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It is possible to make image reconstruction based on the dose dependence ofthe therapeutic XA (X-ray induced acoustic signal) amplitude which is then usedto make dose mapping. We give further explicit parametrization for the acousticsignal in terms of the absorption parameters based on a physical model of theabsorption process. The first step is to obtain pressure waveform due to apoint dose absorption by solving the thermo-acoustic equation governing theheat absorption-pressure induction process based on the analytic integrationtechnique. Then, clinically relevant XA signal profile at the detection pointis obtained by generalizing point-dose-gradient induced acoustic signal tosurface-dose-gradient of a uniform spherical 3D dose distribution based on thereciprocity principle for pressure waves in fluid media. Therapeutic XA signalinduced from the surface of the uniform spherical dose distribution due toX-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. XAwaves obtained in previous empirical studies are simulated and compared bymeans of shape and relative amplitude. Considering the previous studies on thissubject, we believe that the significance of this study is the foundation of anovel and self-contained analytic approach to simulate the therapeutic X-rayacoustic waves based on the physical parametrization of the energy transferprocess. This not only provides a better understanding of the physicalphenomena underlying the medical technique in terms of the medically relevantparameters such as field size, pulse duration, absorbed dose per pulse etc.together with the physical assumptions used to obtain a solution to thephoto-acoustic equation, but also brings consistent simulation results withprevious experimental and k-Wave results.

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