Tato disertační práce se zabývá tématikou analýzy strukturálních změn ve svalové tkáni a metodikou optického měření. I přesto, že existuje nezanedbatelné množství metod pro detekci konkrétních změn ve svalovině, především pak v konzumním mase, drtivá většina z nich se zaměřuje na jeden konkrétní proces a vyžaduje komplikované postupy a drahé přístroje. Předmětem prezentovaného výzkumu není tedy nalézt metody přesnější a specifičtější, než jsou ty již exitující, ale raději zvolit alternativní přístup k problematice. Součástí je pak i snaha najít možnosti jak obejít technologické nároky moderních postupů a přitom se přiblížit co nejvíce jejich informačnímu přínosu. Za tímto účelem je potřeba mít dostatečné teoretické znalosti a experimentální zkušenosti především v oboru fyziky, optiky a postupů měření, ale také široké povědomí o problematice biologických tkání a procesů v nich probíhajících. Na základě získaných informací a pochopení pochodů ve svalové tkáni jsou navrhnuty a testovány tři rozdílné přístupy. Vytvořené metody pracují s fotony v transmisním i reflexním uspořádání. Pomocí pozorování změn absorpce, rozptylu a polarizace světla po interakci se vzorkem svalové tkáně jsou posouzeny jeho další optické vlastnosti především index lomu a optická anizotropie. Identifikace změn optických vlastností vzorků za různých podmínek umožňuje společně se simulací Monte Carlo posoudit rozdíly mezi vzorky čerstvými, starými, sušenými a jednou či dvakrát zmraženými a rozmraženými.

This master’s thesis is focused on the electrical properties of biological tissues and flesh in particular. Their electrical characteristics depend on the physical and chemical parameters that determine the concentration and mobility of ions in metabolic fluids. From the electrical point of view, flesh can be simply substituted by a field of elongated conductive cells which are separated by the insulating membrane from each other. In the next part, the Fricke model is introduced. The model describes the measurement of impedance of the tissue at low and high frequencies. The aim of the work is to assess how the impedance of the dielectric sample is dependent on the frequency of the electrical signal during the optimal aging or ripening of flesh.

Within the master thesis a computational model of biaxial tension test of soft biological tissues was developed. The tested specimen can be attached using clamps or hooks. The number and the size of clamps and hooks have a significant impact on the distribution of stress and strain in the centre of the specimen, where deformation is measured. Using the developed computational model, a sensitivity analysis of number and size of clamps and hooks and a sensitivity analysis of placement of clamps was elaborated. The number and size of clamps and hooks were optimized in such a way that the material’s parameters obtained by the tension test correspond to the utmost to the actual parameters of the material. By analyzing the placement of clamps, the influence of selected deviations on the outcome of the tension test was determined. Finally, a plan of the next course of action has been proposed.

La connaissance des propriétés diélectriques des tissus biologiques constitue un enjeu majeur pour la santé. Ces propriétés traduisent la manière dont un tissu stocke ou dissipe l’énergie électromagnétique transmise par un champ extérieur ; étant liées à la composition et à la structure du milieu organique, elles traduisent également la nature et l’état physiologique d’un tissu. Leur estimation fine permet donc, le cas échéant, de détecter et/ou de suivre l’évolution d’une pathologie. Parmi les méthodes de caractérisation diélectrique des tissus possibles, nous nous sommes concentrés sur une technique de caractérisation électromagnétique par antenne inductive exploitée en émission/réception, qui permet une mise en œuvre sans contact entre le système de mesure et le tissu. Celle-ci opère dans la gamme des radiofréquences (RF) ce qui présente l’avantage de rendre le dispositif sensible à la fois à la conductivité électrique et à la permittivité diélectrique du tissu. Cette technique travaillant en champ proche nécessite l’utilisation d’un modèle électromagnétique 3D des interactions sonde / tissu pour être mise en œuvre de manière pertinente. Dans ces travaux, nous nous sommes donc intéressés au problème de la modélisation des interactions, ainsi qu’à la résolution du problème inverse qui consiste à estimer les paramètres diélectriques recherchés à partir des données de mesure fournies par l’antenne et du modèle élaboré. Pour cela, nous nous sommes concentrés sur une configuration canonique, constituée d’une antenne RF filiforme circulaire, interagissant avec un milieu diélectrique homogène « sain » dont les paramètres diélectriques macroscopiques sont représentatifs d’un tissu organique (conductivité de 0.6 S/m et permittivité relative de 80), et d’une inclusion sphérique représentative d’une lésion présentant un contraste de 10% à 50% avec les paramètres du milieu « sain ». Nous avons établi un modèle d’interactions électromagnétiques 3D reposant sur une formulation semi – analytique à sources distribuées (DPSM) adaptée à cette configuration. Une étude paramétrique de la mise en œuvre du modèle, validée dans des configurations simples par rapport à des modèles analytiques et des expérimentations, a permis de construire un modèle qui montre des écarts inférieurs à 5 % par rapport à l’expérimentation, et qui établit un compromis acceptable entre exactitude et ressources informatiques nécessaires pour calculer la solution. Enfin, nous nous sommes intéressés à la résolution du problème inverse, consistant à retrouver les paramètres géométriques et diélectriques d’une lésion enfouie dans un milieu diélectrique « sain », à partir des variations d’impédances de l’antenne RF. Pour cela, nous avons construit un modèle inverse à réseaux de neurones artificiels (RNA) à partir de banque de données produites par le modèle DPSM. Une étude paramétrique a permis d’identifier les configurations de mise œuvre (fréquences, positions des antennes) les plus pertinentes permettant d’estimer les propriétés diélectrique, la taille et la position de l’inclusion dans le tissu, avec des erreurs d’estimation de l’ordre de 7% avec une antenne unique monofréquence, pour la caractérisation d’une inclusion de 3 cm de rayon enfouie jusqu’à 6 cm de profondeur. Ces travaux ouvrent la voix à des techniques de diagnostics de dans des milieux plus complexes (tissus stratifiés…) avec des techniques d’investigation multi-antennes et/ou multifréquences particulièrement prometteuses. / The characterization of the dielectric properties of organic tissues is a major issue in health diagnosis. These properties reflect the way organic material stores or dissipates the electromagnetic energy transmitted by an external field. They are related to the composition and the structure of the organic medium. Furthermore, they are also related to the nature and the physiological state of a tissue. For that reason the estimation of these properties is very valuable for detecting and/or monitoring the evolution of tissue pathology.Among the existing dielectric characterization methods, we focused on a characterization technique using an inductive antenna, which acts as a transmitter/receiver sensor and allows a contactless implementation between the measuring system and investigated tissue to be carried out. This system is operated in the radio-frequency (RF) band. Indeed, in the RF the device is equally sensitive to both the electrical conductivity and the dielectric permittivity of the tissue. This technique operates in a near-field and therefore a 3D electromagnetic modeling technique is required to accurately model the interactions between the sensor and the investigated tissue.This work deals with the 3D modeling and with the resolution of the inverse problem required to estimate the dielectric parameters of tissues starting from the data provided by the antenna and the outputs of the model. For this purpose, a canonical configuration featuring a filiform circular antenna is considered. This antenna interacts with a “healthy” homogeneous dielectric medium, which possess the macroscopic dielectric parameters of a typical organic tissue (i.e. conductivity 0.6S/m and relative permittivity of 80 at 100 MHz). Meanwhile, a spherical inclusion buried within the tissue is considered to simulate a tissue lesion. This inclusion features a dielectric contrast of 10% up to 50% by reference to the parameters of the “healthy” medium. A 3D modeling of the sensor/tissue interactions is established, which is based on the distributed point source method (DPSM), a versatile semi-analytical modeling technique. The model is adjusted using a parametric study and validated against analytical models (in simplified configurations) and experiments. The implemented DPSM modeling was found to feature a 5% accuracy error, compared to the experimentations, together with offering an acceptable trade-off between accuracy and the computation cost. Finally, we focused on the solving of the inverse problem which consists in estimating the geometric and dielectric parameters of a buried lesion in the “healthy” dielectric medium, starting from the variations of the impedance of the RF antenna. To do so, a behavioral model build up using an artificial neural network (ANN) was established. The model is build using a data base elaborated using the DPSM model. The parameters of the ANN is discussed in order to identify the relevant configuration (frequency, position of the antenna) to estimate the dielectric properties, the size and the position of the inclusion in the tissue. For a single antenna operated at a single frequency, an inclusion of 3cm radius buried as deep at 6 cm within the tissue was located and characterized with estimation errors of the order of 7%.The methodologies developed in these works open the way to the diagnosis of more complex material (such as layered tissues), using promising techniques such as multi-frequency non contact RF antenna arrays.

Electrical impedance imaging is an imaging technique which has the capability of revealing the spatial distribution of the electrical impedance inside biological tissues. Classical electrical impedance imaging including Electrical Impedance Tomography (EIT) typically has low resolution. Advances in electrical impedance imaging typically involve methods that either increase image resolution or image contrast. This study investigates the possibility of the resolution improvement for electrical impedance imaging using motion, and presents a novel high-resolution and calibrated impedance imaging method called Scanning electrical Impedance Imaging (SII). SII uses an electrical probe held at a known voltage and scanned over a thin sample immersed in a conductive medium on a grounded conducting plane to obtain high-resolution calibrated impedance images of samples. For system improvement and image reconstruction, a numerical model is developed to describe the SII system. This model simulates the measurement process by solving a 3-D electrostatic field at each scanning position using a modified approach of the finite difference method (FDM). The simulation consists of a quasi-statics problem involving inhomogeneous media with a complicated boundary condition. This 3-D model is used to optimize both the probe height and the shield-spacing for probe fabrication and also to evaluate system parameters including the frequency and the resistor in the peripheral circuit. Based on this model, an approach is also developed to quantifying conductivity values using the SII system. However, a large computational cost due to the motion involved in SII leads to challenges for a fast and accurate image reconstruction based on this 3-D model. Alternative fast models are derived as a replacement of the 3-D model for quick image reconstruction. In particular, the Modified Linear Approximation (MLA) involving two conductivity-weighted convolutions based on the reciprocity principle, explains the function of the special shield design introduced in the SII system reasonably well. Based on the MLA a nonlinear inverse method using total variation regularization and the Polak-Ribi'{e}re variant of the nonlinear conjugate-gradient method is developed for fast image reconstruction of the SII system. The inverse method is accelerated using convolution which eliminates the requirement of a numerical solver for the 3-D electrostatic field. 2-D images of small biological tissues and cells are measured using the SII system. The corresponding conductivity images are reconstructed using the MLA method. The successful improvement of resolution shown in both simulation and experimental results demonstrates that the idea of this approach can potentially be expanded to other imaging modalities for resolution improvement using motion.

This dissertation elucidates the instrumentation and application of a hybrid ambient ionization source, laser electrospray mass spectrometry (LEMS), for the direct analysis and molecular imaging of biological tissue without matrix deposition. In LEMS, laser pulses from a Ti:Sapphire laser amplifier (60 fs, 800 nm, and 1 mJ) interact with surface analytes and transfer them from the condensed phase into the gas phase without the requirement of either exogenous matrix or endogenous water in the sample. The laser vaporized analytes are captured and ionized by an electrospray source, and finally detected by a mass analyzer. It was found that a turn-key, robust femtosecond fiber laser with longer wavelength, longer duration, and lower pulse energy at 1042 nm, 425 fs, and 50 µJ, respectively, provided comparable results with the Ti:Sapphire laser. Vaporization of intact, dried or aqueous cytochrome c and lysozyme samples was demonstrated by the fiber laser. A charge states distribution at lower charge states indicating folded conformation of proteins and the hemoglobin α subunit-heme complex from whole blood was observed. Endogenous anthocyanins, sugars, and other metabolites were detected and revealed the anticipated metabolite profile for the flower petal and leaf samples by the fiber laser. Phospholipids, especially phosphatidylcholine, were identified from a fresh mouse brain section sample. These lipid features were suppressed in both the fiber laser and Ti:Sapphire LEMS measurement in the presence of optimal cutting temperature compounds which are commonly used in animal tissue cryosectioning. This dissertation also details the design of an automated mass spectrometry imaging source based on the Ti:Sapphire LEMS. The laser, translation stage, and mass analyzer are synchronized and controlled using a customized user interface to enable step-by-step scanning of the area of interest on a given tissue sample. The imaging source is coupled with a high resolution accurate mass quadrupole time-of-flight (QTOF) mass analyzer with tandem mass analysis capability. A lateral resolution of 60 µm was demonstrated on a patterned ink film by LEMS imaging. Plant metabolites including sugar and anthocyanins were directly imaged from a leaf sample. Small metabolites, lipids and proteins were simultaneously imaged from a single tissue section of a pig liver sample. Biomarkers of blood-brain barrier damage and traumatic brain injury (TBI) that occurred during the injury were detected and imaged from a TBI mouse brain. The loading values from principal component analysis (PCA) were shown to be useful for identification of features of interest from the large LEMS imaging dataset. / Chemistry

Aplicamos a teoria de representação de funções isotrópicas para determinar o número mínimo de invariantes independentes necessários para caracterizar completamente a densidade de energia de deformação de sólido hiperelástico com duas direções de simetria material. Expressamos a densidade de energia em termos de dezoito invariantes e extraímos um conjunto de dez invariantes para analisar dois casos de simetria material. No caso de direções ortogonais, recuperamos o resultado clássico de sete invariantes e oferecemos uma justificativa para a escolha dos invariantes encontrados na literatura. Se as direções não são ortogonais, descobrimos que o número mínimo também é sete e corrigimos um erro em fórmula encontrada na literatura. Uma densidade de energia deste tipo é usada para modelar, na escala macroscópica, materiais de engenharia, tais como compósitos reforçados com fibras, e tecidos biológicos, tais como ossos. / We determine the minimum number of independent invariants that are needed to characterize completely the strain energy density of a hyperelastic solid having two distinct material symmetry directions. We use a theory of representation of isotropic functions to express this energy density in terms of eighteen invariants and extract a set of ten invariants to analyze two cases of material symmetry. In the case of orthogonal directions, we recover the classical result of seven invariants and offer a justification for the choice of invariants found in the literature. If the directions are not orthogonal, we find that the minimum number is also seven and correct a mistake in a formula found in the literature. An energy density of this type is used to model, on the macroscopic scale, engineering materials, such as fiber-reinforced composites, and biological tissues, such as bones.

Les travaux de cette thèse s'inscrivent dans le cadre du développement de méthodes d'identification inverse de paramètres matériau. On porte un intérêt particulier à la biomécanique des tissus souples renforcés par des fibres de collagène (artère, disque intervertébral, peau, tendon, ligament, etc.), dans le cadre de leurs réponses viscoélastiques et en grandes déformations et en grands déplacements (hyperélasticité). Fortement non-linéaires et anisotropes, les lois constitutives en biomécanique contiennent un nombre important de paramètres matériau. Le problème inverse qui permet de les identifier est de grande dimension et fortement non linéaire. En raison de difficultés numériques liées à sa résolution avec des méthodes à base de gradient, nous avons développé deux nouvelles méthodes d’identification inverse de paramètres nommées GAO (Genetic algorithms & Analytical Optimization) et MMIM (Maximum-Minimum Identification Method).La méthode GAO combine de manière avantageuse les méthodes déterministes de type gradient avec les algorithmes génétiques. Son originalité consiste à introduire des calculs analytiques pour la partie déterministe, ce qui permet d’accélérer et d’améliorer la convergence des algorithmes génétiques. Cette stratégie est appliquée dans le cadre de l’hyperélasticité anisotrope.En ce qui concerne la méthode MMIM, elle opère selon un critère d’identification basé sur la norme infinie et elle utilise les algorithmes génétiques. Elle permet d’identifier les paramètres de lois viscoélastiques quasi-linéaires. Elle garantit une réponse visqueuse constante qui est caractéristique des tissus souples qui sont insensibles à la vitesse de chargement.Les méthodes GAO et MMIM ont identifié avec succès des paramètres de tissus artériels et de tissus du disque intervertébral. Les propriétés de ces tissus sont décrits par ailleurs dans le mémoire dans un contexte plus général où on expose l'anatomie, l'histologie et le mécanisme de déformation aux différents niveaux hiérarchiques (nano-échelle à milli-échelle) d’un tissu souple renforcé par des fibres de collagène. Ceci permet de comprendre le rôle des efforts dans la relation liant la structure à la fonction en biologie. / This thesis focuses on research and development of inverse identification methods of material parameters. A particular attention is attributed to the viscoelastic response of collagen-reinforced soft tissues (artery, intervertebral disc, skin, tendon, ligament, etc) submitted to large displacements and large deformations (hyperelasticity). Highly non-linear and anisotropic, biomechanical constitutive laws account for a large number of material parameters. The inverse problem that allows their identification is of high non-linearity and of large dimension. By reason of numerical difficulties related to its resolution with gradient-based methods, we developed two new identification methods labelled GAO (Genetic algorithms & Analytical Optimization) and MMIM (Maximum-Minimum Identification Method).GAO advantageously combines deterministic methods of gradient type with genetic algorithms. Its originality consists in introducing analytical computations for the deterministic part leading to a gain in the speed up and in the convergence of genetic algorithms. This strategy is used in the context of anisotropic hyperelasticity.Regarding MMIM method, it operates according to an identification criterion that is expressed with the infinite norm and uses genetic algorithms. MMIM method identifies parameters of quasi-linear viscoelastic laws. It guarantees a constant viscous response that characterises the insensitivity of soft tissues to strain rate. GAO and MMIM methods successfully identified parameters of arterial wall and intervertebral disc tissues. The properties of these tissues are described in a more general context that exhibits the anatomy, histology and deformation mechanism at different hierarchical levels (nano-scale to milli-scale) of collagen-reinforced soft tissues. This gives understanding of the role of forces in relating structure to function in biology.

Photoacoustic tomography (PAT), as well as thermoacoustic tomography (TAT), utilize electromagnetic radiation in its visible, near infrared, microwave, and radiofrequency forms, respectively, to induce acoustic waves in biological tissues for imaging purposes. Combining the advantages of both the high image contrast that results from electromagnetic absorption and the high resolution of ultrasound imaging, these new imaging modalities could be the next successful imaging techniques in biomedical applications. Basic research on PAT and TAT, and the relevant physics, is presented in Chapter I. In Chapter II, we investigate the imaging mechanisms of TAT in terms of signal generation, propagation and detection. We present a theoretical analysis as well as simulations of such imaging characteristics as contrast and resolution, accompanied by experimental results from phantom and tissue samples. In Chapter III, we discuss the further application of TAT to the imaging of biological tissues. The microwave absorption difference in normal and cancerous breast tissues, as well as its influence on thermoacoustic wave generation and the resulting transducer response, is investigated over a wide range of electromagnetic frequencies and depths of tumor locations. In Chapter IV, we describe the mechanism of PAT and the algorithm used for image reconstruction. Because of the broad bandwidth of the laser-induced ultrasonic waves and the limited bandwidth of the single transducer, multiple ultrasonic transducers, each with a different central frequency, are employed for simultaneous detection. Chapter V further demonstrates PAT’s ability to image vascular structures in biological tissue based on blood’s strong light absorption capability. The photoacoustic images of rat brain tumors in this study clearly reveal the angiogenesis that is associated with tumors. In Chapter VI, we report on further developing PAT to image deeply embedded optical heterogeneity in biological tissues. The improved imaging ability is attributed to better penetration by NIR light, the use of the optical contrast agent ICG (indocyanine green) and a new detection scheme of a circular scanning configuration. Deep penetrating PAT, which is based on a tissue’s intrinsic contrast using laser light of 532 nm green light and 1.06 µm near infrared light, is also presented.

Aplicamos a teoria de representação de funções isotrópicas para determinar o número mínimo de invariantes independentes necessários para caracterizar completamente a densidade de energia de deformação de sólido hiperelástico com duas direções de simetria material. Expressamos a densidade de energia em termos de dezoito invariantes e extraímos um conjunto de dez invariantes para analisar dois casos de simetria material. No caso de direções ortogonais, recuperamos o resultado clássico de sete invariantes e oferecemos uma justificativa para a escolha dos invariantes encontrados na literatura. Se as direções não são ortogonais, descobrimos que o número mínimo também é sete e corrigimos um erro em fórmula encontrada na literatura. Uma densidade de energia deste tipo é usada para modelar, na escala macroscópica, materiais de engenharia, tais como compósitos reforçados com fibras, e tecidos biológicos, tais como ossos. / We determine the minimum number of independent invariants that are needed to characterize completely the strain energy density of a hyperelastic solid having two distinct material symmetry directions. We use a theory of representation of isotropic functions to express this energy density in terms of eighteen invariants and extract a set of ten invariants to analyze two cases of material symmetry. In the case of orthogonal directions, we recover the classical result of seven invariants and offer a justification for the choice of invariants found in the literature. If the directions are not orthogonal, we find that the minimum number is also seven and correct a mistake in a formula found in the literature. An energy density of this type is used to model, on the macroscopic scale, engineering materials, such as fiber-reinforced composites, and biological tissues, such as bones.