^{1,a)}, Scott C. Davis

^{1}, David M. McClatchy

^{1}, Rongxiao Zhang

^{2}, Brian W. Pogue

^{3,a)}and David J. Gladstone

^{4}

### Abstract

**Purpose:**

A novel technique for beam profiling of megavoltage photon beams was investigated for the first time by capturing images of the induced Čerenkov emission in water, as a potential surrogate for the imparted dose in irradiated media.

**Methods:**

A high-sensitivity, intensified CCD camera (ICCD) was configured to acquire 2D projection images of Čerenkov emission from a 4 × 4 cm^{2} 6 MV linear accelerator (LINAC) x-ray photon beam operating at a dose rate of 400 MU/min incident on a water tank with transparent walls. The ICCD acquisition was gated to the LINAC sync pulse to reduce background light artifacts, and the measurement quality was investigated by evaluating the signal to noise ratio and measurement repeatability as a function of delivered dose. Monte Carlo simulations were used to derive a calibration factor for differences between the optical images and deposited dose arising from the anisotropic angular dependence of Čerenkov emission. Finally, Čerenkov-based beam profiles were compared to a percent depth dose (PDD) and lateral dose profile at a depth of *d* _{ max } from a reference dose distribution generated from the clinical Varian ECLIPSE treatment planning system (TPS).

**Results:**

The signal to noise ratio was found to be 20 at a delivered dose of 66.6 cGy, and proportional to the square root of the delivered dose as expected from Poisson photon counting statistics. A 2.1% mean standard deviation and 5.6% maximum variation in successive measurements were observed, and the Monte Carlo derived calibration factor resulted in Čerenkov emission images which were directly correlated to deposited dose, with some spatial issues. The dose difference between the TPS and PDD predicted by Čerenkov measurements was within 20% in the buildup region with a distance to agreement (DTA) of 1.5–2 mm and ±3% at depths beyond*d* _{ max }. In the lateral profile, the dose difference at the beam penumbra was within ±13% with a DTA of 0–2 mm, ±5% in the central beam region, and 2%–3% in the beam umbra.

**Conclusions:**

The results from this initial study demonstrate the first documented use of Čerenkov emission imaging to profile x-ray photon LINAC beams in water. The proposed modality has several potential advantages over alternative methods, and upon future refinement may prove to be a robust and novel dosimetry method.

This work has been funded by National Institutes of Health (NIH) Grant Nos. RO1CA120368 and PO1CA084203.

I. INTRODUCTION

II. THEORY

III. MATERIALS AND METHODS

III.A. Experimental setup

III.B. Image processing

III.C. Monte Carlo simulations of Čerenkov emission angular distributions

III.D. Calibration factor determination

III.E. Imagecalibration

III.F. Signal to noise ratio (S/N)

III.G. Measurement variability

III.H. Percent depth dose (PDD) and lateral dose profile comparison

III.I. Reference dose distribution

IV. RESULTS

IV.A. Monte Carlo simulations of Čerenkov emission angular distributions

IV.B. Calibration factor determination

IV.C. Signal to noise ratio

IV.D. Measurement variability

IV.E. Percent depth and lateral dose profile comparison

V. DISCUSSION

VI. CONCLUSIONS

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## Figures

In (a) the Čerenkov angle, ζ, (b) collisional and Čerenkov emission energy losses per unit path length, and (c) CSDA range for an electron traveling through water, tissue, and polystyrene plastic are plotted as a function of particle energy.

In (a) the Čerenkov angle, ζ, (b) collisional and Čerenkov emission energy losses per unit path length, and (c) CSDA range for an electron traveling through water, tissue, and polystyrene plastic are plotted as a function of particle energy.

A side view of the system is shown in (a) with the radiation beam vertically entering the tank and inducing Čerenkov light emission, which is captured by a camera placed at an imaging distance L = 45 cm from beam center. The definition of the polar angle of emission θ is shown with respect to the camera field of view. In (b) an aerial view of the system is shown, with the corresponding definition of the azimuthal angle of emission ϕ.

A side view of the system is shown in (a) with the radiation beam vertically entering the tank and inducing Čerenkov light emission, which is captured by a camera placed at an imaging distance L = 45 cm from beam center. The definition of the polar angle of emission θ is shown with respect to the camera field of view. In (b) an aerial view of the system is shown, with the corresponding definition of the azimuthal angle of emission ϕ.

In (a)–(c), the Monte Carlo derived histograms of Čerenkov emission, *P*(*x*, ϕ), for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam. The histograms of Čerenkov emission, *P*(θ, *z*), for all three field sizes are shown in (d)–(f).

In (a)–(c), the Monte Carlo derived histograms of Čerenkov emission, *P*(*x*, ϕ), for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam. The histograms of Čerenkov emission, *P*(θ, *z*), for all three field sizes are shown in (d)–(f).

In (a) the Monte Carlo derived phase function, *P*(*z*, θ), for Čerenkov emission from a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at depths of *z* = *d* _{ max }, 10, 20, 30, and 40 cm. In (b) the normalized phase functions from (a) in comparison to the normalized phase function in the buildup region at *z* = 0.2 cm for all three field sizes is plotted.

In (a) the Monte Carlo derived phase function, *P*(*z*, θ), for Čerenkov emission from a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at depths of *z* = *d* _{ max }, 10, 20, 30, and 40 cm. In (b) the normalized phase functions from (a) in comparison to the normalized phase function in the buildup region at *z* = 0.2 cm for all three field sizes is plotted.

In (a)–(c) the Monte Carlo derived Čerenkov emission light profiles, *P*(θ_{ lens }, *z*), as a function of depth for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at imaging distances of L = 45, 100, and 150 cm. In (d)–(f) lateral light profiles, *P*(*x*, ϕ_{ lens }), for the same three field sizes and imaging distances. The solid lines denote the total light (i.e., angularly integrated emission profiles), expected to be a surrogate for the deposited dose in the medium.

In (a)–(c) the Monte Carlo derived Čerenkov emission light profiles, *P*(θ_{ lens }, *z*), as a function of depth for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at imaging distances of L = 45, 100, and 150 cm. In (d)–(f) lateral light profiles, *P*(*x*, ϕ_{ lens }), for the same three field sizes and imaging distances. The solid lines denote the total light (i.e., angularly integrated emission profiles), expected to be a surrogate for the deposited dose in the medium.

In (a)–(c) the horizontal calibration factor, *C*(*x*), is plotted for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at imaging distances of L = 45, 100, and 150 cm. In (b) the vertical calibration factor, *C*(*z*), for all three field sizes at each imaging distance is plotted.

In (a)–(c) the horizontal calibration factor, *C*(*x*), is plotted for a 4 × 4, 10 × 10, and 20 × 20 cm^{2} 6 MV beam at imaging distances of L = 45, 100, and 150 cm. In (b) the vertical calibration factor, *C*(*z*), for all three field sizes at each imaging distance is plotted.

In (a)–(j) the full resolution captured images of a 10 × 10 cm^{2} FOV for a 4 × 4 cm^{2} 6 MV beam after temporal median filtering of a various number of frames denoted by the numbers in the bottom right of each image. The scale bar in the bottom left of each image corresponds to 1 cm.

In (a)–(j) the full resolution captured images of a 10 × 10 cm^{2} FOV for a 4 × 4 cm^{2} 6 MV beam after temporal median filtering of a various number of frames denoted by the numbers in the bottom right of each image. The scale bar in the bottom left of each image corresponds to 1 cm.

The signal to noise ratio as a function of delivered dose is plotted for a 4 × 4 cm^{2} 6 MV beam. The corresponding coefficient values after regression to a square root power law are shown.

The signal to noise ratio as a function of delivered dose is plotted for a 4 × 4 cm^{2} 6 MV beam. The corresponding coefficient values after regression to a square root power law are shown.

In (a) the PDD from the TPS and Čerenkov emission light profile before and after correction are plotted. The corresponding dose difference as a function of depth between the TPS and corrected signal is shown in (b). In (c) the lateral profile comparison between the TPS and corrected and uncorrected light profiles at a depth of *d* _{ max } is shown. The corresponding dose difference is shown in (d).

In (a) the PDD from the TPS and Čerenkov emission light profile before and after correction are plotted. The corresponding dose difference as a function of depth between the TPS and corrected signal is shown in (b). In (c) the lateral profile comparison between the TPS and corrected and uncorrected light profiles at a depth of *d* _{ max } is shown. The corresponding dose difference is shown in (d).

## Tables

Relevant optical parameters of Čerenkov emission in water, tissue, and polystyrene plastic.

Relevant optical parameters of Čerenkov emission in water, tissue, and polystyrene plastic.

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