ABSTRACT: Biological effect of radiation can be enhanced with hypofractionation, localized dose escalation, and, in particle therapy, with optimized distribution of linear energy transfer (LET). The authors describe a method to construct inhomogeneous fractional dose (IFD) distributions, and evaluate the potential gain in the therapeutic effect from their delivery in proton therapy delivered by pencil beam scanning.For 13 cases of prostate cancer, the authors considered hypofractionated courses of 60 Gy delivered in 20 fractions. (All doses denoted in Gy include the proton's mean relative biological effectiveness (RBE) of 1.1.) Two types of plans were optimized using two opposed lateral beams to deliver a uniform dose of 3 Gy per fraction to the target by scanning: (1) in conventional full-target plans (FTP), each beam irradiated the entire gland, (2) in split-target plans (STP), beams irradiated only the respective proximal hemispheres (prostate split sagittally). Inverse planning yielded intensity maps, in which discrete position control points of the scanned beam (spots) were assigned optimized intensity values. FTP plans preferentially required a higher intensity of spots in the distal part of the target, while STP, by design, employed proximal spots. To evaluate the utility of IFD delivery, IFD plans were generated by rearranging the spot intensities from FTP or STP intensity maps, separately as well as combined using a variety of mixing weights. IFD courses were designed so that, in alternating fractions, one of the hemispheres of the prostate would receive a dose boost and the other receive a lower dose, while the total physical dose from the IFD course was roughly uniform across the prostate. IFD plans were normalized so that the equivalent uniform dose (EUD) of rectum and bladder did not increase, compared to the baseline FTP plan, which irradiated the prostate uniformly in every fraction. An EUD-based model was then applied to estimate tumor control probability (TCP) and normal tissue complication probability (NTCP). To assess potential local RBE variations, LET distributions were calculated with Monte Carlo, and compared for different plans. The results were assessed in terms of their sensitivity to uncertainties in model parameters and delivery.IFD courses included equal number of fractions boosting either hemisphere, thus, the combined physical dose was close to uniform throughout the prostate. However, for the entire course, the prostate EUD in IFD was higher than in conventional FTP by up to 14%, corresponding to the estimated increase in TCP to 96% from 88%. The extent of gain depended on the mixing factor, i.e., relative weights used to combine FTP and STP spot weights. Increased weighting of STP typically yielded a higher target EUD, but also led to increased sensitivity of dose to variations in the proton's range. Rectal and bladder EUD were same or lower (per normalization), and the NTCP for both remained below 1%. The LET distributions in IFD also depended strongly on the mixing weights: plans using higher weight of STP spots yielded higher LET, indicating a potentially higher local RBE.In proton therapy delivered by pencil beam scanning, improved therapeutic outcome can potentially be expected with delivery of IFD distributions, while administering the prescribed quasi-uniform dose to the target over the entire course. The biological effectiveness of IFD may be further enhanced by optimizing the LET distributions. IFD distributions are characterized by a dose gradient located in proximity of the prostate's midplane, thus, the fidelity of delivery would depend crucially on the precision with which the proton range could be controlled.
