Random walks classici e quantistici

Questa tesi si propone di fornire uno studio sul random walk. Partendo da un approfondimento sulla teoria della probabilita` alla base di tale processo ed in particolare le distribuzioni Binomiale e Gaussiana, si `e potuto studiare il caso del random walk classico, sia nel caso del reticolo monodimensionale che per reticoli a piu` dimensioni. Sempre nell’ambito classico si sono analizzati anche i processi stocastici dipendenti dal tempo, detti Processi di Markov, e il moto browniano, per cui si sono ricavate le equazioni del moto della particella browniana, ovvero le equazioni di Langevin. Si sono in seguito definiti i quattro postulati della meccanica quantistica, introducendo il concetto di quantum bit, per cui si `e fornito un confronto con il bit classico. Si `e inoltre trattato il calcolo quantistico, definendo il concetto di porta logica e affrontando l’esempio importante del gate di Hadamard, utile nel caso del random walk quantistico. Quest’ultimo `e stato introdotto separando il caso nel discreto e nel continuo, cercando di sottolineare le differenze che presenta con il caso classico

A Cationic Contrast Agent in X-ray Imaging of Articular Cartilage: Pre-Clinical Evaluation of Diffusion and Attenuation Properties

The aim of this study was the preliminary assessment of a new cationic contrast agent, the CA4+, via the analysis of spatial distribution in cartilage of ex vivo bovine samples, at micrometer and millimeter scale. Osteochondral plugs (n = 18) extracted from bovine stifle joints (n = 2) were immersed in CA4+ solution up to 26 h. Planar images were acquired at different time points, using a microCT apparatus. The CA4+ distribution in cartilage and saturation time were evaluated. Tibial plates from bovine stifle joints (n = 3) were imaged with CT, before and after 24 h-CA4+ bath immersion, at different concentrations. Afterward, potential CA4+ washout from cartilage was investigated. From microCT acquisitions, the CA4+ distribution differentiated into three distinct layers inside the cartilage, reflecting the spatial distribution of proteoglycans. After 24 h of diffusion, the iodine concentration reached in cartilage was approximately seven times that of the CA4+ bath. The resulting saturation time was 1.9 ± 0.9 h and 2.6 ± 2.9 h for femoral and tibial samples, respectively. Analysis of clinical CT acquisitions confirmed overall contrast enhancement of cartilage after 24 h immersion, observed for each CA4+ concentration. Distinct contrast enhancement was reached in different cartilage regions, depending on tissue's local features. Incomplete but remarkable washout of cartilage was observed. CA4+ significantly improved cartilage visualization and its qualitative analysis

Dual energy computed tomography techniques applied to the characterization of cartilage tissue

The study and visualization of articular cartilage are of great interest for different pathological conditions. Currently, 3D tomographic methods considered for the study of cartilage tissue are Magnetic Resonance Imaging (MRI), which is considered the gold standard technique, and Computed Tomography (CT). However, these have various limitations. MRI is characterized by long acquisition times and difficulties in the presence of metal implants and in the visualization of bones; while CT has difficulties in differentiating soft tissues, characterized by lower attenuation of X-rays. Therefore, in this thesis work, we want to study the properties of Dual Energy Computed Tomography (DECT), which with a single acquisition provides multiple material-specific information using virtual monochromatic and material density reconstructions. In particular, we want to study if DECT without the use of contrast agents, allows a satisfactory visualization of cartilage. Subsequently, we want to investigate how the combined use of DECT and a new cationic contrast agent, called CA4+, can further increase the quality of images. For this purpose, three bovine tibiae supplied by the food chain were considered for a pre-clinical testing. Initially, acquisitions without the use of contrast medium were performed. Afterward, the tibiae were immersed in the contrast medium at three different concentrations (one for each tibia considered). It has been observed that DECT without contrast medium does not allow satisfactory visualization of cartilage, even exploiting the properties of material density and virtual monochromatic reconstructions. On the other hand, the presence of CA4+ contrast medium allows a direct visualization of cartilage and improved distinction with surrounding tissues by exploiting monochromatic and material density reconstructions