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Theses

Mathematical modelling for hybrid and nanoparticle imaging

Abstract : In this thesis we study the mathematical modelling of new experimental imaging techniques. It is divided in two parts. The first one contains work on hybrid imaging techniques based on the interactions betwenn different types of waves. The second part is devoted to the study of the behavior of metallic nanoparticles embedded in electromagnetic fields. The first part contains three chapters in which three different imaging techniques are studied : - magneto-acoustic tomography by Lorentz force, - magneto-acoustic tomography with magnetic induction, - optical coherence tomography based elastography. In the first two chapters we give a mathematical model for the experiments studied as well as explicit reconstruction formulas for the associated inverse problems. We introduce a new direct reconstruction method ("viscosity method") allowing the recovery of the electrical conductivity of the medium. In the third chapter we give an optimisation method to reconstruct the shear modulus of the medium from a displacement field. The second part contains two chapters in which are studied the diffraction of light by small metallic nanoparticles. We study: - plasmonic resonances, - second harmonic generation. The plasmonic resonances are studied within the Maxwell frame. We give an asymptotic formula for the electromagnetic fields within a small volume approximation.
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  • HAL Id : tel-01769044, version 1

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Pierre Millien. Mathematical modelling for hybrid and nanoparticle imaging. Medical Imaging. Ecole normale supérieure - ENS PARIS, 2015. English. ⟨NNT : 2015ENSU0010⟩. ⟨tel-01769044⟩

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