Non-invasive foetal heartbeat rate extraction from an underdetermined single signal

doi:10.4236/health.2009.12018

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Vol.1, No.2, 111-116 (2009)

doi:10.4236/health.2009.12018

SciRes

Health

Non-invasive foetal heartbeat rate extraction from an

underdetermined single signal

Ranjan Acharyya1, Neil L Scott1, Paul D Teal2

1Industrial Research Ltd, Wellington, New Zealand; r.achary ya@i rl.c ri.nz, [email protected]

2Victoria University of Wellington, Wellington, New Zealand; mailto:[email protected]

Received 17 June 2009; revised 20 July 2009; accepted 23 July 2009.

ABSTRACT

Extraction of foetal heartbeat rate from a single

passive sound sensor on the mother’s abdomen

is demonstrated. The extraction is based on the

assumption that a disjoint band of frequencies

exist and foetal signal is concentrated in this

band, and further that it can be represented

conveniently as a set of wavelet coefficients.

The algorithm has been applied to each stream

of data obtained from six different channels and

the detection performance is elaborated. The

algorithm has also been tested on signals from

non-pregnant abdomens to show successful

rejection of adult heartbeat. The extraction of

the desired signal is done in two stages so as to

eliminate components from the maternal heart-

beat.

Keywords: Underdetermined System; Foetal

Heartbeat Rate; Wavelet, Blind Source Separation;

Non-Invasive; Passive.

1. INTRODUCTION

Monitoring of foetal heartrate using a non-invasive tech-

nique is still a challenging problem with a variety of

approaches [1,2]. Usually, foetal heartbeat is monitored

using a Doppler ultrasound device which transmits ul-

trasonic sound waves into the uterus. Most researchers

consider that the power used in these devices is perfectly

safe, although there are some exceptions [6]. In many

cases women prefer that ultrasound is not used on them.

Detailed motivation for development and use of accurate,

non-invasive techniques for monitoring the foetal heart

is covered in the excellent introduction of [1]. This paper

describes a method for detection of the foetal heart with

a passive acoustic monitoring device (PAM). The proc-

ess involves collection of signals with microphones and

subsequent signal processing.

The passive monitoring of foetal heartrate may be

considered as one class of Blind source separation (BSS)

problem, which has been an active research area for sev-

eral decades now. It refers to the problem of estimating

the original sources from a mixture. In most cases the

mixing system and the number of sources are unknown.

Sensors placed on the maternal abdomen provide signals

which are mixtures of an unknown number of sources

and the nature of the mixing is also unknown. In this

section a quick review of other techniques and overview

of the technique of this paper is given.

Independent Component Analysis (ICA) is a tech-

nique to obtain statistically independent components

from a mixture and a solution technique for BSS prob-

lems. One way to categorise BSS problems is based on

the number of sensor and source signals. Three different

scenarios are, the number of sensors are greater than,

equal to or less than the number of sources. The third

case, which is equivalent to solving for an underdeter-

mined system or for an overcomplete basis, resembles

the problem at hand. Detail and an in-depth analysis of

algorithms can be found in [3,4,5]. A well known algo-

rithm for sparse sources is known as DUET (degenerate

unmixing estimation techniques) [5], which does time-

frequency masking. The applicability of the algorithm

depends on a W disjoint orthogonal [5] condition of the

sources and availability of at least two sensor signals.

Extraction of foetal heartrate using ICA [7] has been

attempted in [8] and some interesting results were ob-

tained. In this paper a new algorithm is developed based

on certain assumptions on the foetal heartbeat signal.

This paper is an extension of an earlier work [9] demon-

strating estimation of the foetal heartrate by frequency

masking. A crucial difference of this paper compared to

[9] is that it avoids filtering of the signal in the time do-

main. Filtering in the time domain was done in [9] to

suppress the maternal heartbeat. The issue of suppress-

ing the maternal signal in the overlap region is addressed

in this paper by performing the filtering in two steps. In

addition to filtering in the frequency domain the resolu-

tion of the signals is enhanced by using a wavelet trans-

formation. The process is discussed in detail in later sec-

tions. The method described in this paper requires only

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one mixture provided the sources satisfy certain condi-

tions.

The work reported in [10,11] using SCICA (sin-

gle-channel independent component analysis) is perhaps

the closest to this work in its assumption of disjoint fre-

quency bands for the noises in the mixtures.

In Section 2, the experimental setup and the sensor

structure is shown. The assumptions on the sources are

explained in Section 3. In Section 4 the algorithm is dis-

cussed in detail. Results of the application of the algo-

rithm to a mixture of signals from a pregnant maternal

and a non-pregnant abdomen is elaborated in Section 5.

Finally, in Section 6 the conclusion and future work are

discussed.

2. EXPERIMENTAL SETUP

The sensor is similar to that described in [9] which was

designed for work using multiple sensors. The sensor

structure array is an array of 16 piezo film (PVDF, Poly-

vinylidene Fluoride) contact microphones of type CM-

01B in a mat placed against the mother’s abdomen. Use

of the existing 16-sensor array allowed recording multi-

ple channels simultaneously, although the algorithm

proposed here uses only a single sensor signal. The sig-

nals are conditioned in a 16 channel low noise amplifier

with band pass filtering (7.2 – 130Hz) and then recorded

in a data logger. Figure 1 shows the block diagram of

the Passive Acoustic Monitor (PAM) and Figure 2 the

complete sensor array.

3. ASSUMPTIONS ON SOURCES

The model is that the sensor signal is a mixture of sig-

nals from multiple sources including foetal heartbeat,

maternal heartbeat, other noises internal to the mother’s

abdomen and external noises from the environment. In

addition the mixing system seems to vary with time. The

most important assumption is that sound from the foetal

heart is band limited and part of the band is isolated

from the other sources, including maternal heartbeat. In

other words, sources do not share the whole band of the

foetal heart beat sound. This conclusion is motivated by

the assumption that the characteristics of sound have

direct relation to the size of the object generating the

sound. The foetal heart is considerably different in size

from the maternal heart or any other sound sources in-

side the maternal abdomen. However, it is expected that

there may be overlap of the frequency band of the foetal

heart and the maternal heart beat. The maternal heart

beat is considered to be the strongest noise present with

respect to the desired signal. In addition to being band

limited the foetal heartbeat sound is also expected to be

compact in the time domain. This implies the signal is

assumed to be absent for short periods between heart-

beats. Hence, application of wavelet transformation to

Figure 1. Block diagram of Passive Acoustic Monitor (PAM).

Figure 2. The 16 channel sensor array.

the signal is expected to enhance detection of the heart-

beat. The effect of the wavelet transformation will be

shown in the next section.

There are further assumptions on the energy content

of the signal. In each data block, after initial processing

the energy of the processed data in the foetal band needs

to be more than a specified threshold value. This is es-

sential to reduce the risk of accepting the adult heartbeat

as the foetal one. The energy of the foetal heartbeat

needs to be more than a specified threshold value at two

different stages. This has a disadvantage that if the signal

strength of the foetal heartbeat is very weak then the

algorithm can fail to detect it at any particular time. It

has been observed that the foetal heartbeat sound is loca-

tion dependent and it is strong at a certain portion of the

maternal abdomen; the strength of the signal is not equal

at every point on the abdomen. Further the position

where the signal is strongest may vary from time to time.

4. DETAILS OF THE ALGORITHM

The algorithm has been developed to exploit the beha-

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viour of the signals given the assumptions mentioned

above. The mixture signal obtained from an acoustic

sensor is subjected to filtering in both the frequency and

wavelet domains. The procedure is an extension of the

process discussed in [9], where both maternal and foetal

heartbeat were extracted. The algorithm developed here

can be extended to extract the maternal heartbeat as well

although it is not required for estimation of the foetal

heart rate. First, we describe the components of the algo-

rithm and then provide a step by step algorithm descrip-

tion.

The first filtering step is performed in the frequency

domain. The spectrum of the mixture signal is multiplied

by a profile derived from a Gaussian mixture before in-

verse Fourier transform. The procedure to derive the

profile of the mixture of the Gaussians is as in [9]. The

Gaussian mixture so obtained is then modified such that

20 406080100 120140 160

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0. 7

0. 8

0. 9

Frequency in Hz

Mixture of Gaussians and flat spectrum

Figure 3. The solid line is mixture of Gaussian and the dashed

line is the derived one.

05 10 15 20 25 30 35

-0. 25

-0. 2

-0. 15

-0. 1

-0. 05

0.05

0. 1

0.15

0. 2

0.25

Time in msec

Wavelet coefficients and filtered signal

Figure 4. Comparison between filtered signal and its wavelet

coefficients (dashed).

a range of values around the peak of the mixture are set

to unity. This makes the frequency profile flat around the

middle portion. The reason for this modification is that

the peak energy frequency bin may vary from foetal

heart to heart or it may fluctuate from beat to beat.

Therefore a general form of frequency profile in the

first stage of filtering seems to be more appropriate.

Figure 3 shows the frequency profile derived in [9] and

the profile that is utilized in this paper. The mixture sig-

nal is filtered by this derived spectrum.

After filtering, the energy of the signal is compared to

the energy of the signal prior to filtering. The filtered

signal must meet the energy criterion which is set by a

specified threshold value, in order to proceed to the next

stage of processing, which is carried out for the portions

of signals which are expected to have a foetal heartbeat.

Next, a stationary wavelet transform (SWT) of type

Discrete Meyer as defined in MATLAB, is applied to the

signal. The number of coefficients in each level of sta-

tionary wavelet transform has the same number of sam-

ples as the original signals. The approximate coefficients

of the 5th level are considered [12]. Figure 4 shows a

small block of the filtered signal and the corresponding

5th level wavelet coefficients.

As can be seen in the figure, the portion where the

foetal heart beat is expected i.e. higher energy portion of

the signal is inflated. Next, the locations of the foetal

heartbeat in a block are estimated by determining the

peaks of the energy of the wavelet coefficients. The al-

gorithm should detect the peaks corresponding to each

heartbeat. Often the change of sign of the derivative is

used for detecting a peak. However, the foetal heart sig-

nal is essentially oscillatory in nature, each heartbeat

event includes several oscillation peaks hence, the

change of sign of the derivative would return many

peaks which are not of interest. To get rid of this prob-

lem the change of sign of derivative algorithm is applied

twice. An algorithm returns the first peak estimator as

the points of change of sign of the derivative. The same

algorithm is then applied to the absolute values of the set

of first peaks to determine the overall peak estimates.

Figure 5 shows the peaks detected by the algorithm in

the first and second stages. The arrows mark the final

peaks detected by the algorithm. The two stage peak

detector is an alternative to the other peak estimation

methods that require a strict threshold value.

The peaks obtained from the second stage are close to

the actual maxima, as observed by eye.

The signal around the peaks so selected is expected to

be made up of foetal heartbeat signal. At this stage a few

peaks may remain from maternal heartbeats. Next, the

signal is multiplied by a window function around the

peak values. The window function is shown in Figure 6.

The purpose of this window function is to attenuate all

other sources near the desired foetal heartbeat. Emphasis

may be given to the point that the objective of this paper

is to recover the foetal heartbeat rate rather than the

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05 10 15 20 25 3035

-0.2

-0.15

-0.1

-0.05

0.05

0.1

0.15

Peaks detected by the algorithm

Time in msec

Figure 5. The ‘o’ are the peaks obtained first and arrow shows

the accepted peaks.

05 10 15 20 25 30 35 4045

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time in msec

Window function

Figure 6. Window to multiply the time domain signal.

waveform. The use of the window function may change

the actual waveform of the foetal heartbeat but it is ex-

pected not to affect the foetal heartbeat rate. This ends

the first stage of the algorithm.

The signal obtained after applying the window func-

tion is subjected to another filtering step in the frequency

domain. The spectrum of the signal is once again multi-

plied by a profile derived from a set of Gaussians before

inverse Fourier transformation. These new set of Gaus-

sians are obtained in the same way as before [9]. How-

ever, the band of the spectrum is shifted towards higher

frequencies. For example if the frequency range of the

mixture of Gaussians were 15 to 45 Hertz earlier the

derived frequency range would be from 30 to 60 Hertz.

The motivation for this shifting is to pass the signals

which have only foetal heart beat. As mentioned before,

the lower part of foetal spectrum overlaps with the ma-

ternal heartbeat spectrum. The second step is expected to

minimize the energy in the overlap and hence the con-

tribution from the maternal heartbeat. To remove the

maternal part this second step of filtering is performed.

The maternal heartbeat is much stronger than the foetal

one and hence this type filtering helped recover the foe-

tal signal from the noise floor. Similar to the previous

step, the filtered signal must meet an energy criterion

which is set by a specified threshold value, in order to

consider it to be a foetal heartbeat. In the final steps the

signal is passed through a peak detector twice (like the

previous step) so that only those parts of the signal with

relatively large peaks can be considered as foetal heart-

beat.

The complete steps of the algorithm are given below:

• The data is divided into equal sized blocks. Each of

which is filtered by the following steps. In our case the

block size is 14400 samples; 6 seconds of data at the

sampling frequency 2400 samples per second.

• Multiply in the frequency domain the block of data

by the mixture of Gaussians derived as in [9] with flat all

pass section at mid band.

• Check the energy content of small blocks of con-

tiguous 2000 samples and compare the ratio of total en-

ergy before and after filtering. If a block has a ratio of

the energy, after and before filtering greater than the

threshold value of 0.005 the block is accepted for the

next step of processing. A small block of 2000 samples

is chosen instead of 14400 samples so the a whole block

of 6 sec data is not lost.

• Perform a stationary wavelet transform and retain

the approximate coefficients (low pass filtered part) of

level 5 for further processing. The Discrete Meyer

wavelet is utilized.

• Find the peaks of each block by passing data

through a peak detector twice. The peak detector is

based on the change of sign of the derivative of the sig-

nal. The peak detector output is passed on if it exceeds

the specified threshold value of 0.0067.

• Multiply the frequency content of the block of data

with the spectrum derived from the mixture of Gaussians

with flat all pass in the mid band.

• Window the signal with a 1000 sample window

about each peak.

• Multiply the frequency content of the block of

wavelet coefficients with the mixture of Gaussians and

perform an inverse Fourier transform.

• Check the energy content of small blocks of wave-

let coefficients of 2000 samples and compare the ratio of

total energy before and after filtering. If a block has a

ratio of the energy of the signal after and before filtering

is greater than the threshold value of 0.1 the block is

accepted for the next step of processing.

• Find the peaks of each block by passing data

through a peak detector twice. Pass all peaks exceeding a

specified threshold value of 0 .02.

• Count the number of peaks per minute to find the

heart beat rate.

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• Multiply the signal with a window of 1000 samples

so that only selected portions of the energy are kept to

produce an audible confidence signal.

5. RESULTS

The algorithm was applied to four different datasets.

Two sets of data came from pregnant women and two

from non-pregnant abdomens. The purpose was to verify

that the algorithm can detect foetal heartbeat while not

falsely detecting a heartbeat when none is present. Data

sets were collected with equipment comprising either 6

or 16 sensor. The sensor elements are identical while the

6-sensors equipment samples at 2400 data samples per

second and the 16-sensor at 300 samples per second.

Data sets were regularized by decimating the 2400 data

to 300. As the Gaussian mixture algorithm was designed

for 2400, both data types were then up-sampled to 2400

samples per second. It has been observed that the foetal

05 10 15 20 25 30 35 4045

-1

-0.8

-0.6

-0.4

-0.2

0. 2

0. 4

0. 6

0. 8

Time in secs

Foetal heartbeat in 40 seconds

Figure 7. Foetal heartbeat for 40 seconds.

0123456

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

Time in secs

Foetal heartbeat in 5 seconds

Figure 8. Foetal heartbeat for 5 seconds.

heart beat sound is prominent at one sensor at a time.

This has been noticed in two different sets of data.

Figures 7 and 8 show the foetal heartbeat for a period

of 40 seconds and 5 seconds respectively. In the 40 sec-

ond data one can observe that the foetal heartbeat sound

has been missed a few times. From the signals illustrated,

a heartbeat rate of 144 beats per minute can easily be

estimated. A separate Doppler sensor used at the same

time reported a rate between 135 and 160 beats per min-

ute. Similar results were obtained from the other foetal

data set.

Data were collected from non-pregnant abdomens for

a total of 10 minutes being 5 minutes each from two

people. There were 16 channels and altogether the total

number of adult heartbeats expected was 11520 assum-

ing 72 heartbeat per minute. The number of false detec-

tions as foetal heart beat signal was 154 which is 1.3%

of 11520. In addition the 154 falsely detected pulses

were randomly scattered which indicated that they won’t

contribute significantly to the calculations of foetal heart

rate.

6. CONCLUSIONS

It has been shown that foetal heartbeat rate can be ex-

tracted from a single microphone sensor non- invasively.

The rejection of the adult heart rate by the algorithm is

established. Future research will look into adjustment of

the processing parameters adaptively. In addition the

frequency profile of foetal heart beat may be adjusted

adaptively.

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