Mathematical Analysis of the Photo-acoustic imaging modality using resonating dielectric nanoparticles: The 2D TM-model

Abstract: We deal with the photoacoustic imaging modality using dielectric nanoparticles as contrast agents. Exciting the heterogeneous tissue, localized in a bounded domain $\Omega$, with an electromagnetic wave, at a given incident frequency, creates heat in its surrounding which in turn generates an acoustic pressure wave (or fluctuations). The acoustic pressure can be measured in the accessible region $\partial \Omega$ surrounding the tissue of interest. The goal is then to extract information about the optical properties (i.e. the permittivity and conductivity) of this tissue from these measurements. We describe two scenarios. In the first one, we inject single nanoparticles while in the second one we inject couples of closely spaced nanoparticles (i.e. dimers). This can be done using dielectric nanoparticles enjoying high contrasts of both its electric permittivity and conductivity. These results are possible using frequencies of incidence close to the resonances of the used dielectric nanoparticles. This allows us to solve the photoacoustic inverse problem with direct approximation formulas linking the measured pressure to the optical properties of the tissue. The results are justified in the 2D TM-model.