Maximizing the biological effect of proton dose delivered with scanned beams via inhomogeneous daily dose distributions

Abstract

Purpose: 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.

Methods: 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.

Results: 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.

Conclusions: 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.

Figure 1

Schematic illustration of beam placement for (a) FTP and (b) STP. The transversal cross section of the planning target volume is outlined in green. Two opposed lateral beams were used: right lateral (RL), and left lateral (LL). Open circles represent the pencil beam spots: red for the RL beam and blue for the LL beam. In (a) FTP, both beams targeted the entire gland. In (b) STP, each beam only targeted the respective proximal hemisphere. As the result of expansion of the scanned volume, the spots from RL and LL beams overlap near the midplane.

Figure 2

Workflow used to generate and evaluate IFD plans.

Figure 3

Schematic illustration of construction of intensity maps for two consecutive fractions delivering IFD, which boosted (a) right and (b) left hemisphere of the prostate. Target contour is shown in white; contours of the bladder and rectum are shown in yellow. Intensities of spots within the rectum or bladder (blue) were not modified. Spots outside of organs at risk were doubled on the proximal side of the target, and suppressed on the distal side. The spots within 10 mm of the plane of splitting were further enhanced by 25%.

Figure 4

IFD distributions of two consecutive fractions for a representative patient case. (a) and (b) m = 1 (FTP-sourced IFD); (c) and (d) m = 0 (STP-sourced IFD). In each fraction both fields are used. The summed dose of two fractions is approximately uniform on the whole target. The contour for PTV1 is shown in white. Contours for OARs are shown in yellow. The colorscales are identical in all three subfigures.

Figure 5

Percentage EUD gain in IFD plans constructed with different mixing factors m (i.e., relative weight of FTP) for a representative patient case. The physical dose of the IFD plans was renormalized to eliminate any increase of rectal or bladder EUD. A range of α/β-values was considered. The solid lines correspond to α/β of 1.5 Gy for GTV, 8 Gy for rectum, and 3 Gy for bladder, and nominal beam range. The shadowed bands correspond to the likely interval of the ΔEUD% due to (a) the uncertainty of α/β (±0.5 Gy for GTV, ±2 Gy for rectum, ±1 Gy for bladder) and (b) range shift (2.5 mm SD).

Figure 6

Dose-volume histograms (DVHs) of the prostate (GTV) for the standard uniform-dose FTP course of 78 Gy in 39 fractions (red), the hypofractionated FTP course of 60 Gy in 20 fractions (green), and the 20-fraction IFD course ($m=\frac{1}{3}$, blue), for a representative patient case. (a) Physical dose; (b) ED2Gy.

Figure 7

LET distributions calculated with Monte Carlo for (a) FTP, (b) STP, and (c) IFD course ($m=\frac{1}{3}$), for a representative patient case. Contours for GTV and PTV1 are shown in white. Contours for OARs are shown in yellow. The colorscales are identical in all three subfigures.

Figure 8

Maximum target EUD gain for 13 patients and the corresponding mixing factor m, (i.e., relative weight of FTP contribution). The physical dose of the IFD plans was renormalized to eliminate any increase of rectal or bladder EUD. The data points corresponding to the three patients treated with endorectal balloon for immobilization are circled.