Rheography and Spirography Signal Analysis by Method of

Nonlinear Dynamics

Anna Кiseleva

, Peter Luzhnov

, Alexander Dyachenko

and Yuriy Semenov

Department of Biomedical Techniques, Bauman Moscow State Technical University, Moscow, Russian Federation

Russian Academy of Sciences, Moscow, Russian Federation

Keywords: Rheocardiographic Signal, Spirography, Nonlinear Filtering, Nonlinear Dynamics.

Abstract: The method for identifying rheocardiographic signal reference points was considered by means of nonlinear

dynamics. Its application was shown for the analysis with the spirographic signals together. Seven male

volunteers participated in the study as test subjects. Comparative analysis and efficiency of the developed

algorithm were demonstrated.

1 INTRODUCTION

Biological signals have supplied vital information

for diagnosis of disease for many years. Traditional

algorithms of analysis are based on a priori

information about the structure of the biosignals.

Therefore, the main disadvantages of such methods

are their complexity and poor adaptation for signals

having an atypical structure. Also, such methods

cannot remove the noise without signal damage.

In recent years, researchers have discovered that

biosignals show nonlinear dynamical behaviour and

chaos phenomenon. This discovery made it possible

to apply methods of nonlinear dynamics to living

systems (Cohen M.E., Hudson D.L., 2004). At

present, methods of nonlinear dynamics are used in

various fields of medicine. First of all, it is the

processing of the most commonly diagnostic

biosignals such as the electrocardiogram (ECG)

(Ming-rong Ren, Pu Wang, Hui-qing Zhang, 2008),

the electromyogram (EMG) (Diab A., Falou O.,

Hassan M. 2015; Padmanabhan P., Puthusserypady

S., 2004), the electroencephalogram (EEG) (Akar

S.A., Kara S., Agambayev S., Bilgic V., 2015).

Also, these methods are used in processing

biomedical images (Mendonca A. M., Campilho A.,

2006). One of the main advantages of methods of

nonlinear dynamics is the ability to process signals

in real time (Dhivya R., Premkumar R., Nithyaa,

A.N., 2015).

In this paper, we consider methods of nonlinear

dynamics with respect to signals of the rheography

and the spirography. An algorithm for signal

processing was considered based on the analysis of

attractors of phase trajectories. The proposed

algorithm allows without destroying and losing

useful information about the signal to filter these

signals.

2 MATERIALS AND METHODS

Nonlinear dynamics offers the following methods of

analysis: calculation of Lyapunov's exponents and

determination of the time for forgetting the initial

conditions, evolution of phase volume, analysis of

attractors of phase trajectories (Morgavi G., et al.,

2002).

The analysis of attractors is one of the simplest

and most obvious ways of analyzing a nonlinear

system. This method is one of the most common in

the analysis of biosignals (Charlton P.H., Bonnici T.,

Tarassenko L., 2015; Aston P.J., Manasi N., Christie

M.I., Huang Y.I., 2014; Velez A.H., Gonzalez-

Hernandez H.G., Reyes Guerra, B., 2014). It

determines the dependence of each subsequent value

on the previous one with a temporary delay. Blurring

of the pseudo-phase portrait occurs after forgetting

the initial conditions by a nonlinear system. The

non-linear system parameters represents the

dynamics of the cardiovascular system.

Kiseleva A., Luzhnov P., Dyachenko A. and Semenov Y.

Rheography and Spirography Signal Analysis by Method of Nonlinear Dynamics.

DOI: 10.5220/0006579301360140

In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIODEVICES 2018), pages 136-140

ISBN: 978-989-758-277-6

2.1 Data Set

The rheography allows to investigate a tissues

hemodynamic in physiological conditions.

Description of an impedance cardiac system are

presented in the paper (Kubicek W.G., Karnegis

J.N., Patterson R.P., 1966). Now are used a

tetrapolar system of electrodes usually. It means that

four electrodes are positioned on a body surface on

one straight line. The pair measuring electrodes is

between pair current electrodes (Shamaev D.M.,

Luzhnov P.V., Iomdina E.N., 2017). Tetrapolar

rheocardiography is a noninvasive method for the

measurement of cardiac output, cardiac index,

systolic time intervals, and other hemodynamic

parameters (Vasilyeva R.M., 2017). Rheographic

signals are depend on many physiological factors:

pulse blood flow, blood pressure (Luzhnov P.V.,

Shamaev D.M., Iomdina E.N. et al., 2017), breath.

Our research was aimed to study the reaction of

the human cardiovascular system to breath

(Semenov Yu.S., Dyachenko A.I., Popova Yu.A., et

al. 2017). In order to analyze the nonlinear system

for isolating its main mathematical dependencies, a

study was conducted based on the rheocardiographic

and spirographic signals. Seven male volunteers

aged 22 to 35 years participated in the study as test

subjects. None of the subjects took medication and

did not suffer from chronic or acute diseases. The

study was performed in 2014 in the Institute of

BioMedical Problems of the Russian Academy of

Sciences. Informed consent from test subjects was

received prior to study. The experiment was adopted

by the Bioethics Committee of the Institute of

BioMedical Problems.

2.2 Pre – processing of Signals

2.2.1 Selection of the Stationary Signal

Sections

The choice of stationary sites during the study is

important, as the stationary condition, as a rule,

limits the sample size for subsequent analysis. We

used without artefact 30 seconds records as the

considering sections of the signal.

2.2.2 Pre - filtration

The selected sites were pre-filtered. A second-order

Butterworth high-pass filter with a cut off frequency

of 0.05 Hz was used to process the

rheocardiographic signals, and then a second order

Butterworth filter with a cut off frequency of 30 Hz

was used. A moving average filter was used (the

window width was 20 samples) to smooth the noise

on the spirographic signal.

2.3 The Nonlinear Filter Implementing

The correct offset must be selected to calculate the

parameters (Palit K., Mukherjee S., Bhattacharya

D.K. 2013). It is known that if the reconstruction

window is too small, then the image of the attractor

turns out to be "compressed", if it is large, then the

image is "stretched and folded". In both cases, it is

necessary to distinguish very small scales to study

the details (Palit K., Mukherjee S., 2011). Usually,

the bias is chosen so that each next reconstructed

vector adds the most information about the attractor

or correlates as little as possible with the previous

one. Researched signals and the filter points are

presented on the figures below:

Figure 1: The filter points – the rheocardiographic and

spirographic signals.

Figure 2: The filter points – the rheocardiographic filter

points.

We set the displacement as suggested in the

paper (Gracia J., Seppa V-P., Pelkonen A., 2017).

2.3.1 Definition of Points Attraction

We defined the moments of the beginnings of an

inspiration and an exhalation for the spirographic

signal. For the analysis allocated six whole cycles of

breath. On the basis of the obtained value, we

constructed pseudo-phase portraits of signals and

determined the main points of attraction on them. It

is the systolic peak, the pulse wave beginning, and

the diastolic wave for a rheocardiographic signal.

The coordinates of the obtaining centres are

presented in Table 1.

Table 1: Coordinates of the reference points centres.

Reference

point

Systolic peak,

Ohm

0,147

0,086

0,042

Pulse wave

beginning,

Ohm

0,120

0,071

0,066

Diastolic wave,

Ohm

0,086

0,058

0,070

2.3.2 Identification of Reference Points by

Analyzing Its Pseudo-phase Portraits

Geometric shapes (cube, sphere, ellipsoid) were

used to identify the local points of the signal,

namely, the data was located in the centres of the

points of attraction of the registered signals (see

figure 3).

Figure 3: Identification of the rheocardiographic signal

reference points.

The size of these shapes was selected from the

consideration of the difference between the

maximum and minimum value of the received

signals. Table 2 shows the main parameters of

geometric shapes (the units correspond to the value).

Table 2: The main parameters of geometric shapes.

Shapes

Systolic

peak

Pulse wave

beginning

Diastolic

wave

Cube, the

edges length,

Ohm

0,162

0,154

0,148

Sphere, the

radius, Ohm

0,140

0,133

0,128

Ellipsoid, the

X1-axis, Ohm

0,018

0,010

0,101

Ellipsoid, the

X2-axis, Ohm

0,105

0,068

0,084

2.3.3 The Error Analysis

We estimated the error in identifying the reference

points of the signal using the coordinates and sizes

of the obtained geometric shapes and performed a

correlation analysis to determine the optimal

geometric shape.

The maximum value of the correlation

coefficient is 0.81 for spherical area. So the most

optimal shape is the sphere for nonlinear filtering

with the purpose of selecting reference points of

rheocardiographic signals.

3 RESULTS

On the basis of the chosen geometric shape, a

contour analysis of the signal section was carried

out. In particular, its main structure elements were

marked. It is the systolic peak, the pulse wave

beginning point, and the diastolic wave for a

rheocardiographic signal.

Figures 4, 5, 6 show a contour analysis of signal

carried out with the help of the obtained method of

nonlinear filtering.

Figure 4: The example of main point selection for the

rheocardiographic signal – the rheocardiographic signal in

phase space.

Figure 5: The example of main point selection for the

rheocardiographic signal – the projection of the

rheocardiographic signal portrait on the X1 and X2 axis.

Figure 6: The example of main point selection for the

rheocardiographic signal – the rheocardiographic signal

with selection of the main points.

4 CONCLUSIONS

In this paper, we considered a new complex method

for analysing biosignals. The received technique is

presented on rheocardiographic signals. The study

showed that analysis of the attractors is the way to

reference points of rheocardiographic signals with

breath identify. For the purpose of the analysis,

stationary signal sections were selected, as well as

the optimal displacement time. A nonlinear filtering

method based on filtering by geometric shapes

(sphere and ellipsoid) in phase space - was proposed

on the basis of the data obtained. A correlation

analysis was performed to evaluate the error of the

filtration.

This work is a continuation of the work of

analyzing the signals of the cardiovascular system

(Aston PJ, Nandi M, 2004; Ming-Rong Ren, Pu

Wang, Hui-Qing Zhang, 2008) and the respiratory

system (Gracia J., Seppa V-P., Pelkonen A.,

Kotaniemi-Syrjanen A. et al., 2017).

In the future, the non-linear filtering method will

serve as a basis for processing signals in real time.

Analysis of pseudo-phase portraits can be used as a

diagnostic method for assessing the state of the

cardiovascular and respiratory systems.

5 CONFLICT OF INTEREST

The authors declare that they have no conflict of

interest.

REFERENCES

Akar S.A., Kara S., Agambayev S., Bilgic V. (2015)

Nonlinear analysis of EEG in major depression with

fractal dimensions. 37th Annual International

Conference of the IEEE on Engineering in Medicine

and Biology Society: 7410–7413.

Aston P.J., Manasi N., Christie M.I., Huang Y.I. (2014)

Comparison of Attractor Reconstruction and HRV

Methods for Analysing Blood Pressure

Data, Computing in Cardiology 41: 437-440.

Aston P.J., Nandi M., Christie M.I. and Huang Y.H.

(2004) Continuous information extraction from blood

pressure data using attractor reconstruction. J. Am.

Coll. 44: 1164-1171.

Charlton P.H., Bonnici T., Tarassenko L., et al. (2017)

Extraction of respiratory signals from the

electrocardiogram and photoplethysmogram:

Technical and physiological determinants.

Physiological Measurement 38(5): 669-690. doi:

10.1088/1361-6579/aa670e.

Cohen M.E., Hudson D.L. (2004) Diagnostic Potential of

Nonlinear Analysis of Biosignals. IEEE Engineering

in Medicine and Biology 26: 5396-5399.

Dhivya R., Premkumar R., Nithyaa A.N. (2015) Real time

secured transmission of biosignal using chaotic

communication system. Engineering and Technology

(ICETECH). doi: 10.1109/ICETECH.2015.7275045.

Diab A., Falou O., Hassan M. et al. (2015) Effect of

filtering on the classification rate of nonlinear analysis

methods applied to uterine EMG signals. 37th Annual

International Conference of the IEEE Engineering in

Medicine and Biology Society (EMBC): 4182-4185.

doi: 10.1109/EMBC.2015.7319316.

Gracia J., Seppa V-P., Pelkonen A., Kotaniemi-Syrjanen

A. et al. (2017) Nonlinear Local Projection Filter for

Impedance Pneumography. European Medical and

Biological Engineering Conference 65: 306-309.

Kubicek W.G., Karnegis J.N., Patterson R.P. (1966)

Development and evaluation of an impedance cardiac

output system. Aerospace medicine 37(12): 1208-

1212.

Luzhnov P.V., Shamaev D.M., Iomdina E.N. et al. (2017)

Using quantitative parameters of ocular blood filling

with transpalpebral rheoophthalmography. IFMBE

Proceedings 65: 37-40. doi: 10.1007/978-981-10-

5122-7_10.

Mendonca A. M., Campilho A. (2006) Segmentation of

retinal blood vessels by combining the detection of

centrelines and morphological reconstruction. IEEE

Trans. Med. Imaging. 25(9): 200–1213.

Ming-rong Ren, Pu Wang, Hui-qing Zhang (2008)

Nonlinear Local Projection Technique for ECG. IEEE

Trans. Biome: 2195-2198.

Morgavi G., et al. (2002) Chaotic Signals: Attractor

Reconstruction and Local Prediction, Proc. 34th

Midwest Symposium on Circuits and Systems 1: 48-51.

Padmanabhan P., Puthusserypady S. (2004) Nonlinear

analysis of EMG signals - A chaotic approach, IEEE

Eng. Med. Biol. 1: 608-611.

Palit K., Mukherjee S., Bhattacharya D.K. (2013) A high

dimensional delay selection for the reconstruction of

proper phase space with cross auto-correlation.

Neurocomputing 113: 49-57.

Palit K., Mukherjee S. (2011) Generalized auto-

correlation and its application in attractor

reconstruction. Bull. Pure Appl. Math. 5(2): 218–230.

Semenov Yu.S., Dyachenko A.I., Popova Yu.A. (2017)

Reaction of the human cardiovascular system to

respiration with additional negative pressure at breath

during 15-hour head-down hypokinesia.

Aviakosmicheskaya i Ekologicheskaya Meditsina

51(3): 22-30. doi: 10.21687/0233-528X-2017-51-3-

22-30.

Shamaev D.M., Luzhnov P.V., Iomdina E.N. (2017)

Modeling of ocular and eyelid pulse blood filling in

diagnosing using transpalpebral rheoophthalmo-

graphy. IFMBE Proceedings 65: 1000-1003. doi:

10.1007/978-981-10-5122-7_250.

Terrill P.I., Wilson S.J., Suresh S., Cooper D.M., Dakin C.

(2008) Investigating parameters participating in the

infant respiratory control system attractor.

Engineering in Medicine and Biology Society. 2120-

2123.

Vasilyeva R.M. (2017) Rheocardiography, an advanced

noninvasive circulatory system test in children and

adults: Progress and prospects. Human Physiology

43(2): 229-239. doi: 10.1134/S0362119717020165.

Velez A.H., Gonzalez-Hernandez H.G., Reyes Guerra, B.

(2014) Attractor reconstruction for plethysmographic

biosignals. 24th International Conference on

Electronics, Communications and Computers

CONIELECOMP: 94-98. doi: 10.1109/

CONIELECOMP.2014.6808574.