This work presents an analytical approach for the solution of the tissue diffusion equation based on the bound- ary measurements. We consider a bioluminescent point source in both homogeneous and heterogeneous circular turbid media. The point source is described by the Dirac delta function. Analytical expressions for the strength and position of the point source are obtained introducing boundary measurements and then applying appropriate boundary conditions. In addition, numerical simulations are performed for the position of the source. Calculations show that that the analytical results are in a good accordance with the numerical results.
The representation theorems of the convolution type and the correlation type are used to obtain the superposition of the Green's function and its time reversal counterpart for the photoacoustic wave equation. Based on the representation theorems, an interferometry relation providing the Green's function between sources and receivers is obtained. The reciprocity theorems for a spherical geometrical system consisting of sources located on the boundary of the inner spherical region and transducers located on the outer boundary are utilized. Therefore, the measurement would be observed at one of the detectors if there were a photoacoustic point source at the other one.