Optimizing a three-stage Compton camera for measuring prompt gamma rays emitted during proton radiotherapy

Abstract

In this work, we investigate the use of a three-stage Compton camera to measure secondary prompt gamma rays emitted from patients treated with proton beam radiotherapy. The purpose of this study was (1) to develop an optimal three-stage Compton camera specifically designed to measure prompt gamma rays emitted from tissue and (2) to determine the feasibility of using this optimized Compton camera design to measure and image prompt gamma rays emitted during proton beam irradiation. The three-stage Compton camera was modeled in Geant4 as three high-purity germanium detector stages arranged in parallel-plane geometry. Initially, an isotropic gamma source ranging from 0 to 15 MeV was used to determine lateral width and thickness of the detector stages that provided the optimal detection efficiency. Then, the gamma source was replaced by a proton beam irradiating a tissue phantom to calculate the overall efficiency of the optimized camera for detecting emitted prompt gammas. The overall calculated efficiencies varied from ∼ 10(-6) to 10(-3) prompt gammas detected per proton incident on the tissue phantom for several variations of the optimal camera design studied. Based on the overall efficiency results, we believe it feasible that a three-stage Compton camera could detect a sufficient number of prompt gammas to allow measurement and imaging of prompt gamma emission during proton radiotherapy.

Figure 1

Diagram of the 3-stage Compton camera setup in parallel-plane geometry showing (on left) the Compton scatter angles (θ₁, θ₂) and the gamma ray energy (E₀, E₁, E₂) as it travels through the detectors (D1, D2, D3), as well as the projected cone used to reconstruct the images. On the right, an identical Compton camera setup with the prompt gamma originating from a proton beam irradiating a tissue phantom producing a prompt gamma ray that subsequently interacts in the Compton camera with the interaction position and energy deposition in each detector shown.

Figure 2

Transport efficiencies for all three detector stages, D1 (•), D2 (∇) and D3 (■) as a function of their respective widths at initial gamma energy of 6.13 MeV. The D1 transport efficiency is the percentage of prompt gammas that enter D1, shown with a data fit (dashed line) using the solid angle equation (5) at a distance of 15 cm from the source. The calculated transport efficiencies were found to be independent of thickness for all three detector stages. Therefore an arbitrary thickness of 3 cm was set for all three stages.

Figure 3

(a) The interaction efficiencies (solid symbols) and transport efficiencies (empty symbols) for all three detector stages, D1 (circles), D2 (triangles) and D3 (squares) as a function of their respective thicknesses at initial gamma energy of 6.13 MeV. (b) The product of $e_i^1\cdot e_t^{12}$ (•) and $e_i^2\cdot e_t^{23}$ (∇) as function of detector thickness at initial gamma energy of 6.13 MeV. The detector width for each stage was set to a ‘practical’ value of 10 cm.

Figure 4

Percent change in the overall efficiency of the optimized three-stage detector with adjusting the distance between the detectors stages, with three different scenarios. First, varying the gap between D1 and D2 while holding the D2–D3 gap constant (•). Second, holding the D1–D2 gap constant while adjusting the D2–D3 gap (∇). Lastly, changing both the D1–D2 inter-detector gap and the D2–D3 gap (■).

Figure 5

Overall efficiency results from the isotropic gamma source for energies 0–15 MeV including the characteristic prompt gamma peaks (symbols) of 2.31, 4.44 and 6.13 MeV. Five detector configurations are shown: the practical detector, 3 × 10, 3 × 10, 10 × 10 cm (•), 3 × 20, 3 × 20, 10 × 20 cm (∇); 3 × 50, 3 × 50, 10 × 50 cm (▲); 3 × 10, 3 × 100, 10 × 100 cm (■); 3 × 100, 3 × 100, 10 × 100 cm (◇).

Figure 6

Overall efficiency results (left axis) for detection of prompt gammas produced during proton irradiation from 50 to 250 MeV for the four detector configurations: 3 × 10, 3 × 10, 10 × cm (•); 3 × 20, 3 × 20, 10 × 20 cm (∇); 3 × 10, 3 × 100, 10 × 100 cm (■); 3 × 100, 3 × 100, 10 × 100 cm (◇). On the right axis is the estimated triple scatter events detected for a typical proton treatment beam delivery of 4 × 10¹¹ protons entering the patient.