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Open Access Research article

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

Javier O Rodríguez1*, Signed E Prieto2, Catalina Correa3, Pedro A Bernal4, Germán E Puerta5, Sarith Vitery5, Yolanda Soracipa6 and Diana Muñoz7

Author Affiliations

1 MD. Insight Group Director - Investigation Center, Clínica del Country. Professor and Director of the research area: "Mathematical and Physical Theories Applied to Medicine". Universidad Militar Nueva Granada, Cr 11 No. 101-80, Bogotá, Colombia

2 Insight Group researcher - Investigation Center, Clínica del Country. Bogotá, Colombia

3 Psychologist. Insight Group researcher- Investigation Center, Clínica del Country. Bogotá, Colombia

4 Systems Engineering Student. Universidad Nacional de Colombia. Insight Group researcher - Investigation Center, Clínica del Country. Bogotá, Colombia

5 Medicine student. Universidad Militar Nueva Granada, Bogotá, Colombia

6 Degree in Physics student. Universidad Pedagógica Nacional. Insight Group researcher- Investigation Center, Clínica del Country. Bogotá, Colombia

7 Medicine student. Universidad Militar Nueva Granada, Bogotá, Colombia. Special Internship: "Mathematical and Physical Theories Applied to Medicine

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BMC Medical Physics 2010, 10:1  doi:10.1186/1756-6649-10-1

Published: 17 September 2010

Abstract

Background

Fractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications. Starting from a previous work, here we made a theoretical research based on a geometric generalization of the experimental results, to develop a theoretical generalization of the stenotic and restenotic process, based on fractal geometry and Intrinsic Mathematical Harmony.

Methods

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.

Results

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.

Conclusions

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.