Space of phases: Space of 2 or more dimensions, in which the dynamics of a system is represented geometrically, by means of the graphic representation of ordered pairs of values of a dynamic variable consecutive in time.
Fractal Dimension of Box-Counting: It is defined from the following equation:
D is the fractal dimension; N is the number of frames occupied by the object in the grid with partition degree k.
Simplified Box-Counting equation: Obtained by Equation 1, applied to two squares with a proportion of ½ in its dimensions, obtaining the formula:
Kp represents the number of squares occupied in the smallest grid and Kg those corresponding to the large grid.
Exponential law of cardiac chaotic dynamics17-20 It is obtained after a clearing of Equation 2 and is expressed as follows:
450 continuous electrocardiographic and Holter records were taken, evaluated in 21 hours by an expert cardiologist, of subjects older than 21 years, 100 corresponded to cases diagnosed as normal by the clinician and 350 corresponded to patients with cardiac pathologies. The records came from databases of previous investigations of the Insight group, which allowed for a retrospective study.
The clinical diagnoses established by the expert were masked. The maximum and minimum values of the heart rate were taken every hour and the beats per hour, in 21 and 16 hours. With these data, a quasi-random sequence of heart frequencies was generated by an equiprobable algorithm. Then, the cardiac attractors were constructed, plotting one frequency against the next in time in the phase space. The fractal dimension was calculated with the Box-Counting method (Equation 2) through the superposition of two grids, with which the spatial occupancy in Kp and Kg of the attractors was determined.
From Equation 3, the mathematical diagnosis of the records was determined, according to the previously developed law17-20, according to which, the dynamics of acute cardiac pathologies exhibit occupation spaces in the Kp grid below 73, normality it presents occupation spaces in this grid over 200, and the evolution towards the disease presents occupation spaces between 73 and 200. The mathematical diagnosis was compared in 16 and 21 hours, with which the agreement between both was established.
The diagnoses established by the clinical expert were taken as Gold Standard, according to conventional clinical parameters and were compared with the mathematical diagnosis in 16 hours, once the agreement of the diagnoses established by the mathematical law was confirmed at 16 and 21 hours. For the purposes of the statistical analysis, cases with acute and normal disease were taken. False negatives, false positives, true positives and true negatives were calculated. From a 2x2 contingency table, sensitivity and specificity were determined. Also, the Kappa coefficient was calculated.
This research is governed by the ethical, technical and scientific principles set forth in the Declaration of Helsinki of the World Medical Association. According to the provisions of Resolution 8430 of 1993 of the Colombian Ministry of Health, it is defined as a minimum risk investigation, since physical-mathematical calculations are made from non-invasive and non-invasive reports and tests requested and performed according to conventionally established protocols. protecting the information and integrity of patients.