Spectral power density of the random excitation for the photoacoustic wave equation

Hakan Erkol,Mehmet Burcin Unlu

doi:10.1063/1.4894524

Abstract

The superposition of the Green's function and its time reversal can be extracted from the photoacoustic point sources applying the representation theorems of the convolution and correlation type. It is shown that photoacoustic pressure waves at locations of random point sources can be calculated with the solution of the photoacoustic wave equation and utilization of the continuity and the discontinuity conditions of the pressure waves in the frequency domain although the pressure waves cannot be measured at these locations directly. Therefore, with the calculated pressure waves at the positions of the sources, the spectral power density can be obtained for any system consisting of two random point sources. The methodology presented here can also be generalized to any finite number of point like sources. The physical application of this study includes the utilization of the cross-correlation of photoacoustic waves to extract functional information associated with the flow dynamics inside the tissue.

Highlights

It is shown that photoacoustic pressure waves at locations of random point sources can be calculated with the solution of the photoacoustic wave equation and utilization of the continuity and the discontinuity conditions of the pressure waves in the frequency domain the pressure waves cannot be measured at these locations directly
With the calculated pressure waves at the positions of the sources, the spectral power density can be obtained for any system consisting of two random point sources
The tissue absorbs the laser energy and the absorbed light leads to thermal expansion generating a pressure wave

Summary

INTRODUCTION

The photoacoustic phenomena was described by Alexander Graham Bell in 1881 but its application as an imaging method has attracted much attention after the improvement of the laser, computer and transducer technologies.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] Photoacoustic imaging (PAI) uses absorption of the electromagnetic energy as a contrast mechanism to analyze the system.[13]. It is well known that in acoustics, the cross-correlation of observed waves due to the excited random sources can yield the extraction of the Green’s function.[19,20] For example, Snieder obtained the Green’s function from the diffusive and the acoustic waves due to sources described by the Dirac delta functions.[20,21] This method is utilized when the sources are placed inside a domain or on its surface.[20]. Obtaining the Green’s function by the correlation of the waves resulting from the randomly distributed sources has attracted much intention. Beard[35] quantify Doppler time shifts using the cross-correlation of photoacoustic signals. The motivation behind the use of the cross-correlations is that the motion of the red blood cells cause fluctuations in the photoacoustic signal. It is very important to note that red blood cells inside the blood can be modeled as randomly distributed (spatially uncorrelated) point sources.[36]

METHOD

OBTAINING THE PRESSURE WAVES AT THE LOCATIONS OF THE RANDOM POINT SOURCES

DISCUSSIONS