Is the dose-averaged LET a reliable predictor for the relative biological effectiveness?

PURPOSE

The dose-averaged linear energy transfer (LET ) is frequently used as representative quantity for the biological effectiveness of a radiation field. Moreover, relative biological effectiveness (RBE) values measured or calculated in mixed radiation fields are typically plotted vs the LET . In this study, we will investigate whether the LET is an appropriate quantity to describe the RBE of any mixed radiation field of protons and heavier ions and discuss potential limitations.

METHODS

To study the reliability of LET , we investigate model predictions of RBE in monoenergetic beams under track segment conditions and pristine Bragg peaks as well as spread out Bragg peaks (SOBP) in water. Both, the pristine Bragg peaks and the SOBPs are regarded as mixed radiation fields in this analysis, that is, they are characterized by a certain width of the energy spectrum of the projectile, although the underlying energy distribution is much broader in the case of an SOBP as compared to a pristine peak. For both cases, the corresponding RBE values are compared to those of strictly monoenergetic particles under track segment conditions, characterized by a single LET value. For the planning we use the treatment planning software TRiP98 together with the Local Effect Model to predict the RBE of protons, helium, and carbon ions. We further compare our model predictions for protons with a simplistic linear RBE-LET relationship representative for the phenomenological models in literature.

RESULTS

Regarding pristine Bragg peaks in water, the deviations in RBE compared to monoenergetic particles under track segment conditions for the same LET value are low (mostly 0-5%), except for the distal fall-off region. The situation changes in SOBPs for which we found deviations in the order of up to 25% for the lighter particles and even more pronounced deviations for heavier particles like carbon ions.

CONCLUSIONS

The analysis showed that LET is a sufficiently accurate predictor for RBE only in regions with comparably narrow, but not in regions with broad, LET distribution as in a single SOBP or in multiple overlapping fields. The deviations are caused by the nonlinearity of the RBE(LET) relationship in the case of track segment conditions. Thus, independent of the underlying RBE model and the particle type regarded, as long as the RBE(LET) relationship deviates from being purely linear, LET is not a good predictor for RBE, and especially for heavier particles like carbon ions knowledge of the underlying LET distribution is mandatory to describe the RBE in mixed radiation fields.