STATISTICAL NATURE OF BLOOD PRESSURE AND FLOW WAVES*

STATISTICAL NATURE OF BLOOD PRESSURE AND FLOW WAVES*

By

B. Szucs and E. lVIo"os

Department of Automation. Technical Lniversity. Budapest (Received :1Iarch 18. 1972)

Presented by Prof. Dr. F. CS"i.KI

Introduction

As it -u-as shown earlier, statistiealmethods of control engineering might be properly applied for studying dynamics of the cardiovascular system (CVS). In our previous experiments system analysis of the adrenal circulation was performed on the basis of the slow, third-order pressure and flow waves

[1-5].

Then we turned to the study of dynamics of the fast, first-order pulsatile waves in the circulatory system [6, 7].

Recently, integration of measuring and data processing techniques is aimed at, likely to be convenient

1. for simultaneous and comparative analysis of first-order and third- order blood pressure and flow waves in the same experiment from the point of view of signal structure and system dynamics:

2. for quantitative analysis of the nonlinear properties of CVS:

3. for analysis of pathological changes in haemorrhagic shock from side of the signal structure and system dynamics.

The present paper offers a short sun-ey of studies in point 1 and of thl' probll'm of stationarity of pulsatile waves.

Methods

The experiml'nts were performl'd on 12 dogi3. Chloralose anaesthesia and Flaxedil immobilisation were used with artificial respiration. The experiments were divided into two groups in respect to type of haemorrhage: a) graded hypotension by steps of 20 mmHg; b) standardized haemorrhagic shock.

Four circulatory variables were observed in both cases. The blood pres- sure was measured in the ascending aorta, right iliac artery and right atrium 'with Statham inductive transducers. For measuring the velocity of the blood flo'w in the left iliac artery a \'\7 ard ultrasonic flow meter was used. The analogue electrical signals were recorded by a Hottinger instrument tape-recorder and hy

* Presented at the IMC Symposium on ~lea5urement and Procesi' Identification by Correlation and Spectral Techniques, Bradford. 1973.

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an Alvar polygraph. The mean pressure levels 'were stabilized by a buffer erservoir system. The schematic diagram of experimental set-up is presented in Fig. 1. At each m ~an pressure level an obseryation period of 30 min duration was applied after the transient elicited by the bleeding off.

Based ^UpO:l general properties of th~ measured signals in the frequency domain, every single circulatory variablc was automatically decomposed into three componcnts during playback fro.m the magnetic tape. As it is shown in Fig. 2, the power density spectrum can be divided into the follo,,-ing fre- quency ranges: the pulsatile component above 2 Hz, the respiration waves with frequency of 0.·:1, Hz and the Traube-Hel'ing-Mayer wan's below 0.2 Hz.

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The signal decomposition was performed by means of a Solartron analogue computer according to the flow chart in Fig. 3. The damped respiratory waves were indicatpd both at the first- and third-order components. The primary data reduction 'I'as extended to the determination of auto- and cross-correla- tion functions, variance, trajectories and amplitude spectrum of the pulsatile 'I-avcs, and that of auto- and cross-correlation functions and power density spectrum of the Mayer-'I-aves recorded at several arterial mean pressure levels (normotension; stabilized levels at 1.50, 130, llO, 90 and 70 mmHg; retrans- fusion).

The actual state of CYS was characterized by statistical parameters deriyed from further processing of results of the primary data reduction (about 800 correlation functions, power density spectra, etc.). Various signal components of about 80000 heart cycles were processed in the computations.

The detailed discussion of final statistical parameters, appropriate to draw physiological conclusions too, exceeds the limits of this paper.

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Stationarity in practice

According to the available stochastic mcthods of control engineering the 'wayes selTing as input and/or output signals -- must be stationary:

that is, the basic statistical characteristics of the signals under study mu,s t

not change during the period of registration.

In theoretical statistical investigations the stationarity of the processes is generally supposed. But in practice, the statistical characteristics of signals of technical and biological systems can undergo essential alterations.

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The changes of statistical characteristics (correlation functions, spectra, means and mean square Yalues, etc.) determined for real processes by compu- tation are due not only to the instationarity of the process or signal under -examination but also to the shortness of the observation period (OP). The shortening of OP is accompanied by increasing deviations in the statistical characteristics computed for different sections of a stationary signal with the same OP. It follo'ws that the OP used in practical studies of stationary signals must at least be increased up to the value, where the relative changes of the measured statistical characteristics will be less than the specified relatiye accuracy of the computing deyice. The aboye minimal OP yalue can be called necessary OP.

For strictly stationary signals a simple approximate connection can hc giyen to determine the necessary OP [8]. Some kinds of relative errors of correlation functions (CF),

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xx' computed from square waye signals in compari- son with theoretical CF, qu, are shown in Fig. 4. The change of errors is giyen in dependence of the multiplication of the fundamental freqnellcy (fn;n,' Hz) in the signal and the averaging time constant (T, sec). The lower horizontal curve sho'ws the limit determined hy the specified accuracy (1⁰ Q) of the {;orrelator.

399

On the basis of the desired maximal error, mean absolute or mean square error, the averaging time constant (integration time) can be determined in dependence of the low boundary frequency of the signal to be investigated.

The necessary OP, To should be at lcast double of T.

If an averaging time constant cnsuring the desired accuracy of the computation is applied, the instationarity of the signal during an essentially longer OP than necessary can be quantitatiyely dcscribed by the yalue of the observed changcs in the computed CF and in other statistical characteristics.

In the case of simpler systcms optional statistical characteristics can he chosen for the stationarity test. In the study of complex processes and! or multivariable systems it is more suitable to simultaneously examine the formation of some statistical characteristics. It is to be noted that the sensitiv- ity of stationarity tests is influenced by the averaging method used in forming the statistical parameters. Based upon analysis of the variance of a stochastic signal x(t) 'with zero mean value, the 1- and T-averaging methods, generally applied in practice, will be dcmonstrated.

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processes thc real changes in the mean square yalue can he follo\red more closely and sensitin'ly hy the T-ayeraging method than hy the I-ayeraging onc.

Stational'ity ill CVS

The stationarity of circulatory variables mentioned earlier was examined hy T-ayeraging techniques. As it is seen in Fig. 2, the components of circulatory ,,·aves can he found in a frequency range of sc\-eral decades, and the formation

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observation period). (a) l\Iean yalue changes of the complete signal. (1)) "'.lean square yalue changes of thc pulsatile component. (c)-(f) .-\utocorrelation functions of the pulsatile compo-

ncnt, obtained for different starting times ^tb of computation (T 100 sec, To = 7 min)

BLOOD PRESSURE 401

of the individual components is expected to be influenced by effects originated from different parts of the organism. Therefore the mean value of the circu- latory variables and the variance of the pulsatile ·waves were simultaneously computed and recorded. The formation of the mean value during th~ experi- ments is likely to characterize the stationarity of the AIayer-waves in the first place, and the mean square value to demonstrate the changes in statistical structure of the pulsatile components.

As an example, the diagrams obtained from measuring series of blood flow in normotension are shown in Fig. 5. The mean value of blood flow does

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not essentially change, although the averaging time IS the smallest in this case. But the variance of the pulsatile component has decreased by about 25⁰0

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;:tructure of the pulsatile blood flow signal. Fig. 5 demonstrates the fact;; that the procei's may be regarded as a stationary one (except the last quarter) and that the individual statistical characteristics of the samp signal may change in different manller.

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Similarly, the changes of a given statistical characteristic. derived from different, simultaneously observed signals of the system under test can demon- strate various tendencies as it is shown in Fig. 6. The variance of pulsatile pressures measured in the ascending aorta, iliac artery and right atrium and that of pulsatile flow obtained in the iliac artery exhibits different kinds of changes. In this experiment, the periods marked by shaded areas (Fig. 6) may he regarded as stationary.

As a conclusion, pulsatile pressure and flow waves can be regarded at a good approximation as stationary for periods of ahout 10 min. It is concluded that the statistical characteristics of the circulatory parameters have to he checked during application of the methods of control engineering. The pulsatile processes of the CVS do not seem he invariahly stationary, not even in anaesthe-

tized animal under standard circumstances.

Summary

A complex statistical study of the cardiovascular system in nor mo- and hypotensive states is presented. Signals derived from ascending aorta, iliac artery and right atrium were analysed in anaesthetised dogs during observation periods of 30 min. Circulatory waves decom- posed by frequency analysis were statistically reduced by correlation functions, power density spectra, etc.

A practical view of obtaining the necessary length of observation period and that of stationary test is given.

Pulsatile pressure and flow waves can be regarded at a good approximation as stationary for periods of about 10 min. The pulsatile processes of the CVS are likely not to be invariably stationary, not even in anaesthetized animal under standard circumstances.

References

I. }lo;:-,-os, E., Szucs, B.: Study on dynamic properties of changes in adrenal blood flow and arterial pressure during stochastic peripheral nerve stimulation. Acta Physiol. Acad.

Sci. Hung. Suppl. ad T. 32, 93 (1967).

2. The 34th Annual Conference of the Hungarian Phvsiological Societv. Akademiai Kiad&

Budapest. 1970. p. 123, 126. ~ . ~ .

3. Identification and Apparatus for Statistical Studies. Xauka, Moscow, 1970. p. 80-8'~.

(In Russian).

4. SZ[C5. B .. :110;:-'-05. E.: Circulatory system analysis by a stochastic method using an analogue correlator. Intern. J. Bio-Medical Computing I, 87-102 (1970).

S. Sz[c~. B .• Mo:"os. E .. CS"tKL F.: On a method for identification of the cardiovascular svs- tern. Preprints of the 2nd Prague IFAC Symposium, 2, ]970 pp. 1-7. • 6. }lo:"os. E.. Sz[cs, B.: Statistical nature of pulsatile blood pressure waves studied by correla-

tion functions in dogs. Proc. Il'PS, }Iunich. Vol. IX. p. 4·01, 1971.

7. }Io2\"os. E., Sztcs, B.: Analysis of pulse-synchronous blood pressure waYes "'ith correlation functions. _-\cta Physiol. Acad. Sci. Hung. 39, 252 (1971).

8. Sz[cs. B .. CS"tKI. F.: On evaluation of statistical charaeteristics of stochastic signals. Pre- prinst of Congress BIEKO Y. D-Th-25. 1970.

B6la Sztcs, 1052 Budapest XI., Garami E. t6r 3, Hungary

Emil iVlol'Oos, Experimental Research Department. Semmeh\-eis Medical rniHl'sity, 1082 Budapest, UUoi lit i8/a, Hungary.