Abstract
BackgroundFractal 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.MethodsStarting 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.ResultsA 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.ConclusionsThe 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.
Highlights
Fractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications
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 Intrinsic Mathematical Harmony (IMH), which allows to compare the fractal dimensions of parts and whole artery
This concept is mathematically defined as the similarity degree or difference between units and first three decimal ciphers - known as significant ciphers, to compare fractal dimensions of parts and totality of artery
Summary
Fractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications. 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 Intrinsic Mathematical Harmony (IMH), which allows to compare the fractal dimensions of parts and whole artery. This concept is mathematically defined as the similarity degree or difference between units and first three decimal ciphers - known as significant ciphers-, to compare fractal dimensions of parts and totality of artery. These values compared by the IMH determined the difference between healthy and diseased arteries, with values of 3, 3 and 3 for artery 17, while artery 10 presents values equals to 0, 0 and 1
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
