An analysis of beam parameters on proton-acoustic waves through an analytic approach

It has been reported that acoustic waves are generated when a high-energy pulsed proton beam is deposited in a small volume within tissue. One possible application of proton-induced acoustics is to get real-time feedback for intra-treatment adjustments by monitoring such acoustic waves. A high spatial resolution in ultrasound imaging may reduce proton range uncertainty. Thus, it is crucial to understand the dependence of the acoustic waves on the proton beam characteristics. In this manuscript, firstly, an analytic solution for the proton-induced acoustic wave is presented to reveal the dependence of the signal on the beam parameters; then it is combined with an analytic approximation of the Bragg curve. The influence of the beam energy, pulse duration and beam diameter variation on the acoustic waveform are investigated. Further analysis is performed regarding the Fourier decomposition of the proton-acoustic signals. Our results show that the smaller spill time of the proton beam upsurges the amplitude of the acoustic wave for a constant number of protons, which is hence beneficial for dose monitoring. The increase in the energy of each individual proton in the beam leads to the spatial broadening of the Bragg curve, which also yields acoustic waves of greater amplitude. The pulse duration and the beam width of the proton beam do not affect the central frequency of the acoustic wave, but they change the amplitude of the spectral components.