Medical Physics Support, Inc., 7110 Pelican Island Dr., Tampa, FL 33634, USA.
Phys Med. 2019 Nov;67:185-191. doi: 10.1016/j.ejmp.2019.10.022. Epub 2019 Nov 18.
to determine optimal fractionation schedule which provides maximum biologically effective dose (BED) in the targeted tumor in the case of heterogeneous radiosensitivity of malignant cells in combination with a spatially varying sparing factor for the organ at risk.
the mathematical framework used in the current study is based on the linear-quadratic (LQ) model with heterogeneous parameters alpha and beta for malignant cells. To determine optimal fractionation, we consider changes in BED in the treatment target (BED) under the condition of fixed BED in the affected normal tissue (BED).
we demonstrate both analytically and via numerical calculations that there exists an optimal number of fractions for which biologically effective dose in the uniformly irradiated target is at maximum. It is also shown that dependence of BED on number of fractions is generally non-monotonic and is affected by the variances σ and σ of the alpha and beta radiosensitivities, respectively. In a particular case when σ and σ are sufficiently small, expression for the optimal target dose which maximizes BED was derived analytically.
the obtained results demonstrate that in the presence of heterogeneous alpha and beta in the tumor, hypofractionation can either increase or decrease BED depending on the variances σ and σ. Consequently, intratumor heterogeneity is an important factor which can affect radiobiological comparison of different fractionation regimens.
在恶性细胞存在不均匀放射敏感性的情况下，结合器官风险的空间变化保护因子，确定为靶肿瘤提供最大生物有效剂量（BED）的最佳分割方案。
目前研究中使用的数学框架基于具有不均匀参数α和β的线性二次（LQ）模型恶性细胞。为了确定最佳分割，我们考虑在受影响的正常组织（BED）中固定 BED 的情况下，治疗靶区（BED）中的 BED 变化。
我们通过分析和数值计算证明，存在一个最佳的分割次数，使均匀照射靶区的生物有效剂量达到最大值。还表明，BED 与分割次数的依赖性通常是非单调的，并且分别受α和β放射敏感性的方差σ和σ的影响。在特定情况下，当σ和σ足够小时，可以通过解析推导得出最大化 BED 的最佳靶剂量的表达式。
研究结果表明，在肿瘤中存在不均匀的α和β的情况下，分割次数的减少可能会增加或减少 BED，具体取决于方差σ和σ。因此，肿瘤内异质性是一个重要的因素，可能会影响不同分割方案的放射生物学比较。
