Fractal sets and their applications in medicine

La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.

Polymer-liquid crystal interface: a molecular dynamics study

Liquid crystals (LCs) are an interesting class of soft condensed matter systems characterized by an unusual combination of fluidity and long-range order, mainly known for their applications in displays (LCDs). However, the interest in LC continues to grow pushed by their application in new technologies in medicine, optical imaging, micro and nano technologies etc. In LCDs uniaxial alignment of LCs is mainly achieved by a rubbing process. During this treatment, the surfaces of polymer coated display substrates are rubbed in one direction by a rotating cylinder covered with a rubbing cloth. Basically, LC alignment involves two possible aligning directions: uniaxial planar (homogeneous) and vertical (homeotropic) to the display substrate. An interesting unresolved question concerning LCs regards the origin of their alignment on rubbed surfaces, and in particular on the polymeric ones used in the display industry. Most studies have shown that LCs on the surface of the rubbed polymer film layer are lying parallel to the rubbing direction. In these systems, micrometric grooves are generated on the film surface along the rubbing direction and also the polymer chains are stretched in this direction. Both the parallel aligned microgrooves and the polymer chains at the film surface may play a role in the LC alignment and it is not easy to quantify the effect of each contribution. The work described in this thesis is an attempt to find new microscopic evidences on the origin of LC alignment on polymeric surfaces through molecular dynamics (MD) simulations, which allow the investigation of the phenomenon with atomic detail. The importance of the arrangement of the polymeric chains in LCs alignment was studied by performing MD simulations of a thin film of a typical nematic LC, 4-cyano-4’-pentylbiphenyl (5CB), in contact with two different polymers: poly(methyl methacrylate)(PMMA) and polystyrene (PS). At least four factors are believed to influence the LC alignment: 1. the interactions of LCs with the backbone vinyl chains; 2. the interactions of LCs with the oriented side groups; 3. the anisotropic interactions of LCs with nanometric grooves; 4. the presence of static surface charges. Here we exclude the effect of microgrooves and of static surface charges from our virtual experiment, by using flat and neutral polymer surfaces, with the aim of isolating the chemical driving factors influencing the alignment of LC phases on polymeric surfaces.