Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony

Starting from all the possibilities of space occupation in box-counting space, all arterial prototypes differentiating normality and disease were obtained with a computational simulation. Measures from 2 normal and 3 re-stenosed arteries were used as spatial limits of the generalization.A new methodology in animal experimentation was developed, based on fractal geometric generalization. With this methodology, it was founded that the occupation space possibilities in the stenotic process are finite and that 69,249 arterial prototypes are obtained as a total.The Intrinsic Mathematical Harmony reveals a supra-molecular geometric self-organization, where the finite and discrete fractal dimensions of arterial layers evaluate objectively the arterial stenosis and restenosis process.The fractal geometry, developed by Benoit Mandelbrot, allows irregular objects characterization, through fractal dimensions [1,2]. There are several fractal dimension definitions and different methodologies for calculation, applied according to measured object [2]. For wild fractals, such as those that characterize the morphology, box counting method is used. Fractal geometry have been used in experimental and clinical applications [3,4], for example to differentiate cardiac lesion degree in angiography, to characterize pre-neoplasic cervical cells or normal and abnormal erythrocyte morphology [5-7]. However, in some cases, isolated fractal measures not differentiate normality and disease, and could present limitations for their effective application [8].This problem was analyzed [9] in the restenosis phenomena. Although arteries present irregular form and structure, it is common to do Euclidean measurements of their shape for their posterior statistical analysis [10,11]. Rodríguez et al. [9] demonstrated that isolated fractal dimensions of whole artery or parts can not differentiate between groups with and without restenosis, and developed a new methodology for differentiation based on Intrins