# Determining the Optimal Inhale-to-Exhale-Ratio for Resonance Breathing and HRV Biofeedback Training

## Introducing the Idea of a “Resonance Ratio.”

It is well established that breathing at a certain frequency, known as the resonance frequency, triggers a strong cardiovascular response that maximizes heart rate variability (HRV). Determining this frequency, which varies from person to person, usually forms the starting point for HRV biofeedback training.

What is however less often considered is that the ratio of inhale to exhale duration can also impact the response of the autonomic nervous system.

In many cases this ratio is simply fixed without further consideration, usually either at the equal ratio of 0.5, or the slightly more “sophisticated” value of 0.4 which puts a stronger emphasis on the exhale, the part of the breathing cycle that stimulates the calming parasympathetic nervous system (see this article for more details on the mechanisms behind this).

In my latest self-study I test this common assumption, applying a similar protocol as is used to determine the resonance frequency to the inhale/exhale ratio, determining the ratio with the strongest HRV response — what I shall call the “**resonance ratio**.”

[Side-note: technically the ratio values I’m referring to are the fraction of the breath cycle that are spent in the inhale phase, i.e. inhale / (inhale + exhale), but in this article I will call this inhale/exhale ratio for convenience.]

In a previous self-study I determined my own personal resonance frequency to be at around 5.4 breaths per minute (equivalent to 11.11 seconds per breathing cycle), so I used this as the basis for my breath ratio experiment.

With this fixed breathing frequency, I used a modified version of the *Yudemon* HRV Biofeedback app to test all the inhale/exhale ratios between 0.25 (corresponding to 2.78 seconds inhale and 8.33 seconds exhale) and 0.75 (8.33 seconds inhale and 2.78 seconds exhale) in steps of 0.05.

Specifically, I collected data from ten individual breathing sessions, where in each session I would breathe at each of the 11 unique ratios for 90 seconds (and just like in my previous experiment, I chose the ordering of ratios in each session at random to avoid potential bias from a continuous progression).

Combining all the HRV data gives the following results:

The solid line represents the mean HRV at each inhale/exhale ratio, and the box plots show the spread of the data at each ratio across the ten sessions.

This plot shows a very clear and strong correlation between HRV and inhale/exhale ratio, with a maximum average HRV at a ratio of 0.35.

Given the data I can say that at a breathing frequency of 5.4 breaths/minute, my resonance ratio lies somewhere in the interval (0.3, 0.4), and probably very close to 0.35.

While this resonance ratio is not too far off from the commonly used 0.4, it does give me an improvement of over 5% over the standard ratio. And compared to the equal ratio of 0.5 it shows a very significant improvement of over 25%.

For me this raises the question of whether a test of optimal inhale/exhale ratio should be included in the HRV biofeedback protocol.

I should note that first determining my resonance frequency and then finding my resonance ratio at this fixed frequency does not guarantee that this is the optimal frequency/ratio-combination.

To really determine the optimal parameter values I would have to repeat the same experiment at several different frequencies, exploring the full two-dimensional parameter space. But this might be overkill.

The present experiment already goes beyond most standard considerations and gives me a very optimised/personalised protocol.

It is also interesting and informative to not just look at the HRV for each ratio, but the shape of the heart rate curve over a full breath cycle.

I segmented all available heart rate data into the individual breath cycles, and overlaid them for each ratio. The following plot shows these individual segments (in blue), as well as their average (in red) for the extreme ratios of 0.25 and 0.75, as well as the equal ratio of 0.5.

It is interesting to see that only for the equal ratio does the HR maximum coincide with the transition from inhale to exhale. For the extreme ratios the heart response lags behind or precedes the breathing change.

Looking only at the averages, we can combine all the different ratios into a single plot.

This shows a very clear pattern.

Roughly, the larger the ratio the more the HR peak is shifted towards the latter stages of the breath cycle, but not much exceeding the mid-point even for long inhales. In addition, above a ratio of 0.4 the amplitude of the HR oscillation gets significantly smaller, in line with the lower HRV values.

To get a slightly cleaner picture, we can single out the extreme and equal ratios from above, as well as my resonance ratio 0.35.

Interestingly, at least for me, the highest HRV does not seem to necessarily correspond to the “smoothest” (in the sense of most sine-like) heart rate oscillation. Rather it seems to have a more gentle acceleration stage which already starts towards the end of the exhale, and a sharper deceleration stage beginning just after the end of the inhale.

The most sine-like behavior (including a phase that’s more or less perfectly aligned with the beginning and end of the cycle) actually coincides with the lowest HRV value, at an inhale/exhale ratio of 0.75

This concludes my experiment on the optimal inhale/exhale ratio for HRV biofeedback training. I would love to see other people repeat this experiment to get some insight whether the resonance ratio is also highly personal, just like the resonance frequency, or more or less universal (or maybe at least universal as a function of resonance frequency).

While I have determined my resonance ratio to be close to 0.35, I will actually choose to practice at the slightly higher ratio of 0.375 = 3/8 going forward.

One of my key goals with Yudemon is to improve biofeedback training through generative sounds and music. The value of 8 (and 16, 32, etc) is extremely important in music. With most (modern) music being written in a 4/4 time signature, 8 bars (or multiples thereof) is one of the most common durations for a musical phrase.

The fact that 0.375 splits 8 bars into exactly 3 and 5 full bars for the inhale and exhale respectively allows me to play around with different sonic characteristics for these two phases that still align with the beat and feel perfectly “musical.”

I’m excited to dive much deeper into this sound/music aspect from now on.

My next self-study will be a first small step into the world of sound, exposing myself to a few different types of soundscapes during resonance breathing and trying to see if they have any measurable effect on my HRV.

Stay tuned for the results of that experiment, as well as my explorations into generative and responsive sound.