驗證此數值程式於能量損失模擬方面的準確性。
材料與方法：新的數值計算程式採用Moliere的理論來模擬傳播過程中電子的角度散射機率分佈，能量損失分佈則是以Landau的游離能量損失理論來處理。由制動輻射所造成的能量損失則暫未包含在本研究中。本報告針對20 MeV、10 MeV以及6 MeV的單能電子射束在簡化的一度空間條件下（未包含角度散射），進行水中的碰撞質量阻擋本領計算、並在相同條件下模擬電子於水中的傳播過程。為驗證數值計算程式的正確性，我們採用EGS4蒙地卡羅程式作為計算驗證的工具。
結果：在未包含角度散射的條件下，數值程式所計算的碰撞質量阻擋本領與ICRU提供的資料比較，其誤差於高能量（20 MeV、10 MeV）下小於2 %；低能量（6 MeV）下則約在3％左右。而應用於絕對深度劑量分佈曲線計算中，50％劑量深度誤差均在3 mm以內；粒子射程（practical range）誤差則均在2 mm以內。
結論：研究結果證實Landau 的理論可以準確的模擬電子在水中的游離能量損失，且等機率取樣方法並不會在劑量計算上產生太大的誤差。

Purpose : A numerical electron dose calculation algorithm was introduced in 1992 by McLellan who used equal space sampling method to simulate electron energy loss and angular scattering distribution. The drawback of this numerical algorithm was its long calculation time. In our study, an equal probability sampling method was adopted in hope that less sampling points were necessary while the same calculation accuracy can still be maintained. Calculation results for electron energy loss process in homogeneous media were reported.
Material and Methods : The multiple scattering theory of Moliere was used in the modified numerical algorithm to simulate electron angular scattering; while Landau’s ionizational energy loss theory was used to simulate electron energy loss process. At present, energy loss due to bremsstrahlung production was not included in the algorithm. Test calculation of collisional stopping power for 20, 10 and 6 MeV electrons incident into water under simplified condition (excluding electron multiple scattering) was performed. The energy loss process for the same setup was also simulated. In order to verify the calculation accuracy of the numerical code, EGS4 Monte Carlo code was adopted to perform benchmark calculation.
Results : When excluding electron multiple scattering, the calculation of collisional stopping power shows discrepancy of less than 2% between numerical calculation and ICRU reports for high energy electrons (20 and 10 MeV). For low electrons (6 MeV), this discrepancy is close to 3%. The calculation results of absolute depth-dose distribution demonstrate that the calculated depths of 50% dose agree with EGS4 to within 3 mm and the calculated electron ranges to within 2 mm.
Conclusion : Landau’s theory is suitable for simulating electron ionizational energy loss in homogeneous media and the error due to equal probability sampling of electron energy loss distribution is acceptable.