Abstract
d anaerobic threshold (AnT) using dynamical detrended fluctuation analysis (DDFA). Conventionally, the thresholds are estimated in laboratory settings, where the subject performs an incremental exercise test on a cycloergometer or treadmill. We compared DDFA- based
Pirkanmaa Regional Fund, Grant/ Award Number: 50231659; The European Regional Development Fund, Grant/Award Number: R- 00083 Abstract We study the estimation of aerobic threshold (AeT) and anaerobic threshold (AnT) using dynamical detrended fluctuation analysis (DDFA). Conventionally, the thresholds are estimated in laboratory settings, where the subject performs an incremental exercise test on a cycloergometer or treadmill. We compared DDFA- based thresholds (DDFAT 1 and DDFAT 2) with lactate thresholds (LT 1 and LT 2) and examined thresholds derived from theoretical and measured maximal heart rates (HR). The analysis was conducted on 58 subjects undergoing an incremental treadmill running test. Our findings indicate significant discrepancies between thresholds derived from theoretical and measured maximal HRs compared to lactate thresholds. Specifically, theoretical maximal HR thresholds consistently underestimated lactate thresholds, exhibiting systematic bias. Measured maximal HR thresholds also showed a consistent underestimation, though with improved alignment to lactate thresholds. In contrast, the DDFA- based method demon- strated reasonable agreement with lactate thresholds and lacked systematic bias. The DDFA- based approach offers a simple and accurate alternative for estimat- ing AeT and AnT. Its potential for continuous monitoring makes it suitable for integration into wearable devices such as smartwatches and heart rate monitors. KEYWORDS aerobic threshold, anaerobic threshold, exercise physiology, heart rate variability
2 of 12 | KANNIAINEN 1234. gas exchange (VT 1, VT 2) (Binder et al., 2008). LT 1 is de- fined as the point where the rate of lactate production becomes greater than the rate of lactate clearance in the body, but is still able to reach a steady state for the current exercise work rate. LT 2, on the other hand, corresponds to the point where the lactate production overcomes the lactate clearance, and steady state in the production/ clearance is not achievable any more even though the exercise rate is steady (Faude et al., 2009). The lactate thresholds correspond to changes in metabolic activity caused by the exercise intensity, but the determination of the lactate thresholds is often costly, cumbersome and time- consuming, so the measurements are not carried out regularly except for professional endurance athletes. The lactate thresholds are often determined by a professional exercise physiologist in laboratory settings. However, the determination of the thresholds is subjective and ambig- uous due to the different metabolic responses and initial lactate levels of the individuals, and there is no universal method to be referred as the golden standard (Jamnick et al., 2018; Newell et al., 2007). On the other hand, ventilatory thresholds correspond to the changes in the cardiopulmonary activity. Akin to lactate thresholds, the determination of VTs also requires a specialized test environment with strict quality con- trol and trained personnel (Cannon et al., 2009; Gaskill et al., 2001). Although VTs are closely related to and cor- relate with LTs, they do not correspond quantitatively (Cerezuela-Espejo et al., 2018). This has led to controversy over the methodologies used to study the well- defined physiological and metabolic changes that occur during exercise. Consequently, there is a growing need for stan- dardized methods that more accurately reflect the phys- iological changes at these thresholds (Chavez- Guevara et al., 2024; Sperlich & Gronwald, 2024). Heart rate (HR) and HR variability (HRV) measure- ments are becoming increasingly more popular due to enhanced signal quality of the wearable devices such as smartwatches. This allows a variety of possibilities for analysing physiological signals, such as electrocar- diogram (ECG) and RR interval (RRI) series during ex- ercise. Current smartwatches
at these thresholds (Chavez- Guevara et al., 2024; Sperlich & Gronwald, 2024). Heart rate (HR) and HR variability (HRV) measure- ments are becoming increasingly more popular due to enhanced signal quality of the wearable devices such as smartwatches. This allows a variety of possibilities for analysing physiological signals, such as electrocar- diogram (ECG) and RR interval (RRI) series during ex- ercise. Current smartwatches have several measures to determine physiological changes, for example, the train- ing zones during exercise based on HR or HRV measure- ments with varying reliability and applicability (Campen et al., 2020; Cottin et al., 2006). Several wearable devices utilize the estimated maximal HR (HR max) to assess the training zones. Typically, the first HR threshold (HR maxT 1) is estimated to be around 60%–70% of the HR max, and the second HR threshold (HR maxT 2) around 80%–90% of the HR max, respectively (Marx et al., 2018). It is still widely used in fitness and exercise applications, even though it has gained considerable criticism (Colantonio & Peduti Dal Molin Kiss, 2013; Robergs & Landwehr et al., 2002). The estimates have been shown to fail to account for the population- wide individual variability and there- fore provide unreliable results for, for example, highly trained athletes (Faff et al., 2007; Shookster et al., 2020). Furthermore, the relative percentages of the maximal HR associated with the physiological thresholds are strongly individual. HRV describes the variability between successive heart beats, that is, interbeat intervals (Goldberger, 2020). HRV methods can be used to analyse the physiological response to both rest and exercise (Gronwald & Hoos, 2020). There are several different HRV metrics based on different ap- proaches (Shaffer & Ginsberg, 2017). For example, the frequency- domain methods have been used for threshold estimation in multiple studies (Di Michele et al., 2012; Ramos-Campo et al., 2017). However, in recent years, non- linear HRV metrics have received considerable attention in sport applications. For example, the short- term scaling exponent α 1 of detrended fluctuation analysis (DFA) (Peng et al., 1995)—which describes the characteristic correla- tions of the RRI series (see below)—has shown potential in the assessment of exercise load and intensity, as well as the thresholds compared to the ventilation measurements (Gronwald et al., 2021; Rogers et al., 2021). In
have received considerable attention in sport applications. For example, the short- term scaling exponent α 1 of detrended fluctuation analysis (DFA) (Peng et al., 1995)—which describes the characteristic correla- tions of the RRI series (see below)—has shown potential in the assessment of exercise load and intensity, as well as the thresholds compared to the ventilation measurements (Gronwald et al., 2021; Rogers et al., 2021). In this study, we utilize an extension of DFA, that is, dynamical detrended fluctuation analysis (Molkkari et al., 2020) (DDFA), to estimate the AeT and AnT. The DDFA algorithm expands the analysis of DFA by calcu- lating the scaling exponents dynamically as functions of both time t and scale s , thus providing a comprehensive view of the changing physiological conditions during exercise. Increased exercise intensity has been shown to decrease the scaling exponent values for both DFA and DDFA (Rogers et al., 2021; Gronwald et al., 2021; Kanniainen et al., 2023). The algorithm for estimating the physiological thresholds with DDFA was first intro- duced in (Kanniainen et al., 2023), where the thresholds were calculated for 15 subjects during a cyclo- ergometer test and compared to conventional methods. The pres- ent study serves as the further validation for the method with a larger dataset of incremental running treadmill exercise tests. There are significant physiological dif- ferences in cycling and running; for example, the mus- cle pump efficiency, the ventilatory response, and the heart rate levels for maximal and submaximal intensi- ties are different between the two (Millet et al., 2009). Furthermore, the biomechanics of running and cycling are fundamentally different due to the use of different muscle groups, and the exercise settings such as cadence and treadmill incline have an effect on the respiratory rate and heart rate variability of the subjects during ex- ercise (Lunt et al., 2011). Therefore, it is important to 2051817x, 2025, 9, Downloaded from https://physoc.onlinelibrary.wiley.com/doi/10.14814/phy2.70241, Wiley Online Library on [27/04/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
to 2051817x, 2025, 9, Downloaded from https://physoc.onlinelibrary.wiley.com/doi/10.14814/phy2.70241, Wiley Online Library on [27/04/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
| 3 of 12KANNIAINEN 1234. study the validity of the method based on the RR in- terval correlations irregardless of the exercise mode. We calculate the first and second DDFA- based thresh- olds (DDFAT 1 and DDFAT 2), respectively, and compare them against the lactate thresholds determined by an experienced exercise physiologist. We also evaluate the validity of the thresholds determined from the max- imal HR, which are conventionally used in the wear- able devices to estimate the training zones. We show that the previously consistent results in cycloergometer tests are also valid in treadmill running tests, and the results are relatively comparable to the lactate thresh- olds. Furthermore, we study the relationship between the behavior of the DDFA scaling exponents and lactate concentration in detail. 2 | METHODS AND DATA 2.1 | Participants For this study, 71 participants were recruited as part of a larger study conducted in the University of Jyväskylä. Data collection was performed during an ongoing study project, “Performance variation and health monitoring of recreational runners,” that monitors training, health, and recovery of recreational and endurance runners for one calendar year. The study protocol was approved by the ethics committee of the University of Jyväskylä (534/13.00.04.00/2023). Participants signed a written in- formed consent to participate in the study project. The participants had a very different training background, where some of the participants did occasional recreational exercise and some participants had a background in regu- lar endurance exercise. All of the participants performed a maximal V̇O2 test (Buttar et al., 2019). The information for sex, age, maximal heart rate, maximal V̇O2 intake, maximal lactate concentration, maximal reached speed, and the test duration is shown in Table 1, which includes only the subjects who were remaining after the preproc- essing (see Section 2.3). 2.2 | Test protocol The performed exercise test was an incremental treadmill test with the H/P/Cosmos Saturn 300/100 r treadmill with a constant incline of 1%, and the speed of the treadmill was increased every 3 min by 1 km/h. Ventilation parameters were measured breath- to-breath with Jaeger VyntusTM CPX. Lactate concentration was measured from capillary blood samples from the fingertip and analysed
protocol The performed exercise test was an incremental treadmill test with the H/P/Cosmos Saturn 300/100 r treadmill with a constant incline of 1%, and the speed of the treadmill was increased every 3 min by 1 km/h. Ventilation parameters were measured breath- to-breath with Jaeger VyntusTM CPX. Lactate concentration was measured from capillary blood samples from the fingertip and analysed with the Biosen S- line Lab+ lactate analyser before the first stage and after each stage. The treadmill was shortly paused after each level to obtain the blood sample. Starting speed was determined individually according to the assessment of the study physiologist and possible previous threshold test history. Starting speed was esti- mated to be 2–3 km/h below the aerobic threshold aiming at total test duration of less than 30 min when test is com- pleted until exhaustion. 2.3 | Preprocessing The exercise measurements included a short warm- up period, the exercise, and the recovery phase. The meas- urements were divided manually so that only the exer- cise phase was considered, beginning with the starting level and ending with the highest level reached at the end of the training. The RR intervals were preproc- essed to ensure good data quality for the analysis. First, the RRI time series was filtered with a rolling median filter, with a window of 21 beats. The RRIs which de- viated from the median by more than ± 5% were dis- carded. In addition, the RRI values deviating more than 200 ms from the preceding RRIs were discarded. The recordings of the subjects for which 5% or more of the intervals were filtered were discarded from the analy- sis. Furthermore, there was one sample for which our method could not determine the DDFAT 2, even though the LT 2 and HR maxT 2s were found. This sample was omitted not to neglect the error of our method in deter- mining the threshold for the sample in question, but to be able to directly compare the resulting DDFATs, LTs, and HR maxTs for all tested subjects. This left us with the exercise tests of 58 subjects. TABLE 1 Statistical
2 and HR maxT 2s were found. This sample was omitted not to neglect the error of our method in deter- mining the threshold for the sample in question, but to be able to directly compare the resulting DDFATs, LTs, and HR maxTs for all tested subjects. This left us with the exercise tests of 58 subjects. TABLE 1 Statistical information of the participants, as mean value ± standard deviation: Sex (male = M, female = F), age (years), maximal heart rate HR max (BPM), maximal V̇O2 intake V̇O2 max (mL/kg/min), maximal lactate concentration Lactate max (mmol/l), maximal reached speed Speed max (km/h), and the test duration (min:sec). Variable Studied subjects Sex (M/F) 31/27 Age 33 ± 8 HR max (BPM) 192 ± 9 V̇O2 max (mL/kg/min) 47.1 ± 8.0 Lactate max (mmol/l) 10.0 ± 2.2 Speed max (km/h) 14.5 ± 2.3 Test duration (s) 24:09 ± 4:06 2051817x, 2025, 9, Downloaded from https://physoc.onlinelibrary.wiley.com/doi/10.14814/phy2.70241, Wiley Online Library on [27/04/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
4 of 12 | KANNIAINEN 1234. 2.4 | Lactate thresholds The lactate thresholds were defined by the study physi- ologist (VLR), and any ambiguous cases were examined carefully by VLR and EH. The aerobic threshold was determined based on a 0.3 mmol/L increase from the lowest measured reading of the test, and the anaerobic threshold using the intersection of two fitting lines. The first fitting line was determined according to the lactate value of the load before and after the aerobic threshold, and the second fitting line based on each lactate value that increased by more than 0.8 mmol/L from the pre- vious load. Analyses were performed using K- lab 3.1.25 software and adjusted subjectively by study physiologist (VLR) if needed. 2.5 | Heart rate and heart rate variability thresholds 2.5.1 | Maximal HR- based thresholds We calculated the thresholds based on maximal HR anal- ysis. In the analysis, we calculated the theoretical age- dependent maximal HR with the conventional formula of HR theor max = 220 – AGE according to (Robergs et al., 2002), but also considered the measured maximal HR values HR meas max which the subjects actually reached in the exer- cise test. Based on both theoretical HR theor max and the meas- ured HR meas max we calculated the thresholds by setting the first threshold HR maxT 1 at 70% of the HR max value, and the second threshold HR maxT 1 at 85% of the HR max value as in (Kanniainen et al., 2023). In Section 3 we assess the differences between the thresholds derived from the two different definitions, HR theor max and HR meas max . 2.5.2 | DDFA-based thresholds Our method is based on DDFA (Molkkari et al., 2020) and the computational method to estimate the physi- ological thresholds was first introduced in (Kanniainen et al., 2023). The DDFA scaling exponents utilized in the threshold estimation are calculated as follows (Kanniainen et al., 2023; Molkkari & Räsänen, 2023): 1. Perform dynamic segmentation for each scale s, where the segment length l = 5 s. 2. Compute the second- order DFA fluctuation function (Peng et al., 1995) for each segment at scales s − 1, s, s + 1. The logarithmic fluctuation function is thus denoted as F
et al., 2023). The DDFA scaling exponents utilized in the threshold estimation are calculated as follows (Kanniainen et al., 2023; Molkkari & Räsänen, 2023): 1. Perform dynamic segmentation for each scale s, where the segment length l = 5 s. 2. Compute the second- order DFA fluctuation function (Peng et al., 1995) for each segment at scales s − 1, s, s + 1. The logarithmic fluctuation function is thus denoted as F t(s − 1), F t(s) and F t(s + 1) at the corre- sponding scales. 3. In each segment, compute the dynamic scaling expo- nent α(t,s) by the finite difference approximation where h − = log(s) − log(s − 1) and h + = log(s + 1) − log(s ) are the logarithmic backward and forward differences. During the computation of the time- and scale- dependent scaling exponents α(t,s), the mean HR values of the segments can be calculated, and the scaling proper- ties can be represented as a function of aggregated mean HR and scale, α(HR,s). This HR- dependent scaling expo- nent distribution is then utilized in the determination of the thresholds as follows: 1. Calculate the second- order DDFA (DDFA- 2) for the RRI time series with 20 logarithmically spaced in- teger scales between 5 and 64 RRIs. The range of scales corresponds to the joint scales of DFA α 1 and α 2. 2. Calculate the scaling exponents α(HR,s) as a function of HR and scale s, where HR corresponds to the average of each segment. Sort the HR values by binning them to the nearest integer and assign α(HR,s) values to the corresponding bins. For each scale s, take the mean value of the scaling exponents within the bins, which results in a distribution of α(HR bin,s). 3. Calculate an individual baseline to take the individual physiological starting conditions into account. First, the scaling exponents are determined for the first two speed levels corresponding to roughly 6 min of the be- ginning of the measurement. The lactate measurement break at the end of the second level is not considered in the baseline. A mean value of the scaling exponents for each scale is calculated and added together, thus obtaining the individual baseline value. The baseline value is then subtracted from α(HR bin,s)
levels corresponding to roughly 6 min of the be- ginning of the measurement. The lactate measurement break at the end of the second level is not considered in the baseline. A mean value of the scaling exponents for each scale is calculated and added together, thus obtaining the individual baseline value. The baseline value is then subtracted from α(HR bin,s) over the whole measurement. 4. Calculate the mean value of α (HR bin,s) over each scale s of a HR bin. Smoothen the resulting α (HR bin) curve with a mean filter with a kernel size of 5 HR bins to focus on the trend rather than the small local fluc- tuations. Thus, the mean smoothed scaling exponent 1 HR bin 1 is obtained. The first DDFA- derived thresh- old is the point, where 1 HR bin 1 distribution drops below the baseline ( 1 HR bin 1 = 0). The determination of this point is derived through the following calcula- tion. First find the points where 1 HR bin 1 distribution crosses the baseline. If the intersection is not stable, that is, 1 HR bin 1 keeps fluctuating around the base- line, move to the next one until a stable intersection is found. We find that sufficient stability can be found (t,s)≈ h 2 −1F t(s+1)+ 1 h 2 + −h 2 − 2 1F t(s)−h 2 +1F t(s−1) 3 4 h − h + 1 h + +h − 25 , 2051817x, 2025, 9, Downloaded from https://physoc.onlinelibrary.wiley.com/doi/10.14814/phy2.70241, Wiley Online Library on [27/04/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Description
This study compares DDFA-based thresholds with lactate thresholds in endurance running.