Heart rate variability, multifractal multiscale patterns and their assessment criteria

Both the central nervous system and the autonomic nervous system are complex physiological networks which modulate the heart rate. They are spatially extended, have built-in delays and work on many time scales simultaneously-nonhomogeneous networks with multifractal dynamics. The object of our research was the analysis of human heart rate variability (HRV) using the nonlinear multiscale multifractal analysis (MMA) method for several cardiovascular diseases. The analysis of HRV (night-time recordings) involved six groups of patients: 61 healthy persons, 104 cases with aortic valve stenosis, 42 with hypertrophic cardiomyopathy, 36 with atrial fibrillation, 70 patients with coronary artery disease and 19 with congestive heart failure. 85% of patients formed a training data set (282 subjects) and 15% formed a test data set (50 subjects).

Multiscale multifractal analysis allows one to analyze the complexity of HRV and find the scaling properties of its fluctuations. The main result of MMA is the Hurst surface, the shape of which changes depending on the medical case analyzed. We prepared six criteria to distinguish a multifractal pattern for healthy subjects. We also prepared additional criteria, enabling one to recognize atrial fibrillation.

For the training data set, we obtained the following accuracy statistics in distinguishing the patients from the healthy: 68% for coronary artery disease, 67% for hypertrophic cardiomyopathy, 88% for atrial fibrillation, 74% for aortic valve stenosis and 83% for congestive heart failure. For the complete training data set we obtained an accuracy of 73%, and 80% for the test data set (mean for ten random selections of the test data set).

The results of MMA presented here provide an additional input into the diagnostic process and may help to create a paradigm for future studies on medical screening methods, especially in that MMA focuses on very low frequencies of HRV not easily accessible by standard medical techniques. Satisfactory statistics for screening using both MMA and the unfiltered version of LF/HF indicate that the nature of the complete network moderating heart rhythm needs to be studied and that sinus rhythm in clinical patients may not always be separated from arrhythmia when its incidence is large.