Modelling of a double-scattering proton therapy nozzle using the FLUKA Monte Carlo code and analysis of linear energy transfer in patients treated for prostate cancer

Abstract

Background: The dose-averaged linear energy transfer (LET_D) in proton therapy (PT) has in pre-clinical studies been linked to the relative biological effectiveness (RBE) of protons. Until recently, the most common PT delivery method in prostate cancer has been double-scattered PT, with LET_D only available through dedicated Monte Carlo (MC) simulations. However, as most studies of the relationship between LET_D and RBE in double scattered PT have been focused on the head and neck region, existing MC implementations have not been capable of calculating LET_D for the longer field ranges used, for example, in the pelvic region.

Purpose: The initial aim of this study was to implement a MC code allowing for LET_D calculations in double-scattered PT of prostate cancer. Additionally, we explored LET_D profiles and LET_D as a function of field configuration, by performing MC calculations for a large prostate cancer cohort treated with double-scattered PT.

Methods: The components of a passive scattered clinical treatment nozzle used for delivery of extended field ranges, with two associated modulation wheels, were implemented into an existing FLUKA MC framework for LET_D calculations. The code was validated to spread out Bragg peak (SOBP) measurements conducted using the treatment nozzle with 11 different range and modulation width configurations. After validation, LET_D distributions were calculated on the planning computed tomographies of 582 prostate cancer patients treated with two-field double-scattered PT. All patients had symmetric field configurations with respect to the sagittal plane, with one pair of posterior oblique, lateral opposing, or anterior oblique fields. Dose and LET_D volume parameters and the mean LET_D ratio between the bladder and rectum were compared across the three groups.

Results: The range differences were below 1 mm for all SOBP scenarios used for calibration. For 9 of 11 SOBP scenarios, the modulation width differences were below 2 mm. For the patient simulations, the mean gamma pass rates (3 mm/3%) were at least 98% in the PTV, bladder, and rectum. Comparing anterior to posterior field configurations, the mean LET_D in the bladder increased within both the 10 and 70 Gy iso-dose regions, and conversely, the mean LET_D decreased for the rectum. There was a marked difference in the mean bladder-to-rectum LET_D ratios between anterior oblique, lateral opposing and posterior oblique field configurations.

Conclusion: A MC code allowing for accurate calculations of dose and LET_D in double-scattered PT of prostate cancer was implemented and validated. The LET_D distributions in the rectum and bladder showed a systematic dependence on the field configuration.

Keywords: FLUKA; Monte Carlo; linear energy transfer; prostate cancer; proton therapy.

FIGURE 1

Sketch of the double scattering proton therapy treatment nozzle. Distances and sizes are not to scale. The second ionization chamber and the field mirror are not visualised. The proton beam is traversing from left to right and shown as the red line.

FIGURE 2

Top‐panel: Absolute differences in modulation widths (MW) between FLUKA MC simulations and measurements as a function of MC simulation zero‐angle for range‐modulation wheel 1. Note the dashed green line indicating a difference of 2 mm. Bottom panel: Range differences between FLUKA MC simulations and measurements as a function of MC simulation zero‐angle for range‐modulation wheel 1. The difference is calculated as the FLUKA MC range subtracted from the measured range and the dashed green lines indicate plus and minus 1 mm range. The requested ranges and modulation widths are written as RxxxxMyyyy, where xxxx is the range in 10⁻¹ mm and yyyy is the modulation width in 10⁻¹ mm.

FIGURE 3

Dose depth curves for all measured and simulated SOBPs using range modulation wheel 1. The dashed blue lines represent the FLUKA MC calculated dose, and the red line represents measurements. The dashed vertical lines represent the D90% ranges (proximal and distal) for FLUKA MC (green) and measurements (orange). The requested ranges and modulation widths are written as RxxxxMyyyy in the upper left corners, where xxxx is the range in 10⁻¹ mm and yyyy is the modulation width in 10⁻¹ mm.

FIGURE 4

Dose, LET_D, and dose with LET_D > 4 keV/um distributions for three patients, shown in the central axial plane of the prostate. Contours are, from the bottom to the top of each picture, rectum, CTV, and bladder (if present). Only voxels receiving more than 2 Gy are colourised. Top row: Patient treated with anterior oblique fields (82/278). Middle row: Patient treated with lateral opposing beams (90/270). Bottom row: Patient treated with posterior oblique fields (98/262).

FIGURE 5

Boxplots of mean LET_D above two dose thresholds in the rectum (orange) and bladder (blue) for patients treated with symmetric anterior oblique, lateral opposing or symmetric posterior oblique fields. The dose thresholds used were 10 and 70 Gy in the left and right panel, respectively. The posterior oblique group accounts for 74 patients, while the lateral opposing and anterior oblique groups contain 37 and 471 patients, respectively.

FIGURE 6

Ratio of $\overline{{\mathrm{LET}}_D}(D_T)$ between bladder and rectum for all patients, grouped into anterior oblique, lateral opposing, and posterior oblique fields scattering (blue, green, and red, respectively). The shaded regions represent the 95% confidence interval in each patient group and the solid lines represent the mean. The black, dashed line represents a ratio of 1, indicating an equal ratio. There are 471 patients in the anterior oblique group, 74 in the posterior oblique group, and 37 in the lateral opposing group.