The diagnostic and prognostic power of the fractal complexity measure ‘α’ 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 α, 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 α1 and 0.98 (P < 0.0001) for α2. Third, we predict mathematically that even in conventional (unweighted) spectral analysis there should be approximate counterparts to DFA, namely that α1 and α2 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 α1 (r = 0.73, P = 0.01); the effect on VLF/(LF + VLF) correlates markedly with that on α2 (r = 0.76, P < 0.01). Likewise, with voluntary periodic breathing the reduction in α2 correlates strongly with that in VLF/(LF + VLF) (r = 0.88, P < 0.001); effects on α1 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 α1 and LF/(HF + LF). We conclude that the α1 and α2 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 α1, while periodic breathing → high VLF/LF → high VLF/(LF + VLF) → high α2. Prognostic associations of α are no longer mysterious.
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