Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources
Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources
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DOI：
10.1118/1.3456927
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发表时间：
2010-08-01
期刊：
影响因子：
3.8
通讯作者：
Carlone, Marco
中科院分区：
文献类型：
--
作者：
Guerrero, Mariana;Carlone, Marco
目的：近年来，提出了几个模型，修改了标准的线性二次（LQ）模型，使预测的生存曲线在高剂量线性。这些模型大多数是纯现象学的，只能应用于每部分急性剂量的特定情况。作者认为，在分次剂量实验和指数衰减源的情况下，一个线性二次线性（LQL）模型的机制制定。该模型提供了一个全面的描述，辐射反应的任意剂量率和分馏只有一个额外的parameter.Methods：作者使用的LQL模型从文献中的房室制剂。他们解析求解模型的微分方程的情况下，一个分裂剂量实验和一个指数衰减源。他们比较的解决方案的存活分数与标准LQ方程和与致死潜在致死（LPL）model.Results：在分裂剂量实验的情况下，LQL模型预测的回收率作为剂量的函数，偏离标准LQ的平方律的每一个分数。存活分数作为分数之间的时间的函数遵循与LQ类似的指数规律，但向LQ参数β添加了乘法因子。分次剂量实验的LQL解非常接近LPL预测。对于衰减源，LQL和LQ的解决方案之间的差异可以忽略不计时，源的半衰期远大于特征修复时间，这是临床相关的case.Conclusions：房室制剂的LQL模型可以用于任意剂量率，并提供了一个全面的描述剂量反应。当急性剂量的存活分数对于高剂量是线性的时，也预测了对于分次剂量的恢复率的平方律公式的偏差。(C)2010年美国医学物理学家协会。[DOI 10.1118/1.3456927]
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. (C) 2010 American Association of Physicists in Medicine. [DOI: 10.1118/1.3456927]