Cherenkov emission-based external radiotherapy dosimetry: II. Electron beam quality specification and uncertainties

Abstract

Purpose: Cherenkov emission (CE) is ubiquitous in external radiotherapy. It is also unique in that it carries the promise of 3D, micrometer-resolution, perturbation-free, in-water dosimetry with a beam quality-independent detector response calibration. Our aim is to bring CE-based dosimetry into the clinic and we motivate this here with electron beams. We Monte Carlo (MC) calculate and characterize broad-beam CE-to-dose conversion factors in water for a clinically representative library of electron beam qualities, address beam quality specification and reference depth selection, and develop a preliminary uncertainty budget based on our MC results and relative experimental work of a companion study (Paper I).

Methods: Broad electron beam CE-to-dose conversion factors $k_C^{\theta \pm \delta \theta }$ include CE generated at polar angles θ ± δθ on beam axis in water. With modifications to the EGSnrc code SPRRZnrc, $k_C^{\theta \pm \delta \theta }$ factors are calculated for a total of 20 electron beam qualities from four BEAMnrc models (Varian Clinac 2100C/D, Clinac 21EX, TrueBeam, and Elekta Precise). We examine beam quality, depth, and detection angle dependence for $\theta \pm \delta \theta ={90}^{\circ }\pm {90}^{\circ }$ (4π detection), ${90}^{\circ }\pm 5^{\circ }$ , ${45}^{\circ }\pm {45}^{\circ }$ , and ${90}^{\circ }\pm {45}^{\circ }$ . As discussed in Paper I, 4π detection offers the strongest CE-dose correlation and $\theta ={90}^{\circ }$ with small δθ is most practical. The two additional configurations are considered as a compromise between these two extremes. We address beam quality specification and reference depth selection in terms of the electron beam quality specifier $R_{50}$ , obtained from the depth of 50% CE $C_{50}$ , and derive a best-case uncertainty budget for the CE-based dosimetry formalism proposed in Paper I at each detection configuration.

Results: The $k_C^{\theta \pm \delta \theta }$ factor was demonstrated to capture variations in the beam spectrum, angle, photon contamination, and electron fluence below the CE threshold (∼260 keV in the visible) in accordance with theory. The root-mean-square deviation and maximum deviation of a second-order polynomial fit of simulated $R_{50}$ values in terms of $C_{50}$ were 0.05 and 0.11 mm at 4π and 0.20 and 0.33 mm at ${90}^{\circ }\pm 5^{\circ }$ detection, respectively. The fit performance on experimental data in Paper I was in agreement with these values within experimental uncertainties (±1.5 mm, 95% CI). A two-term power function fit of $k_C^{\theta \pm \delta \theta }$ in terms of $R_{50}$ at a reference depth $d_{\mathrm{ref}}=a{R}_{50}+b$ resulted in total $d_{\mathrm{ref}}$ -dependent dose uncertainty contribution estimate of 0.8% and 1.1% and preliminary best-case estimate of the combined standard dose uncertainty of 1.1% and 1.3% at 4π and ${90}^{\circ }\pm 5^{\circ }$ detection, respectively. The results and corresponding uncertainties with the two intermediate apertures were generally of the same order as the 4π case. In addition, a theoretically consistent downstream shift of the percent-depth CE (PDC) by the difference between $R_{50}$ and $C_{50}$ improved the depth dependence of the 4π conversion by an order of magnitude (±2.8%). Therefore, a large aperture centered on a θ value between ${45}^{\circ }$ and ${90}^{\circ }$ combined with a downstream PDC shift may be recommended for beam-axis CE-based electron beam dosimetry in water.

Conclusions: By delivering $R_{50}$ -based CE-to-dose conversion data and demonstrating the potential for dosimetric uncertainty on the order of 1%, we bring CE-based electron beam dosimetry closer to clinical realization.

Keywords: Cerenkov; Cherenkov; conversion factor; dosimetry; electron beam quality; uncertainty budget.