Integral equation models for thermoacoustic imaging of acoustic dissipative tissue

The main task of thermoacoustic imaging is the estimation of a function, denoted by phi, which depends on the electromagnetic absorption function and the optical scattering properties of the tissue. In the absence of acoustic dissipation, the parameter function phi can be estimated from one of the three types of projections (spherical, circular or planar). In the case of acoustic dissipative wave propagation in tissue, it is no longer possible to explicitly calculate the projection of phi from the respective pressure data (measured by point, planar or line detectors). The goal of this paper is to derive for each of the three types of pressure detectors, an integral equation that allows estimation of the respective projections of phi. The advantage of this approach is that known reconstruction formulas for phi using the respective projection data can then be exploited.