Example of the misleading results caused by LQ model in calculating the fractionation effect in radiation therapy

The linear quadratic model (LQM) has been commonly used for calculating radiotherapy and/or radioprotection. It is a mechanistic, biologically-based model with few parameters and is used to do quantitative predictions of dose fractionation dependences for cases such as radiation protection, and radiotherapy. Here we demonstrate that LQM does encounter serious pitfalls both from a theoretical and phenomenological point of view. LQM is traced back to the famous Drosophila experiments (Muller, 1927). Scientists had believed that mutation was cumulative and irreversible until the dose-rate effects were found by Russell mega-mouse project (Russell. Unfortunately, this message was not taken correctly except for the difference between low and high dose-rate cases and people were content with such notions as dose and dose rate effectiveness factor (DDREF), dose rate effectiveness factor (DREF), and low dose effectiveness factor (LDEF). However, the concept should have been seriously taken into account the important evidence existing in the biological organism, namely the mutation frequency can be reduced by repairing and cell exclusion mechanisms. Especially an apparent inconsistency of the notion of ‘fractionation effect’, which was thought to be related somehow to the so called Elkind-type Recovery, and is utilised in the treatment of cancer in radiation therapy. Here we take a simple thought experiment to show such fractionation calculus leads complete inconsistent result. Why does it happen? The answer is simple: LQM predicts that the risk stays constant so far as D does not change. In actual cases, however, the risk function changes over time due to preventing mechanism. To this end, we have constructed the ‘Whack-A-Mole’ (WAM) Model to take account of input and output processes. Indeed, calculations of clinical circumstances are getting important. Due to this the mutated cells decreases over time after the irradiation stops, while LQM predicts no change since the accumulated total dose, D remains constant. The details will be seen in a separate ICRP publication.