Feasibility Study of Heartbeat Detection from Optical Interferometric

Signal by using Convolution Kernel Compensation

Sebastijan Šprager, Aleš Holobar and Damjan Zazula

University of Maribor, Faculty of Electrical Engineering and Computer Science,

Smetanova ulica 17, SI-2000 Maribor, Slovenia

Keywords: Heat Rate Estimation, Optical Interferometer, Unobtrusive Monitoring of Human Vital Signs, Biomedical

Signal Processing, Latent Variable Analysis, Convolution Kernel Compensation.

Abstract: In this paper, a feasibility of detecting heartbeat from optical interferometric signal by using convolution

kernel compensation (CKC) latent variable analysis (LVA) approach is examined. Optical interferometer is

a very sensitive device that detects physical elongation of the optical fibre. When used as bed or body

sensor, mechanical and audible activity of the heart produce perturbations in the detected signal that, when

extracted by LVA, allows completely unobtrusive monitoring of heartbeat. We performed an experiment

with fourteen young healthy participants. They exercised on a cycle ergometer until they reached their

submaximal heart rate (85 % of maximal heart rate). During resting period after the exercise optical

interferometric signal was acquired along with the referential ECG signal. CKC-based decomposition of 1-

minute-long signal segments was performed. The obtained efficiency (sensitivity of 97.8 ± 3.0 %, precision

of 93.6 ± 7.6 %) and accuracy (reference-to-detected beat delay of 167 ± 65 ms) are within acceptable limits

indicating that unobtrusive heartbeat detection using the proposed approach is feasible.

1 INTRODUCTION

Classical heartbeat monitoring approaches, such as

electrocardiography (ECG) and plethysmography

require trained physician and controlled clinical

environment to perform measurements with a

number of sensors and electrodes. This procedure

can be uncomfortable, disturbing and impractical for

both the patient and physician. In contrast,

methodologies for unobtrusive monitoring of

heartbeat deploy different types of sensors that can

detect electrical, audible or mechanical heart

activity, even when there is no direct contact

between the sensor and person’s body. A short

survey of such methodologies is given in (Šprager

and Zazula, 2012).

Monitoring of heartbeat by using optical

interferometer has already been examined in

(Šprager et al., 2010); (Šprager et al., 2011);

(Šprager et al., 2012). However, all published

approaches are based on linear processing of a single

interferometric signal (single-input-single-output

system - SISO). By applying nonlinear transforms to

an interferometric signal, additional information

may be emphasised. Taking such signal transforms

as additional observations in parallel with the

original single-channel signal, i.e., by forming

multiple-input-multiple-output (MIMO) system,

multichannel decomposition methods become

applicable. The aforementioned signal extension has

already been proposed in (Šprager et al., 2012),

where a new approach for heartbeat detection from

extended interferometric signal has been introduced

by computing so called activity index of multi-

channel interferometric signal (Šprager et al., 2012).

However, activity index only calculates the

Mahalanobis distance between the detected

interferometer patterns and does not extract the

investigated phenomena, i.e, perturbations due to the

heartbeat, from the measurements.

Recently, LVA has been demonstrated as one of

the most promising tools to analyse multichannel

compound signals, including nonlinear instantaneous

and convolutive mixtures. In this study, we

experimented with previously published CKC

decomposition approach that has demonstrated its

great capability in decomposing multichannel

surface electromyographic signals into constituent

motor unit action potential trains (Holobar et al.,

2009). However, this approach has never been

396

Šprager S., Holobar A. and Zazula D..

Feasibility Study of Heartbeat Detection from Optical Interferometric Signal by using Convolution Kernel Compensation.

DOI: 10.5220/0004328303960400

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2013), pages 396-400

ISBN: 978-989-8565-36-5

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

applied to nonlinear instantaneous mixtures of

interferometric signals.

The manuscript begins with a description data

model and methodology in Section 2. Section 3

explains experimental protocol and evaluates the

obtained results. Discussion and conclusions are

made in Section 5.

2 METHODOLOGY

2.1 Data Model

Optical interferometry is a well-known principle of

measuring external stimuli that triggers changes of

optical-fibre length (Udd, 1991). Due to their high

sensitivity, such sensors can detect micrometric or

even nanometric changes. As a result, tiny variations

of pressure against optical fibre generate high

changes in optical interferometric signal.

The use of optical interferometer for heartbeat

monitoring has already been demonstrated in

(Šprager et al., 2010); (Šprager et al., 2011);

(Šprager et al., 2012). When in direct or indirect

contact with a subject, mechanical or audible

activity of myocardium causes perturbations in

interferometric signal i(n).

In this study, the Michelson optical

interferometer was used combined with laser diode

as an optical source emitting the light with the

wavelength of 1300 nm. This interferometer has a

cosine transfer characteristics with one period

corresponding to the fibre length change that is

equivalent to the half wavelength of the optical

source.

When using optical interferometer for heartbeat

monitoring, we observe minute changes of the

sensing fibre length, caused by heartbeats s(n) along

with all other impacts on fibre elongation







, i.e.

noise from the environment, thermal drift, etc:







() cos () ()in An sn n





(1)

Analytic representation of i(n) can be obtained by

using Hilbert transform:







() () ()

()cos () () sin () ()

xn in j H in

n snnjsnn



 







(2)

where j stands for imaginary unit and H[.] for the

Hilbert transform. The phase angle of analytic signal

x(n) can be expressed from (2) as







sin ( ) ( )

tan () tan () ()

cos ( ) ( )

sn n

nsnn

sn n













(3)

Thus,













() tan ()nsn n xn







(4)

When impact of noise and movement artefacts







is negligibly small, (4) evolves into:









nsn





(5)

Therefore, signal s(n) is obtained by computing





tan ( )



. The latter produces wrapped phase







that must be unwrapped for further decomposition

needs.

2.2 Decomposition of Demodulated

Interferometric Signal by CKC

Multichannel CKC is suitable for decomposition of

linear mixtures of signals comprising finite-length

symbols (Holobar and Zazula, 2007). The observed

symbols are first modelled as channel responses in a

MIMO system, while the channel inputs are

conceptually considered sparse positive pulse trains

(PTs) carrying the information about the symbol

arising times. As demonstrated in (Šprager and

Zazula, 2012), in heartbeat observations, the large

portion of repeating symbols corresponds to fibre-

optic responses to the heartbeats.

Fibre-optic observation s(n) is a single-channel

signal. As such, it is not suitable for the CKC

processing and needs to be transformed to multiple

observations. The latter can be achieved by

nonlinear operation, such as by using Hadamard

entrywise products of s(n) for different lags l.

For each

1, ,mM





and all possible

combinations of lags





0, ,

lL 

, i=1,…,m, the

entrywise product





1 m

nl snl 

calculated between the m lagged versions of s(n).

Obtained set of signals is denoted with s

M,L

(n). This

nonlinear extension of single-channel observation

enhances the non-overlapped signal components

(Istenič and Zazula, 2010).

In the following step, CKC-based decomposition

method is applied to signal s

M,L

(n). Outputs from the

CKC decomposition are reconstructed PTs that

indicate symbol arising times.

Fig. 1.a shows three individual heartbeats as

detected by three different PTs (depicted by black

asterisks, blue crosses, and green circles) along with

referential ECG signal drawn in red. It is evident

that a single heartbeat was decomposed into three

different symbols. We assume that these symbols are

consequence of different contributions in

interferometric signal due to mechanical and audible

FeasibilityStudyofHeartbeatDetectionfromOpticalInterferometricSignalbyusingConvolutionKernelCompensation

397

myocardium activity (Šprager and Zazula, 2012).

However, in multivariate observations s

M,L

(n), new

symbols can also be generated by aforementioned

nonlinear extension of single observation s(n).

Figure 1: Heartbeat detection using CKC method: (a)

Three pulse trains (PTs) obtained by the CKC method are

depicted by asterisks, crosses, and circles; (b) marginal

energy of PTs in 1.a over time; (c) smoothed version of

signal from 1.b by using local regression with weighted

linear least squares. Detected heartbeats are denoted as

local maxima. Referential ECG is depicted in all the three

panels.

Fig. 1.a confirms that the pulses from the same

PT more or less occur at the same time instant after

referential R waves (see pulse sequence of different

colours for each of three heartbeats). Fig. 1.b shows

marginal energy of PTs over time, underpinning the

locations where pulses concentrate and point out

individual heartbeats. From this point of view, the

heartbeat detection step is trivial. The heartbeat time

instants can be estimated as local maxima of

marginal energy of PTs over time.

In this study, the PT marginal energy was

additionally smoothed by local regression using

weighted linear least squares with window length

corresponding to the highest expected heart rate, i.e.

120 beats per minute (Fig. 1.c).

3 EXPERIMENTS AND RESULTS

The proposed method was applied to the signal set

obtained by experimental protocol described in

(Šprager and Zazula, 2012). The experiment

involved 14 subjects, 11 males and 3 females (age of

30 ± 9 years, height of 176 ± 6 cm, and weight of 77

± 15 kg), and was performed on a bed with inserted

6 m long optical fibre. Referential ECG signal was

acquired with four electrodes firmly attached to the

subject’s extremities. ECG lead II was taken as the

referential one. Each of the observed persons was

asked to cycle an ergometer until their submaximal

heart rate (85 % of maximal heart rate, which

computes as 220-age) was achieved. Afterwards,

subjects immediately lied down on the mattress (in

the supine position) and were asked to lie still during

4 minutes long acquisition of interferometric and

referential ECG signals. With such a protocol,

gradual change of heart rate was obtained, which

exposed the detection approach to an aggravated

situation.

Signals were acquired by costume made four-

channel sampling device and digitised by a 12-bit

A/D converter built in the microcontroller

PIC18F4458. Interferometric signals were sampled

at 50 kHz, whereas the referential ECG signals were

sampled at 196 Hz. The two signal sequences were

synchronized by hardware. It has been shown

(Šprager and Zazula, 2012) that, in demodulated

signal, the energy of heartbeat contributions due to

mechanical and audible activity of myocardium is

below 60 Hz. Therefore, after frequency

demodulation of interferometric signal, all signals

were down-sampled to 125 Hz.

Recorded signals were divided into four one-

minute-long segments. Each segment was then

nonlinearly extended by using entrywise products up

to the 5

order (M = 5) with lags up to L = 10

samples and decomposed by CKC decomposition

approach (Holobar and Zazula, 2007).

The acquired referential ECG signals were used

to validate the efficiency and accuracy of the

proposed approach. The validation step was based

on the R waves in the ECG signal as automatically

detected by the method published in (Pan and

Tompkins, 1985).

Detection efficiency was determined according

to each referential R wave. Due to delays of

mechanical activity of the heart in comparison with

the ECG signal, the heartbeats detected from the

interferometric signal fall between two consecutive

referential R waves. In the ideal case, exactly one

detected heartbeat appears in every RR interval. In

this way, all detected heartbeats can be grouped in

the following three classes:

 true positive (TP) – the number of first detected

heartbeats in the RR intervals,

 false positive (FP) – the number of all detected

heartbeats in RR intervals, excluding the first

heartbeat in each RR interval,

 false negative (FN) – the number of all

undetected heartbeats in RR intervals.

With these classes, sensitivity (r

) and precision (r

)

were calculated as follows:

BIOSIGNALS2013-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

398

TP TP

and

TP FN TP FP

rr



(6)

Overall sensitivity and precision for all 14 tested

persons yielded 97.8 ± 3.0 % and 93.6 ± 7.6 %,

respectively.

As accuracy metrics, the reference-to-detected

heartbeat delays and the mean absolute error

between the length of RR intervals and the distance

between two consecutively detected heartbeats were

calculated. The stability of both metrics was

assessed by calculating their standard deviation.

The measured reference-to-detected heartbeat

delays for all subjects are shown in Fig. 2.a. When

averaged over all the participants, the overall

reference-to-detected delay yielded 167 ± 65 ms.

Mean absolute errors are shown in Fig. 2.b. The

overall mean absolute error was 79 ± 57 ms.

When measured on a standard personal computer

with 2.4 GHz 4-core Intel processor and 8 GB of

memory, the average processing time for one-

minute-long segment was 10.1 ±1.2 s.

Figure 2: Accuracy metrics for the proposed method

obtained from 14 participants: (a) reference-to detected

delay; (b) mean absolute error (vertical lines indicate

standard deviations).

4 DISCUSSION AND

CONCLUSIONS

Efficiency metrics for 14 subjects (Fig. 2) show that

heartbeat detection is feasible with the proposed

method. Nevertheless, in comparison to more

advanced methods (Šprager and Zazula, 2012),

obtained results indicate lower efficiency (precision

of 93.6 ± 7.6 %) as well as lower accuracy. This also

contributes to relative high overall variability of

detected heartbeat delays (±65 ms) and relatively

high mean absolute error in estimated inter-beat

interval lengths (79 ± 57 ms). The reason probably

lies in relatively high amount of symbols/PTs

comprising the multichannel observations s

M,L

(n).

While a significant portion of them reflect responses

to heartbeats, the other reflect the repeating

interferences from outer world (e.g., due to

breathing, movements etc.) This is also the main

reason why our heartbeat detection was not made

dependent on single pulses in PTs, but was based on

observation of group of pulses as obtained by

calculating marginal energy of all PTs.

Accuracy of heartbeat detection is additionally

degraded by smoothing operation presented in Fig.

1.c. To avoid smoothing, the detection step should

focus on the individual PT and select only those that

represent the actual heartbeats. This is not a trivial

task. Thus, further research of interferometric signal

properties, their nonlinear extensions and their CKC-

based decomposition is required.

The sampling frequency of demodulated

interferometric signal used in the proposed method

was set to 125 Hz, which is four times lower than in

similar approaches (Šprager and Zazula, 2012,

Šprager et al., 2010, Šprager et al, 2011, Šprager et

al., 2012). This is not a limitation as the down-

sampled interferometric signal still preserves all

spectral energy of components induced by

mechanical and audible activity of myocardium

(Šprager and Zazula, 2012). The selected sampling

frequency was also low enough to guarantee

acceptable decomposition time – about 10 s for 60-

second-long signals.

Considering chosen segment length of

interferometric signal, it must be emphasised that

CKC decomposition relies on statistical signal

properties. This means that the signals must be long

enough to contain adequately high number of

symbol repetitions. One-minute-long segments

turned out to be long enough for our decomposition

purposes, but hindered the tracking of heartbeats in

real-time. The real-time version of CKC method is

currently under development and is yet to be tested

on interferometric signals.

Finally, it would be interesting to use the

proposed method with multi-array sensors that, in

contrast to the optical sensor proposed in this paper,

produce multiple observations.

In conclusion, method for heartbeat detection

using decomposition approach based on convolution

kernel compensation has been introduced. Although

the efficiency and accuracy are slightly lower than in

similar detection methods, the obtained results show

great potential in unobtrusive heart rate

measurements. The proposed approach also opens a

new way of decomposing fibre-optic interferometric

signals.

FeasibilityStudyofHeartbeatDetectionfromOpticalInterferometricSignalbyusingConvolutionKernelCompensation

399

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