In this dissertation, two recent problems from tomographic imaging are studied, and results from numerical simulations with synthetic data are presented. The first part deals with ultrasound modulated optical tomography, a method for imaging interior optical properties of partially translucent media that combines optical contrast with ultrasound resolution. The primary application is the optical imaging of soft tissue, for which scattering and absorption rates contain important functional and structural information about the physiological state of tissue cells. We developed a mathematical model based on the diffusion approximation for photon propagation in highly scattering media. Simple reconstruction schemes for recovering optical absorption rates from boundary measurements with focused ultrasound are presented. We show numerical reconstructions from synthetic data generated for mathematical absorption phantoms. The results indicate that high resolution imaging with quantitatively correct values of absorption is possible. Synthetic focusing techniques are suggested that allow reconstruction from measurements with certain types of non-focused ultrasound signals. A preliminary stability analysis for a linearized model is given that provides an initial explanation for the observed stability of reconstruction. In the second part, backprojection schemes are proposed for the detection of small amounts of highly enriched nuclear material inside 3D volumes. These schemes rely on the geometrically singular structure that small radioactive sources represent, compared to natural background radiation. The details of the detection problem are explained, and two types of measurements, collimated and Compton-type measurements, are discussed. Computationally, we implemented backprojection by counting the number of particle trajectories intersecting each voxel of a regular rectangular grid covering the domain of detection. For collimated measurements, we derived confidence estimates indicating when voxel trajectory counts are deviating significantly from what is expected from background radiation. Monte Carlo simulations of random background radiation confirm the estimated confidence values. Numerical results for backprojection applied to synthetic measurements are shown that indicate that small sources can be detected for signal-to-noise ratios as low as 0.1%.

Spectral computed tomography (CT) has proven an important development in biomedical imaging, yet there are several limitations to this nascent technology. Near-term implementation of spectral CT imaging can be enhanced using a hybrid architecture that integrates a narrow-beam spectral 'interior' imaging chain integrated with a traditional wide-beam 'global' imaging chain. The first study demonstrates the feasibility of hybrid spectral micro-CT architecture with a first-of-its-kind system implementation and preliminary results showing improved contrast resolution and spatial resolution. The second study seeks to characterize the hybrid spectral micro-CT scan protocol for reduction of radiation exposure. In the third study, the spectral 'interior' imaging chain was optimized for K-edge imaging of high-z elemental contrast agents. In the final study, an open-source, low-cost solution for managing digital content in an academic setting was demonstrated. The results of these studies confirm the merits of a hybrid architecture and warrant further consideration in future pre-clinical and clinical spectral micro-CT and CT scanner design and protocols. / Ph. D.

Dans cette thèse, nous introduisons et développons une approche mathématiques originale des techniques d'imagerie biomédicales dites "hybrides". L'idée et d'appliquer une méthode d'imagerie mal posée, tout en perturbant le milieu à imager par des déplacements mécaniques. Ces déplacements provenant d'une équation de type onde élastique perturbent les mesures effectuées. En utilisant ces mesures perturbées, et profitant du caractère local des perturbations mécaniques, il est possible d'augmenter considérablement la résolution de la méthode de base. Le problème direct est donc un couplage d'une EDP décrivant la propagation utilisée pour la méthode de base et d'une seconde décrivant les champs de déplacement mécaniques. Dans toutes cette thèse, on fait l'hypothèse d'un milieu mécaniquement homogène afin d'assurer le contrôle et la géométrie des ondes perturbatrices utilisées. A partir des mesures perturbées, une étape d'interprétation permet de construire une donnée interne au domaine considéré. Cette étape nécessite en général l'inversion d'opérateurs géométriques intégraux de type Radon, afin d'utiliser le caractère localisant des perturbations utilisées. A partir de cette donnée interne, il est possible d'initier une procédure de reconstruction du paramètre physique recherché. Dans le chapitre 1, il est question d'un couplage entre micro-ondes et perturbations sphériques. Dans les chapitres 2, 3 et 4, nous étudions l'imagerie optique diffuse toujours couplée avec des perturbations sphériques. Enfin dans le chapitre cinq, nous donnons une méthode originale de reconstruction de la conductivité électrique par un couplage entre champs magnétique et perturbations acoustiques focalisées. / This thesis aims at developing an original mathematical approach for modeling hybrid biomedical imaging modalities. The core idea is to run an ill-posed imaging method while perturbing the medium using mechanical displacements. These displacements described by an elastic wave equation perturb the collected measurements. Using these perturbed measurements and taking advantage of the perturbation localizing e↵ect, it is possible to significantly overcome the resolution of the basic method. The direct problem here is a coupling between a PDE describing the propagation used for the basic method and a second one describing the mechanical displacements fields. In the whole thesis, we only consider mechanically homogeneous medium in order to assure the control and the geometry of the perturbing wavefronts. From these perturbed measurements, an interpretation step leads to an internal data map inside the considered medium. This step usually requires inversion of geometric integral operators such as Radon transform. This allows to use the geometrical localizing behavior of the perturbations. From this internal data, one can start a recovering procedure for the unknown physical parameter. This recovering step involves a new non physical PDE, non linearly coupled with the main modality equation. In the first chapter, we study a coupling between micro-waves and spherical perturbations. In chapter 2, 3 and 4, we propose a model for di↵use optical imaging coupled with spherical perturbations. In chapter 5, we introduce a new method for imaging the electric conductivity by a coupling between magnetic field and focused acoustic perturbations

The first contribution of this thesis is a new regularity theorem for time harmonic Maxwell's equations with less than Lipschitz complex anisotropic coefficients. By using the L^p theory for elliptic equations, it is possible to prove H¹ and Hölder regularity results, provided that the coefficients are W^1,p for some p = 3. This improves previous regularity results, where the assumption W^1,∞ for the coefficients was believed to be optimal. The method can be easily extended to the case of bi-anisotropic materials, for which a separate approach turns out to be unnecessary. The second focus of this work is the boundary control of the Helmholtz and Maxwell equations to enforce local constraints inside the domain. More precisely, we look for suitable boundary conditions such that the corresponding solutions and their derivatives satisfy certain local non-zero constraints. Complex geometric optics solutions can be used to construct such illuminations, but are impractical for several reasons. We propose a constructive approach to this problem based on the use of multiple frequencies. The suitable boundary conditions are explicitly constructed and give the desired constraints, provided that a finite number of frequencies, given a priori, are chosen in a fixed range. This method is based on the holomorphicity of the solutions with respect to the frequency and on the regularity theory for the PDE under consideration. This theory finds applications to several hybrid imaging inverse problems, where the unknown coefficients have to be imaged from internal measurements. In order to perform the reconstruction, we often need to find suitable boundary conditions such that the corresponding solutions satisfy certain non-zero constraints, depending on the particular problem under consideration. The multiple frequency approach introduced in this thesis represents a valid alternative to the use of complex geometric optics solutions to construct such boundary conditions. Several examples are discussed.

L’approche qui a été développée dans l’équipe imXgam du CPPM est de combiner sur un unique support rotatif les modules de détection de la caméra pour petit animal ClearPET avec un détecteur de rayons X à comptage de photons dans le but d’acquérir simultanément des images anatomiques (TDM) et fonctionnelles (TEP) du même champ de vue. L’étude préliminaire du système hybride ClearPET/XPAD3 menée en simulation avec Gate a permis d’implémenter une nouvelle géométrie de détection TEP à 21 détecteurs phoswich, de fixer les grandes lignes de l’assemblage TEP/TDM, ainsi que d’étudier et de solutionner les difficultés liées au régime de fonctionnement bimodal. Pour finir, l’outil de simulation a également permis d’imaginer comment un tel système pourrait judicieusement exploiter la corrélation spatiale et temporelle des informations anatomo-fonctionnelles.Du point de vue de l’instrumentation, ce projet a vu la mise en œuvre du système hybride simultané ClearPET/XPAD3. Une fois les deux systèmes TEP et TDM opérationnels individuellement,il a été démontré, d’une part que le ClearPET est parfaitement capable d’opérer en régime de fonctionnement simultané moyennant un blindage approprié de ses modules de détection, et d’autre part que la nouvelle génération de caméra à pixels hybrides XPAD3-S/Si s’avère très prometteuse compte tenu de la bonne qualité des premières images reconstruites.Finalement, la preuve de concept d’une acquisition TEP/TDM simultanée avec une source de positons scellée et un tube à rayons X a pu être concrètement démontrée. / The pathway that has been followed by the imXgam team at CPPM was to combine on a single rotating device the detector modules of the small animal PET scanner ClearPET witha photon counting X-ray detector in order to perform simultaneous acquisition of images from the anatomy (X-ray CT) and from the metabolic function (PET) of the common field-of-view.A preliminary study of the hybrid imaging system ClearPET/XPAD3 carried out using Gateled us to form a new PET detection assembly based on 21 phoswich modules, to fix the design of the PET/CT device, as well as to study and solve the difficulties arising from simultaneous hybrid imaging. Last but not least, the simulation tool also allowed us for thinking how wellsuch a system could judiciously use the spatial and temporal correlations between anatomicand functional information.From an instrumentation point of view, we succeeded to set up the ClearPET/XPAD3 prototype.Once both imaging systems were operational individually, we demonstrated on one sidethat the ClearPET prototype was perfectly capable of performing correctly in simultaneousacquisition conditions, providing that the detector modules were appropriately shielded. Onthe other side, the new generation of the hybrid pixel camera using the XPAD3-S chip provedto be quite promising given the good quality of the first reconstructed images.Finally, the proof of concept of simultaneous PET/CT data acquisition was made using a sealed positron source and an X-ray tube.

Micro- and nanorobots (MNRs) are small autonomous devices capable of performing complex tasks and have been demonstrated for a variety of non-invasive biomedical applications, such as tissue engineering, drug delivery or assisted fertilization. However, translating such approaches to an in vivo environment is critical. Current imaging techniques do not allow localization and tracking of single or few micromotors at high spatiotemporal resolution in deep tissue. This thesis addresses some of these limitations, by exploring the use of two optical-based techniques (IR and photoacoustic imaging (PAI)) and a combination of both US and PAI. First, we employ an IR imaging setup to visualize mobile reflective micromotors under scattering phantoms and ex vivo mouse skull tissues, without using any labels. The reflective micromotor reflects more than tenfold the light intensity of a simple particle. However, the achieved penetration depth was ca. 100 μm (when using ex vivo tissues), limiting this technique to superficial biomedical applications. In this regard, PAI plays a role that combines the advantages of US such as penetration depth and real-time imaging with the molecular specificity of optics. For the first time, in this thesis, this method is evaluated for dynamic process monitoring, in particular for tracking single micromotor in real-time below ~1 cm deep phantom and ex vivo tissue. However, the precise function control of MNRs in living organisms, demand the combination of both anatomical and functional imaging methods. Therefore, in the end, we report the use of a hybrid US and PA system for the real-time tracking of magnetically driven micromotors (single and swarms) in phantoms, ex vivo, and in vivo (in mice bladder and uterus), envisioning their application for targeted drug-delivery. This achievement is of great importance and opens the possibilities to employ medical micromotors in a living organism and perform a medical task while being externally controlled and monitored.:ABSTRACT 1 1 INTRODUCTION 5 1.1 Motivation 5 1.2 Background 7 1.2.1 Microrobotics 7 1.2.2 Medical Imaging 9 1.3 Objectives and Structure of Thesis 12 2 FUNDAMENTALS 15 2.1 Optical Imaging 15 2.1.1. Reflection-based Imaging 17 2.1.2. Fluorescence-based Imaging 18 2.1.1 Light-Tissue Interaction 20 2.2 Photoacoustic Imaging 23 2.2.1 Theory 23 2.2.2 Implementation 25 2.3 Ultrasound Imaging 26 2.3.1 Theory 26 2.3.2 Implementation 28 3 MATERIALS AND METHODS 30 3.1 Fabrication of Magnetic Micropropellers 30 3.1.1 3D Laser Lithography of Polymeric Resin 30 3.1.2 Self-assembly of SiO2 Particles 31 3.1.3 Electron Beam Evaporation 32 3.1.4 Surface Functionalization 33 3.2 Fabrication of Phantom Tissue and Microfluidic Channels 34 3.2.1 Fabrication of PDMS-Glycerol Phantom 34 3.2.2 Fabrication of Agarose Phantom 35 3.2.3 Phantom based on Ex vivo Tissues (Chicken Breast and Mice Skull) 36 3.2.4 Microfluidic Channel Platform 37 3.3 Sample Characterization 38 3.3.1 Optical Microscopy 38 3.3.2 Scanning Electron Microscopy 38 3.4 Magnetic Actuation 39 3.4.1 Magnetic Force 39 3.4.2 Magnetic Torque 39 3.5 Ethic Statement for Mice Experiments 41 4 OPTICAL IMAGING OF MICROROBOTS 42 4.1 Concept of Reflective Micromotors 42 4.2 Fabrication of Reflective Micromotors 44 4.3 IR Imaging Actuation Setup 45 4.4 Actuation and Propulsion Performance below Phantom 47 4.5 Actuation and Propulsion Performance below Ex Vivo Skull Tissue 50 4.6 Actuation and Propulsion Performance in Blood 51 5 PHOTOACOUSTIC IMAGING OF MICROROBOTS 55 5.1 Absorbers for Deep Tissue Imaging 55 5.2 Absorber Micromotor Design and Fabrication 56 5.3 Photoacoustic Imaging Setup 58 5.4 Actuation Performance below Phantom Tissue 60 5.5 Actuation Performance below Ex Vivo Tissue 65 6 HYBRID ULTRASOUND AND PHOTOACOUSTIC IMAGING 67 6.1 Hybrid Ultrasound/Photoacoustic System 68 6.2 Fabrication and Characterization of Micromotors 69 6.3 Actuation and Propulsion Performance below Phantom 69 6.4 Actuation and Propulsion Performance below Ex Vivo Tissues 71 6.5 Actuation and Propulsion Performance in Mice 72 6.5.1 Swimming of Micromotors in Bladder 72 6.5.2 Actuation of Micromotors in Uterus 74 6.5.3 3D Multispectral Imaging 76 6.5.4 Towards Targeted Drug Delivery 77 7 SUMMARY AND PERSPECTIVES 80 7.1 Summary 80 7.2 Future Perspectives 83 7.2.1 Contrats Enhancing Labels 84 7.2.2 Novel Imaging Concepts 85 8 REFERENCES 88 9 APPENDIX 105 List of Figures 105 List of Tables 107 Abbreviations 108 List of Publications 109 Acknowledgements 110 Selbstständigkeitserklärung 111 Curriculum Vitae 112

Les technologies d'imagerie intravasculaire c’est à dire l’échographie endo-coronaire (IVUS)et la tomographie par cohérence optique (IV-OCT) sont des outils précieux pour aider audiagnostic de la plaque d’athérosclérose et guider les gestes thérapeutiques.Le chapitre 1 présente les inconvénients de la coronarographie dans la pratique clinique.Dans plusieurs circonstances, l’IVUS et l’OCT ont clairement une valeur supplémentaire quandils sont utilisés comme un outil diagnostique en cas d'ambiguïtés angiographiques. Nousavons récemment rapporté la première observation utilisant l’OCT pour décrire une dissectioncoronaire d'une branche septale perforante responsable d’un infarctus du myocarde.Le chapitre 2 porte sur la reproductibilité de I’OCT entre différents instituts concernant denombreux paramètres qualitatifs et quantitatifs de la plaque d'athérome. Le but de notre étudeétait d'étudier en plus de la reproductibilité inter- et intra-observateur, la variabilité inter-institutsde I’OCT concernant les mesures quantitatives et qualitatives et de la comparer à celle del’IVUS. Dans ce travail, nous avons observé que, dans la mesure de la surface de la lumièreendocoronaire, des diamètres minimum et maximum de cette même lumière endocoronaire,de la surface endo-luminale du stent, des diamètres minimum et maximum endo-luminaux dustent, par des analystes provenant de 2 laboratoires différents, la reproductibilité inter-institutsde I’OCT était nettement supérieure à celle de l’IVUS. Le Chapitre 3 présente 2 nouvelles technologies robustes d'imagerie intravasculaire hybridesdéveloppées dans le laboratoire du Professeur Guillermo J. Tearney: l’OCT couplée à laspectroscopie dans le proche infra-rouge (OFDI-NIRS) et l’OCT couplée à l’autofluorescencedans le proche infra-rouge (OFDI-NIRAF). Les premières procédures d’OFDI-NIRS chezl’homme sont prévues dans un avenir proche. Les premières procédures chez l’homme ontété réalisées chez 12 patients porteurs d’un angor stable entre Juillet 2014 et Janvier 2015.Les résultats de cette étude pilote ont montré que le signal d’autofluorescence recueilli(NIRAF) a été focalement trés élevé dans des endroits de la plaque d’athérome où la plupartdes phénotypes morphologiques en OCT d’une plaque à haut risque de rupture étaientévidents. Les substrats biochimiques de ce signal d’autofluorescence (NIRAF) sont encore àélucider. / Intravascular imaging technologies i.e. IVUS and IV-OCT are valuable tools for interventionguidance and diagnostic plaque imaging.Chapter 1 introduces the drawbacks of coronary angiography in the clinical practice. In severalcircumstances, IVUS and IV-OCT have clearly an additional value when they are used as adiagnosis tool in case of angiographic ambiguities. We recently reported the first observationusing IV-OCT to describe a coronary dissection of a septal perforating branch causing AMI.Chapter 2 focuses on the inter-institute reliability of IV-OCT to determine qualitative andquantitative parameters of atherosclerotic plaque. The purpose of our study was to investigatefurther inter- and intra-observer reproducibility, the inter-institute variability for IV-OCT (OFDI)quantitative and qualitative measurements vs. IVUS measurements using publishedconsensus document definitions. In our work, we observed that in the measurement of lumenCSA, maximum and minimum lumen diameters, stent CSA, maximum and minimum stentdiameters by analysts from 2 different laboratories, inter-institute reproducibility of OFDI wasfound to be more consistent than IVUS.Chapter 3 present 2 new robust hybrid intravascular imaging technologies developed in Dr.Tearney’s laboratory i.e. OFDI-NIRS and OFDI-NIRAF, which may offer supplementary criteriafor plaque vulnerability. First-in-human OFDI-NIRS imaging procedures are anticipated in thenear future. First-in-human OFDI-NIRAF imaging procedures have been performed in a firstpioneering series of 12 stable patients between July 2014 and January 2015. Findings of thispilot study showed that NIRAF was focally elevated in plaque locations where most high-riskmorphologic phenotypes were evident. The biochemical substrates of the NIRAF signal stillhave to be elucidated.