Mathematical modelization of the Photoacoustic effect generated by the heating of metallic nanoparticles

TL;DR

This paper develops a mathematical framework to model and analyze the photoacoustic effect caused by electromagnetic heating of metallic nanoparticles in tissue, including asymptotic models, wave generation, and inverse problem solutions.

Contribution

It introduces new asymptotic models for plasmonic resonances and electromagnetic fields, and formulates an inverse problem to recover tissue permittivity from acoustic measurements.

Findings

Derived asymptotic models for plasmonic resonances.

Established a direct relation between acoustic waves and electromagnetic sources.

Solved the inverse problem for tissue permittivity recovery.

Abstract

This paper is devoted to the modelization of the photoacoustic effect generated by the electromagnetic heating of metallic nanoparticles embedded in a biological tissue. We first derive an asymptotic models for the plasmonic resonances and the electromagnetic fields. We then describe the acoustic generation created by the electromagnetic heating of the nanoparticle. Precisely, we derive the model equations that describes the coupling between the temperature rise in the medium and the acoustic wave generation. We obtain a direct relation between the acoustic waves and the electromagnetic external sources. Finally, we solve the multiwave inverse problem that consists in the recovery of the electric permittivity of the biological tissue from the measurements of the generated acoustic waves on the boundary of the sample.