Los biocombustibles se utilizan principalmente en forma de blends, mezclados con combustibles fósiles, derivados del petróleo. Los blends de nafta + bioetanol juegan un rol muy importante en países tales como Brasil y EEUU. Existen otras alternativas, tales como etanol + diesel y diesel + biodiesel. Cada combinación contempla un rango de composiciones de mezcla. Si sumamos a esto el hecho de que nuevos avances en el procesamiento de la biomasa pueden hacer aparecer nuevos biocombustibles, resulta clara la utilidad de disponer de un modelo termodinámico de soporte que permita predecir propiedades de interés de las mezclas combustibles. Esto permitiría, entre otras cosas, ahorrar tiempo y dinero en experiencias de laboratorio, en la búsqueda de mezclas con buen potencial, descartando aquellas que no satisfagan los criterios fijados. En la presente tesis se estudian en particular los blends naftas + bioalcoholes. La nafta es una mezcla multicomponente constituida principalmente por cuatro familias de hidrocarburos: alcanos normales, ramificados y cíclicos e hidrocarburos aromáticos. La presencia de compuestos oxigenados tiene un fuerte impacto sobre la volatilidad y el comportamiento de fases los combustibles, debido a la no-idealidad típica de mezclas de compuestos polares y no-polares. Por otra parte, las mezclas están formadas por un gran número de compuestos de una misma familia, por lo que los modelos a contribución grupal constituyen la mejor opción para calcular sus propiedades. Comparados con los modelos moleculares, los modelos a contribución grupal requieren un menor número de parámetros para caracterizar las interacciones entre los componentes de una mezcla y ofrecen una mayor capacidad predictiva. En esta tesis se utiliza la ecuación de estado a contribución grupal con asociación GCA-EoS. En el Capítulo I se introduce el tema de tesis y se plantean sus objetivos. En el Capítulo II se describen las características del modelo GCA-EoS y se explican en detalle cada uno de sus términos. Los Capítulos III al VII describen el proceso de parametrización llevado a cabo sobre mezclas de agentes oxigenados (alcoholes y éteres) y agua, con cada tipo de hidrocarburo (alcano normal, ramificado y cíclico e hidrocarburo aromático) presente en las naftas. En el Capítulo VIII se analizan detalladamente las propiedades de volatilidad y tolerancia al agua de las naftas, y el impacto que produce sobre las mismas, el agregado de un compuesto oxigenado como aditivo. El Capítulo IX muestra la simulación del proceso de extracción/deshidratación de etanol mediante un fluido supercrítico (propano), utilizando como soporte termodinámico la ecuación GCA-EoS con los parámetros determinados en esta Tesis. Finalmente, en el Capítulo X se discuten las conclusiones generales de este trabajo de tesis, y se propone trabajo a futuro que permita ampliar las capacidades en el modelado de mezclas de biocombustibles y combustibles fósiles. / Biofuels are mainly used as blends, mixed with fossil fuels derived from crude oil. Bioethanol + gasoline blends play a major role in countries like Brazil and USA. There are other alternative blends, such as ethanol + diesel and biodiesel + diesel. Every combination covers a range of compositions. If we also take into account that new developments in biomass processing can make new biofuels available, it becomes clear the advantage of having a suitable thermodynamic model to predict the properties of the fuel blends. This would allow, among other things, to save time and money in laboratory experiments, in the search of mixtures with good potential as transport fuels, disregarding those that do not meet standard properties. In particular, bioalcohol + gasoline blends are studied in the present thesis. Gasoline is a multicomponent mixture of hydrocarbons, belonging mainly to four families: normal-, branched- and cyclic-alkanes and aromatic hydrocarbons. The presence of oxygenated compounds has a strong impact on the volatility and phase behavior of fuels, due to the typical non-ideality of mixtures having polar and non-polar compounds. On the other hand, a great number of different compounds in these mixtures belong to the same chemical species. For this reason group-contribution models are the best option to calculate their properties. Compared against molecular models, group-contribution models require a lower number of parameters to represent interactions among mixture components and offer a more ample predictive capacity. In this Thesis, the group-contribution with association equation of state GCA-EoS is used. In Chapter I, the research subject and objectives of the Thesis are presented. Chapter II describes the characteristics of the GCA-EoS model and explains in detail each term of the equation. Chapters III to VII explain the parameterization process carried out on mixtures containing oxygenated additives (alcohols and ethers), water and each family of the typical gasoline hydrocarbons (normal-, branched- and cyclic-alkanes and aromatic hydrocarbons). Chapter VIII contains a detailed analysis of the volatility properties and water tolerance of gasoline, and discusses the impact produced on these properties by the addition of oxygenated additives to the fuel. Chapter IX shows the results of the simulation of a supercritical process for the extraction and dehydration of bioethanol from a fermentation broth. The GCA-EoS equation, with the parameters obtained in this thesis, was used to model the phase equilibrium conditions in each of the process units. Finally, Chapter X discusses the general results of the thesis and proposes future work to increase modeling capacity in the area of biofuel-fossil fuel blends.

Assumindo que a matéria nuclear seja um fluido perfeito, estudamos a propagação de perturbações na densidade bariônica. A equação de estado é obtida através de um modelo relativístico em campo médio, o qual é uma variante do modelo não-linear de Walecka. A expansão das equações de Euler e da continuidade na hidrodinâmica relativística em torno das configurações de equilíbrio nos levam a equações diferenciais para a perturbação na densidade. Resolvemos tais equações numericamente para perturbações lineares e esféricas mediante pulsos iniciais. Para perturbações lineares econtramos soluções solitônicas de pulsos isolados e soluções com vários solitons seguidas de ``radiação\'\'. Dependendo da equação de estado um forte amortecimento pode ocorrer. Consideramos também a evolução de perturbações em um meio sem efeitos dissipativos. Nesse caso observamos a formação e quebra de ondas de choque. Depois estudamos todo o formalismo na matéria nuclear em temperatura finita. Nossos resultados podem ser relevantes para análise de dados do RHIC. Eles sugerem que ondas de choque formadas na fase de plasma de quarks e gluons podem sobreviver e se propagar na fase hadrônica. Também estudamos a equação de onda não-linear para perturbações na densidade bariônica e densidade de energia no plasma de quarks e gluons (QGP). Sob certas condições solitons podem existir no QGP. Finalmente discutimos métodos alternativos de soluções de equações di-ferenciais não-lineares. / Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ``radiation\'\'. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. We also study the non-linear wave equation for pertubations in baryon density and energy density in quark-gluon-plasma (QGP). Under certains conditions solitons may exist in QGP. Finally we discuss alternatives methods for solving non-linear differential equations.

Assumindo que a matéria nuclear seja um fluido perfeito, estudamos a propagação de perturbações na densidade bariônica. A equação de estado é obtida através de um modelo relativístico em campo médio, o qual é uma variante do modelo não-linear de Walecka. A expansão das equações de Euler e da continuidade na hidrodinâmica relativística em torno das configurações de equilíbrio nos levam a equações diferenciais para a perturbação na densidade. Resolvemos tais equações numericamente para perturbações lineares e esféricas mediante pulsos iniciais. Para perturbações lineares econtramos soluções solitônicas de pulsos isolados e soluções com vários solitons seguidas de ``radiação\'\'. Dependendo da equação de estado um forte amortecimento pode ocorrer. Consideramos também a evolução de perturbações em um meio sem efeitos dissipativos. Nesse caso observamos a formação e quebra de ondas de choque. Depois estudamos todo o formalismo na matéria nuclear em temperatura finita. Nossos resultados podem ser relevantes para análise de dados do RHIC. Eles sugerem que ondas de choque formadas na fase de plasma de quarks e gluons podem sobreviver e se propagar na fase hadrônica. Também estudamos a equação de onda não-linear para perturbações na densidade bariônica e densidade de energia no plasma de quarks e gluons (QGP). Sob certas condições solitons podem existir no QGP. Finalmente discutimos métodos alternativos de soluções de equações di-ferenciais não-lineares. / Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ``radiation\'\'. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. We also study the non-linear wave equation for pertubations in baryon density and energy density in quark-gluon-plasma (QGP). Under certains conditions solitons may exist in QGP. Finally we discuss alternatives methods for solving non-linear differential equations.

International Telemetering Conference Proceedings / October 30-November 02, 1995 / Riviera Hotel, Las Vegas, Nevada / OSC is presently developing a high-rate telemetry collection and formatting component for NASA's EOS-AM1 spacecraft. This device, called the Science Formatting Equipment, is capable of collecting data at aggregate rates exceeding 130 Mbps. The collected data is formatted into CCSDS compatible data structures, error coded, and then routed either to a downlink output or to a recording device at data rates up to 150 Mbps. This paper serves as a brief introduction to this component.

The Peng-Robinson equation of state (PR EOS) is incorporated with the infinite linear association model and the monomer-dimer association model as well as two different sets of mixing rules to result in four different forms of equations of state. The reformulated PR EOS have been used to represent the vapor pressures and liquid densities of pure associating compounds. The vapor pressure and liquid density values calculated by means of the reformulated PR EOS are in good agreement with the experimental data in the literature.<p>The application of the reformulated PR EOS could be extended to represent the VLE behavior of associating systems. The capabilities of different association-incorporated EOS are compared with the Hong-Hu equation, the AMH equation and the Wilson equation, respectively. The results show that, in general, the reformulated PR EOS are superior to the Wilson equation for all tested systems with the exception of alkanol-hydrocarbon systems and at least as good as the Hong-Hu equation, the AMH equation, although the number of tested systems from Hong and Hu and Nan et al. are less than the one from the present work.<p>The excess molar enthalpies of the ethanol-n-hexane and the ethanol-cyclohexane systems at 298.15 K were measured in an LKB 2107 microcalorimeter and compared with the experimental data in the literature. Additionally, new excess molar enthalpy data, measured at 298.15 K, have been reported for the ethanol-n-hexane-cyclohexane ternary system in the present work. Smooth representations of the results are described and used to construct contours of constant enthalpy on a Roozeboom diagram. The reasonable estimates of the excess enthalpies of the three constituent-binary mixtures can be obtained from both the Liebermann-Fried model and the Flory theory. <p>Finally, an attempt has been made to represent, simultaneously, both VLE and excess enthalpy behavior of the ethanol-n-hexane and ethanol-cyclohexane systems by using the Wilson equation and one of the reformulated PR EOS. Both the reformulated PR EOS and the Wilson equation could be extended to predict the ethanol-n-hexane-cyclohexane ternary system at 298.15 K with the binary interaction parameters determined from the experimental VLE data of the three constituent-binary mixtures. The calculated results show that the reformulated PR EOS is better than or as good as the Wilson equation in predicting the excess enthalpies of selected binary and ternary systems involving one associating species. However, quantitative discrepancies with the experimental data are observed.

The Peng-Robinson equation of state (PR EOS) is incorporated with the infinite linear association model and the monomer-dimer association model as well as two different sets of mixing rules to result in four different forms of equations of state. The reformulated PR EOS have been used to represent the vapor pressures and liquid densities of pure associating compounds. The vapor pressure and liquid density values calculated by means of the reformulated PR EOS are in good agreement with the experimental data in the literature.<p>The application of the reformulated PR EOS could be extended to represent the VLE behavior of associating systems. The capabilities of different association-incorporated EOS are compared with the Hong-Hu equation, the AMH equation and the Wilson equation, respectively. The results show that, in general, the reformulated PR EOS are superior to the Wilson equation for all tested systems with the exception of alkanol-hydrocarbon systems and at least as good as the Hong-Hu equation, the AMH equation, although the number of tested systems from Hong and Hu and Nan et al. are less than the one from the present work.<p>The excess molar enthalpies of the ethanol-n-hexane and the ethanol-cyclohexane systems at 298.15 K were measured in an LKB 2107 microcalorimeter and compared with the experimental data in the literature. Additionally, new excess molar enthalpy data, measured at 298.15 K, have been reported for the ethanol-n-hexane-cyclohexane ternary system in the present work. Smooth representations of the results are described and used to construct contours of constant enthalpy on a Roozeboom diagram. The reasonable estimates of the excess enthalpies of the three constituent-binary mixtures can be obtained from both the Liebermann-Fried model and the Flory theory. <p>Finally, an attempt has been made to represent, simultaneously, both VLE and excess enthalpy behavior of the ethanol-n-hexane and ethanol-cyclohexane systems by using the Wilson equation and one of the reformulated PR EOS. Both the reformulated PR EOS and the Wilson equation could be extended to predict the ethanol-n-hexane-cyclohexane ternary system at 298.15 K with the binary interaction parameters determined from the experimental VLE data of the three constituent-binary mixtures. The calculated results show that the reformulated PR EOS is better than or as good as the Wilson equation in predicting the excess enthalpies of selected binary and ternary systems involving one associating species. However, quantitative discrepancies with the experimental data are observed.

Since the plus fraction of reservoir fluids has some uncertainty in its molecular weight and critical properties, equation-of-state, EOS, are generally not predictive without tuning its parameters to match experimental data. Tuning of the EOS is found to be the best method for improving the predictions of compositional reservoir simulators. The proposed strategy for tuning EOS consists of seven steps: (1) split the laboratory plus fraction to single carbon number groups, SCN, usually up to SCN 44; the last component will be C45+, (2) use set of correlations to calculate the critical properties and acentric factor for each SCN group, (3) match the saturation pressure at reservoir temperature by altering the measured value of the molecular weight of the plus fraction using the extended composition, (4) group SCN groups to multiple carbon number groups, MCN, (5) assign critical properties and acentric factor for each MCN group, (6) rematch the saturation pressure at reservoir temperature using the grouped composition, and (7) match the volumetric data by regressing on volume shift parameters of all components in grouped composition. This research shows an accurate method to split the plus fraction to SCN groups. The most accurate set of correlations to calculate the critical properties and acentric factor for each SCN group that will result in a small adjustment for the molecular weight of the plus fraction when saturation pressure is matched using the extended composition. The proposed strategy groups the extended composition to eight pseudocomponents. The binary interaction coefficients between hydrocarbons and between hydrocarbons and non-hydrocarbons are set to zero which dramatically reduces the simulation time. The strategy proposed in this research for tuning EOS to match experimental data has been tested for a wide range of C7+ mole% (4 – 25) which covers gas condensate and volatile oil samples. Also, using this strategy to tune EOS at reservoir temperature will accurately predict the fluid properties at separator conditions and saturation pressures at different temperatures. The scope of this research is to come up with an accurate and systematic technique for tuning an EOS for use in compositional simulation.

Les facteurs de transcription Eos et Helios ont été décrits comme étant des modulateurs des fonctions des cellules T régulatrices (Treg). Nos résultats suggèrent qu’Eos et Helios ne sont pas nécessaires, ni pour la différenciation, ni pour les principales fonctions des cellules Treg CD4+. Cependant, les cellules Helios-/- présentent une meilleure activité suppressive et à un profil transcriptomique de cellules Treg activées. Pour tester si Eos et Helios coopèrent pour réguler les fonctions des cellules Treg, nous avons analysé les souris doubles mutantes. Nos découvertes indiquent que la perte combinée d’Eos et d’Helios n’a pas d’effet sur la biologie des cellules Treg. De plus, nous avons montré qu’Eos et Helios sont induits dans les cellules Treg CD8+. Néanmoins, seule la perte d’Helios ou celle combinée d’Eos et d’Helios affectent leur différenciation. Tous ces résultats suggèrent donc qu’Eos et Helios ne sont pas requis pour réguler les fonctions essentielles des cellules Treg. / The transcription factors Eos and Helios have been described as modulators of regulatory T cell (Treg) functions. Our results suggest that they are not necessary for the differentiation and essential functions of CD4+ Treg cells. However, Helios-/- cells present a superior suppressive activity and a transcriptional profile of activated Treg cells. To test if Eos and Helios can cooperate to regulate Treg cell functions, we then analyzed double null mice. Our findings indicate that loss of both Eos and Helios has no effect on Treg cell biology during homeostasis. In addition, we showed that Eos and Helios are induced in CD8+ Treg cells. However, only loss of Helios, or both Helios and Eos, affect their differentiation. Altogether, these results suggest that Eos and Helios are not required regulate essential CD4+ Treg cell functions, but the absence of Helios may have an impact on their level of activation. Finally, Helios and Eos may play role of in the CD8+ Treg cell compartment.

Pour satisfaire aux dernières réglementations en matière d'émissions, des progrès importants sont encore attendus des moteurs à combustion interne. De plus, améliorer l'efficacité du moteur pour réduire les émissions et la consommation de carburant est devenu plus essentiel qu'auparavant. Mais, de nombreux phénomènes complexes restent mal compris dans ce domaine, tels que le processus d'injection de carburant. Nombreux logiciels pour la dynamique des fluides numérique (CFD) prenant en compte le changement de phase (comme la cavitation) et la modélisation de l’injection ont été développés et utilisés avec succès dans le processus d’injection. Néanmoins, il existe peu de codes CFD capables de simuler avec précision des conditions d’injection transcritiques, à partir d'une condition de température de carburant sous-critique vers un mélange supercritique dans la chambre de combustion. En effet, la plupart des modèles existants peuvent simuler des écoulements à phase unique, éventuellement dans des conditions supercritiques, ou des écoulements diphasiques dans des conditions sous-critiques. Par conséquent, il manque un modèle complet capable de traiter les conditions transcritiques, y compris la transition de phase possible entre les régimes souscritiques et supercritiques, ou entre les écoulements monophasiques et diphasiques, de manière dynamique. Cette thèse a pour objectif de relever ce défi.Pour cela, des modèles d'écoulement diphasique compressible de fluide réel basés sur une approche eulérienne-eulérienne avec prise en compte de l'équilibre de phase ont été développés et discutés dans le présent travail. Plus précisément, un modèle à 6-équation entièrement compressibles incluant les équations de bilan des phases liquide et gazeuse résolues séparément ; et un modèle à 4-équation qui résout les équations des bilans liquide et gazeux en équilibre mécanique et thermique sont proposés dans ce manuscrit. L’équation d’état Peng-Robinson EoS est sélectionné pour fermer les deux systèmes et pour faire face aux éventuels changements de phase et à la transition ou à la séparation des phases. En particulier, un solveur d'équilibre de phase a été développé et validé. Ensuite, une série de tests académiques 1D portant sur les phénomènes d'évaporation et de condensation effectués dans des conditions sous-critiques et supercritiques a été simulée et comparée aux données de la littérature et aux résultats académiques disponibles. Ensuite, les modèles d'écoulement en deux phases entièrement compressibles (systèmes à 6-équation et à 4- équation) ont été utilisés pour simuler les phénomènes de cavitation dans une buse 3D de taille réelle afin d'étudier l'effet de l’azote dissous sur la création et le développement de la cavitation. Le bon accord avec les données expérimentales prouve que le solveur proposé est capable de gérer le comportement complexe du changement de phase dans des conditions sous-critiques. Enfin, la capacité du solveur à traiter l’injection transcritique à des pressions et températures élevées a été validée par la modélisation réussie de l’injecteur Spray A du réseau de combustion moteur (ECN). / To satisfy latest stringent emission regulations, important progress is still be expected from internal combustion engines. In addition, improving engine efficiency to reduce the emission and fuel consumption has become more essential than before. But many complex phenomena remain poorly understood in this field, such as the fuel injection process. Numerous software programs for computational fluid dynamics (CFD) considering phase change (such as cavitation) and injection modelling, have been developed and used successfully in the injection process. Nevertheless, there are few CFD codes able to simulate correctly transcritical conditions starting from a subcritical fuel temperature condition towards a supercritical mixture in the combustion chamber. Indeed, most of the existing models can simulate either single-phase flows possibly in supercritical condition or two-phase flows in subcritical condition; lacking therefore, a comprehensive model which can deal with transcritical condition including possible phase transition from subcritical to supercritical regimes, or from single-phase to two-phase flows, dynamically. This thesis aims at dealing with this challenge. For that, real fluid compressible two-phase flow models based on Eulerian-Eulerian approach with the consideration of phase equilibrium have been developed and discussed in the present work. More precisely, a fully compressible 6-equation model including liquid and gas phases balance equations solved separately; and a 4-equation model which solves the liquid and gas balance equations in mechanical and thermal equilibrium, are proposed in this manuscript. The Peng-Robinson equation of state (EoS) is selected to close both systems and to deal with the eventual phase change or phase transition. Particularly, a phase equilibrium solver has been developed and validated. Then, a series of 1D academic tests involving the evaporation and condensation phenomena performed under subcritical and supercritical conditions have been simulated and compared with available literature data and analytical results. Then the fully compressible two-phase flow models (6-Equation and 4-Equation systems) have been employed to simulate the cavitation phenomena in a real size 3D nozzle to investigate the effect of dissolved N2 on the inception and developing of cavitation. The good agreement with experimental data proves the solver can handle the complex phase change behavior in subcritical condition. Finally, the capability of the solver in dealing with the transcritical injection at high pressure and temperature conditions has been further validated through the successful modelling of the engine combustion network (ECN) Spray A injector.

L'ostéoporose est une maladie du squelette caractérisée par une perte de la qualité osseuse qui entraîne un risque de fracture accru, notamment au niveau vertébral. Des modèles en éléments finis basés sur la tomodensitométrie permettent d'estimer la résistance vertébrale, et donc le risque de fracture, mais leur utilisation en routine clinique est limitée par le coût et l'irradiation engendrée par la tomodensitométrie. L'estimation la résistance vertébrale à partir d'un modèle en éléments finis basés sur l'imagerie basse dose, telle que l'absorptiométrie biphotonique à rayons X, ou la stéréo-radiographie EOS en double énergie, permettrait une utilisation en routine clinique. Cette thèse contribue au développement de la modélisation à partir de l'imagerie basse dose pour la prédiction du risque de fracture. Un modèle en éléments finis de résistance vertébrale y est évalué par rapport à un modèle basé sur la tomodensitométrie, et une étude de sensibilité identifie les facteurs importants du modèle sont analysés. Des méthodes de maillage hexaédrique morpho-réalistes à partir de la reconstruction 3D, et d'estimation de la distribution de densité à partir d'image 2D de densité y sont développées. De plus, profitant des possibilités du système EOS qui permet de radiographier le patient de la tête aux pieds, une méthode préliminaire est proposée pour estimer l'effort exercé sur les vertèbres in vivo. Nous espérons que nos méthodes pourront être utilisées très prochainement in vivo, et contribuer à l'estimation du risque de fracture ostéoporotique, et à la prise en charge des patients à risque de fracture. / Osteoporosis is a bone disease which decreases bone quantity and quality, and increases fracture risk, notably at the vertebral level. CT-scan-based finite element models allow predicting vertebral strength, and thus fracture risk, but their use in routine clinical practice is limited by the cost and accessibility of CT-scan. However, vertebral strength prediction from a finite element model based on low dose images, such as dual X-ray absorptiometry or EOS stereo-radiography in dual energy, would allow a wider use. This PhD thesis contributes to develop fracture risk estimation by such a model. The low dose approach is evaluated in comparison to CT-based finite element model, and a sensitivity study is performed to identify the most important parameters of the model. Hexahedral morpho-realistic meshing techniques from 3D reconstruction and estimation methods for the 3D bone mineral density distribution from low dose images are developed and evaluated. Moreover, taking advantage of EOS system's possibility to take full body radiographs in standing position, a preliminary method is proposed to estimate the load applied to vertebra in vivo. We hope those methods will be used soon in vivo, and will contribute to estimating osteoporotic fracture risk estimation in clinical situations.