A method is proposed for the investigation of the dynamic parameters of breathing and heartbeat based on

the analysis of a block of coefficients of the wavelet transform of the phase signal assumed by a radiowave

sensor. We note the high sensitivity of the method to local changes in the form of the components of the

signal and its outlook for the creation of expert diagnostic and identification systems.

Keywords: diagnostics, breathing, heartbeat, radiowave sensors, continuous wavelet transform.

For some time, in medicine, there has been great interest in the use of radiowave sensors for investigation of the

parameters of breathing and heartbeat, first represented in [1]. This is connected with the noncontact principle of obtaining

information, which predetermines their advantage compared to traditional methods based on recording of an electrocardio-

gram (EKG; ECG). Such sensors are capable of long-term control of the state of a person, carrying out the modeling of phys-

ical parameters with a maximally sparing and nonstationary method. In this case, the sensors do not require frequent care and

replacement of expendable materials, and have a low cost. Moreover, in the absence of an ECG, radiowave sensors carry

information not about the electric potentials that control the operation of cardiac muscles but about specification of the

mechanical motion of the heart and its separate elements. These data do not simply overlap but considerably supplement each

other, enabling us to broaden the diagnostic possibilities with modern analysis [2, 3].

The methods of investigation for the dynamic parameters of the signals of radiowave sensors carrying information

about breathing and heartbeat, as a rule, are based on spectral Fourier analysis of the results after some substantial observa-

tion time. The harmonics obtained for this complex signal characterize the dynamics of the mechanical motions of the lungs

and heart. We should note, however, that such an analysis gives a distorted representation of the actual process since it is based

on the example of a noncontact period of harmonics of the components of the signal spectrum for expansion in a Fourier

series. In the actual situation, after the observation time there is a constant increase in the artifacts or local time inhomo-

geneities, violating the idealized picture, leading to a broadening of the spectral frequencies of breathing and heartbeat.

Therefore, analysis of the dynamic parameters of the signals of breathing and heartbeat with respect to the harmonics after

spectral decomposition in part adds to the repeatability and prediction of the results.

In contrast to spectral Fourier analysis, wavelet analysis supposes the expansion of the investigated signal not in the

form of a noncontact extended harmonic series but in the form of an energy space of two-dimensional coefficients with

respect to the appropriate scales and times using as a basis a specially determined “soliton-like” function of the source

wavelet. As a result, it becomes possible to analyze a complex signal with frequency and time localizations, enabling us to

establish its global and fine structure [4].

Measurement Techniques, Vol. 57, No. 2, May, 2014

INVESTIGATION OF DYNAMIC PARAMETERS

OF BREATHING AND HEARTBEAT BY

NONCONTACT RADIOWAVE SENSORS

MEDICAL AND BIOLOGICAL MEASUREMENTS

D. V. Khablov UDC 621.396.969

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences (IPU RAN), Moscow, Russia; e-mail: dkhablov@mail.ru.Translated from Izmeritel’naya Tekhnika, No. 2, pp. 65–69, February, 2014. Original article submitted December 10, 2013.

0543-1972/14/5702-0206 ©2014 Springer Science+Business Media New York206

In the present work, we investigate a comparatively new method of wave analysis for signal processing of radiowave

sensors of the vital activity of humans in order to estimate the dynamic parameters of breathing and heartbeat. Advantages in

comparison with traditional methods of Fourier analysis are shown.

Principle of Action. In Fig. 1, we show the simplest diagram of a radiowave sensor using continuous, single-fre-

quency radiation. Electromagnetic oscillations U0cos(2πƒ0) of frequency ƒ0 originate from a superhigh-frequency (SHF) gen-

erator 1 through directed coupler 2, circulator 3, to antenna 4, and are irradiated in the direction of person 5. The signal

reflected from the person is received by the antenna, fed through the circulator, and fed to the input of mixer 6. On the other

hand, at the reference input of the mixer, an electromagnetic wave of the same frequency ƒ0 arrives from generator 1 through

the auxiliary arm of the directed coupler 2. Since the phase of the reflected signal depends on the change in geometric dimen-

sions of the person’s body, the signal at the output of mixer 6, determined by the phase difference between the reference sig-

nal and received signal, repeats these changes. This signal, being the output for the sensor, then can be supplied to computer 7

207

Fig. 1. Diagram of radiowave sensor for breathing and heartbeat of a person:

1) superhigh-frequency (SHF) generator; 2) directed coupler; 3) circulator;

4) antenna; 5) patient; 6) mixer; 7) computer.

Fig. 2. Typical spectrum of output signal of radiowave sensor of breathing and heartbeat.

for processing and analysis. Outside, the output signal suggests a distorted sinusoid and, with the condition of reflection of

the wave only from the surface of the person’s body, is written as

Uout = Acos(ϕb(t) + ϕh(t)), (1)

where A is the amplitude of the signal; and ϕb(t) and ϕh(t) are the change in phase of the signal as a result of the displace-

ments of the chest and tissues of the person for breathing and heartbeat, respectively.

The characteristic spectrum of signal (1) is represented in Fig. 2. Here we can see the characteristic lines connect-

ed with the breathing and heartbeat of the person. In order to obtain such a signal at the output of the mixer 6 with an accept-

able distortion level, we must satisfy a necessary condition: half the wavelength λ0/2 should be comparable with the indi-

cated linear motions of the chest, where λ0 = c/ƒ0 , and c is the velocity of light in air. Since these motions correspond to

about 5 and 0.5 mm, respectively, we have that λ0 ≤ 1.25 cm, which corresponds to frequency ƒ0 = 24 GHz. Here we should

maintain the condition of equality between the reference and assumed signals at the input of the mixer 6 (see Fig. 1), which

can be obtained by introducing into the schematic diagram a sensor for the additional compensating channel [5], regulation

of the position of the antenna or introduction of quadratic processing of the signal [3]. For simplicity, these elements are

omitted in Fig. 1.

With increasing λ0, the sensitivity of the sensor is smoothly reduced with simultaneous increase in the penetrating

power of the signal in the body of the person, which can be considered as a dielectric with losses [6]. As a result, the reflect-

ed signal will be the sum of signals reflected from the surface of the body and internal inhomogeneities (layers of fat, bone,

muscle, and organs). The signal at the output of the mixer can be represented in the form

UΣout = AΣcos(ϕb(t) + ϕh(t) + Σϕi(t)), (2)

where AΣ is the amplitude of the total signal; and Σϕi(t) is the sum of the phase variations of the signals reflected from the

internal inhomogeneities of the person.

The spectrum of the signal owing to phase distortions is flattened, and the form is smoothed, losing the local fea-

tures, which is of value for diagnostics. For example, signals of the heart rate degenerate into the usual sinusoid. The given

factor indicates a frequency of ƒ0 ≈ 8 GHz, which can be considered the lower boundary of frequencies used in the operation

of radiowave sensors for investigation of the dynamic characteristics of breathing and heartbeat. Then, for brevity, we will

use the term “SHF sensor” instead of “radiowave,” since precisely this range corresponds to frequencies 8–24 GHz.

As an alternative SHF sensor, we can use the radiolocation pulsed (RP) sensors considered in [3]. However, small

separations and movements lead to the necessity of applying super-broad-band (SBB) technology, which considerably

increases the cost of devices, without causing any noticeable improvement in the functional characteristics. The selection

zone enables us to decrease the action of possible external interference; however, it is insufficient for reducing the effect of

movements and internal inhomogeneities with account of which the filling frequencies usually consist of 1–2 GHz. Thus for

a filling frequency of 1 GHz and pulse length of about 4 nsec, the potential resolving power or selection zone of the SBB

radiolocation pulsed sensors in free space totals:

where Δƒ0.5 = 300 MHz is the spectrum width of the signal power with respect the level 0.5 from the maximum; and ε is the

relative dielectric permeability of air, equal to unity.

At the same time, in tissues of a person, for which ε ≈ 40, we have ΔR = 7.9 cm. As a result, the SBB radiolocation

pulsed sensor, just as sensors with continuous radiation of frequency below 9 GHz, in the best case, can analyze the breath-

ing frequencies, the pulse, and the variability of the heart rate.

Thus, the most adequate picture of the correspondence of the signals of the SHF sensor by mechanical movements

of the lungs and heart, as was noted in [3], can be obtained only for the case of fixation of the changes caused by the posi-

Δ = Δ =R c f/( ) ..2 0 50 5 ε m,

208

tion of the upper surface of the person’s chest, i.e., instead of (2) it is entirely admissible to use relation (1). What most cor-

responds to these requirements is a SHF sensor with continuous radiation at frequency ƒ ≈ 24 GHz.

Features in the Use of Wavelet Analysis for Signal Processing of a SHF Sensor. Presently used methods for sig-

nal processing of noncontact SHF sensors of breathing and heartbeat are based on the filtration and spectral processing of

the output signal, from which we isolate the harmonics corresponding to breathing and heart contraction, with subsequent

recording of their variations (together or separately) for various people after different types of physical loads, with delay of

breathing or without it, sitting, lying down and standing, on one’s side and upright, during conversation, etc. Used togeth-

er with an ECG, is correlation analysis; we estimate the delay time between the cardiac signal and the signal of the SHF

sensor; however in the framework of the measurement of the frequencies of breathing and pulse, the dynamic characteris-

tics of these processes are not investigated. The local time features of the signal, which carry information about the dynam-

ics of muscle contraction, do not enter into the investigation with such an approach. This result is connected with the same

principle of signal processing by their decomposition into harmonics with noncontact duration, which is characteristic for

spectral Fourier analysis, and with features of the signal being investigated.

Basis functions for expansion in Fourier series are sinusoidal oscillations, which are mathematically defined in the

time interval ±∞ for direct transformation and have parameters that are constant over time. This is also valid in the frequen-

cy region for the inverse Fourier transform. Here, separate features of the signal, e.g., discontinuities, peaks, or phase shifts,

cause insignificant changes in the frequency pattern of the signal over the entire frequency interval ±∞, which are “spread”

over the entire frequency axis, which makes their detection over the spectrum practically impossible. A sharp increase in the

number of harmonics in this case proves to have an effect on the form of the signal and for the limits of its local features.

Here, based on the structure of the high-frequency components of the spectrum, it is practically impossible to estimate the

location of features on the time dependence of the signal and their character. For unsteady signals, namely, those that are

observed by SHF sensors, using breathing and heartbeat, the difficulties of direct and inverse Fourier transforms increase

repeatedly. To a certain degree, the indicated difficulties can be overcome by using a window Fourier transform. However,

this does not eliminate the main shortcoming – the use of a sinusoid as the basis function of the spectral expansion.

Wavelet analysis, in contrast to direct Fourier transformation, is based on the procedure of direct continuous wavelet

transformation (DCWT) of a one-dimensional signal based on a system of basis functions of the form

Ψab(t) = a–1/2Ψ[(t – b) /a], (3)

where a–1/2 is the normalizing factor; a and b are coefficients of variation of the time scale and time shift, respectively; and

Ψ(t) is a function of the parent wavelet.

If the energy of the signal is finite in space V, then the DCWT of signal U(t) is given by analogy

with the Fourier transform by calculation of the wavelet coefficients taking into account the limiting region of the signals R

from the formula

(4)

There exists a large and constant supplementary family of wavelet-forming functions (3), suggesting modulated puls-

es of the sinusoid, functions with drops in the level, etc. This ensures a simple representation of signals with local drops and

discontinuities in the set of wavelets of one type or another, which, as a rule, does not have analytical representation in the form

of a formula and is given by iteration expressions. Thanks to this, an expansion of form (4) reveals not only local time features

of the signal assumed (small discontinuities, variations in the signs of the first and second derivatives, etc.), but also allows us

to visually observe a picture of the interaction of different components of the signal in the frequency–time space of the energy

coefficients C(a, b). This explains the advantages of wavelet analysis in the investigation of signals, by which together with

periodic components, inclusions of unsteady-state and turbulent character are present [4]. Features of the signals of the

radiowave sensors enable us to conclude that it is appropriate to explore methods of wavelet analysis for their processing [7].

C a b U t a t b a dtR

( , ) ( ) [( ) / ] ./= −−∫ 1 2Ψ

U t U t dtR

( ) = 2 ( )∫

209

Modeling of Signal Processing for SHF Sensors Using Continuous Wavelet Transforms. For computer model-

ing, we synthesize the signal from the output of the SHF sensor in the form of the sum of two signals. The first is the breath-

ing signal (Fig. 3):Ub(t) = sin(2πƒbt) + 0.2cos(4πƒbt) + Un(t), (5)

where ƒb = 0.16 Hz is the breathing frequency, and Un(t) is the noise component.

This signal consists of the sum of two harmonics and corresponds approximately to the real movement of a person’s

chest during breathing. Here the breathing phase is somewhat drawn out over time compared with the exhalation phase.

The second signal models the dynamics of heart contractions either in the form of a sinusoid S(t) of frequency 1.2 Hz

or in the form of a sequence of Gaussian single pulses G(t) of the same frequency with parameters, maximally gathered for

imitation of the motions of tissues of a person caused by real heart contractions (see Fig. 3). Here we should note that the

amplitudes of the signals of the heartbeat are less than the signal Ub(t) from (5) by a factor of 100, but on the graphs of Fig. 3

for clarity they are shown in magnified form. The modeling was carried out in the Wavelet Toolbox expansion packet from

Matlab [8] for the two signals

US(t) = Ub(t) + 0.01S(t); UG(t) = Ub(t) + 0.01G(t). (6)

Selection of the form of the wavelet function has important significance for the use of DCWT. Results of analysis

showed that for signals of the given type it is possible to use wavelets of the Daubechies, Symlet, Gauss, and Coiflet fami-

lies. In Fig. 4a and b, we show the results of expansion in the coefficients C(a, b) according to (4) of the model signals US(t)

and UG(t), respectively, from (6) (see Fig. 3) with the use of the third-order Coiflet wavelet Ψcoif3. Here we used a uniform

selection from N = 4000 values of length 0.35 msec for coefficients 1 < a < 700 with step 1. The light regions correspond to

maximum values of C(a, b), and the dark regions correspond to minimal values. In Fig. 4a, we graphically represent four

zones of characteristic behavior of the expansion coefficients: a › 600 is the zone of formation of the low-frequency compo-

nent of the breathing signal; 300 < a < 600 is the zone of the second harmonic of the breathing signal; 80 < a < 300 is the

zone of the heartbeat signal US(t); and 1 < a < 80 is the noise zone. In Fig. 4b, we show that when the signal US(t) is replaced

by UG(t) in the expansion, the first and second zones do not change; on the other hand, the third zone (50 < a < 300) acquires

a distinct fractal structure in accordance with the smallest local features of the signal UG(t), and the noise zone is shifted to

the range 1 < a < 50.

210

Fig. 3. Signals for breathing and heartbeat for numerical modeling: 1) breathing Ub;

2) sinusoid S(t); 3) Gaussian single pulses G(t).

Thus, all the insignificant changes in the form of the heartrate signals from US(t) to UG(t) and a more complex form,

and also in the breathing signal Ub(t) can be isolated and investigated in detail in the general population of the space of the

coefficients C(a, b), taking into account the distinct fractal and transition zones. Here, we carry out the analysis simultane-

ously and continuously over all the signal components, in spite of the large difference in amplitude between them and the

noise component. Investigation of the signal can easily be shifted to the frequency region. The coefficients a are connected

with the heartbeat frequency ƒ, expressed in Hertz, in terms of the transfer function:

F(a) = Fc / (aΔ), (7)

where Fc = 0.70588 is the central pseudofrequency of the wavelet being used (in the present case, this is the third-order Coiflet

wavelet); and Δ is the length of the selection, in seconds.

Thus, according to (7), the frequency ƒ = 1.2 Hz corresponds to coefficient a = 168 in Fig. 4a and b.

Conclusions. Expert systems of analysis of the dynamic parameters of breathing and heartbeat of a person using

SHF sensors, constructed on traditional spectral principles of signal estimation, prove to have little effect on the cause of

the poor repeatability and necessity of a long accumulation of results for reduction of the effect of noise and artifacts [2, 3].

As a rule, they are limited by measurement over time of the frequency of breathing and pulse, and the analysis of their ratios

for a different load for various groups of people and different patients.

The approach proposed in this study estimates the same dynamic parameters over the structure of the space of the

coefficients C(a, b) of the wavelet expansion of the signal of the SHF sensor. Here, we do not need to exactly restore and pre-

serve all the components of the signal for subsequent comparison and isolation of pathologies, but it is sufficient to separate

the detailed, local inhomogeneities of the set signal, which can further serve as a more reliable identifier in expert diagnos-

tic systems.

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