Fast, tissue-realistic models of photoacoustic wave propagation for homogeneous attenuating media

Photoacoustic tomography is an emerging medical imaging modality based on the reconstruction of an initial internal pressure distribution from surface measurements of photoacoustic wave pulses over time. Current methods used for this image reconstruction assume that the propagation medium is acoustically non-attenuating. However, in soft biological tissue, the frequency dependent ultrasonic attenuation is sufficient to cause considerable distortion to photoacoustic waves, even over short propagation distances. This distortion introduces blurring artifacts into images reconstructed under the assumption of a lossless medium. Here, a general lossy wave equation applicable to biological media is developed for which an exact solution (formed in the wavenumber-frequency domain) is derived. Explicit consideration is given to sound speed dispersion which is shown to have a negligible effect on photoacoustic imaging. Given an initial pressure distribution, the developed model allows the complete pressure field within the domain to be computed at an arbitrary time without iteration. The computation relies only on the Fourier transform and a decaying time propagator dependent on the attenuation in the medium. This facilitates the fast calculation of pressure fields in two or three dimensions over large domains. The model is demonstrated through the simulation and reconstruction of an example pulse distribution in a lossy medium.