DFA (Detrended Fluctuation Analysis) for PPG HRV

DFA divides the cumulative sum of the IBI series (mean-subtracted) into non-overlapping windows of size $n$, fits a polynomial trend in each window, computes the root-mean-square fluctuation $F(n)$ after detrending, and repeats for window sizes from 4 to $N/4$ beats. The log-log plot of $F(n)$ vs. $n$ reveals the scaling exponent $\alpha$ as the slope. $\alpha_1$ (computed from $n$ = 4–16 beats) captures short-term cardiac dynamics; $\alpha_2$ ($n$ = 16–64) captures longer-term correlations.

Healthy resting IBI series exhibit $\alpha_1 \approx 1.0$ (1/f noise, indicating long-range correlations), while $\alpha_1 < 0.75$ indicates loss of fractal organization (associated with heart failure, post-MI, and aging), and $\alpha_1 > 1.5$ indicates excessive regularity (associated with severe autonomic neuropathy). In athletic performance monitoring, DFA $\alpha_1$ from PPG during exercise correlates with ventilatory thresholds: $\alpha_1$ transitions from ~1.0 at low intensity to ~0.5 at the aerobic threshold and approaches 0.5 at the anaerobic threshold, providing a non-invasive intensity zone indicator.

Exercise DFA $\alpha_1$ from PPG is less validated but shows promising correlation with lactate threshold-based zone boundaries in preliminary studies. DFA $\alpha_1$ is more robust to occasional IBI detection errors than frequency-domain metrics because the detrending step removes slow artifacts and the scaling analysis averages over multiple window sizes.