Theoretical derivation and clinical dose-response quantification of a unified multi-activation (UMA) model of cell survival from a logistic equation

Objective: To theoretically derive a unified multiactivation (UMA) model of cell survival after ionising radiation that can accurately assess doses and responses in radiotherapy and X-ray imaging. Methods: A unified formula with only two parameters in fitting of a cell survival curve (CSC) is first derived from an assumption that radiation-activated cell death pathways compose the first- and second-order reaction kinetics. A logit linear regression of CSC data is used for precise determination of the two model parameters. Intrinsic radiosensitivity, biologically effective dose (BED), equivalent dose to the traditional 2 Gy fractions (EQD2), tumour control probability, normal-tissue complication probability, BED 50 and steepness (Γ50) at 50% of tumour control probability (or normal-tissue complication probability) are analytical functions of the model and treatment (or imaging) parameters. Results: The UMA model has almost perfectly fit typical CSCs over the entire dose range with R 2 ≥0.99. Estimated quantities for stereotactic body radiotherapy of early stage lung cancer and the skin reactions from X-ray imaging agree with clinical results. Conclusion: The proposed UMA model has theoretically resolved the catastrophes of the zero slope at zero dose for multiple target model and the bending curve at high dose for the linear quadratic model. More importantly, it analytically predicts dose–responses to various dose–fraction schemes in radiotherapy and to low dose X-ray imaging based on these preclinical CSCs. Advances in knowledge: The discovery of a unified formula of CSC over the entire dose range may reveal a common mechanism of the first- and second-order reaction kinetics among multiple CD pathways activated by ionising radiation at various dose levels.