Detecting abnormality in heart dynamics from multifractal analysis of ECG signals

Figure 1. Violin-plot showing the distributions of frequencies with the maximum power for healthy and unhealthy groups for the six chest electrodes.

Figure 2. Two dimensional projections of embedded attractors for ECG signals for three healthy (top panel) and three unhealthy (bottom panel) cases. All the attractors are plotted using the SVD transformation.

Figure 3. Distribution of correlation dimension (D 2) values for healthy subjects (green) and unhealthy ones (red). As can be seen, all the values are less than 4 and so we choose M = 4 as the embedding dimension.

Figure 4. D 2 values as a function of embedding dimension M for four randomly chosen datasets (blue) and their surrogates (magenta). It can be seen that the D 2 values of surrogates sufficiently deviate from that of the original data.

Figure 5. Multifractal spectrum curves for 5 randomly selected subjects from each group. The continuous green curves represent healthy subjects while the dashed red curves are for the non-healthy ones.

Figure 6. Distributions of the difference α 2 − α 1 for healthy(green) and unhealthy(red) groups for different channels. This difference is a measure of the complexity of dynamics underlying the ECG, as described in the text and thus, healthy hearts seem to be more complex than the unhealthy ones.

Figure 7. Scatter plots for electrodes v 1 to v 6 in α 1-γ 1 parameter planes. Green circles in the figure represent the healthy subjects and red squares represent patients. Overall, healthy cases are seen to be clustered whereas the patients are separated from healthy ones and are scattered.

Figure 8. Regions of the parameter plane α 1-γ 1 that separate healthy and unhealthy regions obtained using SVC algorithm for electrodes v 1 to v 6. The actual data points are also shown for comparison with the regions.

Figure 9. Regions corresponding to healthy and unhealthy cases in α 1-α 0 plane found using SVC algorithm.

Figure 10. Accuracy of the SVC algorithm as a function of fraction of training data set. It can be seen that even for the low sizes of the training sample, the algorithm predicts the class labels with extremely high accuracy (>90%).

Figure 11. Violin-plot of α 1 values calculated by replicating several randomly chosen beats for few healthy (top panel) and unhealthy (bottom panel) subjects. Each label on x-axis represents a subject and the α 1 values for time series obtained by replicating different beats of that person are plotted along y-axis. The bigger yellow markers in the plots represent the α 1 values obtained from the complete time series. It can be seen that the actual values for patients tend to fall outside the replicated values.

Figure 12. Distributions of the difference between the mean of the replicated values and the α 1 value for the full time series for healthy and unhealthy groups.