Nonlinear HRV measures describe the pattern of your heartbeat intervals rather than their spread. SDNN SDNN The standard deviation of all NN intervals in a recording, in milliseconds. It measures overall variability, and its value depends strongly on how long the recording lasts. More about SDNN says how far the intervals wander; RMSSD RMSSD Root mean square of successive differences: an HRV metric built from how much each heartbeat interval differs from the next, in milliseconds. It mainly reflects vagal activity. More about RMSSD says how much they jump from beat to beat; the nonlinear measures ask whether the beats remember earlier beats ( detrended fluctuation analysis DFA α1 The short-term scaling exponent of detrended fluctuation analysis. Near 1 the beats have memory at every scale; near 0.5 they behave like noise. α2 is the same slope over longer stretches. More about DFA α1 ), how predictable the next one is (sample and approximate entropy Approximate entropy The older cousin of sample entropy, with no unit: a regularity measure that counts each run of beats as matching itself, which biases it towards low values on short recordings. More about Approximate entropy ), and how the rhythm answers a premature beat Ectopic beat A heartbeat that starts outside the heart's normal pacemaker and usually comes early. Ectopic beats are common, but they distort HRV unless removed or corrected. More about Ectopic beat ( heart rate turbulence Heart rate turbulence The brief speed-up and slower recovery of the heart rhythm after a premature ventricular beat, measured from a 24-hour ECG as two numbers: turbulence onset (%) and turbulence slope (ms per beat). More about Heart rate turbulence , deceleration capacity Deceleration capacity The average size of the heart's slow-downs, in milliseconds, found by averaging the pattern around every beat slower than the one before. A 24-hour vagal measure used after heart attacks. More about Deceleration capacity ). You do not need them to follow your own recovery with a wearable. They appear in research software, and the 2015 European position statement on them concluded that they have advanced understanding of the signal while their use as clinical tools has so far been rather limited.
Why “nonlinear”
Take a recording, shuffle the beats into a random order, and compute SDNN: it does not change. Neither does the histogram, the triangular index HRV triangular index The number of NN intervals in a recording divided by the height of the tallest bar of their histogram. A unitless geometric measure of overall variability that a few bad beats barely move. More about HRV triangular index or the Baevsky index Baevsky stress index A number built from the histogram of heartbeat intervals, with no unit. It rises as the rhythm gets steadier and less variable, which Baevsky read as strain on the body's regulation. More about Baevsky stress index . Those measures only see the spread of the intervals. Shuffling destroys the order, and order is where the physiology lives: the breathing wave, the slower blood-pressure wave, the way one slow beat tends to follow another. Methods that read the order, and whose results are not just sums of the values, are called nonlinear. Peng, Havlin, Stanley and Goldberger made the family famous in 1995 by showing that healthy hearts have long-range correlations that break down in severe heart failure.
The two you will meet
DFA α1: do the beats remember?
Does the rhythm remember?
Five minutes of the teaching recording
- α1 (4–16 beats)
- 0.49
- α2 (16–64 beats)
- 0.65
The rested recording is synthetic: a clean breathing wave every four beats with random noise between beats, so over 4 to 16 beats it looks almost like noise (α1 0.49), and the slower waves give 16 to 64 beats some memory (α2 0.65). Real recordings at rest usually give an α1 of about 1 or higher.
The controls work when JavaScript is on.
A log–log chart of fluctuation against box size from 4 to 64 beats, with dots for each box size and two fitted lines: one over 4 to 16 beats for α1, one over 16 to 64 beats for α2. Readouts give α1 and α2, followed by a sentence explaining them. Four buttons choose the rested recording, white noise, 1/f noise or the recording with ectopic beats; a slider mixes white noise into the chosen series.
Detrended fluctuation analysis asks how the wobble of the series grows as you look at longer stretches of it, on log–log axes. White noise, with no memory, gives a slope of 0.5; 1/f noise, with memory at every scale, gives 1; a random walk gives 1.5. Five minutes of the teaching recording give α1 = 0.49 over 4 to 16 beats and α2 = 0.65 over 16 to 64. Switch to white noise and both slopes sit near 0.5 (α1 0.48); switch to 1/f noise and they sit near 1 (α1 1.04). Real recordings at rest usually come out at about 1 or higher. The teaching recording reads low because it is synthetic: a clean breathing wave once every four beats with random noise between beats, which looks like noise at short scales. A strong, regular breathing swing can pull real α1 values down in the same direction. Exercise pushes it from about 1 towards 0.5 as effort rises, and some training apps show it live for that reason.
Sample entropy: how predictable is the next beat?
How predictable is the next beat?
Five minutes of the teaching recording
- SampEn
- 1.67
- ApEn
- 1.02
- Tolerance r
- 5.7 ms
- m matches
- 13
- m+1 matches
- 1
Rested, m = 2, r = 0.20 × SD = 5.7 ms. The highlighted run of 2 beats matches 13 other runs within 5.7 ms; 1 of them still matches when both runs are one beat longer. Counted over every run in the recording, sample entropy is 1.67: the breathing rhythm makes the next beat partly predictable.
The controls work when JavaScript is on.
A line chart of 64 heartbeat intervals in order. A highlighted box marks a template run of m beats with a tolerance band of plus or minus r milliseconds around each of its beats; lighter boxes mark other runs of m beats that match the template within the band, and darker boxes those that still match when both runs are one beat longer. Readouts give sample entropy, approximate entropy, the tolerance in milliseconds, and the two match counts, followed by a sentence explaining them. Two sliders set m (1 to 4 beats) and r (0.1 to 0.6 times the standard deviation); three buttons choose a periodic series, the rested recording or random beats.
Sample entropy Sample entropy How unpredictable the heartbeat series is: minus the log of the chance that runs of beats that match also match one beat longer. Near 0 is a repeating pattern; 2 or more is close to random. More about Sample entropy takes every run of two beats, finds the runs that match it within a tolerance, and asks how many still match one beat later. Minus the log of that share is the entropy. The teaching recording scores 1.67; a perfectly periodic series scores 0.01, because every match keeps matching; random beats score 2.35. Richman and Moorman built it in 2000 to fix the older approximate entropy, which counted each run as matching itself and drifted with record length. Both depend heavily on the run length , the tolerance and the number of beats, so values from different programs or recording lengths cannot be compared.
The clinical ones
Heart rate turbulence and deceleration capacity were developed as risk markers and tested mainly on 24-hour ECGs of people who had had a heart attack. Turbulence reads the baroreflex Baroreflex The reflex that steadies blood pressure from beat to beat by changing heart rate. Its built-in delay makes heart rate rise and fall about every 10 seconds, the 0.1 Hz rhythm in LF power. More about Baroreflex from the rhythm’s answer to a premature ventricular beat; deceleration capacity averages the heart’s slow-downs over a day. Bauer and colleagues’ 2006 study of 1,455 heart-attack survivors, validated in two more cohorts, found deceleration capacity predicted death better than ejection fraction or SDNN. These are risk markers for cardiologists, not wellness numbers, and wearables do not report them.
The verdict
Sassi and colleagues reviewed the whole family in 2015 for the European Society of Cardiology’s e-Cardiology working group and the European Heart Rhythm Association: fractal measures, entropy, symbolic dynamics and chaos. Their conclusion is that the methods have improved understanding of the signal, that results from specialist laboratories in selected patients are interesting but do not establish clinical use, that success in building clinical tools such as risk identification has been rather limited, and that new prospective studies are needed. Shaffer and Ginsberg’s 2017 overview lists the measures beside the Task Force ones and notes, for example, that DFA was designed for recordings spanning several hours.
Do you need them?
For a morning or overnight reading from a wearable, no. RMSSD or lnRMSSD lnRMSSD The natural logarithm of RMSSD, with no unit. Taking the log evens out the spread of RMSSD values, which makes day-to-day changes easier to compare and analyse. More about lnRMSSD against your own baseline Baseline Your own usual HRV level and range, built from weeks of readings taken the same way. Comparing a reading with your baseline says more than comparing it with other people. More about Baseline answers the question those readings are good for, and the nonlinear numbers need cleaner, longer recordings than a wrist sensor gives and settings you would have to hold fixed. They are worth knowing about if you read research papers, use Kubios HRV or a similar program, or see DFA α1 in a training app. The glossary pages on DFA α1, sample entropy, approximate entropy, heart rate turbulence and deceleration capacity give each one its formula and worked example, and What do LF, HF, VLF and nu mean in my HRV app? covers the frequency numbers that usually sit next to them.