A prediction of bone remodeling thanks to a mechanical signal on cells - Predizione del rimodellamento osseo a partire da un segnale meccanico sulle cellule

This text wants to explore the process of bone remodeling. The idea supported is that the signal, the cells acquire and which suggest them to change in their architectural conformation, is the potential difference on the free boundaries surfaces of collagen fibers. These ones represent the bone in the nanoscale. This work has as subject a multiscale model. Lots of studies have been made to try to discover the relationship between a macroscopic external bone load and the cellular scale. The tree first simulations have been a longitudinal, a flexion and a transversal compression force on a full longitudinal fiber 0-0 sample. The results showed first the great difference between a fully longitudinal stress and a flexion stress. Secondly a decrease in the potential difference has been observed in the transversal force configuration, suggesting that such a signal could be taken as the one, who leads the bone remodeling. To also exclude that the obtained results was not to attribute to a piezoelectric collagen effect and not to a mechanical load, different coupling analyses have been developed. Such analyses show this effect is really less important than the one the mechanical load is responsible of. At this point the work had to explore how bone remodeling could develop. The analyses involved different geometry and fibers percentage. Moreover at the beginning the model was to manually implement. The author, after an initial improvement of it, provided to implement a standalone version thanks to integration between Comsol Multiphysic, Matlab and Excel.

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.