Journal of the Autonomic Nervous System, 40 (1992) 63-70 63 © 1992 Elsevier Science Publishers B.V. All rights reserved 0165-1838/92/$05.00

JANS 01300

Three-dimensional analysis of systolic blood pressure and R-R interval: proposal of self-sounding spiral theory

O s a m u S h i m o d a a, Ta t suh ik o K a n o b and T o h r u M o r i o k a c

a Department o f Anesthesiology, Kumamoto Rosai Hospital, Yatsushiro, Japan b Surgical Center, and c Department of Anesthesiology, Kumamoto University Hospital, Kumamoto, Japan

(Received 3 March 1992) (Revision received and accepted 23 April 1992)

Key words: Three-dimensional analysis; Systolic blood pressure; R-R interval; Self-sounding spiral theory

Abstract

Having noted the findings that the frequency spectrum of fluctuation in blood pressure resembles that in R-R interval on ECG, and that both fluctuations are continuous time-related changes, we attempted three-dimensional analysis of blood pressure, R-R interval and time. The serial values in systolic arterial pressure and R-R interval which were simultaneously taken in 17 healthy volunteers (24.8 _+ 3.5 years old) were later analyzed using a personal computer. When dots of systolic pressure and R-R interval were plotted in order in a three-dimensional manner, they depicted spiral movements around an imaginary axis. The magnitude and angle of dot movement was then expressed quantitatively, by assuming the movements as a group of vectors. The vectors were uniformly distributed in four quadrants. The directions of the vector's connections were clockwise in about 75%, while their angles showed no particular tendency. Based on these three-dimensional morphological features of fluctuations in blood pressure and R-R interval, we propose a hypothesis called 'self-sounding spiral theory' for a mechanism preserving the cardiovascular homeostasis.

Introduction

Blood pressure and R-R interval are regulated by autonomic nervous activity in response to changes in the body condition and the environ- ment. When viewed over a short period, blood pressure, even at rest, manifests some periodic fluctuations in addition to beat-to-beat fluctua- tion, respiration-linked fluctuation (Traube-Her- ing wave), and Mayer's wave. Frequency spec-

Correspondence to: O. Shimoda, Department of Anesthesiol- ogy, Kumamoto Rosai Hospital, 1670 Takehara-cho, Yat- sushiro-shi 866, Japan.

trum analysis of the R-R interval at sinus rhythm also disclosed two independent components, i.e. respiratory sinus arrhythmia and Mayer wave re- lated sinus arrythmia [1,5,6]. Noting that both blood pressure and R-R interval show continuous time-related changes, we attempted a three-di- mensional analysis of blood pressure and R-R interval by introducing a factor of time to their relationship. This analysis revealed that the serial plotting of blood pressure and R-R interval de- picts spiral movements. Further analysis, by as- suming these movements as a group of vectors, has led to a hypothesis called 'self-sounding spiral theory' for a biological mechanism preserving the cardiovascular homeostasis.

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Subjects and Methods

The subjects consisted of 17 healthy male vol- unteers with ages ranging from 20 to 40 years (mean: 24.8 _+ 3.5 years). Subjects were randomly selected from hospital staff and medical students. They had no signs of cardiovascular disease or autonomic nervous dysfunction.

Arterial pressure and ECG recordings A 22G Teflon needle was placed into the left

radial artery under local anesthesia, and was con- nected to a pressure transducer (P231D, Gould, Germany). The arterial pressure and Lead I! ECG were monitored on a cardioscope (Life- scope 6, Nihon Kohden, Japan) with the subjects in the supine position. A data recorder (R71, TEAC, Japan) was set so that analogue waves of arterial pressure and lead II ECG were stored whenever needed for later computer analysis, by connecting the output terminals of the cardio- scope and the input terminals of the recorder.

The present experiment was conducted in a quiet room where the temperature was main- tained at 23-26°C. Before starting the experi- ment, each subject had been instructed to per- form regular, smooth breathing with their eyes closed. The subjects were allowed at least 5 min to adjust themselves to the environment. After confirming arterial pressure and heart rate to be stable, the arterial pressure and lead II ECG were recorded simultaneously for 2 min.

Analysis of arterial pressure and R-R intereal The data of arterial pressure waves stored in

the data recorder were imputed via an A / D converter (AB98-05, Adtec System Science, Japan) into a personal computer (PC9801-VX2, NEC, Japan) at a sampling time of 50 ms. The serial changes of blood pressure were expressed digitally at a pressure resolution of 0.125 mmHg.

For measurement of R-R interval, the recorded ECG waves were first imputed into waveform rectifier. Using a band-pass (15-20 Hz) filter, only R waves were passed into a slicer circuit, from which rectangular waves (200 ms, 0.75 V) coinciding with the rising portion of the R wave were obtained. The rectangular waves were then

imputed into a personal computer to analyze the R-R interval (interval between two successive sig- nals) at a time resolution of 0.5 ms.

We confirmed that systolic blood pressure (SBP) were paired with the R-R intervals deter- mined at the same phase, and without allowing a time lag between them. They were simultaneously imputed into two different channels of the per- sonal computer.

Three-dimensional analysis Three-dimensional analysis of SBP and R-R

interval at the same phase was carried out on the personal computer by adding a time factor to their mutual relationships.

First, SBP and R-R interval were plotted on a two-dimensional plane, with the SBP on the Y- axis and R-R interval on the X-axis. Next, each dot was moved one point down and to the right, according to the time series. Each two successive dots were connected with a line. To allow visual- ization of linear changes, changes in SBP were projected onto the right vertical plane, and changes in the R-R interval were projected onto the lower horizontal plane.

Analysis of vector components Assuming the transfer of dots as a group of

vectors, we at tempted quantitative analysis. Be- cause the magnitude of SBP differed from that of the R-R interval, we amplified SBP so that abso- lute value of the mean SBP would become almost equal to that of the mean R-R interval. This equalization was done in each of the 17 subjects. Therefore the amplification rate varied in each subject. Using the amplified SBP and the corre- sponding R-R interval, the vector components were calculated as follows.

First, variances in SBP and the corresponding R-R interval were calculated using the following equations:

ASBPi = SBPi + 1 - SBPi

ARRi = RRi + l - RRi

where ASBPi denotes the variance in the number

' i ' SBP, and ARRi indicated the variance in the number ' i ' R-R interval.

With the R-R interval on the X-axis, SBP on the Y-axis and the positive X-axis direction as 0 degree, we can obtain the magnitude of dot m o v e m e n t (i.e. v ec t o r ' s size) us ing the Pythagorean theorem, and the angle of the dot movement (i.e. angle of the vector) using the inverse tangent:

Si = SQR( ASBPi 2 + ARRi 2)

Ai = (a rcTAN( ZlSBPi/A RRi ) ) × 180/rr

where Si denotes the size of the number ' i ' vec- tor, SQR denotes the square root, Ai indicates the angle of the number ' i ' vector (expressed in units of 360 degrees) and arcTAN indicates the inverse tangent.

Using the above-mentioned equations, we cal- culated the size and angle of individual vectors. Angles of vectors were divided into 18 20-degree ranges. For each range, the size of vector (i.e. the magnitude of dot movement) was totalled. The percentage of the individual range's total vector size in the sum total for all ranges was then calculated.

R - R i n t e r v a l

500 600 700 800 900 1000 1 1 0 0 m s e c . . , , , , , . , . ' . ' , ,

1 2 ' " . • .

' . . . g . "

~ 11 " '- . .

Time ~ ~ 1 ~ N

Fig. 1. Three-dimensional analysis of a healthy 21 year old man. The abscissa shows R-R interval, and the ordinate shows SBP. Two-dimensional plotting was done on the frontal plane, and dots were transferred directly downwards by 1 point according to the time series and linked. From the three-di- mensionally displayed line, only changes in R-R interval were projected on the lower horizontal plane and those in SBP on

the right vertical plane.

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Analysis of two successive vector's angle We then calculated the angle formed by two

successive vectors (the inside angle if the two vectors showed a connection in the clockwise direction, and the outside angle if the two vectors showed a connection in the counter-clockwise direction). If the angle is greater than 0 degree and smaller than 180 degrees, it means a connec- tion in the clockwise direction. If the angle is greater than 180 degrees and smaller than 360 degrees, it means a connection in the counter- clockwise direction. The degrees 0 and 360 indi- cate a line. The degree 180 indicates a turn. The angles were divided into eight 45-degree ranges. The percentage of each range's number of vec- tors in all vectors was calculated.

Results

Figures 1, 2 and 3 show three-dimensional analysis of SBP and R-R interval, an analysis of vector components and an analysis of two succes- sive vector 's angles respectively, in representative adult male who was in the supine position. The three-dimensional analysis revealed a movement which depicted coils around as imaginary axis (Fig. 1). The analysis of vector components dis- closed a distribution of components in all four quadrants, without showing any shift in particular quadrants. The vector components distributed symmetrically along X and Y axes, although the symmetry was not complete (Fig. 2).

Table I shows the results of vector components analysis for all subjects. The vector size decreased as the angle increased from 0 to 90 degrees. The size increased as the angle increased from 90 to 180 degrees. It decreased as the angle increased from 180 to 270 degrees. The vector size then increased as the angle increased from 270 to 360 degrees. The vector size for angle ranges 0-20, 160-180, 180-200 and 340-360 was about 3 - 4 times that for the ranges 80-100 and 260-280.

In the analysis of two successive vectors' an- gles, a comparatively slight clockwise rotation (90-135 degrees) was the most frequent (39.1%) of all pairs of vectors. Although counter-clock- wise rotation (180-360 degrees) was also ob-

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, , , , , , , , , , , . , , , , . , , , , , , , , , , , , . , , , , , , 0 90 180 2 7 0 360

d e g r e e

range o f d e g r e e : percentage

0 < 20 < ~0 < 60 < 8o <

100 < 120 < 1~.0 < 16o <

< 20 : 12.11 180 < < u,O : 5 .86 200 _K < 60 : 1 .64 220 < 80 : 1 .311 2110 < < I00 : 1 .53 260 < < 120 : 3 . 7 6 2 8 0 <

< 140 : /4 .21 3 0 0 < < 1 6 0 : a . 7 3 3 2 0 < < 180 : 1 3 . 0 3 3 ~ 0 _<5

r a n g e o f d e g r e e : p e r c e n t a g e

< 2 0 0 : 8 . 6 4 < 2 2 0 : 6 . 2 1 < 2~40 : 7 . I 1 < 2 6 0 : O. 97 < 2 8 0 : 3 . 8 5 < 300 : 3 . 8 1 < 3 2 0 : 3 . 1 7

< 3 ~ 0 : ~. 83

< 360 : 13.19

Fig. 2. Vector component analysis in Fig. 1. The angle and size of each vector was calculated and arranged with the original point as the center and the positive X direction as 0 degree (upper left figure) expanded between 0 and 360 degrees (upper right). The angles were divided into 18 20-degree ranges. For each range, the size of vector was totalled. The percentage of the individual

range's total vector size in the sum total for all ranges was calculated (lower).

s e r v e d in 2 0 . 7 % . T h u s , t h e r o t a t i o n o f v e c t o r s w as

n o t a lways c lockwi se a n d t w o succes s ive v e c t o r s '

a n g l e s was n o t r e g u l a r (Fig. 3).

T a b l e II s h o w s t h e r e s u l t s o f t h e ana ly s i s o f

two succes s ive v e c t o r s ' a n g l e in all sub jec t s .

C l o c k w i s e r o t a t i o n ( 0 - 1 8 0 d e g r e e s ) w a s o b s e r v e d

in 7 4 . 1 4 % o f all p a i r s o f v e c t o r s .

180

o

: % b o .:: :~,::. ;:9:: : i ~ ~:i :: ~e~

360 degree

range of degree : f r e q u e n c y 0 < < 115 : 10

4 5 ! < 9 0 : 75 9 0 ~ < 1 3 5 : a 3

135 ~ < 180 18 1 8 0 < < 2 2 5 : 13 225 <5 < 2 7 0 : 2 270 ~ < 315 : 5 3 1 5 ~ < 3 6 0 : 4 0 , 1 8 0 , 3 6 0 : 0

: p e r c e n t a g e : 9 . 1 : 1 3 . 6 : 3 9 . 1

1 6 . 4 : 11.8 : 1.8

~.5 : 3.6

0.0

Fig. 3. Two successive vector analyses in Fig. 1. The angle formed by two successive vectors was determined. The. angle was plotted against time. The dots were linked by broken lines (upper). The angles were divided into eight 45-degree ranges. The percentage of the number of individual range's vectors in

all vectors was calculated (lower).

TABLE 1

Analysis of cector components

Angle (degree) Percentage

0 <, < 20 9.58-+4.32(0.76) 20 <, < 40 5.27_+2.57(0.45) 40_<, < 60 3.78+ 2.45(0.43) 60 <, < 80 3.67_+ 2.84(0.50) 80 <, < 100 3.00-+ 2.51(0.44)

100 <, < 120 3.84 + 2.06(0.36) 120 <, < 140 4.23_+2.16(0.38) 140 <, < 160 5.82+3.30(0.58) 160 <, < 180 8.22+4.79(0.85) 180 <, < 200 7.28+4.26(0.75) 200 <, < 220 6.87_+3.01(0.53) 220 <, < 24(1 5.08 + 2.74(0.48) 240 <, < 260 4.34_+ 2.64(0.47) 260 <, < 280 3.78+3.19(0.56) 280 <, < 300 3.03_+ 1.83(0.32) 300 <, < 320 3.87 + 2.49(0.44) 320 _<, < 340 5.98_+3.11(0.55) 340 _<, < 360 12.18_+5.59(0.99)

Mean + S.D. (S.E.)

D i s c u s s i o n

C h r o n o l o g i c a l ana ly s i s o f t h e r e l a t i o n s h i p be -

t w e e n S B P a n d R - R i n t e r n a l , w h i c h was a t -

t e m p t e d in t h e p r e s e n t s tudy , m a y c o n t r i b u t e to

t h e c l a r i f i c a t i o n o f t h e h o m e o s t a s i s p r e s e r v i n g

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TABLE II

Analysis of two successive vectors' angle

Angle (degree) Percentage

0 < , < 45 14.47 + 5.66 (1.05) 45 < , < 90 22.31+ 7.79 (1.44) 90 < , < 135 21.16+7.23 (1.34)

135 < , < 180 16.20+ 6.91 (1.28) 180 < , < 225 8.34+3.90 (0.72) 225 < , < 270 5.51 + 3.50 (0.65) 270 < , < 315 4.09+3.23 (0.60) 315 < , < 360 6.14+2.71 (0.50) 0, 180, and 360 1.31 +_0.96 (0.18)

Mean _+ S.D. (S.E.)

mechanism of the cardiovascular system, al- though this approach involves a few unsolved problems.

With this approach, the time of SBP and R-R interval measurements is important. It is neces- sary to define optimum pairs of SBP and R-R interval (i.e. optimum times of SBP and R-R interval measurements to be paired for this analy- sis).

Short-term fluctuations in the SBP and R-R interval are known to involve autonomic nerve activity, physical and physiological features of the heart and thorax, and other factors. Previous spectral analyses of these fluctuations revealed three components: below 0.05 Hz (low frequency fluctuation; LFF), around 0.1 Hz (mid frequency fluctuation; MFF) and around 0.25 Hz (high fre- quency fluctuation; HFF) [1,5,6]. Both the fluctu- ations in the SBP and those in the R-R interval represent autonomic reflexes (e.g. reflex of the pressure receptors). They are closely related to each other [3,4]. To analyze the relationship be- tween fluctuations in the SBP and R-R interval, De Boer et al. [2] conducted cross-spectral analy- sis by which MFF and HFF of the SBP and R-R interval were isolated and analyzed. In that study, the MFF of the SBP appeared earlier (by about two beats) than that of the R-R interval, while the HFF of the SBP appeared simultaneously with that of the R-R interval.

Bearing in mind a previous report that the HFF (around 0.25 Hz) represents respiration-re- lated fluctuation that is primarily caused by phys-'

ical factors related to the movement of the thorax [3], it is easy for us to understand the report of De Boer et al. that the HFF of the SBP appeared simultaneously with that of the R-R interval. However, fluctuations in the SBP and R-R inter- val also serve as a secondary stimulus to the reflex system and consequently affect the SBP and R-R internal with some time lag. Therefore, there is some time lag in the interactions between around 0.25 Hz fluctuations in the SBP and those in the R-R interval.

To make the argument simpler, let us assume SBP fluctuations as a × sin(0), and R-R interval fluctuations as /3 × sin(0 + d). If the time lag (d) is 90 degrees, the dots of SBP and R-R interval depicts a clockwise circular rotation. If the time lag is - 9 0 degrees, they depict a Counter-clock- wise circular rotation. If the time lag is 0 or 180 degrees, they depict an oblique linear movement. The angle formed by two successive vectors, which is calculated by assuming dot transfer as vectors, agrees with the time lag (d) at each time point.

In the present study, clockwise rotation was observed for a majority of the pairs of vectors, although counter-clockwise rotation was also ob- served in about 24.08%. The angle formed by two successive vectors was not constant but changed. If this result is simulated on the above-mentioned sine curve, the time lag seems to fluctuate.

In practice, the fluctuations in the SBP and R-R interval are not simple but involve multiple components. Each component involves some time lag. We think it appropriate to regard the fluctua- tions in the angle formed by two successive vec- tors as representing an accumulation of the time lag of the several influential factors.

Because the fluctuations in the SBP and R-R interval involve many frequency components and because the phase varies between individual com- ponents, it is difficult to designate an appropriate pair of SBP and R-R interval (i.e. appropriate times of SBP and R-R interval measurements to be paired). For this reason, we tentatively paired SBP with R-R interval determined at the same phase, with the aim of exploring the relationship between the SBP and R-R interval.

In the present study, the sampling time for arterial blood pressure waves was 50 ms. This

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sampling time may appear to be too short. How- ever, because approximately similar results were obtained at a sampling time of 25 ms, it is un- likely that the sampling time adopted in the pre- sent study was inappropriate.

In the analysis of vector components, we am- plified the SBP to match the mean R-R interval. Because the SBP and R-R interval are expressed in different units (mmHg and ms, respectively), it is necessary to make this adjustment for the pur- pose of presenting the results in a clearer form. However, in analyzing the size and angle of indi- vidual vectors, the amplification rate plays an important role. The angle formed by two succes- sive vectors is also affected by the amplification rate. On the other hand, the direction of connec- tion between two successive vectors is not af- fected by it.

When the relationship between the SBP and R-R interval was three-dimensionally analyzed, incorporating the factor of time, the dots de- picted a spiral movement around an imaginary axis. From this finding, we propose a 'self-sound- ing spiral hypothesis' about the homeostasis in the cardiovascular system. This homeostasis-pre- serving mechanism may serve for other biological functions of the living body also.

In order that homeostasis can be maintained, it is necessary for the living body to detect a difference between the actual state and the ideal state at a given time point. However, it is difficult for the living body to respond to constant stimuli or parameters because the receptors for them tend to reduce their sensitivity with time. For this reason, it is likely that the body checks for changes in these stimuli or parameters by intentionally producing minute qualitative changes. In other words, it is likely that the body detects a depar- ture from the ideal state be analyzing the feed- back information after inducing changes in the stimuli to the reflex mechanism. By repeating such a check, the body can maintain homeostasis. This regulation also allows the body to avoid excessive changes when the homeostasis needs to be adjusted in response to the stimuli from outer and inner environments.

This method of regulation is reasonable and allows minute adjustment. A similar regulation

may be found in the other mechanisms of home- ostasis equipped with a feedback system. For example, we may detect a spiral phenomenon in the relationship between blood glucose level and insulin secretion if appropriate designation of the amplification rate and continuous measurement is possible.

Spiral movement is composed of vector com- ponents (i.e. angles and quantity of movement). As the vectors rotate, the imaginary center is shifted slightly. The imaginary central axis seems to represent a tendency of change in the home- ostasis.

In the present study, the vector size (i.e. the magnitude of dot movement) tended to be higher along the X-axis and Y-axis when it was analyzed for each angle range. However, the size was ap- proximately the same in each of the four quad- rants. Such a well-balanced distribution of vector components is probably explained by the fact that healthy adults in the supine position were exam- ined in this study. If homeostasis is lost, the distribution of vector components will be altered remarkably. This approach seems to have the potential of allowing the development of a new monitoring system which can detect imbalance in the cardiovascular regulation.

Conclusion

Cardiovascular regulation could be visualized by serial analysis of the relationship between the SBP and R-R interval. The self-sounding spiral theory, which we propose from the results of this study, will contribute to clarifying not only the homeostatic mechanism of the cardiovascular sys- tem but also various regulatory mechanisms of the living body.

Acknowledgements

We express deep thanks to Mr. Sanzo Kushiyama, Kumamoto General Medical Welfare School, for his cooperation in the production of the computer program in this study.

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