Sviluppo di un tomografo multi-energy per lo studio pre-clinico di nuove metodiche diagnostiche finalizzate al riconoscimento precoce della patologia tumorale

A new multi-energy CT for small animals is being developed at the Physics Department of the University of Bologna, Italy. The system makes use of a set of quasi-monochromatic X-ray beams, with energy tunable in a range from 26 KeV to 72 KeV. These beams are produced by Bragg diffraction on a Highly Oriented Pyrolytic Graphite crystal. With quasi-monochromatic sources it is possible to perform multi-energy investigation in a more effective way, as compared with conventional X-ray tubes. Multi-energy techniques allow extracting physical information from the materials, such as effective atomic number, mass-thickness, density, that can be used to distinguish and quantitatively characterize the irradiated tissues. The aim of the system is the investigation and the development of new pre-clinic methods for the early detection of the tumors in small animals. An innovative technique, the Triple-Energy Radiography with Contrast Medium (TER), has been successfully implemented on our system. TER consist in combining a set of three quasi-monochromatic images of an object, in order to obtain a corresponding set of three single-tissue images, which are the mass-thickness map of three reference materials. TER can be applied to the quantitative mass-thickness-map reconstruction of a contrast medium, because it is able to remove completely the signal due to other tissues (i.e. the structural background noise). The technique is very sensitive to the contrast medium and is insensitive to the superposition of different materials. The method is a good candidate to the early detection of the tumor angiogenesis in mice. In this work we describe the tomographic system, with a particular focus on the quasi-monochromatic source. Moreover the TER method is presented with some preliminary results about small animal imaging.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.