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

Abstract

Recently, considerable effort was focused on unifying various aspects of cardiac pathophysiology in terms of nonlinear dynamics, particularly through application of chaos theory and the concept of fractal geometry. 1–5 Goldberger et al 4–7 have suggested that the specialized cardiac conduction network, the His-Purkinje system, has a fractal geometry. Fractals, first described by Mandelbrot 8 and found ubiquitously in nature, are self-similar geometric structures composed of subunits that in turn are composed of smaller subunits in a cascade down to microscopic scales. Each subunit appears as a smaller but otherwise identical version of the super-structure. The normal QRS complex is a broad-band wave-form, 9,10 and its power spectrum has been shown to fall with frequency according to the following relation: P(f) = kf β (1) where k is a positive constant and β is a negative constant. 6 This type of frequency dependence is generally referred to as an inverse power law, or more simply, a power law. Goldberger et al 6 have provided a theoretical argument suggesting that the power-law nature of the QRS spectrum is a direct consequence of the proposed fractal geometry of the His-Purkinje system. We sought to test this hypothesis by studying the power spectra of QRS complexes from both normally and abnormally conducted beats. During a ventricular premature beat or an exogenously ventricular-paced beat, involvement of the His-Purkinje system in ventricular depolarization is reduced or absent. 11 Thus, comparing power spectra for these beat types with spectra for normally conducted beats provides a means for establishing the importance of the conduction system in determining QRS spectral morphology.