Department of Medical Radiation Physics, Lund University, Lund, Sweden.
Phys Med Biol. 2013 Mar 7;58(5):1529-48. doi: 10.1088/0031-9155/58/5/1529. Epub 2013 Feb 13.
We have previously shown analytically that the biologically effective dose (BED), including effects of repair during irradiation and of incomplete repair between fractions, can be formulated using a convolution between the absorbed dose rate function and the function describing repair. In this work, a discrete formalism is derived along with its implementation via the fast Fourier transform. The implementation takes the intrinsic periodicity of the discrete Fourier transform into consideration, as well as possible inconsistencies that may arise due to discretization and truncation of the functions describing the absorbed dose rate and repair. Numerically and analytically calculated BED values are compared for various situations in external beam radiotherapy, brachytherapy and radionuclide therapy, including the use of different repair models. The numerical method is shown to be accurate and versatile since it can be applied to any kind of absorbed dose rate function and allows for the incorporation of different repair models. Typical accuracies for clinically realistic examples are in the order of 10(-3)% to 10(-5)%. The method has thus the potential of being a useful tool for the calculation of BED, also in situations with complicated irradiation patterns or repair functions.
我们之前已经从理论上证明，包括照射过程中修复和分次间不完全修复影响在内的生物有效剂量（BED）可以通过吸收剂量率函数和修复描述函数之间的卷积来构建。在这项工作中，我们推导出了一种离散形式，并通过快速傅里叶变换（FFT）实现了它。该实现考虑了离散傅里叶变换的固有周期性，以及由于吸收剂量率和修复描述函数的离散化和截断可能导致的不一致性。我们比较了外照射放疗、近距离放疗和放射性核素治疗中各种情况下的数值和解析计算的 BED 值，包括使用不同的修复模型。该数值方法被证明是准确且通用的，因为它可以应用于任何类型的吸收剂量率函数，并允许纳入不同的修复模型。对于临床实际示例，典型的精度在 10(-3)%到 10(-5)%之间。因此，该方法有可能成为计算 BED 的有用工具，即使在辐射模式或修复函数复杂的情况下也是如此。
