Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships

Abstract

Objective: Earlier radiobiological equivalence relationships as derived for low-linear energy transfer (LET) radiations are revisited in the light of newer radiobiological models that incorporate an allowance for relative biological effectiveness (RBE).Methods: Linear-quadratic (LQ) radiobiological equations for calculating biologically effective dose at both low-and high-LET radiations are used to derive new conditions of equivalence between a variety of radiation delivery techniques. The theoretical implications are discussed. Results:The original (pre-LQ) concept of equivalence between fractionated and continuous radiotherapy schedules, in which the same physical dose is delivered in each schedule, inherently assumed that low-LET radiation would be used in both schedules. LQ-based equivalence relationships that allow for RBE and are derived assuming equal total physical dose between schedules are shown to be valid only in limited circumstances. Removing the constraint of equality of total physical dose allows the identification of more general (and more practical) relationships. Conclusion:If the respective schedules under consideration for equivalence both involve radiations of identical LET, then the original equivalence relationships remain valid. However, if the compared schedules involve radiations of differing LET, then new (and more restrictive) equivalence relationships are found to apply. Advances in knowledge:Theoretically derived equivalence relationships based on the LQ model provide a framework for the design and intercomparison of a wide range of clinical techniques including those involving high-and/or low-LET radiations. They also provide a means of testing for the validity of variously assumed tissue repair kinetics.

Report of the AAPM TG‐256 on the relative biological effectiveness of proton beams in radiation therapy

“…There have been concerns that RBE may be under‐ or overestimated for certain tumors or organs at risk (see Section 4.B.). Theoretical studies have addressed the issue of RBE variations in patients and have analyzed the potential impact of RBE on fractionation in proton therapy . In general, RBE effects will be more prominent in tumors involving low α / β tissues, which makes prostate, breast, sarcoma, and certain brain tumors sites to be cautious with.…”

“…There is a need to understand whether or not differences in plans optimized using (LET d times dose) vs (RBE times dose) for relevant molecular or cellular endpoint are large enough to be clinically relevant when viewed against the uncertainties and gaps in our understanding of the underlying clinical endpoint and patient‐specific biology. An increasing number of proton centers are treating patients with proton beam scanning, and it has been shown that variations in RBE might be greater in scanned beams relative to passive scattered beams . IMPT delivered with scanning pencil beams holds the greatest therapeutic potential and will be employed at the majority of new proton centers. Recent theoretical studies have addressed the issue of RBE spatial variations in patients and have analyzed the impact of fractionation on RBE in proton therapy . There is thus increased interest in understanding the clinical relevance of RBE spatial variations.…”

Proton Relative Biological Effectiveness – Uncertainties and Opportunities

“…Furthermore, it implies that hypofractionated regimens will result in lower RBE values [57]. Several theoretical studies have addressed the issue of RBE spatial variations in patients [57–59] and have analyzed the impact of RBE on fractionation [10, 60, 61]. …”

Mathematical Modeling in Radiation Oncology

“…Fractionation schemes are often compared with dose equivalence calculations that are typically based upon the LQ model (Holloway and Dale 2013). In addition to BED-and LQ-based calculations of dose equivalence, tumor growth models can be incorporated into optimization algorithms that explicitly model changes in tumor volume.…”