Modelling of RBE differences in selected points within similar spread-out Bragg-peaks (SOBP) placed at superficial and deep water phantom locations in passively scattered beams but not in scanned pencil beams: A hypothesis.

Purpose: To model relative biological effectiveness (RBE) differences found in two studies which used spread-out Bragg-peaks (SOBP) placed at (a) superficial depth and (b) at the maximum range depth. For pencil beam scanning (PBS), RBE at similar points within the SOBP did not change between the two extreme SOBP placement depths; in passively scattered beams (PSB), high RBE values (typically 1.2-1.3) were found within superficially- placed SOBP but reduced to lower values (1-1.07) at similar points within the extreme-depth positioned SOBP. The dose, LET (linear energy transfer) distributions along each SOBP were closely comparable regardless of placement depth, but significant changes in dose rate occurred with depth in the PSB beam.

Methods: The equations used allow α and β changes with falling dose rate (the converse to FLASH studies) in PSB, resulting in reduced α/β ratios, compatible with a reduction in micro-volumetric energy transfer (the product of Fluence and LET), with commensurate reductions in RBE. The experimental depth-distances, positions within SOBP, observed dose-rates and radiosensitivity ratios were used to estimate the changes in RBE.

Results: RBE values within a 5 % tolerance limit of the experimental results for PSB were found at the deepest SOBP placement. No RBE changes were predicted for PBS beams, as in the published results.

Conclusions: Enhanced proton therapy toxicity might occur with PBS when compared with PSB for deeply positioned SOBP due to the maintenance of higher RBE. Scanned pencil beam users need to be vigilant about RBE and further research is indicated.