Coherence

Coherence, as HeartMath defines it, is the power of the tallest peak in the 0.04–0.26 Hz part of the HRV spectrum divided by the power of everything else. It has no unit.

Why this measure exists

McCraty and Shaffer describe a “coherent” heart rhythm as a smooth, sine-like wave in the beat-to-beat intervals with one narrow, tall peak in the LF LF LF power The variance of the heartbeat intervals that falls in the 0.04 to 0.15 Hz band, in ms²: rhythms repeating every 7 to 25 seconds. Once read as sympathetic activity, which is now disputed. More about LF power region and no large VLF VLF VLF power The variance of the heartbeat intervals in the 0.003 to 0.04 Hz band, in ms²: rhythms repeating every 25 seconds to 5 minutes. It needs at least a 5-minute recording and is best read over 24 hours. More about VLF power or HF HF HF power The variance of the heartbeat intervals that falls in the 0.15 to 0.40 Hz band, in ms²: the range of normal breathing. It mainly reflects vagal activity when breathing is 9 to 24 breaths a minute. More about HF power peaks. They designed the ratio to score that shape, and the Institute of HeartMath’s Inner Balance and emWave products report it. The same paper notes that the body’s resonance frequency is about 0.1 Hz, so breathing at around 6 breaths a minute drives heart rate into exactly this pattern. The disclosure in that paper records that McCraty is employed by the Institute of HeartMath, which sells one of the biofeedback devices discussed.

The formula

$$\mathrm{Coherence} = \frac{P_{\mathrm{peak}}}{P_{\mathrm{total}} - P_{\mathrm{peak}}},\qquad P_{\mathrm{peak}} = \int_{f_0 - 0.015}^{f_0 + 0.015} P(f)\,\mathrm{d}f$$

Find the tallest peak $f_0$ between 0.04 and 0.26 Hz, add up the power $P(f)$ in a window 0.030 Hz wide centred on it, and divide by the power in the rest of the spectrum. A single sharp peak gives a high ratio; power spread across many rhythms gives a low one. Apps turn the ratio into a score or a low, medium or high label.

Worked example

Take the rhythm apart

Five minutes of the teaching recording

Power at each frequency, Hz Breathing

VLFLFHF

0 0.1 0.2 0.3 0.4 0.5

ULF

needs 24 h

VLF

3 ms²

LF

120 ms²

HF

635 ms²

Total

758 ms²

LF nu

15.9

HF nu

84.1

LF/HF

0.19

Peak

0.250 Hz, HF

Rested, 15 breaths a minute (0.250 Hz), 5 minutes, Welch's method after detrending. The breathing peak sits at 0.250 Hz in the HF band, with the ~0.1 Hz blood-pressure wave as a smaller LF peak. LF/HF is 0.19.

Rested Stressed Drifting Ectopic beats

Breathing rate 15 breaths a minute Recording length 5 minutes

Welch (FFT) Lomb–Scargle

Detrend first (smoothness priors, λ = 500)

The controls work when JavaScript is on.

A line chart of power against frequency from 0 to 0.5 Hz with the VLF (0.003–0.04 Hz), LF (0.04–0.15 Hz) and HF (0.15–0.4 Hz) bands shaded and a marker at the breathing frequency. Readouts give ULF, VLF, LF, HF and total power in ms squared, LF and HF in normalised units, the LF/HF ratio and the peak frequency, followed by a sentence explaining what changed. Controls: a breathing-rate slider from 5 to 20 breaths a minute, a recording-length slider, a detrending checkbox, Welch or Lomb–Scargle buttons, and four preset buttons for a rested, stressed, drifting or ectopic recording.

Set the breathing rate breathing rate Breathing rate How many breaths you take a minute. It moves HRV on its own: slower, deeper breathing makes the beat-to-beat swing larger, and below about 9 breaths a minute it shifts from the HF band into LF. More about Breathing rate to 6 a minute. The breathing peak lands at 0.100 Hz, where the ~0.1 Hz blood-pressure wave already sits, and the two merge: LF power reads 4939 ms² against 20 ms² in HF, with LF nu LF nu Normalised units LF or HF power as a percentage of their sum (LF + HF), rather than in ms². The two always add up to 100, so they carry one piece of information between them. More about Normalised units at 99.6. Almost all the power is under one peak, which is a high coherence score. At 15 breaths a minute the spectrum has two separate peaks, the breathing peak at 0.250 Hz and a small LF one, so the ratio is low. The nervous system did the same thing in both cases; the breathing pace changed.

What moves it

Breathing pace and steadiness, above all: Lehrer and Gevirtz explain that at the resonance frequency heart rate and blood pressure oscillate 180° out of phase, so the baroreflex 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 adds to each swing and produces the single large peak, and Shaffer, McCraty and Zerr put that frequency between 4.5 and 6.5 breaths a minute in adults. A calm, regular rhythm raises it; irregular breathing, talking or movement lower it.

When it misleads

When it is read as a measure of emotional state rather than of breathing. Anyone who breathes slowly and evenly scores high, whatever they feel; anyone who talks scores low. It is also the same physiology the Task Force’s LF band captures, so a high coherence score usually comes with a high LF power. McCraty and Shaffer describe the coherent state as correlated with wellbeing and with cognitive, social and physical performance; those are correlations, and much of the work they cite comes from HeartMath’s own research.

Where you will see it

HeartMath’s Inner Balance and emWave apps and sensors, as a coherence score; some other breathing apps borrow the word. The Task Force does not define it. HRV biofeedback covers the training the score was built for, and the resonance breathing finder on this site looks for your own peak.