DFA2

DFA alpha2: long-term fractal correlations of heart rate.

DFA2 — the long-term scaling exponent α2 of detrended fluctuation analysis — describes the fractal correlation properties of heartbeat intervals over longer scales (about 16–64 beats). It reflects how slow fluctuations of heart rate are organised in time. The clinical evidence for α2 as an independent prognostic marker is less extensive than for α1, but several observations are clinically relevant.

Heart rate variabilityNonlinear dynamicsFractal analysisLong-range correlations

Typical in health≈ 1.0

Scale16–64 beats

Unitdimensionless

Requireslonger, stable recordings

What DFA2 measures

DFA calculates how the residual fluctuation F(n) of the integrated heartbeat series grows with the window size n. For short windows the slope is α1; for longer windows (16–64 beats) it is α2. In healthy people both exponents are around 1, indicating fractal ("1/f") behaviour across scales. The point where the slope changes — the crossover — shows that different mechanisms govern short-term and long-term heart-rate dynamics: fast breathing-related vagal effects at short scales and slower baroreflex, hormonal and central influences at longer scales.

Figure 1. Detrended fluctuation analysis: α2 (green) is the slope of log F(n) versus log n at scales of 16–64 beats.

F(n) ∝ n^α · α2 = slope of log F(n) versus log n for n = 16–64 beats

Clinical interpretation

α2 ≈ 1 — normal fractal organisation of slow heart-rate fluctuations.
Changes with sleep stages: in non-REM sleep long-range correlations of heart rate almost disappear, whereas in REM sleep they resemble those of wakefulness, reflecting changes in central autonomic control.
Ageing and disease: loss of the normal difference between α1 and α2 (crossover) and deviations of α2 from about 1 have been described with ageing, heart failure and after myocardial infarction, as signs of reduced complexity.
Atrial fibrillation: irregular ventricular rhythm produces α values close to 0.5 (random) and makes DFA unsuitable for assessing autonomic regulation.

Measurement

Reliable α2 requires enough beats to fill many 64-beat windows — usually at least 10–20 minutes of stable recording, ideally longer. Results depend on the software settings and should be compared only with the same method.

When to see a doctor

DFA2 is a research-oriented index and is not used alone for diagnosis. Discuss it with a cardiologist if HRV analysis shows several abnormal indices or if you have symptoms such as palpitations, breathlessness or fainting.

References

Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5(1):82–87. doi:10.1063/1.166141
Huikuri HV, Mäkikallio TH, Peng CK, Goldberger AL, Hintze U, Møller M. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction. Circulation. 2000;101(1):47–53. doi:10.1161/01.CIR.101.1.47
Bunde A, Havlin S, Kantelhardt JW, Penzel T, Peter JH, Voigt K. Correlated and uncorrelated regions in heart-rate fluctuations during sleep. Phys Rev Lett. 2000;85(17):3736–3739. doi:10.1103/PhysRevLett.85.3736
Voss A, Schulz S, Schroeder R, Baumert M, Caminal P. Methods derived from nonlinear dynamics for analysing heart rate variability. Philos Trans A Math Phys Eng Sci. 2009;367(1887):277–296. doi:10.1098/rsta.2008.0232

This article is for general information and does not replace a consultation with a doctor.

Published on 6 July 2026