Fractal and euclidean geometric generalization of normal and | 17859
International Research Journals

Fractal and euclidean geometric generalization of normal and restenosed arteries


Javier Rodríguez, Signed Prieto, Catalina Correa, Fernando Polo, Yolanda Soracipa, Vanessa Blanco and Andrés Rodríguez

Euclidean geometry characterizes regular objects, w hile fractal geometry studies irregular objects. Building on previous work, it will be developed a g eneralization of all normal and diseased arterial prototypes in experimental models of restenosis in porcine based on fractal and euclidean measures. Fractal dimension and number of spaces occupied by parts and the whole in the generalized Box Counting space were evaluated in 10 normal and 10 r estenosed arteries. Based on these spatial limits, it was developed a computer simulation of all the poss ibilities of spatial occupation of the layers (islands), determining all the possible arterial pr ototypes. The normality presented values below 100 on the surface of its three islands, while restenosis presents values equal to or greater than 100 in at least one of its three islands. The generalization makes possible to determine a total of 44267 arteries: 36 770 restenosed and 7497 normal. The geometric self-orga nization of the parties with respect to the whole artery, assessed by fractal and euclidean simultane ous measures, allows to determine a finite number of fractal arterial prototypes. It makes possible t o differentiate restenosis and normality, as well a s quantifying their evolution; so its implementation could reduce costs in experimental models.

Share this article