DDFA – Dynamical Detrended Fluctuation Analysis

Author: M. Rummel, AI Endurance

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?

Suunto has recently introduced DDFA for real-time measurement of aerobic and anaerobic thresholds in Suunto devices. Like DFA, it promises real-time evaluation of your aerobic and anaerobic thresholds and how those may change daily and during an activity.

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, which require access to a physiology lab.

DDFA looks at your in-activity HRV data, specifically 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 never precisely 0.5 seconds. It could, for example, be 0.499, 0.501, 0.498, … and there is a lot of information that can be deduced from these variations in your heartbeat, hence the term heart rate variability.

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

How is DDFA different from DFA?

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 index values can be gauged against either gas exchange measurements (VT) or lactate (LT) in the lab to proxy exercise thresholds.

A few key differences exist in 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]. We don’t know that Suunto 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 cautiously.

Segmentation

• DFA: The RR time series is first chopped into 2-minute intervals, and then each 2-minute 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 five times the scale. 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, 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.

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). Interestingly, 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, it also 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), which might differ 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 the DFA algorithm has other small differences, including smoothing of the a(HR) result, these are the main qualitative differences, as outlined in [3, 4].

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 heartbeat correlations during running – Matti Molkkari, Giorgio Angelotti, Thorsten Emig, Esa Räsänen – Sci. Rep. 10, 13627 2020

More: AI Endurance, SuuntoPLUS app Zone SENSE (Suunto.com)