Abstract
The spatial resolution achievable in photoacoustic imaging decreases with the imaging depth, resulting in blurred images for deeper structures. Apart from technical limitations, the ultimate resolution limit results from the second law of thermodynamics. The attenuation of the optically generated acoustic waves on their way from the imaged structure to the sample surface by scattering and dissipation leads to an increase of entropy. The resulting loss of spatial resolution for structures embedded in attenuating media can be compensated by numerical methods that make use of additional available information. In this article, we demonstrate this using experimental data from plane one-dimensional (1D) acoustic waves propagating in fat tissue. The acoustic waves are optically induced by nanosecond laser pulses and measured with piezoelectric transducers. The experimental results of 1D compensation are also relevant for photoacoustic imaging in 2D or 3D in an acoustically attenuating medium by dividing the reconstruction problem into two steps: First, the ideal signal, which is the solution of the un-attenuated wave equation, is determined by the proposed 1D attenuation compensation for each detector signal. In a second step, any ultrasound reconstruction method for un-attenuated data can be used for image reconstruction. For the reconstruction of a small step milled into a silicon wafer surface, which allows the generation of two photoacoustic pulses with a small time offset, we take advantage of non-negativity and sparsity and inverted the measured, frequency dependent acoustic attenuation of the fat tissue. We were able to improve the spatial resolution for imaging through 20 mm of porcine fat tissue compared to the diffraction limit at the cut-off frequency by at least a factor of two.
Highlights
At depths larger than the range of the ballistic photons, i.e. more than a few hundreds of microns in tissue, light is scattered several times and the spatial resolution in photoacoustic imaging is limited by acoustic attenuation, which is caused by acoustic absorption, dispersion, and scattering
Acoustic attenuation defines the ultimate spatial resolution limit, other factors such as detector bandwidth, element size and the area over which the acoustic signals are recorded at the sample surface – the detection aperture – can be limiting factors in practice [2]
In 2016 we have introduced sparsifying temporal transforms for compressed sensing in photoacoustic tomography [41], and sparsity / non-negativity constraints have been used for 2D and 3D photoacoustic image reconstruction, but not for the compensation of acoustic attenuation [42,43,44]
Summary
Photoacoustic (or optoacoustic) imaging uses the thermo-elastic expansion following a rapid temperature rise after illumination of light absorbing structures within a semitransparent and turbid material, such as a biological tissue. The physical reason for the illposedness is the second law of thermodynamics: acoustic attenuation is an irreversible process and the entropy production, which is the energy decay during wave propagation due to attenuation divided by the temperature, is equal to the information loss for the reconstructed image [14]. The spatial resolution is diffraction limited and corresponds to the wavelength at the cut-off frequency To reach this thermodynamic resolution limit for compensation of acoustic attenuation experimentally, it is necessary to measure the broadband ultrasonic attenuation parameters of tissues or liquids very accurately [22] and to evaluate the existing mathematical models to get an adequate description of attenuation [23]. That the proposed method for evaluating the principle resolution limit is applicable to any acoustic attenuation model described by a complex wave number
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