The RBE of accelerated protons in different parts of the Bragg curve

Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer

“…Some reports did not mention any of the parameters α x , β x , α, β, or LET d so that the survival curves had to be extracted from the publications and fitted (using matlab (Mathworks Inc.)) in addition to simulating LET d values (Robertson et al 1975, Hall et al 1978, Williams et al 1978, Raju et al 1978b, Bettega et al 1979, Sakamoto et al 1980, Fuhrman Conti et al 1988, Ogata et al 2005, Kagawa et al 2002, Baek et al 2008, Butterworth 2012, Grosse et al 2014, Zhang et al 2013, Aoki-Nakano 2014. In some incidents the LET d values were reported but the α and β values for all measured conditions as a function of proton energy or position in the Bragg curve had to be manually extracted (Wainson et al 1972, Inada et al 1981, Hei et al 1988a, Wouters et al 1996, Ogheri et al 1997, Moertel et al 2004, Yang et al 2007, Ristic-Fira et al 2011, Doria et al 2012.…”

“…In addition to measurements in pristine or spread-out Bragg peak depth dose curves semimonoenergetic proton beams were used with low energy (<6 MeV) (Bettega et al 1979, Bird et al 1980, Perris et al 1986, Hei et al 1988a, 1988b, Belli et al 1989, 1992a, 2000a, Folkard et al 1989, Prise et al 1990, Ogheri et al 1997, Sgura et al 2000, Schettino et al 2001, Baggio et al 2002, Antoccia et al 2009, Wera et al 2011, 2013, Fiorini et al 2011, Yogo et al 2011, Doria et al 2012, Jeynes et al 2013 and higher energies (>6 MeV) (Wainson et al 1972, Perris et al 1986, Fuhrman Conti et al 1988, Bettega et al 1990, Green et al 2001, Moertel et al 2004, Yang et al 2007.…”

Relative biological effectiveness and dose-averaged linear energy transfer studies for proton therapy Monte Carlo treatment planning

“…Research has shown clearly that RBE 1.1 is not a good representation of the biological effect in proton therapy especially at the distal end of an SOBP despite being a conservative estimate. In a work reported by McNamara et al 52 , their RBE model c) and (f), there is a higher biological dose in the target region when using their RBE model compared to RBE 1.1. Hence, this relates to having more doses being delivered to the target when using variable RBE models.…”

“…Till date, many RBE models have been developed to address the issue of RBE variations in patients 39,[47][48][49][50][51][52][53][54][55] . These models are mainly based on the concepts of either Linear Quadratic Model (LQM), Local Effect Model (LEM) 56 or Microdosimetric-Kinetic Model (MKM) 57 .…”

“…In this work, the LQM-based RBE model is adopted with the assumption that the use of experimental data to derive the model would be more accurate. These RBE models have assumed that 𝐿𝐸𝑇 𝑑 has a linear relationship with RBE [52][53][54][55]61,62 , while others assumed that there is a non-linearity between them 48,63 . where Δ is the energy cut-off value of secondary electrons, 𝑆 𝑒𝑙 is the linear electronic stopping power and 𝑑𝐸 KE,Δ is the mean sum of the kinetic energy larger than Δ of all electrons released by the charged particle per unit path length 𝑑𝑙 27 .…”