by Markus Rummel. We present the first results of AI Endurance's new capability to calculate Respiration Frequency (RF) from in-activity heart rate variability (HRV) data. RF demonstrates its potential in assessing the validity of HRV threshold determination.

How we calculate Respiration Frequency

How can we calculate RF from HRV data, specifically the RR interval time series? RR intervals are the precise time between each successive heart beat.

Why we can calculate Respiration Frequency from HRV

Respiration Frequency can be determined from RR intervals because of the natural influence of breathing on HRV, particularly through a phenomenon known as respiratory sinus arrhythmia [1]. During inhalation, the heart rate typically increases, and it decreases during exhalation, creating rhythmic fluctuations in the RR intervals—the intervals between consecutive heartbeats. These variations arise due to the autonomic nervous system’s response to breathing patterns, modulating the heart rate in sync with the respiratory cycle.

By analyzing these RR interval fluctuations, it becomes possible to estimate the frequency of respiration, even outside of controlled environments. This approach provides insights into respiratory patterns and reveals the coupling between cardiovascular and respiratory systems, offering valuable information for monitoring physiological states and stress levels in both daily life and athletic performance contexts.

Other ways to measure Respiration Frequency for athletes

There's a few options to measure your Respiration Frequency more direct although these options are less affordable than simply wearing a heart rate monitor (HRM) chest strap that measures high quality HRV data such as the Polar H10:

1. Smart clothing such as the Hexoskin smart shirts and Tyme Wear garments integrate sensors into the fabric to monitor respiratory metrics among other physiological data.
2. Gas exchange measurements either obtained in the lab or in the field. Options include COSMED - K5 and VO2 Master. These are naturally much less affordable and also provide deeper physiological insights than RF.

For a blog post comparing alphaHRV RF calculated from HRV to Hexoskin 'directly' measured RF, see this blog post by Bruce Rogers. While awaiting more in-depth studies of comparisons of this nature, the results are very encouraging in that the alphaHRV RF algorithm is clearly doing an excellent job in estimating RF. Also alphaHRV has actually improved the RF algorithm since the above evaluation.

AI Endurance is now using the same RF algorithm as developed by alphaHRV. As expected, the RF calculation in AI Endurance compares very closely to that of alphaHRV:

Fig 1: alphaHRV vs AI Endurance RF calculation for an easy ride with some intensity at the end. The slight shift to the right of the AIE green curve is due to alphaHRV calculating the data in real time while AIE calculates after the activity has been completed. AIE centers the interval of HRV data to calculate RF around a given timestamp while alphaHRV does this at the 'right edge' with all HRV data in the past of the current timestamp due to the real time constraint.

Improved HRV threshold detection

So how can we make use of this new metric Respiration Frequency to improve HRV threshold [2, 3] detection? An obvious choice seems sanity checks: if we are detecting thresholds with increasing power/pace in the order

1. baseline (a₁ > 1)
2. aerobic (a₁=0.75)
3. anaerobic (a₁=0.5)

We would also expect respiration rate to increase at each threshold. If this is not the case we can discard thresholds.

Fig 2: baseline (a₁ > 1), aerobic (a₁=0.75) and anaerobic (a₁=0.5) power and RF thresholds.

This is an example of cluster threshold detection in every day activities over a 2 week time span. Cluster thresholds simply look at the distribution of power/pace around the characteristic a₁ values (>1 for baseline, 0.75 for aerobic, 0.5 for anaerobic) for each workout before significant fatigue is expected to kick in. The threshold is the average pace/power of each distribution.

In this example, while as far as power is concerned there's a monotonic increase in all detected thresholds from baseline to 0.75 to 0.5, this is not the case in the mirror plot for RF. We would discard the green, light blue and blue-gray bottom three data sequences because the RF at 0.5 is actually lower than the RF at 0.75. We would only keep the yellow and purple threshold detection.

Failed attempts at RF only cluster threshold detection

Ideally, we would be able to detect the aerobic and anaerobic threshold independently of a₁, purely within the Respiration Frequency metric. Combining a₁ and RF threshold estimation can lead to improved accuracy and reduced bias [4, 5]. The procedure is not necessarily easy to automate though as we will discuss.

A common method is to look for breakpoints in breathing patterns at the gas-exchange thresholds [6]. This is usually done as an analysis of time vs RF in a ramp protocol. Breakpoints are identified after fitting a 6th degree polynomial and identifying local maxima of the second derivative of the latter as the breakpoints/thresholds.

We tried to take this method one step further by looking at intensity in terms of power/pace or heart rate vs RF: For a given workout, we bin each data point by heart rate and calculate RF as the average of all data points in the bin.

Fig 3: Binned heart rate vs average RF in each bin with 6th degree polynomial fit.

As expected, we get a steadily increasing average RF with increasing intensity. In this example with heart rate vs average RF. We can do the polynomial fit and look for local maxima in the second derivative, just like in [6].

Fig 4: Second derivative of the 6th degree polynomial fit in Fig 3 with local maximum.

However, we found that we can not reliably detect local maxima in an automated way over our dataset, as demonstrated by the example in the above figure.

Other attempts include change point detection in various metrics: RF, first derivative of RF, RF/a₁, first derivative of RF/a₁. Again, these did not yield a reliable threshold detection method.

While we continue to work towards improved threshold detection with the help of Respiration Frequency data, we are grateful for any input or ideas from the community. Feel free to reach out at info@aiendurance.com.

1. Respiratory sinus arrhythmia: why does the heartbeat synchronize with respiratory rhythm? - Fumihiko Yasuma, Jun-Ichiro Hayano - Chest. 2004 Feb;125(2):683-90. doi: 10.1378/chest.125.2.683
2. A new Detection Method Defining the Aerobic Threshold for Endurance Exercise and Training Prescription Based on Fractal Correlation Properties of Heart Rate Variability - Bruce Rogers, David Giles, Nick Draper, Olaf Hoos, Thomas Gronwald - Front. Physiol. 2021
3. Detection of the Anaerobic Threshold in Endurance Sports: Validation of a New Method Using Correlation Properties of Heart Rate Variability - Bruce Rogers, David Giles, Nick Draper, Laurent Mourot, Thomas Gronwald - J. Funct. Morphol. Kinesiol. 2021
4. Improved Estimation of Exercise Intensity Thresholds by Combining Dual Non-Invasive Biomarker Concepts: Correlation Properties of Heart Rate Variability and Respiratory Frequency - Bruce Rogers, Marcelle Schaffarczyk, Thomas Gronwald - Sensors 2023, 23(4), 1973
5. Heart Rate Variability Based Ventilatory Threshold Estimation – Validation of a Commercially Available Algorithm - Timo Eronen, Jukka A. Lipponen, Vesa V. Hyrylä, Saana Kupari, Jaakko Mursu, Mika Venojärvi, Heikki O. Tikkanen, Mika P. Tarvainen - https://doi.org/10.1101/2024.08.14.24311967 (preprint)
6. Evidence of break-points in breathing pattern at the gas-exchange thresholds during incremental cycling in young, healthy subjects - Troy J. Cross, Norman R. Morris, Donald A. Schneider, Surendran Sabapathy - Eur J Appl Physiol. 2012 Mar;112(3):1067-76. doi: 10.1007/s00421-011-2055-4.