Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships

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.Radiobiological equivalence relationships continue to play an important role in radiation oncology, providing a means of intercomparing alternative radiotherapy treatment schedules in terms of their biological effectiveness and, in principle, allowing the fine-tuning and optimisation of treatments. Such relationships allow any treatment schedule to be converted into a therapeutically equivalent (or improved) alternative through manipulation of various schedule parameters (fraction size, dose rate etc.) or through the consideration of different physical methods of dose delivery (brachytherapy, targeted therapy, permanent implants etc.).In this paper, the original concept of radiobiological equivalence (the so-called Liversage equivalence, applicable only to intercomparisons between fractionated and continuous schedules) is revisited and re-assessed in the light of more recent advances in radiobiological modelling. In doing so, we demonstrate that Liversage-type equivalence is a special and restricted case of a much wider range of possible equivalence relationships, including, for example, those involving radiations with increased linear energy transfer (LET). High-LET therapies such as those using protons or light ions have been the subject of much interest in recent years because of the therapeutically advantageous dose distributions afforded by the Bragg-peak phenomenon and (especially in the case of light ions) on account of their improved radiobiological effectiveness [1]. Updating equivalence relationships to include allowance for relative biological effectiveness (RBE) is therefore timely. In the same way that the concept of equivalence currently assists in assessing low-LET therapies, it is expected that this will become increasingly relevant in the high-LET domain as these therapies emerge and mature, especially in relation to clinical trials where comparisons will inevitably need to be made with low-LET treatment outcomes. This article does not attempt to provide a clinical evaluation of these equivalence relationships but rather seeks to update the theoretical model by incorporating what is now known about RBE and to discuss some important implications.