Is the power spectrum of the QRS complex related to a fractal His-Purkinje system?

Why Ablation of Sites With Purkinje Activation Is Antiarrhythmic: The Interplay Between Fast Activation and Arrhythmogenesis

Ablation of sites showing Purkinje activity is antiarrhythmic in some patients with idiopathic ventricular fibrillation (iVF). The mechanism for the therapeutic success of ablation is not fully understood. We propose that deeper penetrance of the Purkinje network allows faster activation of the ventricles and is proarrhythmic in the presence of steep repolarization gradients. Reduction of Purkinje penetrance, or its indirect reducing effect on apparent propagation velocity may be a therapeutic target in patients with iVF.

Nonlinear measures of heart period variability: decreased measures of symbolic dynamics in patients with panic disorder

Time series of heart period are not linear and recent studies illustrated the importance of using nonlinear methods to quantify the complexity of these time series. We compared different techniques to quantify the nonlinear complexity of these time series in patients with panic disorder and normal controls and correlated these measures with spectral powers in different bands of interest. Twenty-four hour ECG was recorded in 23 normal controls and 29 patients with panic disorder by using Holter records. Time series of heart period were analyzed by using approximate entropies, slopes of 1/f scaling, two algorithms to calculate fractal dimension, and word sequences using symbolic dynamics. Measures using symbolic dynamics, especially word count (WC-100), showed highly significant differences between the two groups similar to some of the frequency domain (spectral) measures, while the other techniques were relatively ineffective to distinguish between the two groups. Different nonlinear techniques may relate to different aspects of nonlinear complexity of the time series. These nonlinear techniques were also not uniform in showing the differences between awake and sleep periods. Some correlate with the measures of respiratory sinus arrhythmia and some measures obtained from symbolic dynamics may reflect not only the nonlinear complexity of the time series but also the total variability in the 24 hr HP time series, especially power in the ultra-low frequency band (< 0.0033 Hz). However, word count (WC-100) had only weak correlations with other measures and discriminated best between the two groups and showed that this nonlinear measure was of additional value to the linear measures in classifying the two groups.

New approach to studies on ECG dynamics: extraction and analyses of QRS complex irregularity time series

How to extract information intensively from ECGs for the diagnosis of cardiovascular diseases and assessment of heart function is a topical subject. Using a method based on the wavelet transform to calculate the irregularity of the QRS complex, which may relate to inotropy, the QRS complex irregularity time series is successfully extracted from original ECG signals. This provides a new approach to studies of ECG dynamics. With the help of non-linear dynamics theory, the QRS complex irregularity time series of eight subjects from the MIT/BIH arrhythmia database are studied qualitatively and quantitatively, and the characteristics of ECG dynamics are analysed extensively. The power spectrum, phase portrait, correlation dimension, largest Lyapunov exponent, time-dependent divergence exponent and complexity measure all verify the fact that ECG dynamics are dominated by an underlying 5-6-dimensional non-linear chaotic system, whose complexity measure is about 0.7. The QRS complex irregularity time series contains abundant information about all parts of the heart and the regulation of the autonomic nervous system, and so further analyses are of great potential theoretical and clinical significance to patho-physiology studies and ambulatory monitoring.

Power spectrum of the QRS complex in patients with panic disorder and normal controls

We performed spectral analysis on the QRS complex of the electrocardiogram obtained using standard limb leads, sampled at 500 Hz with 12 bit precision in 20 normal subjects and 15 patients with panic disorder. We divided the frequency range of the QRS into two bands based on spectral patterns before and after the postural challenge-mid frequency (MF): 7.8-20 Hz; and high frequency (HF): 21-250 Hz. Postural change from supine to standing produced a significant increase in absolute (P = 0.003) and relative HF power (P = 0.00001). Patients with panic disorder had a significantly decreased QRS HF power (P = 0.003). The increase in QRS HF power may have been due to the shortening of the QRS interval in standing posture. The decreased QRS HF power in patients with panic disorder should be further investigated due to the recent reports of an association of phobic anxiety and fatal coronary heart disease, and the possible association of decreased high frequency components of QRS in myocardial infarction.

Nonlinear time series analysis of electrocardiograms

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.

Of the British coastline and the interest of fractals in medicine

We review a certain number of medical applications of a new non-euclidean geometry: the fractal geometry described by Mandelbrot. Examples come from anatomy, cytology, general physiology and physiopathology. Furthermore, real clinical applications are shown, in particular, in cardiology, neurology, ophtalmology, radiology and other imaging techniques. An easy reading mathematical approach is added. Some of the fractal images will certainly capture your attention and spur your interest for further applications of this new concept.