Wavelet $p$-Leader Non Gaussian Multiscale Expansions for Heart Rate Variability Analysis in Congestive Heart Failure Patients

Objective: Numerous indices were devised for the statistical characterization of temporal dynamics of heart rate variability (HRV) with the aim to discriminate between healthy subjects and nonhealthy patients. Elaborating on the concepts of (multi)fractal and nonlinear analyses, the present contribution defines and studies formally novel non Gaussian multiscale representations. Methods: A methodological framework for non Gaussian multiscale representations constructed on wavelet p-leaders is developed, relying a priori neither on exact scale-free dynamics nor on predefined forms of departure from Gaussianity. Its versatility in quantifying the strength and nature of departure from Gaussian is analyzed theoretically and numerically. The ability of the representations to discriminate between healthy subjects and congestive heart failure (CHF) patients, and between survivors and nonsurvivor CHF patients, is assessed on a large cohort of 198 subjects. Results: The analysis leads to conclude that (i) scale-free and multifractal dynamics are observed, both for healthy subjects and CHF patients, for time scales shorter than 170 s; (ii) a circadian evolution of multifractal and non Gaussian properties of HRV is evidenced for healthy subjects, but not for CHF patients; (iii) non Gaussian multiscale indices possess high discriminative abilities between survivor and nonsurvivor CHF patients, at specific time scales (~20 s and ~85 s). Conclusions: The non Gaussian multiscale representations provide evidence for the existence of short-term cascade-type multifractal mechanisms underlying HRV for both healthy and CHF subjects. A circadian evolution of this mechanism is only evidenced for the healthy group, suggesting an alteration of the sympathetic-parasympathetic balance for CHF patients. Significance: Results obtained for a large cohort of subjects suggest that the novel non Gaussian indices might robustly quantify crucial information for clinical risk stratification in CHF patients.