Analytical modeling of depth-dose degradation in heterogeneous lung tissue for intensity-modulated proton therapy planning

Abstract

Background and purpose: Proton therapy may be promising for treating non-small-cell lung cancer due to lower doses to the lung and heart, as compared to photon therapy. A reported challenge is degradation, i.e., a smoothing of the depth-dose distribution due to heterogeneous lung tissue. For pencil beams, this causes a distal falloff widening and a peak-to-plateau ratio decrease, not considered in clinical treatment planning systems.

Materials and methods: We present a degradation model implemented into an analytical dose calculation, fully integrated into a treatment planning workflow. Degradation effects were investigated on target dose, distal dose falloffs, and mean lung dose for ten patient cases with varying anatomical characteristics.

Results: For patients with pronounced range straggling (in our study large tumors, or lesions close to the mediastinum), degradation effects were restricted to a maximum decrease in target coverage (D ₉₅ of the planning target volume) of 1.4%. The median broadening of the distal 80-20% dose falloffs was 0.5 mm at the maximum. For small target volumes deep inside lung tissue, however, the target underdose increased considerably by up to 26%. The mean lung dose was not negatively affected by degradation in any of the investigated cases.

Conclusion: For most cases, dose degradation due to heterogeneous lung tissue did not yield critical organ at risk overdosing or overall target underdosing. However, for small and deep-seated tumors which can only be reached by penetrating lung tissue, we have seen substantial local underdose, which deserves further investigation, also considering other prevalent sources of uncertainty.

Keywords: Bragg peak degradation; Depth-dose degradation; Heterogeneous lung tissue; Non-small-cell lung carcinoma; Proton therapy; Radiotherapy planning.

Fig. 1

Model validation. Integrated pristine depth-dose curves for pure water (right peak) and integrated degraded depth-dose curves (left peak) were measured, Monte Carlo (MC)–simulated, and calculated with matRad. The degraded curves were obtained behind a 30 mm-thick lung phantom (Gammex lung 455, Sun Nuclear Corporation, serial no. 45564732). The proton energy was 108.88 MeV. The pristine and degraded depth doses were normalized to the area under the curve for energy conservation.

Fig. 2

Two-dimensional dose distribution of patient S06 for homogeneous lung tissue (a) and corresponding dose difference distribution by introducing heterogeneity correction (b). In (b), the blue areas indicate volumes that received lower doses with heterogeneity correction than without. The prescribed dose was 11 Gy (RBE) with the use of three coplanar treatment field orientations (gantry at 40°, 300°, and 340°; couch at 0°).

Fig. 3

Dose-volume histograms of patients S08 (a) and S06 (b, c). Histograms for homogeneous lung tissues are indicated by solid lines and histograms for heterogeneous lung tissues by dotted lines. (c) Hot spots in target dose decreased upon heterogeneity correction.

Fig. 4

(a) Distal falloff values, z_80-20, of heterogeneous and homogeneous lung tissue, and their difference, Δz_80-20. The phantom setup was a proton beam impinging on a 30 mm-thick water-equivalent chest wall, a lung-phantom slab (relative electron density 0.30 and variable geometrical distance, z_geo), and a water-equivalent cubic target with an edge length of 80 mm. The plans were optimized for homogeneous lung tissue and recalculated with heterogeneity correction on. The mean and standard deviation values of more than 1500 rays are shown. The connection lines are for visual guidance only. (b, c) Different optimizations of the distal end of a spread-out Bragg peak (SOPB). Colored solid lines represent the single Bragg peaks composing the integrated depth dose of the SOBP. A high weight on the highest-energy Bragg peak leads to a steep pristine dose falloff (b), more similar weights on all single Bragg peaks lead to a wider pristine dose falloff (c).