Simple analytic model for radiotherapeutic X-ray induced acoustic signal as a function of absorption parameters

It is possible to make image reconstruction based on the dose dependence of the therapeutic XA (X-ray induced acoustic signal) amplitude which is then used to make dose mapping. We give further explicit parametrization for the acoustic signal in terms of the absorption parameters based on a physical model of the absorption process. The first step is to obtain pressure waveform due to a point dose absorption by solving the thermo-acoustic equation governing the heat absorption-pressure induction process based on the analytic integration technique. Then, clinically relevant XA signal profile at the detection point is obtained by generalizing point-dose-gradient induced acoustic signal to surface-dose-gradient of a uniform spherical 3D dose distribution based on the reciprocity principle for pressure waves in fluid media. Therapeutic XA signal induced from the surface of the uniform spherical dose distribution due to X-ray irradiation onto $5x5$ $cm^2$ field of the water surface by $1~\mu s$ pulses delivering $1.7$ mGy/pulse is simulated in time and frequency domain. XA waves obtained in previous empirical studies are simulated and compared by means of shape and relative amplitude. Considering the previous studies on this subject, we believe that the significance of this study is the foundation of a novel and self-contained analytic approach to simulate the therapeutic X-ray acoustic waves based on the physical parametrization of the energy transfer process. This not only provides a better understanding of the physical phenomena underlying the medical technique in terms of the medically relevant parameters such as field size, pulse duration, absorbed dose per pulse etc. together with the physical assumptions used to obtain a solution to the photo-acoustic equation, but also brings consistent simulation results with previous experimental and k-Wave results.