HEART RATE VARIABILITY MEASUREMENT USING THE

SECOND DERIVATIVE PHOTOPLETHYSMOGRAM

Mohamed Elgendi, Mirjam Jonkman and Friso DeBoer

School of Enigneering and Information Technology, Charles Darwin University, Australia

Keywords: Heart Rate, HRV, Plethysmography, SDPTG.

Abstract: Heart-rate monitoring is a basic measure for cardiovascular functionality assessment. The electrocardiogram

(ECG) and Holter monitoring devices are accurate, but their use in the field is limited.

Photoplethysmography is an optical technique that has been developed for experimental use in vascular

disease. Because of its non-invasive, safe, and easy-to-use properties, it is considered a promising tool that

may replace some of the current traditional cardiovascular diagnostic tools. A useful algorithm for a-wave

detection in the second derivative plethysmogram (SDPTG) is introduced for heart–rate monitoring. The

performance of the proposed method was tested on 27 records measured at rest and after exercise. Statistical

HRV measures can be calculated using the a-a interval of the SDPTG.

1 INTRODUCTION

Heart rate variability has considerable potential to

assess autonomic nervous system fluctuations in

normal healthy individuals and in patients with

various cardiovascular and non-cardiovascular

disorders. Heart rate variability (HRV) studies could

enhance our understanding of physiological

phenomena, the actions of medications, and disease

mechanisms.

Traditionally, HRV measures are based on

cardiac inter-beat intervals using the

electrocardiogram (ECG). Some practitioners,

however, have used a distal measurement of the

arterial pulse like the fingertip photoplethysmogram

to measure the heart rate. However, there are some

potential obstacles to obtaining precise inter-beat

intervals from arterial pressure pulses, especially

when measured from a distal source like fingertip

photoplethysmogram. The lack of sharp peaks in

blood pressure pulses compared to the R-peaks in

the ECG makes the accurate determination of heart

rate challenging. Also the shape and timing of the

pulse waveform may be influenced by ventricular

pressure, flow rate, time period, or other parameters

of cardiac output. Peripheral effects, such as changes

in vascular tone, may also influence distal pulse

peak detection.

(Berntson et al., 1997) reported these potential

drawbacks of the fingertip plethysomograph.

Therefore, they strongly advised the usage of R-R

intervals from ECG signals to determine interbeat

intervals. However, they also stated that “the use of

intra-arterial pressure pulses and a sophisticated

peak detection algorithm may be acceptable,” and

also recommended, Their opinion is that indirect

measures, such as photoplethymographic signals

require further validation.

(Giardino et al., 2002) proved that distal pulse

pressure is adequate for determining the heart rate

variability under resting conditions. Their results

provided grounds for some caution in the use of

finger plethysmography in experimental studies,

where manipulations may alter the relationship

between cardiac chronotropic control and distal

blood pressure changes in unpredictable ways. They

recommended further studies that include test–retest

reliability assessment of different data collection

techniques.

The the second derivative of

photoplethysmogram (SDPTG) was developed as a

method to allow more accurate recognition of the

inflection points and easier interpretation of the

original plethysmogram wave.

In literature, the second derivative of

photoplethysmogram (SDPTG) has also been called

acceleration plethysmogram (APG). In this paper,

the abbreviation SDPTG will be used.

Elgendi M., Jonkman M. and DeBoer F. (2010).

HEART RATE VARIABILITY MEASUREMENT USING THE SECOND DERIVATIVE PHOTOPLETHYSMOGRAM.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 82-87

DOI: 10.5220/0002743300820087

 SciTePress

Figure 1: Signal Measurements (a) Original fingertip

photoplethysmogram (b) second derivative wave of

photoplethysmogram (SDPTG).

As shown in Fig.1, The heart beat in SDPTG

consists of four systolic waves and one diastolic

waven (Takazawa et al., 1993), namely a-wave

(early systolic positive wave), b-wave (early systolic

negative wave), c-wave (late systolic reincreasing

wave), d-wave (late systolic redecreasing wave) and

e-wave (early diastolic positive wave). The height of

each wave was measured from the baseline, with the

values above the baseline being positive and those

under it negative.

Because the peaks in the SDPTG signal are more

clearly defined than in the original

photoplethysmographic signal is more suitable for

accurate heart rate detection.

(Taniguchi et al., 2007) used a-a interval in the

second derivative photoplethysmogram instead of R-

R interval in the ECG to determine the heart rate

evaluating stress that surgeons experience.

To calculate the heart rate variability (HRV) using

the second derivative photoplethysmogram

(SDPTG), the accurate detection of individual a-

waves is a first essential step.

Although the clinical significance of using

SDPTG signals has been discussed, there is still a

lack of studies focusing on the automatic detection

of a-waves in SDPTG signals.

In this paper, we present an algorithm that can be

used to calculate the heart rate variability using the

finger photoplethysmograph. This investigation

aimed to develop a fast and robust algorithm to

detect a-waves in SDPTG signals. The SDPTG

waveform was measured in a population-based

sample of healthy males at rest and after exercise.

2 DATA

The photoplethysmograms of twenty seven healthy

males volunteers with a mean±SD age of 27±6.9

were measured by a photoplethysmograph (Salus),

equipped with a sensor located at the cuticle of the

second digit of the left hand. Measurements were

performed while the subject was at rest on a chair.

Data were collected at a sampling rate of 200Hz.

The duration of each data segment is 20 seconds.

The test was conducted from 20

of April to 5

of May 2006 at Northern Territory Institution of

Sport (NTIS).

All procedures were approved by the ethics

committee of Charles Darwin University. Informed

consent was obtained from all volunteers.

3 METHODOLOGY

An algorithm to detect a-waves is described below.

The algorithm consists of three main stages: pre-

processing, feature extractions and thresholding. The

structure of the algorithm is shown in Fig. 2.

Figure 2: Algorithm structure.

3.1 Pre-Processing

The pre-processing stage consists of two sub-stages:

bandpass filtering and taking the second derivative

of the photoplethysmogram.

3.1.1 Bandpass Filter

We remove the baseline wander and high

frequencies which do not contribute to a-waves

detection by using a second order Butterworth filter

with passband 0.5-10 Hz.

10Hz).5h(PTG[n],0Butterworts[n] −

Feature

Extraction

Pre-Processing

Result >

Threshold

Yes

PTG

beat

Ignore

feature

HEART RATE VARIABILITY MEASUREMENT USING THE SECOND DERIVATIVE PHOTOPLETHYSMOGRAM

Fig. 3(b) is the result of applying a Butterworth filter

to the original signal shown in Fig. 3(a)

3.1.2 Second Derivative

z[n] shown in Fig. 3(c) is the second derivative of

the filtered photoplethysmogram s[n]. Inflection

points are seen as peaks in the SDPTG.

3.2 Feature Extraction

The feature extraction stage consists of two sub-

stages: squaring and selection of potential blocks.

3.2.1 Squaring

y[n] is the square of the SDPTG signal z[n].

Squaring the signal makes the results positive and

emphasizes large differences

3.2.2 Selection of Potential Blocks

We demarcate the onset and offset of the potential a-

waves in the SDPTG signals by using two moving

averages, based on the normal duration of the ab

interval which for a healthy adult is 187±17 ms.

For a sampling frequency of 200 Hz, the

maximum window size corresponding to the ab

interval is approximately 40 points and the

maximum window size corresponding to complete

heart beat interval is approximately 220 points. We

will use the maximum window sizes to detect a-

waves. The a-waves are detected by comparing two

moving averages.

First moving-window integration: The fist moving

average is., calculated as follows:

y[n]).......2)]-(W-y[n1)]-(W-(y[n

[n]MA

Peak

+++=

Where

40=

W which is the window width of ab

segment. The purpose of the first moving average,

shown as the dotted line in Fig. 3(d), is to emphasize

the a-wave.

Second Moving-window Integration: the second

moving average, shown as the solid line in Fig. 3(d),

is used as a threshold for the output of the first

moving-window integration.

y[n]).......2)]-(W-y[n1)]-(W-(y[n

[n]MA

MaxPeak

+++=

where

220=

W is the window width of a complete

heart beat.

.05

0.1

100

200

300

400

500

600

700

800

Figure 3: Algorithm structure.(a) original SDPTG signal

(b) filtered PTG signal with Butterworth bandpass filter

interest using two moving averages to detect a-waves.

When the amplitude of the first moving average

filter (MA

Peak

) is greater than the amplitude of the

second moving average filter (MA

MaxPeak

), that part

of the signal is selected as a block of interest, as

follows:

Fig. 3(d) shows an example of applying the two

moving averages.

We show four consecutive aa intervals in Fig. 3

(d) to demonstrate the idea of using two filters to

generate blocks of interest. Sometimes, blocks are

generated which do not represent potential a-waves.

These blocks are caused by noise and need to be

eliminated.

3.3 Thresholding

Blocks with a small width are considered as blocks

caused by noise. Blocks which are smaller than half

of the expected size for the ab interval are rejected.

IF [n]MA

Peak

[n]MA

MaxPeak

THEN

BLOCKS[n]

ELSE

BLOCKS[n] =0

END

(a)

(b)

(c)

(d)

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

Table 1:a-wave detection performance on SDPTG Data.

Before Exercise After Exercise 1 After Exercise 2 After Exercise 3

Record

No of

beats

TP FP FN

No of

beats

TP FP FN

No of

beats

TP FP FN

No of

beats

TP FP FN

26 26 0 0 45 45 0 0 43 41 2 0 32 32 0 0

24 24 0 0 44 44 0 0 47 47 0 0 46 46 0 0

17 17 0 0 36 36 0 0 44 43 1 0 32 32 0 0

26 26 0 0 43 43 0 0 38 38 0 0 30 30 0 0

20 20 0 0 33 33 0 0 37 37 0 0 40 40 0 0

20 20 0 0 30 30 0 0 23 23 0 0 Could not continue

22 22 0 0 33 33 0 0 39 39 0 0 42 42 0 0

19 19 0 0 23 23 0 0 27 27 0 0 30 30 0 0

22 22 0 0 25 25 0 0 30 30 0 0 31 31 0 0

19 19 0 0 34 34 0 0 38 38 0 0 39 38 1 0

30 30 0 0 48 48 0 0 48 48 0 0 49 49 0 0

19 19 0 0 33 33 0 0 42 42 0 0 45 45 0 0

23 23 0 0 31 31 0 0 32 32 0 0 32 32 0 0

22 22 0 0 30 30 0 0 35 35 0 0 41 41 0 0

17 17 0 0 28 28 0 0 31 31 0 0 31 31 0 0

23 23 0 0 36 36 0 0 41 41 0 0 38 38 0 0

24 24 0 0 36 36 0 0 37 37 0 0 30 30 0 0

24 24 0 0 35 35 0 0 39 39 0 0 41 41 0 0

18 18 0 0 23 23 0 0 24 24 0 0 33 33 0 0

20 20 0 0 29 29 0 0 31 31 0 0 37 37 0 0

24 24 0 0 29 29 0 0 33 33 0 0 38 38 0 0

17 17 0 0 32 32 0 0 34 34 0 0 40 40 0 0

26 26 0 0 35 35 0 0 34 34 0 0 36 36 0 0

20 20 0 0 29 29 0 0 34 34 0 0 39 38 1 0

22 22 0 0 27 27 0 0 28 28 0 0 29 29 0 0

18 18 0 0 33 33 0 0 36 36 0 0 34 34 0 0

volunteer

584 584 0 0 885 885 0 0 955 952 3 0 946 944 2 0

The expected size for the ab interval is based on

the statistics for healthy adults, as described above.

We reject blocks that are smaller than 50% of the

width that is expected for the ab interval. This

corresponds to:

20KS)width(BLOC <

The rejected blocks are considered as noisy blocks

and the accepted blocks are considered to be

containing a-wave.

The maximum absolute value within each

accepted block is considered to be the a peak. For

this research the algorithm was tested using

annotated a peaks.

The proposed algorithm was tested on 27 SDPTG

records. The volunteers exercised three times. The

photoplethysmogram was recorded before starting

exercise and after each exercise period. Volunteer

C3 discontinued in the third exercise period. No

episodes have been excluded from our analysis

The exercise SDPTG data contains records of

normal SDPTG signals as well as records of SDPTG

signals that are affected by non-stationary effects,

low signal-to-noise ratio, and high heart rate. This

provides the opportunity to test the robustness of the

algorithm in detecting a-waves in SDPTG signals. a-

wave detection may be affected by the quality of the

SDPTG recordings and the irrigular heart rhythms in

the SDPTG signals.

The following statistical parameters were used to

evaluate the algorithm:

FPTP

FNTP

HEART RATE VARIABILITY MEASUREMENT USING THE SECOND DERIVATIVE PHOTOPLETHYSMOGRAM

True Positive (TP): a-wave has been classified as a-

wave.

False Negative (FN): a-wave has been missed.

False Positive (FP): Non a-wave classified as a-

wave.

The sensitivity Se is the percentage of true a-

waves that were correctly detected by the algorithm.

The positive predictivity +P is the percentage of

detected a-waves which are real a-waves.

Table I shows the result of a-waves detection in

27 different records of collected SDPTG before

exercise and after each of the three exercise periods,

containing a total of 3332 heart beats.

As shown in Table 1, records which have

relatively irregular fast heart beats signals like A1-

after exercise 2 , irregular fast heart beats with low

amplitudes like B1-after exercise 2, and non-

stationary SDPTG with irregular fast heart beats and

low amplitudes like E3-after exercise 3 contain a

few false positives (FP).

The number of false negatives (FN) was zero. The

overall average sensitivity for a-waves detection was

100% and the positive predictivity was 99.88%.

4 DISCUSSION

The major reason for the interest in measuring heart

rate variability stems from its ability to predict

survival after a heart attack. In ECG signals analysis,

the interval between adjacent QRS complexes is

termed as the normal to normal (NN) or the R to R

(RR) interval. Heart rate variability (HRV) refers to

the beat-to-beat alterations in heart rate. The results

of a HRV analysis portray the physiological

condition of the patient and are an important

indicator of cardiac disease. Many studies have

shown that reduced HRV predicts sudden death in

patients.

The detection of R peak is the main step to

measure HRV. Precise R-R interval calculations are

necessary to accurately depict the physiological

state. (John, 2000) found that more than 26 different

types of arithmetic manipulations of R-R intervals

have been described in the literature to represent

HRV.

The Task Force of the European Society of

Cardiology and the North American Society of

Pacing and Electrophysiology (Task Force of the

European Society of Cardiology and the North

American Society of Pacing and Electrophysiology,

1996) suggest a number of simple time domain

measures to estimation HRV. It has been discussed

in their paper that the HRV is calculated using the

mean the standard deviation of the length of the

cardiac cycle. This can be determined using either

the R-R intervals of a short ECG segment or the. a-a

intervals With these methods either the heart rate or

the a-a intervals a and SDPTG signal. Table 2 shows

some simple time–domain HRV variables: MAX-

MIN, SDNN, RMSSD, and SDSD that can be

calculated based on SDPTG signals.

Table 2: HRV Statistical Variables.

variable Statistical measurement

MAX-MIN

Difference between shortest and longest a-a

interval

SDNN Standard deviation of all a-a intervals

RMSSD

Root mean square of the difference of

successive a-a intervals

SDSD

Standard deviation of of differences between

adjacent a-a intervals

5 CONCLUSIONS

The second derivative of the photoplethysmogram

(SDPTG) can be used to calculate heart rate

variability provided the a-waves can be detected

accurately. Therefore, we propose an algorithm to

detect a-waves in SDPTG signals with a high

frequency noise, low amplitude, non-stationary

effects, irregular heart beat and after exercise. It

achieved an overall average sensitivity for a-waves

detection 100% and a positive predictivity was

99.88%. over 27 records, containing a total of 3370

heart beats.

The accurate detection of a-waves in the SDPTG

offers a non-invasive method of evaluating cardiac

functioning. The usage of SDPTG can be useful for

HRV analysis and identification of individuals at

risk.

ACKNOWLEDGEMENTS

The authors would like to thank Aya Matsuyama for

collecting the data.

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HEART RATE VARIABILITY MEASUREMENT USING THE SECOND DERIVATIVE PHOTOPLETHYSMOGRAM