Modeling of the heart's ventricular conduction system using fractal geometry: Spectral analysis of the QRS complex

Abstract

Many biological systems having one or more characteristics that remain constant over a wide range of scales may be considered self-similar or fractal. Geometrical and functional overview of the ventricular conduction system of the heart reveals that it shares structures common to a tree with repeatedly bifurcating “branches,” decreasing in length with each generation. This system may further simplify by assuming that the bifurcating and decreasing process is the same at any generation, that is, the shortening factor and the angle of bifurcation are the same for each generation. Under these assumptions, the conduction system can be described as a fractal tree. A model of the heart's ventricles which consists of muscle cells and a fractal conduction system is described. The model is activated and the dipole potential generated by adjacent activated and resting cells is calculated to obtain a QRS complex. Analysis of the frequency spectrum of the QRS complex reveals that the simulated waveforms show an enhancement in the high frequency components as generations are added to the conduction system. It was also found that the QRS complex shows a form of an inverse power law, which was predicted by the fractal depolarization hypothesis, with a highly correlated straight line for a log-power versus log frequency plot with a slope of approximately −4. Similar results were obtained using real QRS data from healthy subjects.