Wavelet Transform Analysis of Heart Rate to Assess Recovery Time for Long Distance Runners

The diagnostics of the condition of athletes has become a eld of special scienti c interest and activity. The aim of this study was to verify the effect of a long (100 km) run on a group of runners, as well as to assess the recovery time that is required for them to return to the pre-run state. The heart rate (HR) data presented were collected the day before the extreme physical effort, on the same day as, but after, the physical effort, as well as 24 and 48 h after. The Wavelet Transform (WT) and the Wavelet-based Fractal Analysis (WBFA) were implemented in the analysis. A tool was constructed that, based on quantitative data, enables one to con rm the completion of the recovery process that is related to the extreme physical effort. Indirectly, a tool was constructed that enables one to con rm the completion of the recovery process. The obtained information proves that the return to the resting state of the body after a signi cant physical effort can be observed after two days entirely through the analysis of the HR. Certain practical measures were used to differentiate between two substantially different states of

was constructed that enables one to con rm the completion of the recovery process. The obtained information proves that the return to the resting state of the body after a signi cant physical effort can be observed after two days entirely through the analysis of the HR. Certain practical measures were used to differentiate between two substantially different states of the human body, i.e., pre- and post-effort states were constructed. The obtained results allow for us to state that WBFA appears to be a useful and robust tool in the determination of hidden features of stochastic signals, such as HR time signals. The proposed method allows one to differentiate between particular days of measurements with a mean probability of 92.2%. Keywords:heart rate; recovery time; runners; wavelet transform 1. Introduction The process of the differentiation of patients' conditions as a function of their physical effort and body positions is an important step in medical diagnostics regarding both healthy and unhealthy individuals [1,2]. Recently, the diagnostics of the condition of athletes has become a eld of special scienti c interest and activity. In the context of medical diagnostics, this is a group of healthy individuals that were subjected regularly to substantial physical effort. Therefore, it is important to evaluate any changes in their body functions based on pre- and post-effort medical assessment. This can be done by regular monitoring of body functions that are represented next as time series, Electronics2020,9, 2189; doi:10.3390/electronics9122189

Electronics2020,9, 2189 2 of 17 related to pre- and post-effort periods [3–6]. It is also possible to continue the monitoring process for a number of days following the effort, which allows for one to estimate the time that is required for body recovery, when all of the body functions return to their pre-effort state, i.e., the time of full recovery [7–10]. As is widely known, a decrease in the vagal tone represents the initial response of a body to physical effort and it is followed by an increase in the sympathetic activity of the autonomic nervous system (ANS). An inverse process occurs after the effort cessation [11]. On the other hand, it is well known that higher effort intensity can lead to a persistent increase in the adrenergic tone, the loss of parasympathetic predominance of the ANS [12–16], or even to a marked shift in the autonomic balance towards sympathetic predominance lasting for many hours after effort cessation [3,17–26]. Most previous studies analysing the effects of intense physical exercise included professional athletes. In contrast, the research dealing with the effects of this type of exercise on the function of ANS in amateur athletes is relatively sparse [15,16,27]. The differences between these two groups of athletes seem to be important in relation to the speci city of their training and the resulting degree of preparedness for overcoming exercise-related load. Nowadays, signal processing, including biomedical signals, is based on a variety of different methods. The leading signal analysis methods are the frequency methods, e.g., the Fourier transform. However, the most important drawback of the Fourier transform lies in a possible loss of certain signal features in the time domain. This may lead to overlooking important information regarding the signal dynamics, which may then result in the loss of information about any transient action of regulation systems. An example can be a resulting apparent dynamic balance between pre- and post-effort states. The following years the development in signal processing techniques have brought about the method of wavelet analysis (WA) [28–31]. This technique, employing the Wavelet Transform (WT), allows for one to analyse signal

then result in the loss of information about any transient action of regulation systems. An example can be a resulting apparent dynamic balance between pre- and post-effort states. The following years the development in signal processing techniques have brought about the method of wavelet analysis (WA) [28–31]. This technique, employing the Wavelet Transform (WT), allows for one to analyse signal at a selected detail level not only in the frequency domain, but also in the time domain. Non-stationary signals, like biomedical signals, are well described by this transformation, in contrast to other signal processing methods, e.g., the Fourier transform, which is dedicated to periodic signals analysis. Nowadays, WA, which is frequently supported by WBFA in order to appropriately assess de ned spectral elements, is a powerful signal processing tool that can be employed to prove or falsify various scienti c hypotheses. WA techniques are proven methods for the investigation of the work of the circulatory system [28,32,33]. The essence of the paper is to investigate changes in the circulatory system in a group of 13 athletes before and after a run over a distance of 100 km, as well as to assess the recovery time that is required for them to return to the pre-run state. The research is based on the analysis of the heart rate and it follows a broadly accepted tendency in the measurements of extreme physical effort, especially in the case of long distance runners. The technical part of the paper is focused on the implementation of novel and robust signal processing techniques, especially the Wavelet Transform (WT) and WBFA, in order to pick up subtle changes in four independent responses (measurements) that were taken from the circulatory system, these being: the heart rate, stroke volume, heather index, and velocity index. However, it should be mentioned that substantial and usable changes for subsequent signal processing were only observed in the case of the heart rate. For that reason, the authors' scienti c interest is mainly concentrated on the thorough assessment and analysis of this single heart related parameter. The scope of the presented article includes a

heather index, and velocity index. However, it should be mentioned that substantial and usable changes for subsequent signal processing were only observed in the case of the heart rate. For that reason, the authors' scienti c interest is mainly concentrated on the thorough assessment and analysis of this single heart related parameter. The scope of the presented article includes a detailed description of measurements that aimed at collecting HR time signals, together with a description of two methodologies that are used to analyse the collected data. The authors focused on one-dimensional CWT and WBFA supplemented with a statistical approach. In the following chapters, the obtained results are presented and discussed.

Electronics2020,9, 2189 3 of 17 2. Methods 2.1. Study Description The main purpose of the research is to investigate the changes in the circulatory system of long distance runners before and after an extreme physical effort. A group of volunteers from the Sport Centre of the Gdansk University of Physical Education and Sport have been selected as the test subjects. They were obligated to take part in regular measurements of their HR before the physical effort, just after the effort, as well as 24 and 48 h after the effort. The volunteers took part in a long distance run. The run covered 100 km on a 3375 m loop with the total altitude difference not being greater than 2 m. The weather conditions during the run were as follows: air temperature of 4–5 degrees C and relative air humidity 86% with no wind. The run started at 7:20 in the morning and it lasted for approximately 10 h. The shortest recorded nishing time was 9 h and 11 min. and the longest was 12 h and 8 min., not including 3-min. breaks for collecting research data. Twelve hours before the race the runners ate dinner, and thenm after a night rest, at 6:30 in the morning, they ate a light breakfast. The runners were dressed according to their individual needs in sports shoes, cotton tracksuits, as well as gloves and hats made of natural materials. During the run, each athlete wore on their chest a telemetric HR meter (Polar Electro, Kempele, Finland), which recorded their heart rate every 5 s. The time intervals of running and breaks between sections were measured by an electronic Timex clock (Zug, Switzerland, 2009) with the current reading visible on a board that was placed next to the starting line. During the run, they consumed individually prepared sets of beverages and nutritional products whenever they reported the need. The administration of food took place at designated stations. A standard meal consisted of low-mineralized water, energy drinks, sandwiches with cheese or ham, energy bars, and bananas. Runners consumed products with an average energy value of 1151

next to the starting line. During the run, they consumed individually prepared sets of beverages and nutritional products whenever they reported the need. The administration of food took place at designated stations. A standard meal consisted of low-mineralized water, energy drinks, sandwiches with cheese or ham, energy bars, and bananas. Runners consumed products with an average energy value of 1151 kcal per person, whereas their average energy demand was at the level of 5610 kcal, which is equivalent to oxygen consumption of 1.6 l/min. Blood samples were collected immediately before the run and after 25, 50, 75, and 100 km of running, as well as after 12 and 24 h of rest. The parameters of acid-base balance (arterial blood gas—ABG) were measured in arterialized blood samples that were drawn from the ngertip. During the analysis of blood parameters, the individual and mean values were taken into account, as well as the reference values (standards): pH (7.35 7.45), base excess in extracellular uids (BE ecf.; 2.3 to +2.3 mEq/L), bicarbonate level (HCO3;21 27mmol/L), oxygen partial pressure (pO2; 75 to 100 mmHg), carbon dioxide partial pressure (pCO2; 32 to 45 mmHg), oxygen saturation of haemoglobin (O2sat.;95% 98%), and lactate level (0.5 2.22mmol/L). The arterial blood gas levels were determined with the use of the analyser type ABL 835 FLEX, which was produced by Radiometer Medical ApS (Brønshøj, Denmark). For the determination of the lactate concentration in blood samples, the enzymatic method with Randox reagent kit was used and reading of the extinction had been done at 37 degrees C while using a spectrophotometer type EPOLL 200, produced by Serw-med s.c. (Warsaw, Poland, 2006). The HR of the runners was measured continuously for 12 min. and thanks to that 450-sample-long time series were collected. All of the HR signals were recorded based on the time intervals between successive R-waves of electrocardiographic signals (ECG). Their measurements were performed with NiccomoTM device (Medis, Ilmenau, Germany). Eight spot electrodes and a cuff manometer were used. The haemodynamic parameters were measured continuously and their values were recorded beat-to-beat. The quality of all the measurements was high and

collected. All of the HR signals were recorded based on the time intervals between successive R-waves of electrocardiographic signals (ECG). Their measurements were performed with NiccomoTM device (Medis, Ilmenau, Germany). Eight spot electrodes and a cuff manometer were used. The haemodynamic parameters were measured continuously and their values were recorded beat-to-beat. The quality of all the measurements was high and no relevant errors were noted. The HR of all volunteers measured before the run was around 64–72/min., while just after the run was around 141–158/min. For further analysis, only HR measurements from 13 male amateur runners were selected. It should be mentioned that the runners represent different training levels that cover between

Electronics2020,9, 2189 4 of 17 25–35 years of running. Apart from running, they are also active in other sports, such as: swimming, cycling, or strength sports. The study was approved by Independent Bioethics Commission for Research at Medical University of Gdansk. Written informed participation consent was obtained from all of the volunteers taking part in the programme. All of the experiments presented were carried out in accordance with the approved guidelines. 2.2. Wavelet Analysis The Wavelet Transform (WT) employed in the current paper is a process of source signal decomposition and its following representation by a linear combination of some base functions, which are known in the literature as wavelets. As mathematical functions, wavelets are characterised by zero mean value, nite signal power, rapid decay, as well as a nite time length. These features of wavelets make them well localised bases in both time (or space) and frequency. For that reason, wavelets are especially useful in the analysis of biomedical signals, in which singular points are omnipresent and where the problem of decomposition and reconstruction of original non-periodic and non-stationary signals is extremely important. Based on the literature available [34–36] related to the analysis of discontinuous, non-stationary signals of high variability, it was decided by the authors to use the Haar wavelet (synonymous with Daubechies 1 [37]) in the present work. These wavelets were used in wavelet decomposition processes that were subsequently used for HR assessment. The rst decomposition process was based on the use of the Continuous Wavelet Transform (CWT), which generated certain coef cients describing the resemblance between a chosen wavelet and the signal under investigation. The schematic diagram that is presented in Figure the methodology employed by the authors based on the application of CWT, which led them to the calculation of the sums of wavelet coef cients. WBFA was chosen as the second method. Its choice was supported by the fact that the analysed HR signals can be understood as time series (stochastic processes). On the other hand, stochastic processes can be well characterised by a physical quantity, known as a spectral power density (PSD). Because

them to the calculation of the sums of wavelet coef cients. WBFA was chosen as the second method. Its choice was supported by the fact that the analysed HR signals can be understood as time series (stochastic processes). On the other hand, stochastic processes can be well characterised by a physical quantity, known as a spectral power density (PSD). Because the PSD represents the signal power that is associated with particular frequenciesw, it becomes possible to investigate the frequency content of stochastic processes as well as identify any periodic behaviour that is associated with them [38]. It should be also underlined, at this point, that HR signals are characterised by the PSD distributions that correspond to1/fprocesses (pink noise), which means, in practice, that their amplitudes are inversely proportional to frequencyf[39,40]. The WBFA allows for an investigation of the HR correlation in a similar manner to that presented by Tan et al. [41]. In their work, they analysed, by fractal methods, the in uence of various drugs on the heart rate variability (HRV) in the case of 10 healthy individuals. They pointed out the fact that increasing the time signal lengths during the assessment, even up to 1.5 h, had no signi cant in uence on the quality of the results. Moreover, they suggested that the most appropriate signal lengths should stay around 15–20 min. This kind of information is vital for the material that is presented in this work, as all analysed time signals of HR include 450 samples, which is approximately equal to 12 min. The self-similarity estimation of the signals under investigation was made based on the spectral exponentg, calculated by WBFA, by: g= Dlog 2 vardm,n Dm (1) wheredm,ndenotes the wavelet coef cients that were obtained by the application of the Discrete Wavelet Transform (DWT) [42]. The wavelet coef cients are dot products of the time signal and a series of base functions. The schematic diagram that is presented in Figure employed by the authors, but, based on the application of DWT using Daubechies base wavelet (db3) and eight decomposition levels, which led them to the calculation

the application of the Discrete Wavelet Transform (DWT) [42]. The wavelet coef cients are dot products of the time signal and a series of base functions. The schematic diagram that is presented in Figure employed by the authors, but, based on the application of DWT using Daubechies base wavelet (db3) and eight decomposition levels, which led them to the calculation of the spectral exponent coef cients.

Electronics2020,9, 2189 5 of 17 In order to decompose a given source time signals(t)by DWT,the signal is first separated into a detailD1and its approximationA1. In the following step, the number of time samples is reduced by half and next detailD2and its approximationA2are obtained. This process can be continued further; however, as the number of time samples is halved, such a discrete process can be carried out on a finite number of decomposition levels. This constraint is not present in the case of CWT that was described above earlier. Differences between the scalograms representing two days of observation, thus a different condition of the patients, can indicate the capture of certain subtle, but signi cant changes. They can also con rm the robustness of the applied methodology and the numerical tool developed. In that context, the essence of the application of CWT or DWT comes from the curves that represent the sums of the wavelet coef cients as a function of the scale. In contrast, the essence of the application of WBFA comes from the spectral coef cients, which carry all necessary resulting information. Figure 1. A schematic diagram for the signal analysis methodology based of the application of Continuous Wavelet Transform (CWT), used for calculation of the sums of wavelet coef cients.

This study analyzes heart rate recovery in long distance runners after a 100 km run.