From physiological complexity to data interactions-A case study of recordings from exercise monitoring.

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

Prediction of peak oxygen consumption using cardiorespiratory parameters from warmup and submaximal stage of treadmill cardiopulmonary exercise test.

This study investigates the quality of peak oxygen consumption (VO2peak) prediction based on cardiac and respiratory parameters calculated from warmup and submaximal stages of treadmill cardiopulmonary exercise test (CPET) using machine learning (ML) techniques and assesses the importance of respiratory parameters for the prediction outcome. The database consists of the following parameters: heart rate (HR), respiratory rate (RespRate), pulmonary ventilation (VE), oxygen consumption (VO2) and carbon dioxide production (VCO2) obtained from 369 treadmill CPETs. Combinations of features calculated based on the HR, VE and RespRate time-series from different stages of CPET were used to create 11 datasets for VO2peak prediction. Thirteen ML algorithms were employed, and model performances were evaluated using cross-validation with mean absolute percentage error (MAPE), R2 score, mean absolute error (MAE), and root mean squared error (RMSE) calculated after each iteration of the validation. The results demonstrated that incorporating respiratory-based features improves the prediction of VO2peak. The best results in terms of R2 score (0.47) and RMSE (5.78) were obtained for the dataset which included both cardiac- and respiratory-based features from CPET up to 85% of age-predicted HRmax, while the best results in terms of MAPE (10.5%) and MAE (4.63) were obtained for the dataset containing cardiorespiratory features from the last 30 seconds of warmup. The study showed the potential of using ML models based on cardiorespiratory features from submaximal tests for prediction of VO2peak and highlights the importance of the monitoring of respiratory signals, enabling to include respiratory parameters into the analysis. Presented approach offers a feasible alternative to direct VO2peak measurement, especially when specialized equipment is limited or unavailable.

Maximal oxygen uptake prediction from submaximal bicycle ergometry using a differential model.

The maximal oxygen uptake (VO2max) estimation has been a subject of research for many years. Cardiorespiratory measurements during incremental tests until exhaustion are considered the golden yard stick to assess VO2max. However, precise VO2max determination based on submaximal tests is attractive for athlete as well for clinical populations. Here, we propose and verify such a method based on experimental data. Using a recently developed model of heart rate (HR) and VO2 kinetics in graded exercise tests, we applied a protocol, which is terminated at 80% of the estimated maximal HR during ergometer cycling. In our approach, initially, formula for maximal HR is selected by retrospective study of a reference population (17 males, 23.5 ± 2.0 years, BMI: 23.9 ± 3.2 kg/m2). Next, the subjects for experimental group were invited (nine subjects of both sexes: 25.1 ± 2.1 years, BMI 23.2 ± 2.2 kg/m2). After calculation of maximal HR using cardiorespiratory recordings from the submaximal test, VO2max is predicted. Finally, we compared the prediction with the values from the maximal exercise test. The differences were quantified by relative errors, which vary from 1.2% up to 13.4%. Some future improvements for the procedure of VO2max prediction are discussed. The experimental protocol may be useful for application in rehabilitation assessment and in certain training monitoring settings, since physical exertion is not a prerequisite and the approach provides an acceptable VO2max estimation accuracy.

Effect of nonlinearity and persistence on multiscale irreversibility, non-stationarity, and complexity of time series-Case of data generated by the modified Langevin model.

Stochastic models of a time series can take the form of a nonlinear equation and have a built-in memory mechanism. Generated time series can be characterized by measures of certain features, e.g., non-stationarity, irreversibility, irregularity, multifractality, and short/long-tail distribution. Knowledge of the relationship between the form of the model and features of data seems to be the key to model time series. The paper presents a systematic analysis of the multiscale behavior of selected measures of irreversibility, irregularity, and non-stationarity vs degree of nonlinearity and persistence. As a time series generator, the modified nonlinear Langevin equation with built-in persistence is adopted. The modes of nonlinearity are determined by one parameter and do not change the half-Gaussian form of the marginal distribution function. The expected direct dependencies (sometimes non-trivial) were found and explained using the simplicity of the model. It has been shown that the change in nonlinearity, although subjected to a strong constraint (the same marginal distribution), causes significant changes in the tested markers of irregularity and non-stationarity. However, a synergy of non-linearity and persistence is needed to induce greater changes in irreversibility.

Heart rate variability comparison between young males after 4-6 weeks from the end of SARS-CoV-2 infection and controls.

Due to the prolonged inflammatory process induced by infection of the novel severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), indices of autonomic nervous system dysfunction may persist long after viral shedding. Previous studies showed significant changes in HRV parameters in severe (including fatal) infection of SARS-CoV-2. However, few studies have comprehensively examined HRV in individuals who previously presented as asymptomatic or mildly symptomatic cases of COVID-19. In this study, we examined HRV in asymptomatic or mildly symptomatic individuals 5-7 weeks following positive confirmation of SARS-CoV-2 infection. Sixty-five ECG Holter recordings from young (mean age 22.6 ± 3.4 years), physically fit male subjects 4-6 weeks after the second negative test (considered to be the start of recovery) and twenty-six control male subjects (mean age 23.2 ± 2.9 years) were considered in the study. Night-time RR time series were extracted from ECG signals. Selected linear as well as nonlinear HRV parameters were calculated. We found significant differences in Porta's symbolic analysis parameters V0 and V2 (p < 0.001), α2 (p < 0.001), very low-frequency component (VLF; p = 0.022) and respiratory peak (from the PRSA method; p = 0.012). These differences may be caused by the changes of activity of the parasympathetic autonomic nervous system as well as by the coupling of respiratory rhythm with heart rate due to an increase in pulmonary arterial vascular resistance. The results suggest that the differences with the control group in the HRV parameters, that reflect the functional state of the autonomic nervous system, are measurable after a few weeks from the beginning of the recovery even in the post-COVID group-a young and physically active population. We indicate HRV sensitive markers which may be used in long-term monitoring of patients after recovery.

Oxyhemoglobin Concentration and Oxygen Uptake Signal During Recovery From Exhaustive Exercise in Healthy Subjects-Relationship With Aerobic Capacity.

This proof of concept study is dedicated to the quantification of the short-term recovery phase of the muscle oxygenation and whole-body oxygen uptake kinetics following an exhaustive cycling protocol. Data of 15 healthy young participants (age 26.1 ± 2.8 years, peak oxygen uptake 54.1 ± 5.1 mL∗min-1∗kg-1) were recorded during 5 min cool down-cycling with a power output of 50 W on an electro-magnetically braked cycle ergometer. The oxygen uptake (VO2) signal during recovery was modeled by exponential function. Using the model parameters, the time (T1/2) needed to return VO2 to 50% of VO2 peak was determined. The Hill's model was used to analyze the kinetics of oxyhemoglobin concentration (Sm, %), non-invasively recorded by near-infrared spectroscopy (NIRS) over the M. vastus lateralis. Analysis of the Pearson correlation results in statistically significant negative relationships between T1/2 and relative VO2 peak (r = -0.7). Relevant significant correlations were determined between constant defining the slope of VO2 decrease (parameter B) and the duration of the anaerobic phase (r = -0.59), as well as between Hill's coefficient and average median Smmax for the final 2 min of recovery. The high correlation between traditional variables commonly used to represent the cardio-metabolic capacity and the parameters of fits from exponential and Hill models attests the validity of our approach. Thus, proposed descriptors, derived from non-invasive NIRS monitoring during recovery, seem to reflect aerobic capacity. However, the practical usefulness of such modeling for clinical or other vulnerable populations has to be explored in studies using alternative testing protocols.

Individual performance progression of German elite female and male middle-distance runners.

Current standards for talent identification often base on age-related cross-sectional or mixed data analyses. Longitudinal studies of elite runners from their very early to their late career are still rare, despite their need for valid talent identification and prognoses. Thus, we analysed individual performance trajectories of German international level middle-distance runners (30 females, 41 males) from an age of 14 until their top performance. Quadratic equations best fitted the individual performances from 14 years to late career in relation to the world record time. The individual trajectories were further used to construct a global performance progression model, providing annual performance estimates (mean and standard deviation of 800, 1000 and 1500 m race times in relation to the current world record time) of later top runners from early to late career. Our analysis implies that, on average, females started from a higher performance level at young age. In contrast, average performance progression of the males was higher until the age of 17 years. Performance peaked at an age of 24.0 ± 3.0 and 23.3 ± 2.6 years for the female and male runners, respectively. The provided average annual performance progressions, as well as their ranges, may help coaches and sport federations in their decision making on age-related performance criteria for talent identification in middle-distance running.

Impact of observational error on heart rate variability analysis.

An observational error of heart rate variability (HRV) may arise from many factors, such as a limited sampling frequency, QRS complexes detection process, preprocessing procedures and others. In our study, we focused on the first two origins of measurement error. We introduced a model of observational error and suggested universal descriptors for the assessment of its resultant magnitude in terms of time, frequency as well as nonlinear parameters. For this purpose, we applied Monte Carlo simulations which showed that the most sensitive to observational error are: pNN50 (the proportion of pairs of successive RR intervals that differ by more than 50 ms) and markers obtained from frequency analysis. On the other hand, the most resistant are other time domain parameters as well as the short and long-term slopes of Detrended Fluctuation Analysis (DFA). We postulate that the observational error should be considered in population studies, when different recorders are used in the research centres. Additionally, in the case of patients with similar etiology of disease but with different heart rhythms abnormalities the scatter of HRV parameters will also be observed due to the subject's the time series variability.

Interlimb Coordination: A New Order Parameter and a Marker of Fatigue During Quasi-Isometric Exercise?

Although exercise-induced fatigue has been mostly studied from a reductionist and component-dominant approach, some authors have started to test the general predictions of theories of self-organized change during exercises performed until exhaustion. However, little is known about the effects of fatigue on interlimb coordination in quasi-isometric actions. The aim of this study was to investigate the effect of exercise-induced fatigue on upper interlimb coordination during a quasi-isometric exercise performed until exhaustion. In order to do this, we hypothesized an order parameter that governs the interlimb coordination as an interlimb correlation measure. In line with general predictions of theory of phase transitions, we expected that the locally averaged values of the order parameter will increase as the fatigue driven system approaches the point of spontaneous task disengagement. Seven participants performed a quasi-isometric task holding an Olympic bar maintaining an initial elbow flexion of 90 degrees until fatigue induced spontaneous task disengagement. The variability of the elbow angle was recorded through electrogoniometry and the obtained time series were divided into three segments for further analysis. Running correlation function (RCF) and adopted bivariate phase rectified signal averaging (BPRSA) were applied to the corresponding initial (30%) and last (30%) segments of the time series. The results of both analyses showed that the interlimb correlation increased between the initial and the final segments of the performed task. Hence, the hypothesis of the research was supported by evidence. The enhancement of the correlation in the last part means a less flexible coordination among limbs. Our results also show that the high magnitude correlation (%RCF > 0.8) and the %Range (END-BEG) may prove to be useful markers to detect the effects of effort accumulation on interlimb coordination. These results may provide information about the loss of adaptability during exercises performed until exhaustion. Finally, we briefly discuss the hypothesis of the inhibitory percolation process being the general explanation of the spontaneous task disengagement phenomenon.

On the nature of heart rate variability in a breathing normal subject: a stochastic process analysis.

Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology.