Download Poincare Plot of Heart Rate Variability Allows

Clinical Science (1996) 91, 201-208 (Printed in Great Britain)
20 I
Poincare plot of heart rate variability allows quantitative
display of parasympathetic nervous activity in humans
Peter Walter KAMEN, Henry KRUM* and Andrew Maxwell TONKIN
Departments of Cardiology and *Clinical Pharmacology, Austin and Repatriation Medical Centre
(Austin Campus), Melbourne, Australia
(Received 24 October 1995/2 April 1996; accepted II April 1996)
1. Time domain summary statistics and frequency
domain parameters can be used to measure heart rate
variability. More recently, qualitative methods including the Poincarb plot have been used to evaluate
heart rate variability. The aim of this study was to
validate a novel method of quantitative analysis of
the PoincarC plot using conventional statistical
techniques.
2. Beat-to-beat heart rate variability was measured
over a relatively short period of time (1&20 min) in
12 healthy subjects aged between 20 and 40 years
(mean 30 f 7 years) during (i) supine rest, (ii) head-up
tilt (sympathetic activation, parasympathetic nervous
system activity withdrawal), (iii) intravenous infusion
of atropine (parasympathetic nervous system activity
withdrawal), and (iv) after overnight administration
of low-dose transdermal scopolamine (parasympathetic nervous system augmentation).
3. The ‘width’ of the PoincarC plot, as quantified by
SD delta R-R (the difference between successive R-R
intervals), was determined at rest (median 48.9, quartile range 20ms) and found to be significantly
reduced during tilt (median 19.1, quartile range
13.7 ms, P< 0.01) and atropine administration
(median 7.1, quartile range 5.7ms, P<O.Ol) and
increased by scopolamine (median 79.3, quartile
range 33 ms, P< 0.01). Furthermore, log variance of
delta R-R intervals correlated almost perfectly with
log high-frequency (0.15-0.4Hz) power (r=0.99,
P< 0.01).
4. These findings strongly suggest that the ‘width’ of
the PoincarC plot is a measure of parasympathetic
nervous system activity. The Poincarb plot is therefore a quantitative visual tool which can be applied to
the analysis of R-R interval data gathered over
relatively short time periods.
INTRODUCTION
Sympathetic-parasympathetic interactions have
been well studied and their importance established
in a number of cardiovascular diseases. Such situations include patients after myocardial infarction
[l], patients at risk of sudden cardiac death [2, 31
and patients with heart failure [4,51, in all of which
increased sympathetic and decreased parasympathetic nervous system activity is common. Various
methods have been used to attempt to quantify
these autonomic influences. Recently, there has been
considerable interest in the measurement of heart
rate variability (HRV) as one such approach and a
number of time and frequency domain indices have
been used to quantify this [6].
Another new method of HRV analysis is the
PoincarC plot, which is a ‘scatterplot’ (return map)
of current cardiac cycle length (the R-R interval on
the ECG) against the preceding R-R interval [7].
The PoincarC plot allows a real time display of
interbeat intervals at the time the patient is being
monitored and can thus provide a visual measure of
parasympathetic nervous system activity. In addition, this method permits immediate recognition of
ectopic beats [S, 91 or artefact which may otherwise
go unobserved [lo, 111.
We have developed a method of quantifying the
Poincart plot which is an extension of a method
developed by Malik et al. [l2] who used the width
of the main peak of the frequency distribution curve
to quantify noisy HRV time series. Our technique of
quantifying the pattern of the PoincarC plot uses
statistical measures of variance of both R-R and
delta R-R histograms. These may provide more
robust measures of HRV in the presence of a low
level of beat recognition error and recording artefact
than more conventional techniques [12).
In this study we sought to validate this new
approach to quantitative assessment of the PoincarC
plot by analysis in healthy subjects of the effects of
standard perturbations of autonomic function.
Moreover, we tried to simplify the assessment of
HRV by collecting R-R interval data over a relatively short time (10-2Omin). Most recent research
has used HRV data acquired over a 24h period
during prolonged ambulatory (‘Holter’) monitoring
of the ECG. This approach has attendant logistic
problems including non-stationarity of the HRV
time series.
Key Words: autonomic nervous system, heart rate variability, parasympathetic nervous system, Poincark plot.
Abbreviations: HF, high frequency; HRV, heart rate variability; LF, low frequency; rMSSD, root mean-squared successive difference.
Correspondence: Dr Peter W. Kamen, Department of Cardiology, ARMC (Austin Campus), Heidelberg, Victoria 3084, Australia.
P. W. Kamen et al.
202
METHODS
. .
14004
Subjects
Twelve healthy subjects (seven males and five
females) aged between 20 and 40 years (mean
30.2 i-7.2) years were studied. Subjects were
included in the study if they were in sinus rhythm,
did not smoke, had no known cardiovascular
abnormalities and were not taking any medications.
All had provided fully informed consent. Ethical
approval was granted by the Austin Hospital Committee of Ethics in Human Research.
f
6001
4001
200
artefact
I
,
,
,”:
,;;
artefact
,
,
200
400
600
800
1000 I200
R-R, interval (ms)
200
400
600
800
I
,
,
1400
1600
1400
1600
Study design
Study subjects were instructed to have a light
breakfast and not consume alcohol or caffeinated
beverages for 12h before the study. All studies were
performed at the same time of day with the subjects
breathing spontaneously and remaining undisturbed
in a quiet, temperature-controlled room. Although
respiratory rate and amplitude are important modulators of HRV [13] we did not control respiration
in our subjects because all phases of the study were
conducted in the resting state where respiration
frequency and amplitude should remain essentially
unchanged and within the range of 16-18 breaths
per min. An intravenous cannula was inserted into
an antecubital vein and subjects then rested for
20 min before commencement of data collection. A
total of 1024 data points (R-R intervals) were
collected for each study segment and used to generate the PoincarC plot. Accordingly, data epochs
varied from approximately 10 to 20min.
The following sequential protocol of autonomic
perturbations was performed. At least 20 min was
allowed between each phase of the study to permit
the return of heart rate to baseline. The study
phases were not randomized.
Baseline study. All baseline studies were conducted in subjects in the post-absorptive state after
resting for 10min in the supine position in a quiet
environment.
Seventy degree head-up tilt. Subjects were tilted to
70” on a motorized table until 1024 data points
were collected. This manoeuvre increases sympathetic and decreases parasympathetic nervous system
activity [14, 151. Collection of HRV data commenced after 5min of tilt to permit the heart rate to
stabilize in the new position.
Atropine infusion. Atropine sulphate, 1.2mg, was
added to 50ml of 5% intravenous dextrose and
infused at a rate of 0.12 mg/min for 5 min and then
at a rate of 0.024mg/min until completion of this
phase of the study. This dose regimen markedly
decreases parasympathetic nervous system activity
[16]. Data collection began 10 min after commencement of the infusion.
Transdermal scopolamine. A low-dose transdermal
scopolamine patch (hyoscine 1.5 mg) was applied
:
:
y
200
1000
1200
R-R, interval (ms)
Fig 1. PoincarC plots. (a) Poincare plot before filtering of ‘noisy’ R-R
interval data showing a ’central cluster’ with outlying data points due to
artefact. (b) Poincare plot after ‘adequate’ filtering. The ‘central cluster’ has
been preserved and the outlying data points have been removed.
overnight to an undamaged hair-free area of skin
behind the ear 1 week after the above studies. The
patch remained in situ for the duration of this
period of the study. Low-dose transdermal scopolamine increases parasympathetic nervous activity
~171.
Data acquisition
R-R intervals were collected using an AMLAB
data acquisition workstation (Associative Measurements, Sydney) with a program that triggers on the
leading edge of the R-wave of the ECG. The
analogue ECG signal was digitized at a sampling
rate of 2kHz. The system was calibrated on a
digital and analogue pulse generator to an accuracy
of + l m s and found to measure R-R intervals to
within k l m s . The Poincark plot and tachogram
were constructed on line using raw data and examined for artefact and ectopic activity.
Technical aspects of the Poincar6 plot
The PoincarC plot is a ‘scatterplot’ (or ‘return
map’) of the current R-R interval against the R-R
interval immediately preceding it, as illustrated in
Fig. 1.
Poincare plot and autonomic perturbations
The Poincark plot can provide a display of
overall as well as beat-to-beat variability [181. This
is because HRV is graphically displayed as a pattern
of points which lends itself to visual analysis more
readily than summary statistical measures such as
the root mean-squared successive difference
(r-MSSD).
Histograms of R-R intervals and delta R-R intervals can be quantified by the analysis of variance of
the respective data [4]. The SD of the R-R interval
histogram relates to the variance of the data of the
Poincark plot projected onto the x-axis. The delta
R-R interval is the difference between successive RR intervals. Thus the SD delta R-R can be used to
quantify the ‘width‘ of the Poincark plot as it relates
to the variance of the distribution of data points
around the line of identity. Mathematical details are
given in the Appendix.
Filtering technique
Artefact and occasional ectopic beats occur in
almost all HRV studies [12]. To reduce the effect of
such ‘noise’, filters can be used to remove selected
portions of the R-R interval data. We identified
artefact or ectopic beats from the original ECG and
related them to the pattern of distribution of points
on the Poincark plot [8] as illustrated in Fig l(a).
The outlying points were then replaced with interpolative R-R interval data using a cubic spline
algorithm 119, 201 (Software for Science, Engineering and Industry for Microsoft Quickbasic 4.xIPCQB-006 Version 7; Quinn-Curtiss, Needham, MA,
USA.). We then examined the filtered Poincark plot
for evidence of distortion of the pattern induced by
excessive filtering and for possible persistence of
outlying points due to inadequate filtering. Figure 1
(b) illustrates the effect of filtering on the Poincark
plot.
Power spectral analysis
The time series was created as a function of
heartbeats and the resulting interval tachogram is
thus a series of R-R intervals plotted as a function
of the interval number, as detailed by De Boer et al.
[21]. Since the interval tachogram is a function of
the interval number rather than time, when used to
compute the fast Fourier transformation the result
in the abscissa is expressed in cycles per interval
rather than Hz. When the total variability is small
in comparison with the mean heart rate, only a
small error arises and the calculated interval spectrum is considered as a true frequency spectrum.
The spectral units must then be divided by the
mean R-R interval in order to obtain a result
expressed in Hz. After detrending and filtering the
raw R-R interval data, an IBM PC 486 with a
commercial software package (Software for Science,
Engineering and Industry for Microsoft Quickbasic
4.xIPC-QB-006 Version 7; Quinn-Curtiss) was used
203
to compute the fast Fourier transformation. Power
spectral measures of R-R variability were then
computed by integrating over their frequency intervals. Two main components of the power spectra of
HRV were identified: a high-frequency (HF) component (from 0.15 to 0.4Hz) and a low-frequency (LF)
component (from 0.01 to 0.15Hz). The total power
(from 0.01 to 0.4Hz) was also calculated.
Statistics
Variables with a normal distribution (age, heart
rate) are presented as mean+SD and skewed data
are expressed as median and quartile range (the
value of the 75th percentile minus the value of the
25th percentile) where 50% of the data points fall
within this range. We used the non-parametric
Friedman repeated-measures analysis of variance on
ranks as all HRV variables showed a skewed distribution. Consequently, Pearson’s correlation coefficient and the corresponding tests of significance
were used to assess the relation between logtransformed frequency and time domain variables.
R-R interval histograms were assessed for normality
by the Kolmogorov-Smirnov method. A two-tailed
P < 0.05 was considered significant.
RESULTS
Results are summarized in Table 1.
HRV in the baseline study
The Poincark plot of all subiects displayed a
clustering of data-points as illustiated in Fig. 2(a),
characterized by SDR-R of 55-142ms, median 69.3
(19.4)ms and SD delta R-R of 27-123ms, median
48.9 (20)ms.
HRV during head-up tilt
All subjects displayed a marked reduction in
variance of delta R-R intervals compared with
baseline, as illustrated in Fig. 2(b). Heart rate
increased significantly during tilting from 60.9 & 9.7
to 80.9f 12.4 beats/min P<O.OOOl). The SDRR
decreased by 22% to 54.4 (24.1)ms (P<O.Ol), but
the coefficient of variation of R-R intervals
remained unchanged compared with baseline values.
The SD delta R-R and coefficient of variation of
delta R-R intervals between baseline and tilt were
reduced by 61% and 51% respectively (P<O.Ol for
both).
Considering analyses in the frequency domain,
LF, H F and total power decreased by 31%, 82%
and 39% respectively (all P <0.05).
P. W. Kamen et al.
204
Table 1. Heart rate and HRV parameters from subjects exposed to various autonomic perturbations. All values are
presented as median (quartile range). Abbreviations: Coeff, coefficient of variation; HF, high-frequency power; LF, low-frequency
power; pNN50, proportion of R-R intervals more than 50ms different; NS. not significant. Statistical significance: *P < 0.05,
**P < 0.01,
Heart rate variability
Time domain
SDR-R (mr)
Coeff R-R
SDAR-R (ms)
Coeff AR-R
pNN50
SDR-R/SDAR-R
Frequency domain
LF (msl)
HF (mrl)
Total power (rnsl)
Baseline
70” tilt
Atropine
Scopolamine
69.3 (19.4)
7.6 (1.3)
48.9 (10)
5.3(2.5)
19.1 (21.8)
I .34 (0.3)
54.4 (24. I)**
7.3 (2.2) (NS)
19.1 (13.7)**
1.6 (I .5)**
I .8 (6.5)**
1.61 (I .O)**
33.6 (8.6)**
4.3 (1.3)**
7.1 (5.7)**
I .I (0.7)**
0.5 (0.3)**
5.4 (l.l)**
90.7 (35.3)**
8. I (I.8) (NS)
79.3 (33.0)**
7.6 (1.7)**
48.6 (20)**
1.1 (0.1) (NS)
858 (695)
303 (412)
1056 (961)
588 (703)*
54 (91)*
641 (8l8)*
142 (150)**
5.0 (7.3)*
147 (IS)**
1477 (134l)(NS)
685 (734)*
2287 (2160)*
HRV during atropine infusion
Heart rate increased significantly in all subjects,
from 60.9 & 9.7 to 83.6 f9.4 beats/min (P < 0.01).
Atropine administration resulted in a 57% reduction
in SDRR to 33.6 (8.6)ms and an 87% reduction in
SD delta R-R to 7.1 (5.7)ms ( P ~ 0 . 0 1for both)
compared with baseline measurements. These
changes were associated with a marked reduction in
‘width’ of the Poincark plot, as illustrated in Fig.
2(c). The reductions in coefficient of variation of RR and delta R-R intervals were also highly significant (P t0.01).
Both LF and H F power decreased; LF power
from 858 (695) to 142 (150)ms’ (P<O.Ol) and H F
power from 303 (412) to 5.0 (7.3)ms2 (P<0.05).
and increases with scopolamine, consistent with
changes in parasympathetic activity.
Correlations between time and frequency domain
parameters
Using all the HRV data, we found an almost
perfect correlation between log H F power and log
variance of delta R-R intervals (r=0.99, P<O.OOOl).
This is illustrated in Fig. 3. Log total power was
also strongly correlated with both log variance of
R-R (r=0.98, P<O.OOOl) and delta R-R intervals
( r =0.95, P <0.0001). This has been reported previously [22, 231 and is supportive of experimental
evidence for the mathematical relationship between
time and frequency domain HRV parameters as
described by Parseval’s theorem. Details appear in
the Appendix.
HRV during lowdose transdermal scopolamine
The scopolamine patch was well tolerated by all
patients, none of whom voluntarily reported adverse
side effects such as dry mouth or drowsiness.
The reduction in heart rate from the baseline
value of 60.5k9.7 to 56.7k8.3 beats/min was not
statistically significant, possibly because of the small
sample size. SDR-R increased by 31% (P<O.Ol) and
SD delta R-R increased by 62% (P<O.Ol) with
transdermal scopolamine. This was reflected by a
marked increase in the ‘width’ of the Poincare plot,
as illustrated in Fig. 2(4. The coefficient of variation
of delta R-R intervals increased by 43% (P<O.Ol),
indicating that the increase in HRV was not simply
due to the reduction in heart rate.
Analysis of the effect of transdermal scopolamine
on measures in the frequency domain paralleled
effects of the drug on time domain parameters.
High-frequency power increased by 126% (P <0.05),
consistent with an increase in parasympathetic nervous system activity.
In summary, the results show that the ‘width‘ of
the Poincart plot, as quantified by SD delta R-R,
decreases from baseline with tilting and atropine
DISCUSSlON
Time series methodologies applied to the analysis
of HRV have mainly been standard time [24] and
frequency [25] domain techniques. The potential for
use of serial correlation techniques [26, 271 has not
been fully explored. The present study strongly
suggests that short-term analysis of HRV using the
Poincark plot and related histograms provides an
accurate method with which to quantify autonomic
activity. We have demonstrated that the ‘cluster’
Poincark pattern can be quantified with conventional statistical methods that correlate closely with
time and frequency domain parameters used to
quantify parasympathetic nervous system activity in
healthy subjects [lS, 16, 281. More complex, nonlinear mathematical methods may be necessary to
accurately quantify other pattern types seen in
patients with cardiac disease [4, 291.
Bigger et al. [22] have previously shown a strong
correlation between H F power and the r-MSSD of
normal R-R intervals. Although SD delta R-R is
mathematically equivalent to r-MSSD (see Appendix), only the delta R-R interval can be used to
Poincare plot and autonomic perturbations
//
500
1W
205
1500
R-R, interval (ms)
0
Q
/
9s
%
/
‘
D
*4
’*., 9@
%
%
Q
A M interval
R-R interval (ms)
R-R interval
histogram
histogram
AR-R interval
histogram
*/
/
R-R. interval (ms)
O 600 800 loo0 I200 1400
R-R interval
histogram
1500,
I
500
MO
1000
R-R, interval (ins)
80
60
40
20
AR-R interval
histogram
0
R-R interval
histogram
histogram
R-R interval
histogram
Fig. 1. Characteristic Poincar6 plots generated by a 36year old female during various phases of the study. (a) Baseline study. The SDs of R-R (SDR-R) and
AR-R (SDAR-R) intervals were 71 and 50ms respectively. (b) Head-up tilt. The SDR-R and SDAR-R were 50 and I I ms respectively. (c) Atropine infusion. The SDR-R
and SDAR-R were 34 and lOms respectively. (d) Transdermal scopolamine. The SDR-R and SDAR-R were 81 and 71 ms respectively.
construct a histogram which relates to the Poincart
plot (all r-MSSD values are positive). Therefore, we
have used S D delta R-R as a measure of the
‘spread‘ of the delta R-R interval histogram and
have proposed this parameter as a method by which
to quantify parasympathetic nervous system activity
during these perturbations.
We have also demonstrated a strong correlation
between frequency and time domain measures used
to quantify HRV. Total power was strongly correlated with SDR-R and SD delta R-R. The total
power of spectral energy has been proposed to
represent both sympathetic and parasympathetic
activity, while H F power is accepted as a measure
of pure parasympathetic activity [30]. Therefore, it
is suggested that the ‘width’ of the Poincart plot as
quantified by SD delta R-R represents a pure
measure of parasympathetic activity.
The use of this method also allows immediate
recognition of ectopics or artefact which may go
unobserved and corrupt HRV data if conventional
analytical methods are used [111. We have used the
Poincark plot to guide filtering algorithms to completely remove ectopic beats and artefact from the
time series data without corrupting the normal sinus
rhythm. Poincark plot analysis is an extension of a
method developed by Malik et al. [12] who used
the width of the main peak of the frequency distribution curve to quantify noise HRV time series.
Although the analysis of histograms using the Malik
P. W. Kamen et al.
206
2
4
6
8
Log variance AR-R interval (ms’)
10
Fig. 3. Relation between time and frequency domain variables. Log
HF power (O.IM.4Hz) correlated strongly with log variance of AR-R
intervals.
algorithm provides the same statistical result as the
Poincart plot technique we have found that the
visual information provided by the latter method
augments the simple statistical analysis of histograms. Furthermore, other methods for analysis of
Poincart plot patterns may demonstrate non-linear
relationships [31] between sympathetic and parasympathetic nervous activity [32-341 which would
otherwise go unrecognized. Therefore the PoincarC
plot provides additional information to complement
current methods of HRV analysis and is a useful
adjunct, especially in the clinical setting where ‘real
time’ analysis of HRV is of critical importance.
In contrast to most, but not all [35] studies of
HRV which have relied on data collected during
prolonged ambulatory monitoring of the ECG, our
patients rested quietly with data collected over a
relatively short time span of 10-20mins. This may
account for the finding that our healthy subjects did
not display Poincart plot patterns with the characteristic ‘comet’ and ‘stem’ shape seen in data from
healthy subjects in the study of Woo et al. [7] who
employed 24 h ambulatory monitoring. The small
‘head’ of their ‘comet’ pattern was probably the
result of increased sympathetic and decreased parasympathetic activity leading to an increase in absolute heart rate and associated reduction in HRV.
Significance and potential applications
Analysis of HRV based on short-term analysis of
the PoincarC plot provides a sensitive, non-invasive
measurement of autonomic input to the heart. Heart
rate variability can be measured in both the time
and frequency domain, and in the present study,
time and frequency domain variables have been
shown to correlate very highly. Time domain indices
used to quantify the PoincarC plot have been shown
to be nearly equivalent to their respective frequency
domain variables. The technique described could
therefore greatly simplify HRV analysis.
Bigger et al. [35] have demonstrated that power
spectral measures of R-R variability calculated from
short (2-1 5 min) electrocardiographic recordings are
remarkably similar to those calculated over 24 h. If
so, short-term HRV analyses based on the Poincark
plot should be as predictive of prognosis as 24h
measures of HRV.
In summary, the present study has demonstrated
that the PoincarC plot is a simple, yet powerful
adjunct to conventional HRV analytical techniques.
It provides complementary information to other
standard procedures such as statistical (time
domain) measures, the tachogram, histogram and
frequency (power spectrum) analysis.
ACKNOWLEDGMENT
We thank AMRAD Operations Pty Ltd and
National Mutual Life Association for their support
of this work.
REFERENCES
I. Stramba-Badiale M, Vanoli E, De Ferrari GM, Cerati D, Foreman RD,
Schwartz PJ. Sympathetic-parasympathetic interaction and accentuated
antagonism in conscious dogs. Am J Physiol 1991; 260: H335-40.
2. Corr PB, Pitt B, Natelson BH, Reis DJ, Shine KI, Skinner JE. Sudden cardiac
death. Neurakhemical interactions. Circulation 1987; 76 (Suppl. I): 1-208-14.
3. Schwartz PJ, La Rovere MT, Vanoli E. Autonomic nervous system and sudden
cardiac death. Experimental basis and clinical observations for post-myocardial
infarction risk stratification. Circulation 1992; 8 5 177-91.
4. Kamen PW, Tonkin AM. Application of the Poincare plot t o heart rate
variability: a new measure of functional status in heart failure. Aust N Z Med
1995; 2 5 1&26.
5. Adamopoulos 5, Piepoli M, McCance A, et al. Comparison of different methods
for assessing sympathovagal balance in chronic congestive heart failure secondary t o coronary artery disease. Am J Cardiol 1992; 70 157682.
6. Kienzle MG, Ferguson DW, Birkett CL, Myers GA, Berg WJ, Mariano DJ.
Clinical, hemodynamic and sympathetic neural correlates of heart rate variability in congestive heart failure. Am J Cardiol 1992; 69: 761-7.
7. Woo MA, Stevenson WG, Moser DK. Trelease RB. Harper RM. Patterns of
beat-to-beat heart rate variability in advanced heart failure. Am Heart J 1992;
lU: 704-10.
8. Anan T, Sunagawa K, Araki H, Nakamura M. Arrhythmia analysis by successive
RR plotting. J Electrocardiol 1990; U: 243-8.
9. Woo MA, Stevenson WG, Moser DK, Middlekauff HR. Complex heart rate
variability and serum norepinephrine levels in patients with advanced heart
failure. J Am Coil Cardiol 1994; U.565-9.
10. Kamen PW, Tonkin AM. Heart rate Poincare plots in heart failure: reply. Aust
N 2 J Med 1995; 25 (4): 372-3.
I I. Myers G, Workman M, Birkett C, Ferguson D, Kienzle M. Problems in
measuring heart rate variability of patients with congestive heart failure. J
Electrocardiol 1992; 25. 214-19.
12. Malik M, Farrell T, Cripps T, Camm A]. Heart rate variability in relation t o
prognosis after myocardial infarction: selection of optimal processing techniques. Eur Heart J 1989 10 1060-74.
13. Novak V, Novak P, de Champlain J. Le Blanc AR. Martin R, Nadeau R.
Influence of respiration on heart rate and blood pressure fluctuations. J Appl
Physiol 1993; 74: 617-26.
14. Butler GC, Yamamoto Y, Xing HC, Northey DR, Hughson RL. Heart rate
variability and fractal dimension during orthostatic challenges. J Appl Physiol
1993; 75 ZMI2-12.
15. Vybiral T, Bryg RJ, Maddens ME, Boden WE. Effect of passive tilt on sympath
etic and parasympathetic components of heart rate variability in normal sub
jects. Am J Cardiol 1989; 63: I117-20.
16. Hayano J,Sakakibara Y, Yamada A, e t al. Accuracy of assessment of cardiac
vagal tone by heart rate variability in normal subjects. Am J Cardiol 1991; 67:
199-204.
17. La Rovere MT, Mortara A, Pantaleo P, Maestri R, Cobelli F, Tavazzi L.
Scopolamine improves autonomic balance in advanced congestive heart failure.
Circulation 1994; 90 (2): 83B-43.
207
Poincare plot and autonomic perturbations
18. Raetz SL, Richard CA, Garfinkel A, Harper RM. Dynamic characteristics of
cardiac R-R intervals during sleep and waking states. Sleep 1991; 14 526-33.
19. Rompelman 0, Coenen AJ, Kitney RI. Measurement of heart-rate variability:
Part I-Comparative study of heart-rate variability analysis methods. Med Biol
Eng Comput 1977; IS:233-9.
20. Albrecht P, Cohen RJ. Estimation of heart rate power spectrum bands from
real world data: dealing with ectopic beats and noisy data. Comp Cardiol. L a
Alamitos, CA, U.S.A.: IEEE Computer Society Press, 1988 31 1-14.
21. De Boer RW, Karemaker J. Strackee J. Comparing spectra of a series of point
events particularly for heart rate variability data. IEEE Trans Biomed Eng 1984;
where R-R, corresponds to the x-coordinate and
R-R, + to the y-coordinate.
Delta R-R interval
The delta R-R interval (AR-R) is defined as
31: 3B4-7.
22. Bigger Jr JT, Albrecht P, Steinman RC, Rolnitzky LM. Fleiss JL, Cohen RJ.
Comparison of time- and frequency domain-based measures of cardiac parasympathetic activity in Holter recordings after myocardial infarction. Am J Cardiol
1989; 64. 536-8.
23. Bigger Jr IT, Fleiss JL, Steinman RC, Rolnitzky LM, Kleiger RE, Rottman JN.
Correlations among time and frequency domain measures of heart period
variability two weeks after acute myocardial infarction. Am J Cardiol 1992; 6 9
891-8.
24. Box GEP, Jenkins GM. Time series analysis: forecasting and control. San
Francisco, U.S.A.: Holden-Day, 1970.
25. Bloomfield P. Fourier analysis of time series: an introduction. New York John
Wiley, 1976.
26. Pincus SM. Greater signal regularity may indicate increased system isolation.
Math Biosci 1994; 122 (2): 161-81.
27. Cox DR. Lewis PAW. The statistical analysis of series of events. London:
Chapman and Hall, 1966.
28. Jaffe RS, Fung DL, Behrman KH. Optimal frequency ranges for extracting
information on autonomic activity from the heart rate spectrogram. J Auton
Nerv Syst 1994; 46: 37-46.
29. Kamen PW, Tonkin AM. Chaos mathematics enables quantitative assessment of
heart rate variability in patients with cardiac failure. [Abstract] Aust N Z Med
1993; 2 3 595.
30. Pomeranz 8, Macaulay RIB, Caudill MA, et al. Assessment of autonomic
function in humans by heart rate spectral analysis. Am J Physiol 1985; 248:
H151-3.
31. Glass L, Kaplan DT. Time series analysis of complex dynamics in physiology
and medicine. Med Prog Techno1 1993; I9 115-28.
32. Woo MS, Woo MA, Gozal D, Jansen MT, Keens TG, Harper RM. Heart rate
variability in congenital central hypoventilation syndrome. Pediatr Res 1992;
31: 291-6.
33. Garfinkel A. Raetz SL, Harper RM. Heart rate dynamics after acute cocaine
administration. J Cardiovasc Pharmacol 1992; I9 453-9.
34. Schechtman VL, Raetz SL, Harper RK, et al. Dynamic analysis of cardiac R-R
intervals in normal infants and in infants who subsequently succumbed to the
sudden infant death syndrome. Pediatr Res 1992; 31: 606-12.
35. Bigger JrIT, Fleiss JL, Rolnitzky LM, Steinman RC. The ability of several
short-term measures of RR variability t o predict mortality after myocardial
infarction. Circulation 1993; 88: 927-34.
APPENDIX
Geometrical interpretation of R-R interval histogram
The relationship between the histogram of R-R
intervals and the corresponding PoincarC plot can
best be illustrated using geometric concepts and
techniques. We make the assumption that the xand y-axes are scaled identically.
We consider first the time series XN
X, =
AR-R,
R-R, - R-R,
+1
If it is assumed that the PoincarC plot has a
symmetric distribution about its mean, then the
AR-R interval distribution has zero mean
A R-R interval histogram
The AR-R interval histogram is a frequency
distribution graph which includes both negative and
920
980
940
960
980
1
I000
IOW
/’
I
i
9001”
I
900
920
’
I
’
I
940
960
R-R, interval (ms)
’
I
980
’
+ 1,
R-R,
+ 2,
Fig. 4. Geometric relationship between the AR-R interval and data
points on the PoincarC plot. Point A is the point with coordinates (R-R,,
R-R,+J, while points B and C lie on the line of identity. The AR-R
interval is quantified by the distance AC. The ‘width’ of the Poincare plot is
derived from the length of AB. a=454
positive values and is centred around zero
(mean = 0) with variance measured by SDAR-R.
SD of AR-R intervals is given by
...,R-RN)
which is equivalent to the r-MSSD given by
Each datapoint on the PoincarC plot corresponds to
the ordered pair.
r-MSSD =
Datapoint, =(R-R,, R-R,+ ,)
I 900
1000
SDAR-R =
(R-R,, R-RZ, ...,R-R,, R-R,
920
(R-R, - R-R,
+ 1)2
P. W. Kamen et al.
208
SDAR-R
and r-MSSD are mathematically
equivalent if AR-R=0, but only the former is a
measure of SD of the AR-R histogram which relates
to the ‘width’ of the Poincare plot.
Geometrical interpretation of the AR-R interval
histogram
(where a = 45”).
A ‘width’ histogram can be constructed from the
transformed data which can then be tested for
normality by the Kolmogorov-Smirnov method. If
the ‘width’ histogram is Gaussian, then the ‘width’
measure is directly related to the width of the
Poincart plot, namely
SD width =
Take two consecutive R-R intervals in the time
series; namely
(R-R, and R-R,
+ 1)
Let A denote the point (R-R,R-R,,,)
which they
determine on the Poincare plot, as illustrated in Fig.
4.
Let C(R-R,, R-R,) denote the projection, in the
direction of the y-axis, of the point A(R-R,, R-R, + 1)
onto the line of identity. Any point above the line of
identity is defined as having a negative AR-R
interval and any point below as having a positive
AR-R value.
Therefore
SDAR-R
Jz
Relationships between time and frequency domain HRV
variables
Parseval’s theorem.
where Y k is the discrete Fourier transform of X ,
and P,(k) is the power spectral density of X w Thus
the signal variance and total spectral power are
equal to each other.
length A C = AR-R,
HF power
Geometrical interpretation of the ‘width’ measure
The term ‘width’ is defined in terms of AR-R(AC)
with respect to AB in Fig. 4. In particular,
A B = A C .sincl= A C * sin-.n=-A C
4Jz
For a continuous R-R time series, X N , with fast
Fourier transform ( Y f ) and power spectral density
function Px(f), the power spectrum of dX(t)/dt is
4 n z f 2 P , ( f ) . Thus, time domain parameters related
to the first derivative or successive differences in the
R-R interval time series are correlated with HF
spectral power.