Extraction of apex beat waveform from acoustic pulse wave by sound sensing system using stochastic resonance

概要

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Extraction of apex beat waveform
from acoustic pulse wave by sound
sensing system using stochastic
resonance
Etsunori Fujita1,2*, Masahiro Horikawa2, Yoshika Nobuhiro2, Shinichiro Maeda2,
Shigeyuki Kojima2, Yumi Ogura2, Kohji Murata3, Tomohiko Kisaka4, Kazushi Taoda5,
Shigehiko Kaneko6 & Masao Yoshizumi1*
With a sound sensing system using stochastic resonance (4SR), it became possible to obtain an
acoustic pulse wave (APW)—a waveform created via a mixture of apex beat and heart sound. We
examined 50 subjects who were healthy, with no underlying cardiovascular diseases. We could
determine boundary frequency (BF) using APW and phonocardiogram signals. APW data was divided
into two bands, one from 0.5 Hz to BF, and a second one from BF to 50 Hz. This permitted the
extraction of cardiac apex beat (CAB) and cardiac acoustic sound (CAS), respectively. BF could be
expressed by a quadratic function of heart rate, and made it possible to collect CAB and CAS in real
time. According to heart rate variability analysis, the fluctuation was 1/f, which indicated an efficient
cardiac movement when heart rate was 70 to 80/min. In the frequency band between 0.5 Hz and BF,
CAB readings collected from the precordial region resembled apex cardiogram data. The waveforms
were classified into five types. Therefore, the new 4SR sensing system can be used as a physical
diagnostic tool to obtain biological pulse wave data non-invasively and repeatedly over a long period,
and it shows promise for broader applications, including AI analysis.
Abbreviations
3SR Sound sensing system using resonance
4SR Sound sensing system using stochastic resonance
ACF Autocorrelation function
ACG​ Apex cardiogram
APW Aortic pulse wave (biological pulse wave collected by 3SR) → acoustic pulse wave (biological pulse wave collected by 4SR)
BMI Body mass index
BF Boundary frequency
CAB Cardiac apex beat
CAS Cardiac acoustic sound
DBP Diastolic blood pressure
ECG Electrocardiogram
F-APW APW measured from the front (precordium) region
F-APW × PCG Power spectrum—frequency diagram which emphasizes the PCG component of F-APW
by addition on double logarithmic axes (multiplication on linear axes)
F-APW × ­PCG−1 Power spectrum—frequency diagram which decreases the PCG component of F-APW by
subtraction on double logarithmic axes (division on linear axes)
1

Department of Cardiovascular Physiology and Medicine, Graduate School of Biomedical and Health
Sciences, Hiroshima University, 1‑2‑3 Kasumi, Hiroshima  734‑8553, Japan. 2Delta Tooling Co., Ltd, 1‑2‑10
Yanoshinmachi, Hiroshima  736‑0084, Japan. 3Graduate School of Nursing, Sanyo Gakuen University, 1‑14‑1
Hirai, Okayama  703‑8501, Japan. 4Office of Research and Academia-Government-Community Collaboration,
Hiroshima University, 1‑2‑3 Kasumi, Hiroshima  734‑8553, Japan. 5Biwako Professional University of
Rehabilitation, 967 Kitasakacho, Shiga  527‑0145, Japan. 6Major in Mechanical Engineering, School of Creative
Science and Engineering, Center for Science and Engineering, Waseda University, 3‑4‑1 Okubo, Tokyo 169‑8555,
Japan. *email: gonzo@deltatooling.co.jp; yoshizum-tky@umin.ac.jp
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Front CAB Cardiac apex beat waveform drawn from F-APW
Front CAS Cardiac acoustic sound waveform drawn from F-APW
HR Heart rate
HRV Heart rate variability
MAV Micro acoustic vibration
PCG Phonocardiogram
SBP Systolic blood pressure
STFT Short time Fourier transform
Visual inspection and forms of palpation and auscultation are used as basic diagnostic ­methods1, which occupy
important positions in physical examination in cardiology. A phonocardiogram (PCG) delivers an objective
graphing of the auscultation method, which is the visualization of vibrations and sounds derived from the heart
and great arteries in the 16 to 1000 Hz audible range. On the other hand, apex cardiogram (ACG), the target vibration frequency range of which is below 10 Hz, corresponds with visual inspection and ­palpation2. However, the
ACG sensor’s major drawback is its susceptibility to n
­ oise3, since piezoelectric elements are commonly employed.
Among previous approaches regarding signal processing to extract information from ACG, the Stretchable
E-Skin Apexcardiogram S­ ensor4 can analyze waveforms and time phase of the A wave, but it was reported that
recording skills might largely affect waveforms other than that of the A wave. And ­gyrocardiography5 has not
been able to reproduce the ACG waveform. Consequently, both methods are mainly used for time phase analysis.
No machine learning method conducting automatic detection of the ACG waveform has been reported so far.
In 2015, we completed a sound sensing system using resonance (­ 3SR6,7) with a mechanical amplification
mechanism using a harmonic oscillator.
In 2019, we developed a new sound sensing system using stochastic resonance (4SR) to measure human
vibration waveforms below 10 Hz. 4SR combines a harmonic oscillator at 20 Hz with a stochastic resonance
­mechanism8. We succeeded in extracting the acoustic vibration information of 0.5 to 80 Hz from the apex by
using this system.
Since the previous ­study9 reported that there was a frequency around 16 Hz which was the boundary between
apex beat and heart sound, we decided to further examine the correlation between heart rate and BF (which is a
boundary between CAB and CAS) by using heart rate variability (HRV) and statistical methods, focusing on BF.
The 3SR system was destined to collect biological information from the back, and we named this information an aortic pulse wave (APW), considering that it mainly captured HRV from heart sound via the aorta.
The 4SR system was developed to extract apex beat waves, with the aim of measuring acoustic signals from the
precordial, back and lumbar regions. Therefore, in this paper, we named the biological information collected by
4SR an acoustic pulse wave, although it uses the same basic APW abbreviation. To avoid confusion, we distinguish these APWs by adding a prefix: APW measured from the precordial region as front acoustic pulse wave
(F-APW), for instance.

Results

Performance of the 4SR sensing system and measurement of F‑APW.  Figure 1a shows the instal-

lation position of the sensor and the component configuration of 4SR to evaluate its sensing performance. 4SR
consists of a gel-pack and an air-pack. The gel-pack consists of gel injected into a soft plastic case and a microphone. The air-pack is sealed with an elastomer film and consists of three-dimensional knitted fabrics known as
3D net (see the sectional photo in Fig. 1a) of 10 mm thickness. It is conceivable that 4SR amplifies vibrations of
0.5 to 80 Hz by the two resonance mechanisms of stochastic resonance and string vibration. Thus, the elastomer
film produces tension by receiving a uniform air pressure, delivering conditions which make it easy to propagate
acoustic vibration.
Micro acoustic vibration (MAV) emitted from the body trunk enables the microphone in the gel-pack to
detect and measure a signal of a certain frequency band caused by the frictional vibration of 3D net in the
air-pack.
During testing, a microphone and 4SR were placed 10 cm left of the chest midline on the left fifth intercostal
space.
Figure 1b shows MAV being measured by the microphone. Since the microphone is attached directly to
the chest, MAV information is unaffected by the amplification effect of stochastic resonance. Figure 1c shows
F-APW measured by 4SR. F-APW is acoustic vibration information which is affected by the responses of the
mechanical vibration system comprising the 4SR sensing system, harmonic oscillator resonance and stochastic
resonance. Then, Fig. 1d shows the amplitude ratios calculated by frequency analysis of the time waveforms of
MAV and F-APW.
The gains of F-APW/MAV were 42 dB in a band of the fundamental vibration of apex beats, slightly more than
30 dB in a band of higher harmonics, and 20 dB in the vicinity of 20 to 30 Hz, which is the band of the harmonic
oscillator and a minimum band of heart sounds. The effect of the response of the mechanical vibration system
and stochastic resonance indicated that the maximum gain was over 40 dB and the minimum was 10 dB, while
its amplitude difference increased by slightly less than 200 times.
Figure 2 shows the time waveforms for 2.5 s of electrocardiogram (ECG), F-APW and PCG of four subjects,
whose average heart rates were 58, 71, 79 and 93/min, respectively. Waveforms in a 1 to 1.5 Hz band were
observed in F-APW.

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Figure 1.  Experimental apparatus and characteristics of 4SR (amplitude ratio). (a) The installation position and
component configuration of 4SR. 4SR is an assembly comprising of a gel-pack (left photo) and an air-pack (right
photo). The gel-pack consists of gel injected into a soft plastic case and a microphone. The air-pack is sealed
with an elastomer film and embedded three-dimensional knitted fabrics called 3D net (see the sectional photo)
of 10 mm thickness. The air-pack and the gel-pack are fixed together by adhesion of the gel. For comparison,
micro acoustic vibration (MAV) was collected using only the microphone. (b) MAV obtained using only the
microphone. (c) F-APW obtained using 4SR. (d) The amplitude of apex beats and heart sounds increased almost
two 100-fold, and the gain was 20 to 42 dB through mechanical vibration system response and the stochastic
resonance effect.

Determination of BF.  Figures 3a-1–a-6 show results of frequency analysis and short time Fourier transform (STFT)10 by the frequency analysis of F-APW and PCG of a subject whose average heart rate for 10 s was
93/min. BF corresponding to a ­breakpoint11 is 15 Hz. ...

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