Abstract

RODRIGUEZ VELAQUEZ, Javier et al. Euclidean and Fractal Generalization of Coronary Arteries. Rev. Lasallista Investig. [online]. 2014, vol.11, n.2, pp.29-35. ISSN 1794-4449.

Introduction. Fractal geometry characterizes irregular objects, including the human body. Objective. Develop a geometric method to differentiate, in an experimental model of restenosis in pig arteries, the normal and the pathologic arteries, by the simultaneous use of fractal and Euclidean geometries. Materials and methods. Seven images of histological slides of normal arteries and seven re-stenosed arteries were taken, simultaneously calculating the fractal dimension of the arterial layers -by the use of the Box-Counting method- and the number of squares occupied by the surfaces of three arterial layers. Then, the intrinsic mathematical harmony was calculated and, finally, the differences between the groups were established. Results. The values of the number of squares occupied by the surfaces of the seven normal arteries oscillated between 27 and 74 and the re-stenosed ones oscillated between 83 and 176. The value of the fractal dimension varied between 0.9241 and 1.2578 for the normal arteries and between 0.7225 and 1.2937 for the re-stenosed ones. Conclusion. The methodology developed in this research work could geometrically differentiate, in an objective way, normal and re-stenosed arteries, making the calculations with their occupation spaces as bases.

Keywords : coronary arteries; Box-Counting; fractal geometry; Euclidian geometry; intrinsic mathematical harmony.

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