Interest into the concept of dose (i.e., the energy deposited in a medium by ionizing radiation) began in 1895 following the discovery of x rays [1]. The importance of accurate dose assessment was elevated with the introduction of the medical linear accelerator (LINAC) and the general clinical adoption of external beam radiation therapy, which requires routine dose calibration and quality assessment [2]. To date, several methods have been developed to spatially resolve the dose distribution from therapeutic electron and photon beams for quality-assurance and dosimetry purposes. Of the several available techniques, the most commonly used and widely accepted method relies on using ionization chambers in which the dose to the surrounding medium (conventionally a water volume, because of its similarity in atomic composition to human tissue) is related to the recorded electrical signal [3]. However, the time-consuming raster-scanning point measurement nature of ionization-chamber systems limits measurements to sparsely spaced one- and two-dimensional data. In addition, many correction factors are necessary to account for perturbation of the radiation by the chamber itself, and the measurement resolution is limited by the finite size of the detectors [4].

Alternative modalities to overcome the prohibitive spatial profiling capabilities of ionization chambers have been proposed, including plastic or liquid scintillation and gel dosimetry, in which the number of emitted scintillation photons or a chemical change in a polymer gel is assumed to scale with imparted dose [5–7]. Although the techniques offer several advantages, each requires a material other than water to record the deposited dose, an unfavorable requirement that introduces dosimetric inaccuracies due to differences in material properties. Therefore, there is immediate interest in a simple, fast, high-resolution, and noninvasive modality capable of reconstructing full three-dimensional (3D) dose distributions originating from the native water volume itself.

Here we present a method to recover volumetric dose distributions in pure water by tomographically capturing optical projection images of the induced Čerenkov radiation from a megavoltage x-ray photon LINAC beam using an intensified charge-coupled device (ICCD). Figure 1(a) presents a schematic of the experimental optical dosimetry system. X-ray photons generated by electron bombardment of a target within a medical LINAC form a pulsed radiation beam (5 μs in duration at 180 Hz) and travel downward into a perpendicularly placed water-filled glass tank, where either the primary collimator (capable of providing rectangular shapes) or the multileaf collimator (capable of producing irregular shapes) dictates the cross section of the propagating radiation beam. The two beam configurations used in the current study, field A and field B, were chosen to explore the ability of the modality to reconstruct axisymmetric and asymmetric distributions. The current produced at the target during electron irradiation is converted into a trigger voltage suitable for opening the shutter, which subsequently closes at the end of the pulse. The process repeats iteratively as signal accumulates on the camera (PI-MAX3, 1024i, Princeton Instruments, Acton, Massachusetts).

 

Fig. 1. (a) Experimental schematic of the proposed optical dosimetry system. The telecentric lens captures optical rays emerging from the transparent water tank that are nearly parallel to the optical axis and focuses them onto the ICCD. The two field shapes corresponding to the primary and multileaf collimator are shown in green. (b) Atomic diagram of the radiation transport interactions governing electron energy loss in water. (c) Electron energy loss per unit path length, resulting in local energy deposition and emitted Čerenkov photons as a function of electron energy.

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As each radiation pulse enters the tank, secondary electrons are liberated from water molecules by photon–electron interactions, which then dissipate their energy through electromagnetic interactions with neighboring water molecules [see Fig. 1(b)]. During propagation, a small fraction of each electron’s energy is emitted as optical photons as a result of the Čerenkov effect, which is focused by a peripherally placed telecentric lens (0.06X Gold Series, Edmund Optics, Barrington, New Jersey). Because of the approximate proportionality between the electron energy loss due to ionizing events leading to energy deposition and the energy released in the form of Čerenkov photons [see Fig. 1(c)], the imaged light serves as a surrogate to indirectly determine the imparted dose distribution [i.e., the number of Čerenkov photons captured is directly correlated to the electron energy deposition at any spatial location in the irradiated medium; see [8] for background theory and definitions of equations used to produce Fig. 1(c)].

To demonstrate tomographic reconstruction of 3D dose distributions, images of the induced Čerenkov radiation ($10\mathrm{cm}\times 10\mathrm{cm}$ field of view) from a 6 MeV x-ray photon beam for both field sizes shown in Fig. 1(a) are recorded by rotating the LINAC collimators through an angle ($0°\le \theta \le 180°$ in 2° increments) to provide the telecentric lens with a number of angled projections (91 total). Each projection is acquired by imaging individual pulses over 18 s and processed for noise induced by indirect irradiation of the ICCD using a $5\times 5\mathrm{pixel}$ median filter, resulting in a 1 mm resolution (0.2 mm native image resolution), and total scan time less than 30 min. Once all projections are captured, a sinogram is constructed at each depth, $z$, in the irradiated water volume corresponding to a single row of pixels in each captured projection. Representative sinograms for fields A and B are shown in Figs. 2(a) and 2(d), respectively, at a depth of $z=1.5\mathrm{cm}$. The resulting sinograms are then used to reconstruct two-dimensional (2D) cross sections of the induced light volume using a parallel-beam back-projection algorithm and cosine filter to prevent amplification of high-spatial-frequency noise in the reconstruction. The recovered cross sections for the sinograms in Figs. 2(a) and 2(d) are, respectively, shown in Figs. 2(b) and 2(e). Finally, the full 3D distributions are created by parsing together the 2D reconstructions from each depth.

 

Fig. 2. (a), (d) Sinograms and (b), (e) reconstructed cross sections for fields A and B, respectively. (c), (f) Full 3D reconstructions of fields A and B. The intensity decreases with depth as a result of exponential attenuation of the radiation beam. The full image data sets used to construct (a) and (d) (Media 3 and Media 4), as well as multimedia files for (c) and (f) (Media 1 and Media 2), are included in the supplementary material.

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To examine the accuracy of the proposed system, a well-characterized and known dose profile along the central depth axis (i.e., $x=0\mathrm{cm}$, $y=0\mathrm{cm}$) of field A from the Varian Eclipse treatment-planning system was compared with the experimentally reconstructed distribution based on the captured Čerenkov light. The results are plotted in Fig. 3, where the recovered light profile decays exponentially and is indicative of the known dose at all depths (within $\pm 3\%$) beyond the dose maximum, before which the difference is higher as a result of the large dose gradient. An alternative accuracy metric in the buildup region is the distance to agreement (i.e., shortest distance to equivalence between the two curves), which is less than 1 mm for the curves presented in Fig. 3.

 

Fig. 3. Comparison of the reconstructed central-axis light profile for field A with the known dose profile.

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In contrast to initial reports investigating the capture of a single 2D projection, the results in the present study extend the concept to optical tomography, a significant advancement providing full 3D distributions [8,9]. We introduce a critical innovation by using a telecentric lens to establish a constant magnification at all imaging distances and thereby avoid parallax (i.e., objects closer appear larger, and vice versa), a technique used previously for bubble-chamber photography [10]. By eliminating the perspective error associated with all conventional imaging lenses, true orthographic projections of the imparted 3D light volume suitable for optical tomography are captured. The use of a telecentric lens also provides a novel solution to the main challenge in quantitatively imaging the anisotropic light volume, an issue that was previously resolved using a Monte Carlo derived correction factor, or a fluorophore to convert the anisotropic Čerenkov light to isotropic fluorescence [8,9]. However, by only accepting rays parallel to the optical axis of the detection system, the telecentric lens samples the same solid angle of the anisotropic phase function of Čerenkov emission from each spatial location within the image, inherently providing accurate results (see [8]).

In conclusion, we report full 3D optical tomography of ionizing radiation beams using only the induced Čerenkov radiation in a pure water volume, at a high speed and with a resolution of 1.0 mm per pixel. With the ability to noninvasively interrogate energy deposition of energetic charged particles, the technique could be applied to additional fields utilizing high-energy ionizing radiation.