heuristic algorithm for photoplethysmography heart rate ... · maximal exercise test56 (imet) on...

Articles in Press, J. Med. Biol. Eng. (November 14, 2011), doi: 10.5405/jmbe.898

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Heuristic Algorithm for Photoplethysmography Heart 1

Rate Tracking during Athletes Maximal Exercise Test 2

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Sonnia María López-Silva1 Romano Giannetti

2* María Luisa Dotor

1 Juan Pedro Silveira

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Dolores Golmayo3 Francisco Miguel-Tobal

4 Amaya Bilbao

4 Mercedes Galindo

4 Pilar Martín-Escudero

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1 Instituto de Microelectrónica de Madrid, CNM-CSIC, C/ Isaac Newton 8, Tres Cantos, Madrid 28760, 7

Spain. 8

2 Departamento de Electrónica y Automática, Universidad Pontificia Comillas, C/ Alberto Aguilera 23, 9

Madrid 28015, Spain. 10

3 Instituto de Ciencias de Materiales de Madrid, CSIC, C/ Sor Juana Inés de la Cruz 3, Madrid 28049, Spain. 11

4 Escuela Profesional de Medicina de la Educación Física y el Deporte, Facultad de Medicina, Universidad 12

Complutense de Madrid, Madrid 28040, Spain. 13

* Corresponding author: Prof. Romano Giannetti 14

Vice-Rector for International Relations 15

Universidad Pontificia Comillas 16

C/ Alberto Aguilera 23, 28015 Madrid (Spain)

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Tel +34-915422800; Fax +34-915411542 18

E-mail: [email protected]

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RUNNING TITLE: PPG Heart Rate Tracking in Athletes21

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* Corresponding author: Romano Giannetti E-mail: [email protected]

mailto:[email protected]


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Abstract 24

Photoplethysmography (PPG) is a non-invasive optical technique that enables to quantify the arterial 25

blood pulse rate. Signal corruption by motion artifacts is a primary limitation in the practical accuracy and 26

applicability of instruments for monitoring pulse rate during intense physical exercise. Here we develop and 27

validate an algorithm, based on linear filtering, frequency domain and heuristic analysis, capable to extract 28

and display the heart rate from PPG signal in the presence of severe motion artifacts. The basis of the 29

frequency selection is the observed high harmonic content of movement artifact signals with respect to the 30

PPG-derived heartbeat. The algorithm has been implemented in an experimental PPG measurement device 31

and has been developed by analyzing a set of PPG data recorded from a first group of athletes exercise in 32

treadmill. After that, an extensive set of tests has been carried out on real time during maximal exercise tests 33

in treadmill in order to validate the instrument by comparison with a reference electrocardiography 34

measurement system. We have used the Bland and Altman method to compare and evaluate the PPG signal. 35

The accuracy of the heartbeat measurement is better than ± 6.5 bpm (≤ 4.2 %) even under maximal exercise 36

conditions. 37

Keywords: Biomedical signal processing, Photoplethysmography (PPG), Motion artifact, Detection 38

algorithm, Heart rate 39

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1. Introduction 44 45

Photoplethysmography (PPG) is a technique offering a simple, useful and compact way to measure several 46

clinical parameters such as oxygen saturation, blood pressure and cardiac output [1,2]. PPG is especially 47

suitable for wearable sensing, that could play an important role in many areas ranging from personal health 48

monitoring to sports medicine. Despite the attractive attributes of PPG and the ease of its integration into 49

wearable devices, the PPG signal is known to be fragile and easily modifiable by motion. In most cases, the 50

noise falls within the same frequency band as the physiological signal of interest, rendering linear filtering 51

ineffective. Research carried on motion artifacts in measured PPG signals has reduced the sensitivity to the 52

artifacts common in the clinical environments, as well as in situations of controlled or moderate motion [1-53

8]. A non-contact, laser emitter remote PPG system, has been proposed [9] and positively evaluated for 54

clinical applications. PPG has been also applied to the evaluation of more severe exercise during incremental 55

maximal exercise test (IMET) on cycle-ergometer, where several parameters are monitored, among them 56

oxygen saturation [10,11] and heart rate [12-15]. Active research efforts are beginning to demonstrate a 57

utility beyond oxygen saturation and heart rate (HR) determination; for instance, the conditions for a correct 58

utilization of PPG HR variability (PPGV) have been recently studied [14] and the authors concluded that 59

PPGV cannot be used during slow walk and cycling exercise. Future trends are being heavily influenced by 60

modern digital signal processing [16]. New commercial developments from the PPG-based prototype [17] 61

support a new interest in the possibilities that PPG technique might offer for HR tracking. 62

Under severe exercise conditions, motion artifacts present one of the most challenging problems for PPG 63

analysis. Design of sensor and packaging can help to reduce the impact of motion disturbances, but it is 64

rarely sufficient for noise removal. Advanced signal processing techniques are often required to discriminate 65

motion artifacts under vigorous activity. Several techniques have been investigated to deal with those 66

artifacts, such as processing context information by additional on-body sensors and light sources [18,19] or 67

adaptive noise cancellation using accelerometers as a noise reference [20]. Very recently, heart rate 68

measurements using a PPG sensor integrated with an adaptive noise cancellation device has been 69

demonstrated at common physical activity, from walking to running up to 8 Km/h [21]. 70


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Spectral analysis, as traditional fast Fourier transform (FFT), is a simple and inexpensive useful tool for 71

separating motion artifact and cardiac physiologic spectra. However, techniques based on spectral analysis 72

will not be applicable to spectra that contain frequency bands close to each other. More sophisticated 73

algorithms have shown significant improvement over FFT for measurements obtained during finger bend 74

manoeuvres [2]. Advanced signal processing techniques can help to overcome this problem. The aim of this 75

work is to present and validate an innovative algorithm able for tracking heart rate from PPG signal during 76

athletes IMET on treadmill. The real-time motion discriminator algorithm, based on linear filtering, 77

frequency domain and heuristic analysis, allows us to extract the heart rate value from PPG signal in the 78

presence of severe motion artifacts. The basis of the frequency selection is the observed high harmonic 79

content of movement artifact signals with respect to the PPG-derived heartbeat. A preliminary version has 80

been already presented, with off-line analysis both of heart rate and oxygen saturation [22]; this paper provides 81

an optimization of the algorithm parameters for the heart rate tracking, as well as real time probes and 82

comparison of the results to the values obtained by a standard technique. The physiological aspects of training 83

are out of the scope of this work. The custom PPG measurement system is based on a transmittance pulse 84

oximetry system [23]. 85

The organization of this paper is as follows. Section 2 describes the materials and methods. Section 3 is 86

devoted to the analysis of the elements for the algorithm design through the analysis of PPG recorded data 87

obtained from a first group of athletes during treadmill IMET. Section 4 is devoted to de development of the 88

algorithm. Section 5 is devoted to present the results of validation of the algorithm both on recorded data of 89

a group T1 of athletes and on real time heart rate tracking during IMET on treadmill of a second group T2 of 90

athletes; we have assessed the agreement between heart rate measured by the new and the reference methods, 91

electrocardiography (ECG), by means of Bland and Altman analysis [24,25] obtaining PPG data that lie 92

within ± 6.5 bpm (beats per minute) with respect to the ECG data. In section 6, we present the discussion of 93

the work. 94

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2. Materials and Methods 96


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Athletes of both sex genders with a training schedule exceeding an average of 7 - 8 hours per week 97

participated in IMET performed on treadmill during separate sessions. Data presented and analyzed in this 98

work correspond only to the heart rate measurements; others like oxygen consumption, carbon dioxide 99

production and blood pressure are out of the scope of the present work. The studies were conducted at the 100

laboratories of effort physiology of the Professional School of Physical Education of Complutense 101

University, Madrid (Spain), after approval by the local Research Ethical Committee. All the athletes gave 102

their written informed consent. 103

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2.1. Subjects 105

A first group T1 was composed by 10 white males, endurance runners tested on the treadmill ergometer. A 106

second group T2 includes 20 athletes tested on the treadmill: 9 white females (one runner, 8 football players), 107

9 white male runners and 2 black female basketball players. The development of the algorithm and 108

optimization of its parameters was carried out after data recorded on the first group T1. The algorithm 109

performance has been evaluated on real time during IMET of the independent group of athletes T2. 110

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2.2. Experimental protocol 112

Heart rate was monitored by electrocardiography (ECG, Burdick, Inc, Model Quest Exercise Stress 113

System) and used as reference. The PPG sensor was placed on one finger with special care to avoid 114

excessive compression of the tissues. The arms movement was not restricted. 115

Next, a complete maximal exercise test was performed, followed by active recovery. The protocol [26] for 116

the treadmill ergometer (HP Cosmos QUASAR 4.0) test established that after one minute at rest (in order to 117

record basal values) and after warming up, the athlete began to walk at 6 Km/h and 1 % slope during 2 min. 118

The athlete then started the effort phase running at 8 Km/h and 1 % slope. During the effort phase, the speed 119

was increased every 2 min by 2 Km/h. The maximum speed achieved varied among individuals. When the 120

speed of 14 Km/h (for female athletes) or 16 Km/h (for male athletes) was reached, the slope was increased 121

to 3 %. Afterwards, the slope was maintained constant, while speed was increased every 2 min by 2 Km/h, 122

until they were unable to continue, then the athlete held the protective bars and jumped off the treadmill. 123


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Active recovery was performed during 2 min at 8 Km/h with a slope of 0 %. At the beginning of the exercise, 124

when walking at 6 Km/h, most of the athletes were adapting to walk on the treadmill and in many cases they 125

took hold of protection bars, which could alter the position of the finger sensor. This will be discussed later. 126

The ECG system computed the heart rate every 10 s, averaging the last eight heart beats. At different stages 127

of the test, once the athlete was running at fixed speed and slope, the full-step rate (SR, in Steps/min) was 128

obtained by counting manually the number of steps in 10 s interval, and the one-foot step was derived from 129

that. When running, steps and waving of the arms are synchronous; hereafter, we will note SR both for the 130

full step and the full arm-waving, which are inseparable issues. 131

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2.3. PPG measurement system 133

The custom PPG measurement system comprises the transmittance sensor, sensor electronics, data acquisition 134

board (DAQ) and a laptop personal computer (PC). The emitter of the sensor is one laser diode with a peak 135

wavelength in the near infrared, at 850 nm, and matches the usual PPG wavelengths. Three BPW34 p-i-n 136

silicon photodiodes connected in parallel and aligned to increase the detection area are used as photo-detector. 137

The emitter driver, further amplification and filtering stages, timing and sample-and-hold (S&H) circuits are 138

connected to the fingertip probe by cables but could be easily replaced by wireless connections. The 139

photodetectors signal is filtered by an anti-aliasing analog low pass filter at 300 Hz, then sampled with a high 140

speed S&H and fed into the analogue inputs of a 12 bit DAQ (DAQ1200, National Instruments) to be digitized 141

at 1000 Samples/second (Sa/s). Finally, a ten-sample moving average followed by a ten-to-one decimation is 142

performed, which results in 100 Sa/s PPG data. 143

This experimental system is connected to a Pentium-class laptop computer that saves files containing the 144

PPG 100 Sa/s data in volts (V). The next stages of the signal processing are carried out digitally. The post-145

processing of stored signals from the group T1 of athletes is made off-line; once the algorithm has been 146

developed, it has been implemented as a virtual instrument using Lab Windows CVITM

, and the validation is 147

made on-line during IMET of the second group T2 of athletes. 148

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2.4. Statistical analysis 150


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Comparisons of HR between the two measuring methods (PPG and ECG) were performed using the Student 151

„t‟ test for paired data. Linear Pearson‟s correlation analysis was used to correlate quantitative variables, as 152

an indication that the two methods evolve in parallel. To compare the values of HR obtained by our PPG 153

technique with the standard ECG, we have used the Bland-Altman (B-A) method. Hereafter, we will use the 154

notation PR and ER for the PPG and the ECG heart rate values, respectively. The differences between the 155

methods (PR-ER, in bpm) are plotted against the average value given by the two methods (PR+ER)/2, in 156

bpm. The results are presented as the differences themselves (PR-ER) and mean difference or bias (M) 157

between the two methods. The standard deviation (Sd) value is used to calculate the limits of agreement (LA) 158

computed as M ± 1.96·Sd, providing an interval within which 95 % of differences between measurements by 159

the two methods are expected to lie. The standard errors and confidence intervals (CIs) were determined for 160

the mean bias and for the upper and lower limits of agreement. We defined agreement as a difference of 161

(PR-ER) within ± 10 bpm [3,12]. 162

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3. Elements for the Algorithm Design 164

Fig. 1 presents the FFT spectra corresponding to PPG signals recorded over 10 s time intervals at rest 165

(time interval finishing at 25.96 s, grey) and when running at 12 Km/h (time interval finishing at 435.56 s 166

dark), during the test performed in treadmill by a male athlete A of group T1. Sampling of ECG- and PPG-167

based measurements are not synchronized, for this reason the match of ECG and PPG readings has been 168

achieved by pairing the nearest values in time. 169

FFT spectra are plotted as power density (V2/Hz) versus frequency in the range 40-240 beats per minute 170

(bpm), corresponding to 0.66 to 4 Hz. For each time interval, the spectra show three main peaks, which are 171

labeled according to their power as P1 (the strongest peak), P2 and P3 (the weakest peak). At rest, the 172

spectrum shows the strongest peak P1 at a frequency coinciding with the recorded ER value for the same 173

time interval, and two other tiny peaks corresponding to harmonics of P1 at frequency 2 x P1 and 3 x P1. 174

When running at 12 Km/h, the spectrum exhibits a quite different peak distribution; for this time interval the 175

recorded ER value coincides with P2 frequency, a peak with an intermediate power; indeed, the one foot-176

step rate coincides with P3 frequency, whereas P1 is the harmonic 2 x P3 corresponding to the full-step rate 177


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SR (steps per minute). 178

Fig. 2 shows the time evolution of peaks P1, P2 and P3 (frequency vs. time) during IMET of athlete A, from 179

rest to maximal effort; time evolution of ER and full-step rate (SR) are also shown, as well as the time 180

interval of walking or running and the stop time. There are three well defined lines with a frequency that 181

increases with time, two of these lines evolves concomitantly, among them a third line evolves steeply with 182

time; the strongest peak is not always associated with the same line but jumps from a line to another The 183

steeper line evolves close to ER values, for this reason we have identified these frequencies as the PPG-heart 184

rate measurements PR. The heartbeat harmonics appears sometimes at a noise level at rest and at the 185

beginning of the IMET and goes out of the plotted range of frequency as the heartbeat increases. Regarding 186

the lower and upper lines, it can be observed that the upper one remains always at twice the frequency of the 187

lower one; furthermore, this upper line evolves close to the full-step rate SR, for this reason we have 188

identified these frequencies as the full-step rate SR, the harmonic of the one-step rate, identified as the lower 189

line. In brief, the time evolution of the spectra peaks defines a pattern composed of three branches, one 190

ascending central branch corresponding to the PR and two branches related to the periodic movement of feet 191

and arms (fundamental and its harmonic, related to the one-foot and the full step rates, respectively) that 192

evolve during exercise at a rate different to the heartbeat. 193

Results obtained from different athletes show that evolution of the peaks follows always the ER and SR 194

evolutions; in some cases, the heartbeat evolves much more steeply than SR and the corresponding line 195

intercepts one of the motion branches at a certain moment of the exercise and there are time intervals where 196

the frequency domains of PR signal and artifacts can overlap. 197

The arterial pulse wave might have higher frequencies but their power content is low or they can be 198

filtered. At low physical activity, the PR value can be obtained by simply looking for the highest peak in the 199

spectrum. The respiratory rate has been detected several times during exercise, at frequencies around 40-50 200

min-1

but it has low power content relative to the heartbeat and movement artifact signals. 201

The algorithm design is based on these observations. Firstly, the algorithm needs a harmonic discriminator, 202

taking into account that movement artifact contribution has higher harmonic content than the heart rate 203

signal. The detection algorithm we have developed is mainly based on analysis of the relative strength of 204


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harmonic content of the PPG signal. Secondly, it is important to have a heuristic algorithm to track the 205

heartbeat, taking into account the past history of the heartbeat itself when PR signal and artifact signal 206

overlap. 207

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4. Development of the Algorithm 209

We have developed the algorithm by analyzing the PPG data recorded from the first group T1 of athletes and 210

comparing them to the ECG ones. 211

The first step is a linear filtering of the 100 Sa/s PPG signal E(t) through band-pass Bessel filtering (cut-off 212

frequencies f1 and f2, order n = 6), in order to get the pulsating component (Eac(t)) and to suppress high 213

frequency noise and ripple. Cut-off frequencies are chosen in the ranges 0.1~0.3 Hz for f1 and 5~30 Hz for f2. 214

After filtering, a frequency domain analysis is performed by applying a fast Fourier transform (FFT) to a 10 215

second, rectangular-shaped, sliding window of the aforementioned data signal, with an overlap of about 75 216

%, delivering a spectrogram data F(ts), expressed in terms of power density (pi) versus frequency (fi). In this 217

step, the electrical PPG signal is transformed into a sequence of FFT spectra, in which each spectrum is 218

computed every 2.56 s and contains data from a time interval of 10.24 s, which gives a frequency resolution 219

of 0.58 bpm. The instant in time ts to which the spectrum is assigned corresponds to the end of the interval. 220

The spectra stream goes onto a peak search algorithm that selects the peaks above the noise floor. In this 221

step, the Gibbs phenomenon produces lateral lobes that, in theory, could create “phantom” peaks due to 222

side-lobe leakage; this is taken into account in the peak search algorithm, which never selects peaks from 223

adjacent FFT bins. We have explored more complex windowing functions and even more complex 224

approaches [27], but the relatively wide window and the experimental tests shows that leakage, albeit 225

present, did not invalidate the effectiveness of the algorithm. 226

Fig. 3 shows schematically the heuristic algorithm. The peak search algorithm eliminates all the peaks that 227

are lower than the noise floor of F(ts ), (Fig. 3 (a)), and selects those peaks that could be the most relevant. 228

pMax is the highest power value of F(ts ), and KC is the “cut-off” parameter of the algorithm. Values for KC 229

have been tuned in the range 50 - 400 by analyzing and comparing the PPG and ECG data recorded from the 230

group T1 of athletes; KC = 100 was adopted as the default value; it means that the cut-off of minor peaks occurs 231


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when amplitudes are approximately from 7 to 20 times lower than the highest peak. When implemented on the 232

PPG system and in order to simplify the computational cost of the algorithm, the peak search selects only 233

the three main peaks. 234

Next, the algorithm chooses a “best candidate” P(ts, f, p) as the heartbeat PR, with a reliability factor C(ts) 235

which express, in the range (0-1), the degree of confidence that P(ts) was the heart rate value, not a 236

movement artifact. To achieve this, the list of three peaks is fed into three classification engines: energy, 237

harmonic and historic classification. The task of the classification engine is to associate to each peak the 238

reliability factor C(ts) defined as above, using different criteria. In all the following discussion and formula, 239

reliability factors saturates to 0 or 1, respectively, when the computed value exceeds these limits. Fig 4b and 240

4c shows the flow diagram of the heuristic algorithm. 241

The power engine (Fig. 3 (b)) compares each pi value to the highest value pMax of F(ts), and assigns to each 242

(fi, pi) pair a first reliability factor Cpi, which expresses how much the peak has a high power content. Cpi is 243

computed in the range (0-1) as the amplitude of the peak relative to the highest peak. 244

The harmonic engine (Fig. 3 (c)) computes the probability that a peak is part of a signal with high 245

harmonic content, assigning to each of the peaks a second reliability factor Chi. The engine compares pairs 246

of frequencies. For each peak, a sliding mask is superposed on the spectrum. The mask is formed by 247

parabolic segments centered on the frequencies multiple of the peak, with a relative width controlled by a 248

parameter KH, that modulates the tolerance accepted in the frequency comparison. Chi is computed in the 249

range (0-1) based on how much the spectrum energy enters the mask, and its value is low for high harmonic 250

content and high for low harmonic content. When implemented on the PPG system and in order to reduce 251

the computational burden, the algorithm computes how near a frequency is to double another frequency of 252

the list, limiting the analysis to the second harmonic. The parameter KH is one of the main parameter of the 253

algorithm. KH has been tuned in the range 5 - 50, and was optimized for a value of 12. For KH < 5, the mask 254

is too wide and all the peaks appear with a harmonic content. For KH > 50, the mask is too narrow and the 255

algorithm never finds any harmonics. When a peak is found to have a strong second-harmonic counterpart in 256

the spectrum, it is automatically invalidated for the selection process, even if it has a very high confidence 257

value under the power engine point of view. On the other hand, at rest, the main peak corresponds to the 258


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heart rate PR, but very small power harmonics can be present; it is the value of KC of the peak search 259

algorithm which must contribute to eliminate this harmonics of the peak list entering the heuristic algorithm. 260

Finally, the memory or historic engine (Fig. 3 (d)) compares frequency fi(ts) of peaks Pi (ts) of F(ts), with the 261

frequency fi’ (ts-1) of the peak P(ts-1) selected as PR in the previous spectrogram F(ts-1). A third reliability 262

factor Cmi is computed by taking into account the proximity of the frequency fi (ts) to f i‟(ts-1) as well as the 263

former value of the reliability factor Cmi. This factor Cmi is zero for all the peaks but for that with the 264

frequency closest to f i‟(ts-1) selected as PR at previous spectrogram; Cmi is computed in the range 0-1, so that 265

a high value means high proximity to the previous PR peak. 266

Fig 4 shows, in more detail, the flowchart of the algorithm. Fig 4a shows the general data processing for 267

selecting the three main peaks of a spectrogram F(ts). Fig. 4b depicts the flowchart of the “power” and 268

“harmonic” engines; Fig. 4c shows the flowchart of the “memory” engine and the final selection step. 269

In the end, for each spectrogram F(ts), the heuristic algorithm compares all the peaks and selects one of 270

them, according to the assigned reliability factors. The selection is made on the basis of the maximum 271

reliability factor value, that is high Cpi (amplitude of the peak), high Chi (low harmonic content) and high Cmi 272

(high proximity to the previous PR peak). The chosen peak is assigned to the PR(ts) value, and the overall 273

confidence index C (ts) is set to the highest reliability index. 274

As an exception, when no a peak achieves a reliability factor greater than 0.5 (the highest peak could have 275

been marked as non valid by the harmonic content analysis, and the other peaks are not sufficiently good by 276

any of the classification techniques) the algorithm simply “jumps” over, giving the PR value selected for the 277

last spectrogram, and it restarts with the next one. This step is permitted just once in a row to avoid the 278

possibility of sticking to a wrong value; i.e., at the next spectrogram, if the reliability factor is again lower 279

than 0.5, the selection is made as described above, even with bad reliability factors. This step allows the 280

algorithm to ignore especially bad points, without corrupting the memory part of the algorithm. 281

Notice that the memory engine assigns to the peak selected in each spectrogram a reliability factor smaller 282

than the one assigned in the previous spectrogram. In this way, if the peak chosen as PR continues to be 283

chosen by means of the memory algorithm, the reliability factor is always decreasing, and this eventually 284

forces the heuristic algorithm to select the PR peak by a different criterion, so that the memory one could not 285


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overtake the others for a long time. This is very important in the case PR peak is very close to a motion peak, 286

because when the algorithm selects a high-power peak, both the power engine and the memory engine will 287

tend to follow this high peak. If the reliability factor Cmi decreases continuously, the memory engine does 288

not find a solution and the harmonic engine will search for a new peak. 289

The parameters KC and KH have been optimized by analyzing the recorded data of group T1 of athletes. 290

The highest computational cost of the algorithm is found in the generation of the FFT spectra, for which we 291

used the standard FFT subroutines offered by standard software. As mentioned before, in order to reduce the 292

computational cost, some simplifications have been used: a) at the search peak stage, the number of selected 293

peaks is culled to three, those with highest power density; b) at the harmonic analysis only the second 294

harmonic is taken into account, given that higher order harmonics are normally outside the measurement 295

range, and c) the harmonic analysis compares only frequencies, independently of their power density. 296

Once the IMET starts, the harmonic engine is the principal component of the algorithm and allows it to 297

discriminate the movement artifact. When the PR peak is very close to a motion peak, the memory engine 298

helps to follow correct peak, but forcing the harmonic engine to act quickly. When one peak is selected, its 299

frequency is then assumed to be the pulse rate PR, and its value is displayed on the screen. 300

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4.1. Signal to Noise Ratio 302

An estimation of the signal-to-noise ratio (SNR) of the selected PR data has been done. The selected PR 303

peak has been used as the signal power density and the sum of discarded peaks as the noise power density. 304

The procedure has been repeated for all the PR peaks selected along the exercise and for the whole group T1 305

of athletes. The highest 10 % and the lowest 10% SNR values were discarded and the remaining data were 306

averaged. The SNR estimated in such a way does not take into account the ground floor noise but just 307

discarded peaks; moreover, the noisiest points have been avoided, those where the algorithm has jumped over, 308

so that the resulting figures are probably an overestimation of the real value. Nevertheless, it constitutes a 309

valuable estimation of the SNR of the selected PR data. We have calculated values of SNR, both averaging 310

over the whole IMET and over the last 20 % of IMET time. From the analysis of group T1 recorded data, the 311

averaged values for “full test” and “last 20 %” are - 1.6 dB and - 2.5 dB, respectively. From that, we have 312


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concluded that the algorithm is able to identify the correct cardiac heartbeat PR even with a SNR as low as -313

2.5 dB. 314

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5. Results 316

5.1. Validation of the algorithm on recorded data of group T1 of athletes. 317

To validate the algorithm, each PR value was compared with the timely nearest ER, within intervals in 318

which the athletes were running, i.e., from 8 Km/h until the maximal effort. The initial periods were not 319

included due to dissimilarities in the athlete actions. The reason is that at 6 Km/h most of the athletes were 320

adapting to walk on the treadmill and in many cases they took hold of protection bars, which could alter the 321

position of the finger sensor and therefore distort the measurement. 322

We have calculated the regression line of ER and PR measurements, for a number of athletes A = 10 and a 323

number of (PR, ER) pairs N = 477, with a correlation R = 0.994 and p < 0.0001. This correlation is an 324

indication that the two parameters evolve in parallel. The histogram of differences between the two methods 325

has confirmed the normal distribution. The Bland and Altman plot of the difference (PR - ER) against the 326

average value given by the two methods ((PR + ER)/2) is shown in Fig. 5. The bias is M = - 1.10 bpm, Sd = 327

2.45 bpm is the standard deviation, and the limits of agreement LA are in the range (- 5.90 bpm, + 3.69 bpm) 328

within the a priori set value of ± 10 bpm. The 95 % confidence intervals are - 1.32 to - 0.88 bpm for the bias, 329

- 6.28 to - 5.52 bpm for the lower limit of agreement (LLA), 3.31 to 4.07 bpm for the upper limit of 330

agreement (ULA). All these intervals are reasonably narrow, the width of limits of agreement is 9.59 bpm 331

and more than 95 % of all (PR-ER) differences fall within LA. The plot reveals that there is no relationship 332

between the differences and the bias. The option of plotting the differences as percentages is useful when 333

there is an increase in variability of the differences as the magnitude of the measurement increases. When 334

plotting as percentages, the values obtained are M = - 0.7 %, LLA = - 4.2 %, ULA = 2.8 %. 335

336

5.2. Results on real time heart rate tracking during IMET on treadmill. 337

The algorithm has been implemented in the experimental PPG system, and has been validated on real time 338

measurements during treadmill ergometer IMET on the second group of athletes T2. The SNR values are - 0.1 339


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dB for “full test” and - 2.1 dB for “last 20 %” respectively. Here again, in spite of the low SNR, the 340

algorithm is able to follow the correct PR value, as shown below. 341

The plot of PR versus ER for the group T2 gives a correlation R = 0.992 and p < 0.0001; the number of 342

athletes is A = 20 and the number of (PR, ER) pairs is N = 1061. We have confirmed the normal distribution 343

of differences between the two methods by their histograms. The (PR, ER) pairs obtained have been 344

displayed in Bland-Altman plots in Fig. 6, as the differences (PR - ER) versus mean value (M) of the 345

differences; the value M = - 0.70 bpm indicates a low negative bias, the standard deviation is Sd = 2.92 bpm. 346

The width of limits of agreement is 11.42 bpm, between - 6.41 bpm (LLA) and + 5.01 bpm (ULA), within 347

the a priori set value of ± 10 bpm. More than 95 % of all the differences obtained for the athletes tested on 348

the treadmill fall within ± 6.5 bpm, even for HR as high as about 200 bpm. The 95 % confidence intervals 349

are - 0.88 to - 0.53 bpm for bias, - 6.72 to - 6.12 bpm for LLA and 4.71 to 5.31 bpm for ULA. For group T2, 350

the values expressed as percentage of the average between the two techniques are M = - 0.4%, LLA = - 4.2 351

% and ULA = 3.4 %. 352

353

6. Discussion 354

The algorithm for the automatic detection of the HR from the PPG signals was found to be efficient, despite 355

the small signal-to-noise ratio. Comparison to ECG measurements, the reference standard, shows very high 356

agreement. The low negative bias obtained on recorded data of group T1 of athletes may be caused by slight 357

differences in beat-to-beat averaging times used in the ECG monitor and the PPG system; if the subject's 358

heart rate is changing rapidly, the different averaging times would influence the results and amplify the 359

calculated errors. Moreover, the small bias might be due to possible errors when collecting data from a 360

variety of sources in which time is recorded by independent and unsynchronized clocks [28] (independent 361

computers for ECG and PPG). The algorithm selects PR values that show high agreement with ER 362

measurements in activities as IMET. The narrow width of limits of agreement, narrower than ± 10 bpm, is 363

an acceptable LA for interchangeability between PR and ER. It should be noted that parameters optimization, 364

carried out on the recorded data, has been performed in a “first step” way. Optimization with an iterative 365

mathematical program should give the best values, but it is not the aim of the present work 366


15

Overall, the system shows a general success to track heart rate during the treadmill probe. The system has 367

also shown good results for IMET on cycle-ergometer [29]. When compared to traditional FFT methods the 368

presented algorithm shows significant improvements for separating motion artifact and cardiac physiologic 369

spectra. The limits of agreement are comparable to the mean absolute error obtained using an algorithm 370

including time-frequency techniques based on the smoothed Wigner Ville distribution [2,8], where six 371

subjects participated in the study realizing four kinds of motions at time, frequency and intensity fixed. 372

When comparing our method with results from a PPG sensor integrated with an adaptive noise cancellation 373

device, we obtained LA values between - 6.41 bpm and + 5.01 bpm (or - 4.2 % and 3.4 %), better than 374

values (-21.15% and 20.52 %) obtained for subjects running at 8 Km/h [21]. 375

The algorithm has been developed by analyzing the recorded data of a group of white men, all of them 376

runners; and it has been evaluated on a very dissimilar group, composed of men and women, black and 377

white skins. The algorithm parameters we have used have been the same for female subjects or for black 378

skins and the accuracy of the technique might be higher when adapted for each case. But in the current form 379

the algorithm is suitable to people without discrimination neither gender or skin color. 380

The basic premise of the algorithm is that the motion artifact created in the PPG signal by human running 381

has a high harmonic content with respect to the PPG derived heart rate. The use of graded treadmill running 382

(or cycling) in IMET may bias the motion artifact in the PPG signal by making it quite regular and rhythmic 383

in nature. Although this seems to be a limitation of the PPG-based technique, athletes running are a regular 384

and stable movement. A significant advancement of the algorithm utility would be to show that it can extract 385

representative heart rates during road running or running on uneven ground. Other apparent limitation is that 386

our PPG system is a fingertip probe; the algorithm can be implemented in other PPG systems, as earlobe 387

probes or ring sensor, provided that a rhythmic movement of the body and /or extremities will have high 388

harmonic contents. It is worth to note that other error sources, like movement of the sensor on the finger, do 389

not cause important signals in the FFT analysis once the athlete arms have free movement; otherwise, ECG-390

derived HR values can also give some errors, when the athlete is sweating and the fixation of the ECG 391

electrodes could be poor and produce wrong readings. 392

393


16

7. Conclusions 394

This work addresses the problem that motion artifacts limit the use of photoplethysmography (PPG) to 395

quantify key cardiovascular variables such as heart rate during human exercise. During human movement, 396

the PPG signal is corrupted at frequencies that fall within the range of interest. With appropriate filtering and 397

signal processing, the portion of the PPG signal caused by motion artifact could be removed and the heart 398

rate identified. We have described and evaluated a new algorithm to process PPG signals collected during 399

treadmill exercise into heart rate. The algorithm identifies three frequencies of interest from the PPG signal 400

and uses decision making logic to identify the two harmonic frequencies that most likely represent motion 401

artifact leaving one frequency to represent PPG derived heart rate. The algorithm is tested using a 402

heterogeneous athletic population transitioning from rest through a graded maximal intensity treadmill test. 403

Electrocardiography is used to validate the PPG-derived heart rates. This would allow for significant 404

advancement in the area of biosensor development as PPG technology is ideally suited to be incorporated 405

into wearable devices. 406

Acknowledgment 407

This work was supported by the Spanish Consejo Superior de Deportes under CSD Grants 03/UPB10/06, 408

01/UPB10/07, and 01/UPB10/08. S. M. López-Silva has been supported by CSIC I3P Program financed by 409

the Fondo Social Europeo. The authors gratefully acknowledge the assistance of Dr. Isabel Gómez Caridad 410

in revising the present manuscript. 411

412

413

414

415


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Figure captions 482 483 484 Fig. 1. FFT spectra corresponding to PPG signals recorded over 10 s time intervals (grey at rest, dark during 485

exercise, running at 12 Km/h); the three main peaks P1, P2 and P3 are labeled following decreasing 486

power density; the values of ER (ECG-derived heart-rate) and SR (full-step rate) for the same time 487

intervals are also shown. 488

Fig. 2. Frequency time evolution of the main peaks (P1, P2, P3) over the whole test; the evolution of ER 489

(ECG-derived heart-rate) and SR (full-step rate) are also plotted. 490

Fig. 3. Description of the heuristic algorithm. After the band-pass linear filtering, in (a), a set of significant 491

peaks is computed, represented by a list of frequency-peak value (power density PD). The selection 492

is made by listing all the peaks that are higher than a noise floor, computed by dividing the highest 493

peak by a parameter Kc. The list is then fed into the three mechanisms that assign a reliability value 494

to each pair. In (b), peaks are classified in function of their relative amplitude; in (c), their harmonic 495

relationship is computed (see a more thorough explanation in the text); finally, in (d), the historic 496

record is taken into account, assigning higher reliability values to the peaks that are near to the 497

previously selected value. 498

Fig. 4. Flowchart of the proposed algorithm. In Fig 4a the general data processing is shown. Fig. 4b depicts 499

the “power” and “harmonic” engines, and Fig. 4c the “memory” engine and the final selection step. 500

Fig. 5. Bland and Altman plot of differences in recorded heart rate measurements versus average values for 501

group T1, with bias value (M) and limits of agreement (M ± 1.96 Sd). Sd is the standard deviation, A 502

is the number of athletes and N is the number of pairs (PR, ER). 503

Fig. 6. Bland and Altman plot of differences in real time heart rate measurements versus average values for 504

group T2, with bias value (M) and limits of agreement (M ± 1.96 Sd). Sd is the standard deviation, A 505

is the number of athletes and N is the number of pairs (PR, ER). 506

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40 60 80 100 120 140 160 180 200 220 2400.000

0.001

0.002

0.003

SR

435.5

6=

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bp

m

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150

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25.9

6=

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pm

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1080 1200 1320 1440 1560 1680 180040

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1080 1200 1320 1440 1560 1680 180040

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stop

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7206004803602401200

athlete A ER

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80 100 120 140 160 180 200 220 240-30

-20

-10

0

10

20

30

M - 1.96Sd = - 5.90 bpm

M + 1.96Sd = 3.69 bpm

M = - 1.10 bpm

T1:

A = 10

N = 477

Sd = 2.45 bpm

Dif

f in

heart

rate

, P

R-E

R (

bp

m)

Average by PPG and ECG, (PR+ER)/2 (bpm)


29

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Fig. 6 690

80 100 120 140 160 180 200 220 240-30

-20

-10

0

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30

M = - 0.7 bpm

M - 1.96Sd = - 6.41 bpm

M + 1.96Sd = 5.01 bpm

T2:

A = 20

N = 1061

Sd = 2.92 bpm

Dif

f in

heart

rate

, P

R-E

R (

bp

m)

Average heart rate by PPG and ECG, (PR+ER)/2 (bpm)

heuristic algorithm for photoplethysmography heart rate ... · maximal exercise test56 (imet) on...

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