线性二次线性（LQL）模型的机理公式：分割剂量实验和指数衰减源。

Mechanistic formulation of a lineal-quadratic-linear (LQL) model: split-dose experiments and exponentially decaying sources.

机构信息

Department of Radiation Oncology, University of Maryland School of Medicine, Baltimore, 21201, USA.

出版信息

Med Phys. 2010 Aug;37(8):4173-81. doi: 10.1118/1.3456927.

DOI:10.1118/1.3456927

PMID:20879577

Abstract

PURPOSE

In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter.

METHODS

The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model.

RESULTS

In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter beta. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case.

CONCLUSIONS

The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

摘要

目的

近年来，提出了几种模型来修改标准的线性二次（LQ）模型，以使预测的生存曲线在高剂量下呈线性。这些模型大多数都是纯粹的唯象模型，只能应用于急性剂量分次的特殊情况。作者考虑了一种线性二次线性（LQL）模型的机制表述，用于分割剂量实验和指数衰减源。该模型仅使用一个附加参数，为任意剂量率和分割提供了全面的辐射反应描述。

方法

作者使用文献中 LQL 模型的分区表述。他们对分割剂量实验和指数衰减源的模型微分方程进行了分析求解。他们将生存分数的解与标准 LQ 方程和致死潜在致死（LPL）模型进行了比较。

结果

在分割剂量实验的情况下，LQL 模型预测了分割剂量中作为剂量的函数的恢复比，该比值偏离标准 LQ 的平方律。作为分割间隔时间的函数的生存分数遵循与 LQ 相似的指数规律，但对 LQ 参数β添加了一个乘法因子。分割剂量实验的 LQL 解非常接近 LPL 预测。对于衰减源，当源的半衰期远大于特征修复时间时，LQL 和 LQ 解之间的差异可以忽略不计，这是临床相关的情况。