PHSOR05 Presentation Time: 12:50 PM: The Effect of Quantum Noise on a Novel Multilateration-Based Brachytherapy Source Localization Approach

Abstract

<h3>Purpose</h3> Multilateration, a mathematical technique for localizing a point source in 3D based on measurements related to its location, can be adapted to single-source (i.e. high-dose-rate or pulsed-dose-rate) brachytherapy applications using measurement information provided by particle detector camera(s). Multilateration could be used as a safety measure to locate and monitor the source position, or as an enabler of novel applications such as reconstruction of the delivered radiation dose. However, the accuracy of this method is limited by quantum noise, a dominant source of noise in planar images from photon-counting systems. This work studies the impact of quantum noise on the accuracy of multilateration for a variety of source strengths, source positions, and photon-counting camera system setups. <h3>Materials and Methods</h3> The effect of quantum noise on the accuracy of multilateration was examined systematically for a variety of source strengths, source positions, and camera system set-ups. Quantum noise was simulated by sampling from the Poisson distribution at each image pixel, with the distribution means based on the expected image flux per pixel derived from physics principles. Source strength was fixed at 40700 U (10 Ci), and acquisition times varied from 0.03 s, chosen to represent real-time planar image acquisition at 30 frames/sec, to 10 s. Image size varied from 32 × 32 pixels² to 256 × 256 pixels², and pixel size varied from 0.05 × 0.05 mm² to 5 × 5 mm². Source-to-camera distances (SCD) varied from 100 mm to 1000 mm, and off-axis displacement varied from 0 mm to 100 mm. These parameter ranges were used to perform multilateration on simulated single- and dual-camera system acquisitions, with further optimization of the dual-camera systems for camera-to-camera orientation and spacing. To improve consistency, each configuration was simulated using different random number generator seeds for quantum noise generation, and the resulting errors were averaged. <h3>Results</h3> The effect of quantum noise on multilateration accuracy depended on source strength, acquisition time, SCD, off-axis displacement, and camera system set-up. Figure 1 shows the achievable resolution as a function of SCD for acquisition times of 0.03, 0.1, 1, and 10 s, recorded with a single-camera with 256 × 256 pixels² (0.5 × 0.5 mm² pixel size), with errors averaged across the range of off-axis displacements. At large SCDs, simulated multilateration accuracy was approximately a cubic function of SCD, which agrees with the results of error propagation theory applied to this system. At SCDs up to 1000 mm, single-camera systems produced sub-mm precision in some realistic acquisition parameter ranges, and dual-camera systems had greater source positioning accuracy. The improvement due to the addition of a second camera was smaller when the source was close to the central axis of the first camera, and the improvement's magnitude depended on the camera system setup. For systems with camera sizes of 256 × 256 pixels² (0.5 × 0.5 mm² pixel size), the second camera improved the accuracy by about 7% on-axis and about 15% off-axis, averaging over the range of simulated SCDs. There was a tradeoff between reducing quantum noise and decreasing intra-pixel averaging which discouraged very small or very large pixel sizes. <h3>Conclusions</h3> Multilateration has the potential to provide sub-mm precision for source localization in single-source brachytherapy, even with the limits imposed by quantum noise. This technique could be implemented for general safety measures and for applications such as dose reconstruction. We note that this analysis was strictly intended for photon-counting systems, where quantum noise was the dominant source of planar image noise. The results may help evaluate existing cameras and guide future camera system set-up for multilateration applications, a subject of our future study.