International Journal of Radiation Oncology*Biology*Physics
Biology ContributionsThe assessment of RBE effects using the concept of biologically effective dose
Introduction
The theory of dual radiation action (1) predicts that high linear energy transfer (high-LET) radiation increases the linear (α) component of radiation damage, while the quadratic (β) component remains unchanged. As a consequence it is generally assumed that the “intrinsic” relative biological effectiveness (RBE) of high-LET radiation compared to a reference (low-LET) quality is the ratio of the initial slopes (at zero dose) of the associated cell-survival curves 2, 3. The measured RBE, as determined from the ratio of doses required to achieve a specific endpoint, is dependent on the chosen biological endpoint, and is therefore variable.
In terms of the linear-quadratic (LQ) model, the slope at zero dose is determined entirely by the α-coefficient of cell kill. Using the nomenclature of Carlsson (4) the apparent value of the linear constant (αH) at high LET is related to the low-LET radiosensitivity (αL) by: where RBEM is the RBE in the highest limit of surviving fraction, i.e., at zero dose.
This article explores how RBEM can be accommodated within the LQ model, using the principal assumption that the β-coefficient of damage is unaltered by changes in LET, i.e., βH = βL.
Section snippets
RBE and fractionated irradiation
Adopting the general LQ symbolism whereby the negative of the logarithm of the surviving fraction is written as E, we have: For single doses (dL) of the reference (low-LET) radiation: where αL and βL are the respective linear and quadratic coefficients at low LET for the particular cell line.
If a high-LET radiation is used instead: where αH reflects the higher radiosensitivity to the higher LET radiation and dH is the lower dose consequently required. Then, from Eq. 1
Discussion
The idea that RBE influences predominantly only the linear-dose coefficient in the LQ model is not new. In a study on the interaction between X-rays and 3 MeV neutrons in the skin of mouse foot, Joiner et al. (2) found that increasing the proportion of photon contamination from 11% to 100% reduced both the α- and β-coefficients, by factors of 4.8 and 1.44 respectively (19). Stenerlöw et al. (19) have also shown experimentally that the β-values for some cell lines appear LET-dependent. No
Acknowledgements
We are greatly indebted to Professors Pierre Scalliet, Andre Wambersie, Jack Fowler (Leuven), Dr. Pat Price (London), and Drs. Lowell Anderson and Clifton Ling (New York) for helpful comments and discussions. Dr. Roland Hawkins (New Orleans) is thanked for providing much useful background material in relation to his own work.
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