Evaluation of bone strength: microtomographic tecniques

This thesis is a part of a larger study about the characterization of mechanical and histomorphometrical properties of bone. The main objects of this study were the bone tissue properties and its resistance to mechanical loads. Moreover, the knowledge about the equipment selected to carry out the analyses, the micro-computed tomography (micro-CT), was improved. Particular attention was given to the reliability over time of the measuring instrument. In order to understand the main characteristics of bone mechanical properties a study of the skeletal, the bones of which it is composed and biological principles that drive their formation and remodelling, was necessary. This study has led to the definition of two macro-classes describing the main components responsible for the resistance to fracture of bone: quantity and quality of bone. The study of bone quantity is the current clinical standard measure for so-called bone densitometry, and research studies have amply demonstrated that the amount of tissue is correlated with its mechanical properties of elasticity and fracture. However, the models presented in the literature, including information on the mere quantity of tissue, have often been limited in describing the mechanical behaviour. Recent investigations have underlined that also the bone-structure and the tissue-mineralization play an important role in the mechanical characterization of bone tissue. For this reason in this thesis the class defined as bone quality was mainly studied, splitting it into two sub-classes of bone structure and tissue quality. A study on bone structure was designed to identify which structural parameters, among the several presented in the literature, could be integrated with the information about quantity, in order to better describe the mechanical properties of bone. In this way, it was also possible to analyse the iteration between structure and function. It has been known for long that bone tissue is capable of remodeling and changing its internal structure according to loads, but the dynamics of these changes are still being analysed. This part of the study was aimed to identify the parameters that could quantify the structural changes of bone tissue during the development of a given disease: osteoarthritis. A study on tissue quality would have to be divided into different classes, which would require a scale of analysis not suitable for the micro-CT. For this reason the study was focused only on the mineralization of the tissue, highlighting the difference between bone density and tissue density, working in a context where there is still an ongoing scientific debate.

Iterative regularization methods for ill-posed problems

This Ph.D thesis focuses on iterative regularization methods for regularizing linear and nonlinear ill-posed problems. Regarding linear problems, three new stopping rules for the Conjugate Gradient method applied to the normal equations are proposed and tested in many numerical simulations, including some tomographic images reconstruction problems. Regarding nonlinear problems, convergence and convergence rate results are provided for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting.

Automotive diesel engine transient operation: modeling, optimization and control

Traditionally, the study of internal combustion engines operation has focused on the steady-state performance. However, the daily driving schedule of automotive engines is inherently related to unsteady conditions. There are various operating conditions experienced by (diesel) engines that can be classified as transient. Besides the variation of the engine operating point, in terms of engine speed and torque, also the warm up phase can be considered as a transient condition. Chapter 2 has to do with this thermal transient condition; more precisely the main issue is the performance of a Selective Catalytic Reduction (SCR) system during cold start and warm up phases of the engine. The proposal of the underlying work is to investigate and identify optimal exhaust line heating strategies, to provide a fast activation of the catalytic reactions on SCR. Chapters 3 and 4 focus the attention on the dynamic behavior of the engine, when considering typical driving conditions. The common approach to dynamic optimization involves the solution of a single optimal-control problem. However, this approach requires the availability of models that are valid throughout the whole engine operating range and actuator ranges. In addition, the result of the optimization is meaningful only if the model is very accurate. Chapter 3 proposes a methodology to circumvent those demanding requirements: an iteration between transient measurements to refine a purpose-built model and a dynamic optimization which is constrained to the model validity region. Moreover all numerical methods required to implement this procedure are presented. Chapter 4 proposes an approach to derive a transient feedforward control system in an automated way. It relies on optimal control theory to solve a dynamic optimization problem for fast transients. From the optimal solutions, the relevant information is extracted and stored in maps spanned by the engine speed and the torque gradient.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.