Physiological basis of fractal complexity properties of heart rate variability in man

The diagnostic and prognostic power of the fractal complexity measure 'alpha' of detrended fluctuation analysis (DFA) has remained mysterious because there has been no explanation of its meaning, particularly in relation to spectral analysis. First, we present a mathematical analysis of the meaning of alpha, in weighted power-spectral terms. Second, we test this hypothesis and observe correlations between DFA-based and weighted spectral methods of 0.97 (P < 0.0001) for alpha1 and 0.98 (P < 0.0001) for alpha2. Third, we predict mathematically that even in conventional (unweighted) spectral analysis there should be approximate counterparts to DFA, namely that alpha1 and alpha2 behave broadly in proportion to the conventional (unweighted) ratios LF/(HF + LF) and VLF/(LF + VLF), respectively, where HF is high frequency, LF is low frequency and VLF is very low frequency. Fourth, we test this hypothesis by physiologically manipulating spectral ratios in healthy volunteers in two ways. The effect of 0.1 Hz controlled breathing on LF/(HF + LF) correlates markedly with the effect on alpha1 (r = 0.73, P = 0.01); the effect on VLF/(LF + VLF) correlates markedly with that on alpha2 (r = 0.76, P < 0.01). Likewise, with voluntary periodic breathing the reduction in alpha2 correlates strongly with that in VLF/(LF + VLF) (r = 0.88, P < 0.001); effects on alpha1 and LF/(HF + LF) again clearly correlate (r = 0.73, P = 0.01). Finally, we examine published literature to identify previously undiscussed evidence of the relationship between alpha1 and LF/(HF + LF). We conclude that the alpha1 and alpha2 indices are simply frequency-weighted versions of the spectral ratios LF/(HF + LF) and VLF/(LF + VLF), respectively, multiplied by two (giving a range of 0-2). We can now understand fractal manifestations of physiological abnormalities: depressed baroreflex sensitivity low LF/HF low LF/(HF + LF) low alpha1, while periodic breathing high VLF/LF high VLF/(LF + VLF) high alpha2. Prognostic associations of alpha are no longer mysterious.