The unique dose deposition of proton beams generates a distinctive thermoacoustic (protoacoustic) signal, which can be used to calculate the proton range. To identify the expected protoacoustic amplitude, frequency, and arrival time for different proton pulse characteristics encountered at hospital-based proton sources, the protoacoustic pressure emissions generated by 150 MeV, pencil-beam proton pulses were simulated in a homogeneous water medium. Proton pulses with Gaussian widths ranging up to 200 µs were considered. The protoacoustic amplitude, frequency, and time-of-flight (TOF) range accuracy were assessed. For TOF calculations, the acoustic pulse arrival time was determined based on multiple features of the wave.

Based on the simulations, Gaussian proton pulses can be categorized as Dirac-delta-function-like (FWHM  < 4µs) and longer. For the δ-function-like irradiation, the protoacoustic spectrum peaks at 44.5 kHz and the systematic error in determining the Bragg peak range is  <2.6 mm. For longer proton pulses, the spectrum shifts to lower frequencies, and the range calculation systematic error increases (≤23 mm for FWHM of 56 µs). By mapping the protoacoustic peak arrival time to range with simulations, the residual error can be reduced. Using a proton pulse with FWHM  =  2 µs results in a maximum signal-to-noise ratio per total dose. Simulations predict that a 300 nA, 150 MeV, FWHM  =  4 µs Gaussian proton pulse (8.0  ×  10⁶ protons, 3.1 cGy dose at the Bragg peak) will generate a 146 mPa pressure wave at 5 cm beyond the Bragg peak.

There is an angle dependent systematic error in the protoacoustic TOF range calculations. Placing detectors along the proton beam axis and beyond the Bragg peak minimizes this error. For clinical proton beams, protoacoustic detectors should be sensitive to  <400 kHz (for  −20 dB). Hospital-based synchrocyclotrons and cyclotrons are promising sources of proton pulses for generating clinically measurable protoacoustic emissions.

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