Proposed by Curtis in 1989, lethal and potentially lethal (LPL) model is one of the most comprehensive mechanism‐based mathematical models for radiation cell survival fraction (SF) study. One important reason why it has not been widely used is due to its rich but complex mathematical structure. Even for simple continuous irradiation with constant dose rate case, there is no general analytic solution for radiation cell SF with arbitrary initial condition. In this paper a closed‐form analytical exact solution of cell radiation SF under continuous irradiation with constant dose rate with or without initial lethal and non‐lethal lesions is presented for LPL model. Also asymptotic behaviors of SF for cells obeying LPL model with low radiation doses at the beginning of irradiation, with high radiation doses after a long time of irradiation, and for radiation delivered at very high or very low dose rate were provided. Connections between LPL model and the conventional linear‐quadratic (LQ) model or traditional target theory were discussed with the help of our exact analytic solutions. We hope our new analytic results will renew interest of LPL model among scientists and facilitate its use, particularly for stereotactic radiosurgery/stereotactic body radiation therapy treatments and delivery time effect on intensity modulated radiotherapy, in radiobiology and radiotherapy communities.
ASJC Scopus subject areas
- Radiology Nuclear Medicine and imaging