Mathematical Law for Evaluating Arrhythmic Cardiac Dynamics: Application for the Arrhythmia Diagnosis

Abstract

The development of a mathematical law for chaotic dynamical systems has allowed to develop a methodology for the mathematical evaluation of cardiac dynamics which quantifies the differen­ces between normality and disease, as well as their evolution. Material and methods: 70 Holter records, 60 with cardiac arrhythmias and 10 normal were taken. From the simulation values of consecutive heart rates, an attractor was built for each Holter. The space occupancy of each at­tractor and its fractal dimension were measured. Mathematical evaluation was applied to each Holter and then the sensitivity, specificity and Kappa coefficient of this evaluation with respect to the Gold Standard was calculated. Results: The cases conventionally diagnosed as arrhythmias presented space occupancy between 29 and 198 for Kp grid, and normal cases had higher values at 200. The sensitivity and specificity were 100 % and Kappa coefficient was 1. Conclusion: The power law quantifies differences between arrhythmias and normal dynamics, assessing the evo­lution dynamics towards normality or to disease, this was evidenced by an increase or decrease of the space occupied by the attractor.

Keywords

• Cardiac dynamics
• Cardiac arrhythmia
• Diagnosis