On the robustness of multilateration of ionoacoustic signals for localization of the Bragg peak at pre-clinical proton beam energies in water

The energy deposited in a medium by a pulsed proton beam results in the emission of thermoacoustic waves, also called ionoacoustics (IA). The proton beam stopping position (Bragg peak) can be retrieved from a time-of-flight analysis (ToF) of IA signals acquired at different sensor locations (multilateration). This work aimed to assess the robustness of multilateration methods in proton beams at pre-clinical energies for the development of a small animal irradiator. The accuracy of multilateration performed using different algorithms; namely, time of arrival and time difference of arrival, was investigated for ideal point sources in the presence of realistic uncertainties on the ToF estimation and ionoacoustic signals generated by a 20 MeV pulsed proton beam stopped in a homogeneous water phantom. The localisation accuracy was further investigated experimentally based on two different measurements with pulsed monoenergetic proton beams at energies of 20 and 22 MeV. It was found that the localisation accuracy mainly depends on the position of the acoustic detectors relative to the proton beam due to spatial variation of the error on the ToF estimation. By optimally positioning the sensors to reduce the ToF error, the Bragg peak could be located with an accuracy better than 90 m (2% error). Localisation errors going up to 1 mm were observed experimentally due to inaccurate knowledge of the sensor positions and noisy ionoacoustic signals. This study gives a first overview of the implementation of different multilateration methods for ionoacoustics-based Bragg peak localisation in two- and three-dimensions at pre-clinical energies. Different sources of uncertainty were investigated, and their impact on the localisation accuracy was quantified and experimentally.