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How To Quantify Heart Coherence (What Most HRV Biofeedback Software Does)

Heart coherence biofeedback apps and devices are becoming increasingly popular as tools for stress and anxiety management, and performance improvement. They help you train something called heart coherence, but what exactly is heart coherence and how do you measure it?

In this article I'm going to attempt to explain as briefly and succinctly as I can, how such software apps arrive at a measure of coherence, without getting too far into the sort of maths that you'd need for a full understanding. 

What Is Heart Coherence?

The concept of heart coherence has been popularised (as a useful parameter for biofeedback) largely by the Heartmath Institute, a not-for-profit research and education body promoting HRV biofeedback.

Heart coherence is a particular pattern of variation seen in heart rate. Here, a picture is worth a thousand words:

heart coherence biofeedback screenshot

The graphic above shows how heart rate varies over a two minute interval, when you're in a state of heart coherence. Heart rate is shown as the red trace, while the blue is a measure of the breath. By showing the two traces together, you can see that the heart speeds up and slows down, regularly, in sync with the breath - speeding up on the inhalation then slowing down on the exhalation.

When you're not in coherence the heart rate either remains pretty static or varies in an apparently random way (i.e. not in sync with the breath).

Features of Heart Coherence

Let's spell out the features of the heart rate variation that make for good or strong coherence. I think there are three main points:

  • There are large swings in heart rate. The larger the swing (or if you like, the bigger the difference between the top and bottom of the "heart wave"), the stronger the coherence.
  • The swings are regular or consistent. In the graphic above, each cycle of the "heart wave" looks roughly the same - as opposed to there being a big one followed by a small one, etc).
  • The heart wave is in sync with the breath - in the graphic the peaks and troughs line up very closely.

Quantifying Coherence

If you're using an app such as Hearthmath's "Inner Balance", the software needs a method of capturing and quantifying this pattern so that it can tell you whether your coherence is high or low or anywhere in between. Easier said than done, especially given that many HRV apps don't measure breath but only heart rate. How do they do it?

Speaking generally, most HRV biofeedback software uses a mathematical method called Fourier Analysis or frequency analysis, also known as spectral analysis.

(I should say that the exact details of the Heartmath algorithm are of course their commercial secret but I'm pretty confident in guessing it's based on frequency analysis.)

(As another aside, actually the same method is used for analysing EEG or brain waves, if you happen to be interested in EEG neurofeedback - component frequencies are known as alpha, theta, etc.)

Frequency Analysis

In mathematics, a "pure" wave looking like this:

sine wave

- is known as a sine wave or a sine function. Don't worry about what exactly a sine function is - what matters is that it's mathematically simple and easy for software to work with. A sine wave has a fixed frequency (defined by the time gap between the peaks) and amplitude (height of the peaks).

In the real world, oscillating signals don't usually have a simple form and fixed frequency and amplitude like this - they vary in a much more complex way. However, they can be described mathematically as a sum of lots of different sine waves (i.e. having differing frequencies and amplitudes) added together.

To get an idea of how this works, consider the following oscillation:

composite wave

Hopefully you can see just by looking at it that this rhythm is the sum of three distinct sine waves:

three sine waves

If complex oscillations can be made by adding lots of sine waves together, then frequency analysis is reverse-engineering the process: it means breaking a complex signal into its component rhythms. You can show frequency analysis as another graph, this time with frequency along the horizontal axis. Again I hope that you can see that such a frequency analysis graph of the above composite oscillation (i.e. the white one) would look like this:

spectral analysis

- so in other words three distinct peaks, one for each of the component rhythms.

Heart Coherence Again

Returning to HRV - you can appreciate that in the state of coherence the heart wave graph looks quite a lot like a simple sine wave (i.e. a single one).

Here is a real frequency analysis plot of a heart rate when in a state of coherence:

heart coherence spectral analysis

A non-coherent heart rate trace has a more complex looking frequency analysis plot, such as this one:

non-coherence spectral analysis

(So one way to think of the level of coherence, is how much the heart rate trace looks like a simple sine wave.)

Essentially, to quantify coherence (using frequency analysis), you can take something like the area of colour under the most prominent peak (in the above graphs, green at around 0.1 Hz) and compare it to the total area of colour elsewhere in the chart.

In HRV analysis apps such as SweetWater HRV (where they're looking to use HRV as a marker for stress) they typically express this as a ratio written as LF / HF. Hopefully you can see that in coherence, LF / HF is high, much higher than in non-coherent states. That said, stress assessment apps like SweetWater HRV aren't trying to measure coherence, so to avoid confusion let's not go to far in that direction.

The Significance of Breathing Rate

Clearly, since the "heart wave" and the breathing trace are synchronised in the state of coherence, the frequency of the heart wave is the same as the breathing rate. That means the point on the frequency analysis graph where you see the prominent peak (when in coherence) is determined by the breathing rate. In the above chart it falls at 0.1Hz, which means 0.1 breaths every second, or 1 breath every 10 seconds, or 6 breaths per minute.

This breathing rate of 6 bpm tends to be where you get maximal coherence. Why? That's complicated to explain, but essentially it's like a kind of resonance point in the system, where two physiological mechanisms feed off each other to maximise coherence.

Time Window for the Coherence Calculation

If you think about it, you'll realise that coherence is not an instantaneous measurement (like, say muscle tension or EMG) but requires at least a few breaths' worth of data to calculate - you need a few cycles before any sine-wave like rhythm can become apparent. That means that in any HRV biofeedback software, or HRV analysis software, the coherence measure is a moving average over a certain period of time. That can range from just a few breaths - probably about 5 breaths or 30 seconds worth of data would be the minimum - to 24 hours or more in the case of analysis software. For biofeedback you'd want a much smaller window (seconds to minutes) for training to be meaningful.

My point here is that you need to take this window into account when interpretting the heart coherence biofeedback - it's not going to change that rapidly.

Other Ways To Calculate Heart Coherence

As far as I know, all HRV biofeedback software uses frequency analysis to quantify coherence, except one, which is my own software, known as Mind-Body Training Tools. I developed a different way of calculating coherence, based on measurements of both heart rate and breath. Exactly how I do it, is the topic of another article, but the advantage is that it's more responsive to changes in breathing: for example, suppose you're breathing steadily at 6 bpm and in a state of nice heart coherence, then you suddenly speed up your breathing. At that point you break the synchrony between the two signals, and that's reflected in the coherence score.

The spectral analysis method has the advantage that it only requires the heart signal and therefore can be used with much cheaper devices that only measure heart rate and not breath.

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