Application of the theory of probability and dynamic systems in the evaluation of cardiac dynamics: Study of diagnostic agreement

Abstract

In the present work a new methodology was applied, to evaluate the cardiac status in 16 hours, in continuous electrocardiographic records and Holter, this by means of the theory of probability, and the occupation of spaces from attractors in the general space of Box-Counting, of recent development. 20 normal and 80 pathological records were analyzed, according to the conventional diagnosis. A simulation of the totality of the dynamics was made, taking into account the number of beats, and their maximum and minimum frequencies per hour, during 21 hours. With these data the attractors were built in a phase space. The calculation of the fractal dimension of the attractors was made from the evaluation of the spatial occupation of each one of them and through probability of occupation in the Box-Counting space, establishing its diagnosis with previous mathematical results. Finally, taking the conventional diagnosis as Goldstandard, this and the mathematical result were compared. In the states of normality, the probability of occupation values of the attractors was between 0.157 and 0.286, while for the pathological states, it was 0.019 and 0.141, thereby differentiating the normal and pathological states.