by Markus Rummel. DDFA (Dynamical Detrended Fluctuation Analysis) is a new method to analyze the changes in your HRV data during exercise. It is an evolution of the DFA analysis based on the research in [1, 2] used by AI Endurance.

What is DDFA?

DDFA has been recently introduced by Suunto for real-time measurement of aerobic and anaerobic thresholds in Suunto devices via their new ZoneSense feature. Similar to DFA, it promises real-time evaluation of your aerobic and anaerobic thresholds and how those may change on a day to day basis and during an activity. For an alternative explanation of DDFA and ZoneSense, check out this post by the 5krunner.

One of the big advantages of (D)DFA is that it only requires you to wear a high quality heart rate monitor (Polar H10 or Suunto HRM) and enable heart rate variability (HRV) logging on your device. It is very cost efficient to use and non-invasive compared to other methods like lactate or gas exchange measurements that at this point require access to a physiology lab.

DDFA looks at your in-activity HRV data, specifically your RR intervals. RR intervals are the times between beats. For example, if your heart rate is 120 bpm, the time between beats is on average 0.5 seconds. However, it is actually never exactly 0.5 seconds, but for example 0.499, 0.501, 0.498, ... and there is a lot of information that can be deduced from these variations in your heart beat, hence the term heart rate variability.

HRV at rest data has been used for a while to assess recovery and readiness to train. In activity, HRV based methods such as DFA alpha 1 and DDFA are a more recent development.

How is DDFA different from DFA?

Both DDFA and DFA are non-linear indices that indicate the level of noise and (anti-)correlation in the RR intervals. The basic idea of both concepts is that the more stress the heart is under, the more the correlation patterns in the RR intervals shift as quantified by the (D)DFA index. Various values of the index can be gauged against either gas exchange measurements (VT) or lactate (LT) in the lab to proxy exercise thresholds.

There are a few key differences on how DDFA is calculated [3, 4] relative to DFA [1, 2]. We'll go through the most important ones step by step. Note that this is the algorithm presented in [3, 4] and we don't know that Suunto ZoneSense is using exactly this algorithm but this is the information from the papers they are referencing. It should be noted that [3] has a rather small population of 15 study participants, hence conclusions shall be interpreted with caution.

Segmentation

• DFA: The RR time series is first chopped into 2 min intervals, then each 2 min interval is segmented into the number of RR measurements divided by the scale. Scales for DFA alpha 1 are chosen to be between 4 and 16. For example, for a heart rate of 120 bpm (240 RRs), the number of RR points per segment varies between 240/4 = 60 (scale=4) and 240/16 = 15 (scale=16).
• DDFA: The number of RRs is chosen 'dynamically' as 5 times the scale. So for example for scale 16 there are 80 RRs. According to the authors of [3, 4], this has the advantage that especially for large scales, there is higher temporal resolution (more RRs in one segment) than in DFA. Furthermore, DDFA uses a larger range of scales: between 5 - 64 which is both the DFA alpha 1 and DFA alpha 2 range.

Scale dependence

• DFA: For every 2 min interval analyzed t, residuals F(t, s) of a linear regression versus the actual RR data are calculated for every scale and then another linear regression is performed in the space log(s), log(F(t, s)). DFA alpha 1 a₁(t) is the slope of this linear regression. In a sense, the scale dependence on s is integrated out for every time step t and what's left is solely a function of time: a₁(t).
• DDFA: In contrast to DFA, the scale dependence is kept for further analysis (at least at first) and instead what is studied is a parameter a(t, s). a(t, s) is the dynamic scaling exponent calculated from the neighboring scales s-1, s, s+1 and the residuals F(t, s-1), F(t, s), and F(t, s+1). By combining heart rate (or presumably pace or power) values at all recorded times, one can then organize a(HR, s) in terms of heart rate and scale.

This graph is from Figure 1 in [3]. It shows a(HR, s) as color coded as a function of scale s and heart rate HR. The black line takes the smoothened average over all scales. The dotted line marks the first and second lactate threshold while the cyan line marks the first DDFA threshold (crosses baseline) and second DDFA threshold (crosses minus 0.5).

Baseline building

• DFA: DFA doesn't have this step. As validated in the research [1,2] and many publications since, a₁ = 0.75 corresponds to the aerobic threshold (VT1) while a₁ = 0.5 corresponds to the anaerobic threshold (VT2). What's interesting is that some studies have shown that 0.75 may overestimate the aerobic threshold in at least some athletes and potentially even systematically.
• DDFA: While DDFA uses a fixed value of minus 0.5 for the anaerobic threshold as well, it uses an individualized baseline for the aerobic threshold. In the example of heart rate, the baseline is the mean a(HR, s) for the lowest 25 integer HR values for each scale. In a way, this is the value of a(HR, s) at the lowest intensity for the activity (hence baseline) and it might be different for each athlete. Hence, this scale dependent baseline value is subtracted from a(HR, s) for further analysis. The aerobic threshold is then identified where a(HR, s) falls below zero.

While there are other small differences to the DFA algorithm, including for example smoothening of the a(HR) result, these are the main qualitative differences of the DDFA algorithm as outlined in [3, 4].

This is Figure 3 from [3]. It compares the DDFA method of evaluating the aerobic and anaerobic thresholds to lactate (used as the reference here), ventilatory thresholds (VT), HR max reserve and DFA alpha 1.

Other recent approaches beyond DFA

There are other recent approaches beyond DFA that may be promising.

alphaHRV

alphaHRV is doing a great job in estimating respiration rate from in-activity HRV data. Combining respiration rate and DFA alpha 1 into a new quantity RRa₁ (respiration rate divided by a₁), can be used to determine thresholds: if respiration rate increases and or a₁ decreases this means exercise stress is increasing. This method may allow for an individualized/baseline dependent aerobic threshold evaluation in a similar spirit as in DDFA.

Kubios

Recently, the authors of [5] presented a study with 64 participants in which they compared the DFA algorithm with a Kubios proprietary algorithm that combines DFA alpha 1, with heart rate reserve and respiration rate to estimate thresholds. Interestingly, their combined algorithm performs better on the aerobic threshold (less bias and smaller error) compared to DFA alpha 1. The performance on the anaerobic threshold is similar to DFA alpha 1.

1. 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
2. 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
3. Estimation of physiological exercise thresholds based on dynamical correlation properties of heart rate variability - Matias Kanniainen, Teemu Pukkila, Joonas Kuisma ,Matti Molkkari, Kimmo Lajunen, Esa Räsänen - Front. Physiol. 14, 2023
4. Dynamical heart beat correlations during running - Matti Molkkari, Giorgio Angelotti, Thorsten Emig, Esa Räsänen - Sci. Rep. 10, 13627 2020
5. Heart Rate Variability Based Ventilatory Threshold Estimation – Validation of a Commericially 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)