Kumar Sudhir, Fenwick John D, Underwood Tracy S A, Deshpande Deepak D, Scott Alison J D, Nahum Alan E
Department of Physics, Clatterbridge Cancer Centre, Bebington CH63 4JY, UK. Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK. Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, CT & CRS building, Anushaktinagar, Mumbai-400094, India. Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai-400 094, India.
Phys Med Biol. 2015 Oct 21;60(20):8187-212. doi: 10.1088/0031-9155/60/20/8187. Epub 2015 Oct 6.
In small photon fields ionisation chambers can exhibit large deviations from Bragg-Gray behaviour; the EGSnrc Monte Carlo (MC) code system has been employed to investigate this 'Bragg-Gray breakdown'. The total electron (+positron) fluence in small water and air cavities in a water phantom has been computed for a full linac beam model as well as for a point source spectrum for 6 MV and 15 MV qualities for field sizes from 0.25 × 0.25 cm(2) to 10 × 10 cm(2). A water-to-air perturbation factor has been derived as the ratio of total electron (+positron) fluence, integrated over all energies, in a tiny water volume to that in a 'PinPoint 3D-chamber-like' air cavity; for the 0.25 × 0.25 cm(2) field size the perturbation factors are 1.323 and 2.139 for 6 MV and 15 MV full linac geometries respectively. For the 15 MV full linac geometry for field sizes of 1 × 1 cm(2) and smaller not only the absolute magnitude but also the 'shape' of the total electron fluence spectrum in the air cavity is significantly different to that in the water 'cavity'. The physics of this 'Bragg-Gray breakdown' is fully explained, making reference to the Fano theorem. For the 15 MV full linac geometry in the 0.25 × 0.25 cm(2) field the directly computed MC dose ratio, water-to-air, differs by 5% from the product of the Spencer-Attix stopping-power ratio (SPR) and the perturbation factor; this 'difference' is explained by the difference in the shapes of the fluence spectra and is also formulated theoretically. We show that the dimensions of an air-cavity with a perturbation factor within 5% of unity would have to be impractically small in these highly non-equilibrium photon fields. In contrast the dose to water in a 0.25 × 0.25 cm(2) field derived by multiplying the dose in the single-crystal diamond dosimeter (SCDDo) by the Spencer-Attix ratio is within 2.9% of the dose computed directly in the water voxel for full linac geometry at both 6 and 15 MV, thereby demonstrating that this detector exhibits quasi Bragg-Gray behaviour over a wide range of field sizes and beam qualities.
在小光子场中，电离室可能会出现与布拉格 - 格雷行为的较大偏差；EGSnrc蒙特卡罗（MC）代码系统已被用于研究这种“布拉格 - 格雷击穿”现象。对于完整的直线加速器束流模型以及6兆伏和15兆伏能量、尺寸从0.25×0.25平方厘米到10×10平方厘米的点源谱，计算了水模体中小水腔和空气腔中的总电子（+正电子）注量。已推导出水 - 空气扰动因子，其定义为在微小水体积中所有能量积分后的总电子（+正电子）注量与“针尖3D腔状”空气腔中总电子（+正电子）注量的比值；对于0.25×0.25平方厘米的场尺寸，6兆伏和15兆伏完整直线加速器几何条件下的扰动因子分别为1.323和2.139。对于15兆伏完整直线加速器几何条件，在场尺寸为1×1平方厘米及更小的情况下，空气腔中总电子注量谱的绝对值大小以及“形状”与水“腔”中的情况显著不同。参考法诺定理对这种“布拉格 - 格雷击穿”的物理原理进行了充分解释。对于15兆伏完整直线加速器几何条件下0.25×0.25平方厘米的场，直接计算得到的MC水 - 空气剂量比与斯宾塞 - 阿蒂克斯阻止本领比（SPR）和扰动因子的乘积相差5%；这种“差异”由注量谱形状的差异解释，并从理论上进行了阐述。我们表明，在这些高度非平衡的光子场中，扰动因子在1的5%以内的空气腔尺寸将小到不切实际。相比之下，对于6兆伏和15兆伏的完整直线加速器几何条件，通过将单晶金刚石剂量计（SCDDo）中的剂量乘以斯宾塞 - 阿蒂克斯比值得到的0.25×0.25平方厘米场中的水剂量，与在水体素中直接计算的剂量相差在2.9%以内，从而表明该探测器在广泛的场尺寸和束流品质范围内表现出准布拉格 - 格雷行为。
