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.

BackgroundHIV diagnosis, prognostic and treatment requires T CD4 lymphocytes’ number from flow cytometry, an expensive technique often not available to people in developing countries. The aim of this work is to apply a previous developed methodology that predicts T CD4 lymphocytes’ value based on total white blood cell (WBC) count and lymphocytes count applying sets theory, from information taken from the Complete Blood Count (CBC).MethodsSets theory was used to classify into groups named A, B, C and D the number of leucocytes/mm3, lymphocytes/mm3, and CD4/μL3 subpopulation per flow cytometry of 800 HIV diagnosed patients. Union between sets A and C, and B and D were assessed, and intersection between both unions was described in order to establish the belonging percentage to these sets. Results were classified into eight ranges taken by 1000 leucocytes/mm3, calculating the belonging percentage of each range with respect to the whole sample.ResultsIntersection (A ∪ C) ∩ (B ∪ D) showed an effectiveness in the prediction of 81.44% for the range between 4000 and 4999 leukocytes, 91.89% for the range between 3000 and 3999, and 100% for the range below 3000.ConclusionsUsefulness and clinical applicability of a methodology based on sets theory were confirmed to predict the T CD4 lymphocytes’ value, beginning with WBC and lymphocytes’ count from CBC. This methodology is new, objective, and has lower costs than the flow cytometry which is currently considered as Gold Standard.

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