Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review
Abstract
:1. Introduction
2. Heart Rate Time Series Analysis
2.1. Feature-Based Time-Domain Methods
- RMSSD, the root mean square of difference between adjacent RR intervals
- SDNN, the standard deviation of all RR intervals
- SDSD or SDDS, the standard deviation of differences between adjacent RR intervals (or RR series)
- MSD, the mean successive difference between adjacent RR intervals
- MASD, the mean absolute successive difference between adjacent RR intervals
2.2. Frequency-Domain Methods
3. Nonlinear Analysis for HR Time Series
3.1. Poincarè Geometry
3.2. Detrended Fluctuation Analysis (DFA)
- For a time series RR(i), the integrated time series y(k) can be expressed as:
- 2.
- The time interval is divided in windows with equal length n, to quantify the vertical characteristic scale of y(k);
- 3.
- In each window n, a least-squares line is fit to the data (representing the trend in that window). The y-coordinate of the straight-line segments is denoted by yn(k). The integrated time series is detrended, y(k), by subtracting the local trend, yn(k), in each window (see Figure 1b in [35]).
- 4.
- The root mean square fluctuation of the integrated and detrended time series is estimated by the formula:
- if 0 < α < 0.5, then the process exhibits anti-correlations;
- if α = 0.5, then the process is a random process, such as white noise;
- if 0.5 < α < 1, then the process exhibits positive correlations;
- if α= 1, a long-range correlation in the time-series occurs, corresponding to the typical 1/f noise, where f is the frequency. The 1/f slope of the log(power) vs. log(frequency) plot was obtained from a linear regression;
- if α > 1, then the process is non-stationary;
- if α = 1.5, the process represents a random walk such as Brownian noise.
3.3. Entropy
3.3.1. Approximate Entropy (ApEn)
3.3.2. Sample Entropy (SampEn)
3.4. Recurrence Quantification Analysis (RQA)
4. HR Time Series Analysis for Detection of Metabolic Thresholds during Exercise
4.1. Feature-Based Methods for the Detection of Metabolic Threshold
4.2. Nonlinear Methods for the Detection of Metabolic Threshold
4.2.1. Poincaré Plots and DFA for the Detection of Metabolic Threshold
4.2.2. RQA for the Detection of Metabolic Thresholds
5. Known Issues in Using Nonlinear Methods
- (i)
- The intrinsic individual variability of the subject and the dependence by his/her fitness level and the body mass status;
- (ii)
- The accumulated sampling error and the noise levels of the devices used to record the HR data (sampling rate, motion, for both ECG or HR beat-by-beat monitor);
- (iii)
- The intrinsic features of the recorded signal, as non-stationarity or the trend;
- (iv)
- The dependence on the parametric values for the chosen analysis method (i.e., input values chosen for the algorithms, type of detrending, etc.).
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Abbreviations
HR | heart rate |
HRV | heart rate variability |
HRVT | heart rate variability threshold |
CPET | cardiopulmonary exercise test |
ECG | electrocardiography |
AerT | aerobic threshold |
AnT | anaerobic threshold |
ANS | autonomic nervous system |
S | sympathetic activity |
PS | parasympathetic activity |
CSI | cardiac stress index |
SD1 | standard deviation of instantaneous beat-to-beat interval variability |
SD2 | standard deviation of continuous long-term R–R interval variability |
DFA | detrended fluctuation analysis |
ApEn | approximate entropy |
RQA | recurrence quantification analysis |
DET | percent of determinism |
FFT | fast Fourier transform |
HF | high frequencies |
LF | low frequencies |
VO2 | oxygen consumption |
Ln(rMSSD) | natural logarithm of root mean square standard deviation |
BLa | blood lactate production |
Appendix A
Authors | Physical Exercise | Non-Linear Method |
---|---|---|
Marwan et al., 2002 [9] | Cycling | RQA |
Censi et al., 2002 [10] | Resting | RQA |
Auber et al., 2003 [11] | Cyclergometer | Frequency analysis |
Tulppo et al., 1996 [12] | Cyclergometer | Poincaré plot |
Mourot et al., 2004 [13,14] | Cyclergometer | Poincaré plot |
Orellana et al., 2015 [15] | Soccer | Descriptive analysis |
Chen et al., 2015 [16] | Cyclergometer | DFA |
Singh 2019 [17] | Resting | RQA, ApEn |
Cottin et al., 2004 [18] | Cyclergometer | Frequency analysis |
Goya-Esteban et al., 2012 [19] | Cyclergometer | DFA |
Wittstein et al., 2019 [20] | Treadmill | DFA |
Hoshi et al., 2016 [21] | Soccer, basketball, handball | RQA |
Blasco-Lafarga et al., 2017 [22] | Cyclergometer | DFA |
Appendix A.1. Statistical Analysis, Accuracy and Reliability
Appendix A.2. Electrocardiogram Derived Respiration (EDR)
Appendix A.3. Determinism and Laminarity Epoch-by-Epoch
Appendix A.4. Software for Creating Figures
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Authors | Subjects | Physical Exercise | HR Detection | Methods | Statistical Validation | Gold Standard |
---|---|---|---|---|---|---|
Buchheit et al., 2007 [81] | 72 Trained boys, runners | Treadmill | CPET Chest belt Polar T61; watch Polar 810s | Spectral analysis HFp and (ln fHFm./HFp) | HRVT2 vs. HRDP for VO2 r = 0.88 *; for HR r = 0.85 * | Gas exchange |
Karapetian et al., 2008 [82] | 24 Healthy adults | Cyclergometer | Watch and chest belt Polar Vantage XL | Time analysis SDNN, MSD | HRVT1 vs. VT1 for VO2 r = 0.89; HRVT 2 vs. LT2 for VO2 r = 0.82 | Gas exchange Blood lactate |
Quinart et al., 2013 [83] | 20 Obese adolescents | Cyclergometer | CPET Chest belt and watch Polar 810s | Spectral analysis HFp and (ln fHFm./HFp) Time analysis RMSSD | HRT1 at VT1 for HR r = 0.91 ** 95% CI (0.84–0.95); HRT2 at VT2 for HR r = 0.91 ** 95% CI (0.83–0.95) | Gas exchange |
Cassirame et al., 2015 [84] | 9 Healthy adults ski-mountaineers | Alpine skiing track | Chest belt Polar T61; portable recorder FRWD B100 | Time–frequency analysis fHF × HFp | HRT2 vs. VT2 for HR r = 0.91; for speed r = 0.92 for HR small LoA (3.6 bpm) | Gas exchange |
Vasconcellos et al., 2015 [85] | 35 Adolescents (15 obese) | Cyclergometer | CPET Chest belt and watch Polar TM RS800cx | Time analysis RMSSD | HRVT1 vs. VT1 for VO2 from r = 0.89 ** and test–retest reliability r = 0.59 * | Gas exchange |
Ribeiro et al., 2018 [86] | 13 Young soccer players | Treadmill | CPET Chest belt and watch Polar F11 HRM | Graphics analysis (shift of RR interval) | HRVT2 vs. VT2 for time r = 0.84 *; for HR r = 0.97 *; for VO2 r = 0.97 * | Gas exchange |
Nascimento et al., 2019 [87] | 19 Male runners | Maximal incremental running test (MIRT) | Chest belt and watch Polar 810s | Poincaré plot, DFA (Dmax) | No correlation for HR1 at LT1 for HR; HRT2 at LT2 for HR r = 0.71 **; HRT1 at LT1 for speed r = 0.46 *, 95% CI (0.9–1.9); HRT2 at LT2; for speed r = 0.48 * 95% CI (0.8–1.6) | Blood lactate |
Novelli et al., 2019 [88] | 68 Untrained subjects | Cyclergometer | Chest belt and watch Polar RS800CX RRinterval | Time analysis, Poincaré plot RMSSD and SD1 | No significant difference (p < 0.05) between the test and retest for any of the variables. All variables at HRVT1 and the heart rate at HRVT2 showed CV ~10%. | Gas exchange |
Zimatore et al., 2020 [65] | 20 Obese adults | Treadmill | CPET Chest belt Polar RS 400 | RQA | HRVT1 vs. VT1 for time r = 0.70 **; for speed r = 0.84 **; no statistically significant differences (p < 0.05) for time, speed, VO2, and MFO; | Gas exchange |
Stergiopoulos et al., 2021 [89] | 15 Healthy adults | Treadmill, multistage running test (MSRT) | ECG TEL100, MP 100A Biopac | Time and apectral analysis HFP | no statistically significant differences between the running speed at VT2 and EDRT (F (2,28) = 0.83, p = 0.45, η2 = 0.05) | Gas exchange |
Zimatore et al., 2021 [66] | 31 Healthy adolescents | Cyclergometer | CPET Chest belt Garmin ^ HRM-Dual™ | RQA | HRVT1 vs. VT1 for HR r = 0.87 *; for workload r = 0.95; for VO2 r = 0.91 *; HRVT2 vs. VT2, for HR r = 0.89; for workload r = 0.97; for VO2 r = 0.97 | Gas exchange |
Rogers et al., 2021 [90] | 17 Male adults | Treadmill | Chest belt Polar H7 | DFA | HRVT1 vs. VT1 for HR r = 0.96 **; HRVT2 vs. VT2 for HR r = 0.78 **; | Gas exchange |
Afroundeh et al., 2021 [91] | 103 Young males | Treadmill | Chest belt Polar T31 | DFA, modified Dmax | HRVT1 at LT1 for HR ICC = 0.88 **; for speed ICC = 0.40 ** | Blood lactate |
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Zimatore, G.; Gallotta, M.C.; Campanella, M.; Skarzynski, P.H.; Maulucci, G.; Serantoni, C.; De Spirito, M.; Curzi, D.; Guidetti, L.; Baldari, C.; et al. Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review. Int. J. Environ. Res. Public Health 2022, 19, 12719. https://doi.org/10.3390/ijerph191912719
Zimatore G, Gallotta MC, Campanella M, Skarzynski PH, Maulucci G, Serantoni C, De Spirito M, Curzi D, Guidetti L, Baldari C, et al. Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review. International Journal of Environmental Research and Public Health. 2022; 19(19):12719. https://doi.org/10.3390/ijerph191912719
Chicago/Turabian StyleZimatore, Giovanna, Maria Chiara Gallotta, Matteo Campanella, Piotr H. Skarzynski, Giuseppe Maulucci, Cassandra Serantoni, Marco De Spirito, Davide Curzi, Laura Guidetti, Carlo Baldari, and et al. 2022. "Detecting Metabolic Thresholds from Nonlinear Analysis of Heart Rate Time Series: A Review" International Journal of Environmental Research and Public Health 19, no. 19: 12719. https://doi.org/10.3390/ijerph191912719