  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.
