Department of Medical Radiation Physics, Lund University, Lund, Sweden.
Phys Med Biol. 2013 Mar 7;58(5):1507-27. doi: 10.1088/0031-9155/58/5/1507. Epub 2013 Feb 13.
This work presents a new mathematical formulation of biologically effective dose (BED) for radiation therapy where effects of repair need to be considered. The formulation is based on the observation that the effects of repair, both during protracted irradiation and of incomplete repair between fractions, can be written using a convolution, i.e. BED(T)=∫(∞)(-∞)R(T)(t)dt+1/(α/β) ∫(∞)(-∞)[R(T)(t)xI(t)]dt where T is the total irradiation time, R(T)(t) is the absorbed dose rate as a function of time t and I(t) is the function describing repair. To validate this formulation, the previously published expressions for instant and protracted irradiation are first summarized. Then, by analytical derivation, it is shown that the new formulation gives identical results. The calculation of BED can thus be treated within one single mathematical framework, applicable in external beam therapy, brachytherapy, radionuclide therapy, or a combination of these treatment modalities. Moreover, the new formulation allows for a straightforward incorporation of different repair models and has the advantage of being numerically applicable.
这项工作提出了一种新的放射治疗生物有效剂量（BED）的数学公式，其中需要考虑修复的影响。该公式基于这样一种观察，即修复的影响，无论是在长时间照射期间还是在分次之间不完全修复期间，都可以使用卷积来表示，即 BED(T)=∫(∞)(-∞)R(T)(t)dt+1/(α/β) ∫(∞)(-∞)[R(T)(t)xI(t)]dt，其中 T 是总照射时间，R(T)(t)是随时间 t 变化的吸收剂量率，I(t)是描述修复的函数。为了验证该公式，首先总结了先前发表的即时和长时间照射的表达式。然后，通过分析推导，表明新公式给出了相同的结果。因此，BED 的计算可以在一个单一的数学框架内进行，适用于外照射治疗、近距离放射治疗、放射性核素治疗或这些治疗方式的组合。此外，新公式允许直接纳入不同的修复模型，并且具有数值适用性的优点。
