Fractal and Euclidean geometric differentiation of normal and restenosed arteries. Mathematical arterial harmony
Diferenciación geométrica fractal y euclidiana de arterias normales y reestenosadas. Armonía matemática arterial
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Abstract
Background: a methodology was developed that differentiates normality of coronary restenosis in a model of experimentation with porcine, based on fractal geometry and the concept of intrinsic mathematical harmony (AMI). Objective: to develop a methodology that allows the mathematical differentiation of normal and restenosed arteries through the simultaneous application of Euclidean and fractal geometry. Materials and methods: images of histological plaques of three normal and three restenosed arteries were measured, calculating the fractal dimension by means of the box-counting method of three islands delimited by the arterial layers and then the AMI was calculated; At the same time, the number of squares occupying the surface of the three defined islands was calculated and differences were established between groups. Results: the fractal dimension of the normal arteries was between 1.0184 and 1.2578 and in the restenosed ones between 0.6881 and 1.1651; the values of the number of squares occupied by the surface of the arteries oscillated between 34 and 76 for the normal arteries and for the restenosed ones between 91 and 162, thus the islands of the normal arteries always had occupation values less than 100, while the restenosadas always presented a greater or equal value in at least one of their islands. Conclusions: a fractal and Euclidean mathematical self-organization of the arterial restenosis process was revealed, which allows to establish differences between these states, quantifying the progress of arterial occlusion. Abbreviations: AMI, intrinsic mathematical harmony; EAC, coronary artery disease.
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