Modeling of the heart's ventricular conduction system using fractal geometry: Spectral analysis of the QRS complex |
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Authors: | Omer Berenfeld Dror Sadeh Shimon Abboud |
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Institution: | (1) Medical Physics Group, School of Physics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Israel;(2) Biomedical Engineering Program, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel |
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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. |
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Keywords: | Heart modeling Fractal geometry ECG simulation Spectral analysis QRS complex |
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