Jian-Yue Jin ^1* Jiankui Yuan ² Xiaohang Qin ¹ Yinghui Li ¹ Huagang Yan ^1* Nancy L. Oleinick ³ Min Yao ^4* Quintin Pan ² Feng-Ming (Spring) Kong ^5,6 Mitchell Machtay ^4*

• ¹ School of Biomedical Engineering, Capital Medical University, Beijing, Beijing Municipality, China
• ² Seidman Cancer Center, University Hospitals, Cleveland Medical Center, Cleveland, Georgia, United States
• ³ Case Comprehensive Cancer Center, School of Medicine, Case Western Reserve University, Cleveland, Ohio, United States
• ⁴ Department of Radiation Oncology, Penn State University Cancer Institute, Hershey, United States
• ⁵ Department of Clinical Oncology, Hong Kong University Shenzhen Hospital, Shenzhen, China
• ⁶ Department of Clinical Oncology, Queen Mary Hospital, Li Ka Shing Medical School, The University of Hong Kong, Hong Kong, Hong Kong, SAR China

We aimed to develop a comprehensive proton relative biological effectiveness (RBE) model based on accumulated cell-survival data in the literature. Our approach includes 4 major components: 1) Eligible cell-survival data with various LETs in the PIDE database (72 datasets in 4 cell-lines); 2) A cell-survival model based on Poisson Equation, with α and β defined as the ability to generate and repair damage, respectively, to replace the classic linear-quadratic model for fitting the cell-survival data; 3) Hypothetical linear relations of α and β on LET, or 𝛼(𝐿𝐸𝑇) 𝛼 𝑥 = 𝑎 𝛼 + 𝑏 𝛼 * 𝐿𝐸𝑇 and 𝛽(𝐿𝐸𝑇) 𝛽 𝑥= 𝑎 𝛽 -𝑏 𝛽 * 𝐿𝐸𝑇; 4) A multi-curve fitting (MCF) approach to fit all cell-survival data into the survival model and derive the aα, bα, aβ and bβ values for each cell-line. Dependences of these parameters on cell-type were thus determined and finally a comprehensive RBE model were derived. MCF showed that (aα, bα, aβ, bβ) = (1.09, 0.0010, 0.96, 0.033), (1.10, 0.0015, 1.03, 0.023), (1.12, 0.0025, 0.99, 0.0085), and (1.17, 0.0025, 0.99, 0.013) for the 4 cell-lines, respectively. Thus, aα = 1.12 ± 0.04, bα = 0.0019 ± 0.0008, aβ = 0.99 ± 0.03, and bβ = 0.013 * αx; and approximately, 𝛼~1.12 * 𝛼 𝑥 , and 𝛽 = (0.99 -0.013 * 𝛼 𝑥 * 𝐿𝐸𝑇) * 𝛽 𝑥 . Consequently, a relative reliable and comprehensive RBE model with dependence on LET, αx, βx and dose per fraction was finally derived for potential clinical application.