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Comparative Biochemistry and Physiology Part A 124 (1999) 447 – 460
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Review
Understanding autonomic sympathovagal balance from short-term
heart rate variations. Are we analyzing noise?
Jordi Altimiras *
Department of Zoophysiology, Institute of Biological Sciences, Uni6ersity of Aarhus, Building 131, Uni6ersitetsparken,
DK-8000 Aarhus C, Denmark
Received 21 September 1998; received in revised form 15 March 1999; accepted 30 March 1999
Abstract
Heart rate variations reflect the output of the complex control of the heart mediated by the autonomic nervous system. Because
of that, they also encode different types of information, namely the efferent outflow of reflex mechanisms involved in the
beat-to-beat control of cardiac function, the efferent activity of neurohumoral elements involved in the control of other
cardiovascular parameters and random noise resulting from the hysteresis of the different controllers. The degree to which power
spectrum estimation methods will uncover the periodic component of heart rate variations is in direct relation with the status of
the system under study. Although the utility of spectral methods is now established in mammalian research, very little is known
on the utility of these techniques in non-mammalian cardiovascular research. This review covers this space by discussing the
physiological significance of heart rate variations in non-mammalian vertebrates. A detailed account of the different steps of the
technique, its limitations and the ways to overcome these problems are also presented. These are: the recording of the cardiac
event signal, the detection and digital processing methods, the satisfaction of stationarity conditions, the problem of spectral
leakage and the different methods to estimate the power spectrum. © 1999 Elsevier Science Inc. All rights reserved.
Keywords: Spectral analysis; Heart rate; Heart rate variability; Respiratory sinus arhythmia; Sympathovagal balance; Power spectrum; Autonomic
nervous system; Cardiac function
1. Introduction
The study of cardiac autonomic regulation using
reductionistic methods, i.e. isolating surgically or pharmacologically the different autonomic effectors implicated in cardiac regulation, has provided a consistent
body of knowledge of the magnitude and the dynamic
time course of the response of the cardiovascular system after different types of perturbations. However, as
a recognized limitation of this experimental approach,
the original system under study needs to be disrupted.
Instead of describing ‘the’ original system, we are
studying ‘a’ perturbed system that may or may not
* Present address: Department of Zoophysiology, Zoological Institute, University of Göteborg, Medicinaregatan 18, Box 463, S-40530
Göteborg, Sweden. Tel.: +46-317-733-693; fax: +46-317-733-807.
E-mail address: [email protected] (J. Altimiras)
display the features aimed to understand. Thus, there is
a need to combine these reductionistic studies with
integrative approaches aiming to characterize the complexities of autonomic cardiac regulation without the
need to experimentally isolate the different components.
Spectral analysis is instrumental in fulfilling such
goal. Under the denomination ‘spectral analysis’ we
include a large set of mathematical tools that permit the
characterization of signals according to its frequency
content. As a crude comparison, spectral analysis is to
time signals what a prism is to light, a tool to unravel
the different spectral components (colors) hidden under
a white light.
Over the last two decades, it has been consistently
demonstrated that the beat-to-beat variations of heart
rate contain information about the activity of the autonomic effectors controlling cardiac output [63]. The
interest of spectral analysis is focused on the quantita-
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J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
tive separation of physiologically relevant mechanisms
from a complex output, the beat-to-beat variations in
instantaneous heart rate or, what has been more appropriately called the heart rate variability signal (HRVS).
Irrespective of the internal intricacies of the system,
which is treated like a black-box, the resulting autonomic drive results from the combination of the
parasympathetic and the sympathetic cardiac autonomic outflow, together with a third component
that encompasses other physiological humoral mechanisms and the intrinsic noise of the control circuitry. In
virtue of their different time constants [20], these mechanisms can be separated as will be discussed in Section
2.4.
Comparative physiologists have made little use
of spectral analysis, despite the interest to study
cardiac regulation in a large set of species with
widely diversified central flow patterns and gas exchange organs and with the capacity to adapt
and survive in constantly changing environments.
The study of non-mammalian vertebrates can be
viewed as an evolutionary showroom of relict and
modern control mechanisms, obvious predecessors
and, at the same time, actual survivors in a process
of distilled missed and successful trials. In this framework, spectral analysis techniques can contribute
to a deeper understanding of the intricacies of autonomic cardiac control through the vertebrate phylogeny.
However, in order to apply these spectral analysis
techniques in a comparative context, it is important to
identify and understand the shortcomings and the requirements of the technique itself. While this is usually
irrelevant in mammalian studies, it acquires an important dimension in comparative research because of the
lack of standardized procedures. If the HRVS is contaminated by artifacts arising from improper recording,
detection or processing, the low signal-to-noise ratio
will be compromised and the results will be difficult to
interpret.
This review intends to discuss critically the detailed
applicability of one specific type of spectral analysis to
HRVS, namely the power spectrum estimation methods. To do this, the paper will be divided in several
sections. First, the physiological significance of heart
rate variations will be discussed to emphasize that
heart rate variations are intrinsically linked to
different mechanisms of cardiac control. In Section 3
the common methodology employed in mammalian
studies will be reported, together with a brief account
of alternative methods. In Section 4, the critical steps to
establish an appropriate analytical protocol will be
presented and discussed with an emphasis on its application in non-mammalian vertebrates. Finally, the last
section will be used as a concluding corollary of the
review.
2. Heart rate variations have a physiological
significance
‘‘Physiologists, both by tradition and design, typically express their data as mean values with some
additional indicator of variance. While this conveys
information on the central tendency in that population
of animals, it de-emphasizes any variation in the data’’
[23]. Referred by Bennett as ‘the tyranny of the golden
mean’ [19], this trend was originally applied to interindividual differences in a given population. It also
applies to a single individual if a physiological variable
recorded over a given period of time is reduced to its
mean value. In this case, the ‘golden mean’ would give
a statistically acceptable estimation of the variable,
neglecting at the same time its intrinsic variation
around the mean value.
But these variations have a physiological significance
because changes in heart rate (HR) are coupled to
changes in cardiac output. The changes in heart rate
originate as part of the homeostatic response to a
perturbation or in response to cyclic oscillations of
cardiovascular parameters. The result is the modification of the inputs to the centers responsible for cardiovascular control, maintaining cardiac function in a state
of homeodynamic balance via, among other systems, a
constant modulation of heart rate.
In the following sections I will stress the significance
of heart rate variations and the possibility to obtain
significant information to understand the cardiovascular control by the application of several specialized
tools. This has only been studied in mammals and what
follows is a general revision of our present knowledge.
2.1. Variations in heart rate distribute o6er a wide
frequency range
In a broad sense, any change in heart rate qualifies as
heart rate variability (HRV). Since the origin of these
changes can differ widely, it is relevant to categorize
them. Six types have been proposed [53]. From slowest
to fastest (Fig. 1):
2.1.1. Age related changes
During embryonic life there is a common increase in
heart rate associated with the functional maturation of
the cardiac muscle [69]. After birth, heart rate tends to
decrease with age due to structural and hemodynamic
changes [65].
2.1.2. Seasonal changes
Hibernating or aestivating species will display
marked seasonal differences in heart rate throughout
the year. Temperature fluctuations and changes in the
hormonal profile are probably the most important
causes behind such changes [52].
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
2.1.3. Circadian or daily rhythms
Guided by internal clocks. In humans they are clearly
seen in 24-h electrocardiographic recordings and reflect
alterations in the autonomic nervous system during the
day [55].
2.1.4. Ultradian rhythms
Submultiples of the circadian rhythm with a period
of 1 –3 h [32,46]. The mechanism of action is not well
understood but hormonal as well as central influences
have been implicated.
2.1.5. Minute changes
Minute changes, associated with neurohumoral oscillations in the epinephrine – norepinephrine and/or angiotensin levels in the circulating blood [53].
2.1.6. Beat-to-beat changes
Beat-to-beat changes, which will be referred as short
heart rate variability (SHRV). Mediated by the autonomic nervous system (ANS), reflect the activity of the
reflex mechanisms involved in cardiovascular control.
This paper will be exclusively committed to discuss
the highest frequency type of variations, i.e. heart rate
changes occurring in a beat-to-beat basis with a time
response roughly inferior to a minute and mediated by
the ANS.
2.2. Short term heart rate 6ariations are associated
with the inner6ation of the cardiac pacemaker
SHRV arise mainly from the innervation of the
sinoatrial node, as has been shown in numerous species.
Human patients with a transplanted heart display a
reduction up to 90% in SHRV [60]. Sympathectomized
rats show an increased HRV [26]. In fish, bilateral
vagotomy reduced SHRV drastically [8]. Blockade of
vagal activity with atropine is responsible for a large
decrease in total HRV in all the species tested, from fish
to humans [13,30,37].
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2.3. Parasympathetic and sympathetic responses ha6e a
different time constant
The spectral range of adrenergic and cholinergic effectors differ due to several factors:
1. Mechanism of elimination of the neurotransmitters
in the synaptic cleft. While norepinephrine is mainly
reuptaken in the sympathetic nerve terminals or
washed out in the coronary circulation, acetylcholine is enzymatically hydrolyzed in the same
nerve terminals [44].
2. Post-synaptic effects. b-adrenoceptors are coupled
to a cAMP pathway, while muscarinic receptors are
directly coupled to specific sarcolemmal potassium
channels that trigger membrane hyperpolarization
within 100 ms of the initiation of vagal stimulation.
As a result, cholinergic dependent responses are
faster than b-adrenenergic dependent responses and this
sets the basis for the analysis of SHRV using spectral
analysis.
2.4. The components of the power spectrum of the
HRV are associated with different mechanisms of
cardio6ascular regulation
The power spectrum of HRV in mammals usually
reveals three spectral components. Taking the pioneering study of Akselrod and co-workers [5] in anesthetised dogs as an example (Fig. 2), these components
are the following:
1. A high frequency component (HF) at 0.4 Hz
2. A low frequency component (LF) centered at 0.12
Hz
3. A very low frequency component (VLF) centered at
0.05 Hz
The HF component is caused by an inhibition of the
vagal tone during inspiration. This inspiratory inhibition is evoked centrally on the cardiovascular center
and explains why heart rate fluctuates with the respira-
Fig. 1. Time – frequency scale of the different types of heart rate variations. Data for the different panels was obtained from the following sources:
panel 1 [12]; panel 2 [33]; panel 3 [55] and panel 4 [46]. 1 - Age-related; 2 - Seasonal; 3 - Circadian; 4 - Ultradian; 5 - Minute; 6 - Beat to beat.
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Fig. 2. Original figures from the pioneering work of Akselrod and co-workers reporting the power spectrum of HRV from anaesthetized dogs [5].
With permission from the publisher.
tory frequency. In addition, peripheral reflexes arising
from thoracic stretch receptors also contribute to this
so-called respiratory sinus arrhythmia (RSA). RSA is
clearly abolished by atropine or vagotomy and the
power of the HF component has been used as an index
of the vagal drive.
The LF component of HRV is usually characterized
by an oscillatory pattern with a period of 10 s. This
rhythm originates from self-oscillation in the vasomotor
part of the baroreflex loop as a result of negative
feedback [47] and it is commonly associated with synchronous fluctuations in blood pressure, the so-called
Mayer waves. Muscarinic and b-adrenoceptor antagonists are known to change the area of the LF peak. In
the dog, the LF component appear to be mainly mediated by the parasympathetic nervous system [4], while
in rats the sympathetic influence accounts for 80% of
the LF area [25].
The very low frequency component (VLF) accounts
for all other heart rate changes, including those associated with thermoregulation and humoral and local
factors. Some of these changes might be oscillatory
(when the period of oscillation is long) while others are
known to be chaotic. For the identification of long
period oscillatory components, long periods of recording of the electrocardiogram are required. For the
identification of chaotic components, special methods
of non-linear analysis have been developed and will be
briefly discussed in Section 3.5.2.
In any case, the deterministic components of the
HRVS associated with autonomic cardiac control are
basically contained in the HF and the LF spectral
components, and these will receive most attention.
2.5. An index of sympatho6agal balance based on the
power spectrum
The two divisions of the ANS are classically seen
working in a reciprocal manner, with increases in one
division associated with decreases in the other [20].
Although this reciprocal modulation does not occur in
some physiological states, a non-invasive index of sympathovagal balance obtained through the analysis of
the power spectrum is clearly of physiological and
clinical use. The relative ratio between the different
components of the power spectrum has been used as
such an index [48].
A linear relation of the area of the HF component
and cardiac vagal tone obtained pharmacologically has
been demonstrated [39,40]. Similarly, a linear relationship between the LF component and sympathetic activity has also been established [22].
The suitability of this index of sympathovagal balance has been shown during mental stress, tilt and mild
exercise [49] but not when sympathetic drive is high
such as during heavy dynamic exercise [49] or during
baroreceptor loading [37].
3. Short-term heart rate variations can be studied with
appropriate techniques and analysed with relatively
simple mathematical tools
A detailed algorithm on how to carry out the spectral
analysis of SHRV has already been published [9]. The
purpose here is to review the different steps of the
procedure, specifically those required for the application of the most commonly used spectral tool, which is
the fast Fourier transform (FFT). In Fig. 3 a step-bystep scheme is provided as a guide through this part,
which will include the accurate detection of each cardiac beat from the signal of choice, the correction of
artifacts and the preparation of the time series for
spectral analysis.
In the second part, the FFT and the autoregressive
method will be described and their limitations discussed
and compared with alternative procedures such as
time–frequency methods, wavelet analysis and non-linear fractal methods.
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
3.1. Accurate detection of instantaneous heart rate
The accurate detection of beat-to-beat heart rate
usually relies on tachographs, analog devices that trigger on the rising slope of the QRS wave and measure
time between trigger pulses in real time. The alternative
is the storage of the analog signal on tape for posterior
analysis, either analog post-processing using tachographs or digital processing via computers (Holter systems, for instance). Nowadays, the complete
digitalization and storage of the signal on digital
devices through analog-to-digital conversion hardware
is the most convenient method to use.
Depending on the way the signal is stored, the detection can be carried out in real-time or offline. Real-time
detection (on-line) with analog or digital tachographs
[56] is convenient in terms of storage capacity because
only the time of each event is stored. On the other
hand, off-line detection is advantageous because the
signal can be analyzed many times and detection artifacts can be easily discovered and corrected. With the
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current prices of digital storage, it is a good advice to
record the entire signal even with good on-line detectors in operation.
3.2. Correction of artifacts in beat-to-beat
instantaneous heart rate series. Need or con6enience?
SHRV analysis requires long periods of recording,
and this usually results in the introduction of errors in
the time data series associated with periods of low
signal quality or artifacts in the QRS detection routine.
Although this is a common problem encountered in
any approach to the analysis of SHRV, it has not been
thoroughly treated. The most common approach consists in manually editing the data series, splitting the
long artifactual R–R intervals caused by missed beats
or joining consecutive short R–R intervals caused by
the detection of P or T waves. As a usual practice, the
data is discarded when more than 5% of the beats need
correction. This solution is probably a good compromise but it still involves a lot of subjective decisions
from the analyst/operator.
This problem is accentuated in experiments on undisturbed animals that are allowed to move freely because
the signal to noise ratio usually decreases. A correction
routine based on non-linear filters and neural networks
that will eliminate some of the subjective criteria associated with the manual edition of the data is currently
under test in my laboratory. With this technique, the
most common artifacts and the appropriate corrections
are used to train the neural network, which can then be
used to process the time series automatically.
3.3. Pre-processing of the time series
Fig. 3. Step-by-step graphical scheme of the methodology for the
estimation of the power spectrum of SHRV. See text for details.
The beat-to-beat heart rate series is, by definition,
sampled at a frequency-modulated rate [68], the instantaneous heart rate itself and because of that has been
named the Interval Tachogram [58]. Some authors
prefer to transform this time series to a time evenly
sampled series using linear interpolation procedures
between consecutive beats. This new series has been
called the Interval Function [58].
Since the pioneering work of Akselrod and co-workers [5], other authors have used the Interval Function as
the basis for spectral analysis [25,27]. In this case, a
proper selection of the sampling frequency of the new
time series is needed. Sampling frequencies from 4 [41],
2 [42] or to 1 Hz [35] have been used in human studies.
Higher sampling frequencies might be required when
working with higher heart rates.
Despite the extensive use of interpolation procedures,
it has been demonstrated that the FFT algorithm operates equally well with the Interval Tachogram because
the resulting interval spectrum is completely equivalent
[29]. By removing the interpolation step, the processing
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tral resolution and to overcome stationarity limitations,
most of our knowledge on SHRV and autonomic cardiac modulation is based on two fundamental algorithms: the FFT and the autoregressive modelling
algorithm.
Fig. 4. Demonstration of the truncation effect depending on the
selection of the finite signal to analyze. In the lower panel note the
introduction of high frequency transients due to the ‘apparent’ truncation of the signal caused by the iteration of a finite signal.
of the time series prior to spectral analysis is greatly
simplified [9,11].
Other alternative ways to derive a variability signal
from the cardiac event series have been reported [58]
but are rarely used.
A second step in the processing of the time series is
important to prevent what is known as spectral leakage.
Because the computation of the FFT requires an infinite data series, the FFT algorithm starts by iterating
the time series infinite number of times, as shown in
Fig. 4. If the whole signal contains exact multiples of
the frequencies included, as happens in Fig. 4 top, no
effects due to a finite data series will be observed in the
power spectrum. However, if the signal is not in phase
with itself, which is the most likely situation when
multiple frequencies are present (shown in Fig. 4 bottom), a truncation effect occurs. This is called spectral
leakage or truncation effect and is due to the presence
of sudden transitions in the data that introduce high
frequency noise in the power spectrum estimate. Spectral leakage can be corrected by applying a tapering
window that smoothes the edges of the finite signal [18].
Many tapering windows are in use: Blackman – Harris
[6]; Exact Blackman [41] or the Hanning window. The
latter, also known as the cosinus taper, is the most
widely used [22,42,62]. Importantly, the tapering window has the effect of reducing the overall variability,
effect that is corrected after the FFT computation by
dividing the spectral power at each frequency by 0.875
(if the Hanning window is used).
3.4. The FFT and autoregressi6e algorithms are the
most commonly used tools to study the SHRV
The final step in SHRV analysis includes the application of power spectrum estimation methods to characterize the frequency components associated with vagal
and/or sympathetic outflow. Although new algorithms
and methods are constantly improved to increase spec-
3.4.1. The fast Fourier transform
Any signal can be described as a sum of sine waves
and this decomposition is called the Fourier transform.
An efficient algorithm to carry out this transformation
is the FFT, which, with some improvements and modifications, is still in use in many applications such as
voice analysis or vibration studies. The analysis of
SHRV is another one of these applications.
FFT algorithms impose some constraints on the signal to analyze because an evenly sampled, infinite and
stationary time series is required. Although HR series
do not fulfil these strict requirements, different techniques to minimize the errors are currently in use and
will be discussed in detail in the framework of SHRV
analysis in Section 4.
3.4.2. Autoregressi6e modeling
An alternative method to the FFT is the autoregressive identification algorithm (AR) combined with power
spectral estimation for the assessment of SHRV [14–
16]. The method fits the data to an a priori defined
model and estimates the parameters of the model. The
power spectrum implied by the model is then computed
[57].
The AR approach offers some advantages over the
classical Fourier analysis [50]:
1. Due to intrinsic quasi-randomness of HRV, AR
methods enhance the extraction of the non-random
oscillations superimposed on a wide-band noise.
This type of noise is characteristic of the power
spectrum estimation obtained with the FFT
algorithm.
2. AR algorithms can automatically furnish the number, amplitude, and center frequency of the oscillatory components without requiring the a priori
decision on which peaks will be considered.
3. AR methods operate efficiently on shorter series of
events that are also more likely stationary.
4. The resolution of AR procedures is higher [61].
AR methods are more complex both in design and
operation and this factor has limited its application.
Although a priori decisions on the spectral components
are not needed, the method still introduces a subjective
consideration of the order of the AR model to evaluate,
and there is no common agreement about it [49,66,67].
3.4.3. FFT or AR modelling, which to choose?
Both methods share a common goal: the estimation
of the power spectrum of a signal. FFT-based methods
are also called non-parametric methods because there is
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
no assumption on how the data were originated. AR
methods are parametric because they require a priori
information of the system under study.
Thus, I suggest that FFT-based methods are still the
best choice for the assessment of SHRV in comparative
studies, where no previous knowledge of the system is
available. In addition, FFT algorithms are readily available in many different languages, even in commercial
statistical packages.
Once the basic spectral content of the system is known
and an initial model of the signal can be formulated, AR
algorithms should be a better choice because they provide
better frequency resolution and avoid the problems of
spectral leakage (see Section 3.3).
3.5. New spectral analysis techniques are in continuous
de6elopment to resol6e new problems and o6ercome
current limitations
FFT and AR methods have served a critical role in the
understanding of basal autonomic cardiac control. However, these algorithms have limitations in the study of
long-term non-linear variations of heart rate as well as
in the analysis of transient alterations of heart rate.
Although a detailed discussion of alternative procedures
to overcome these limitations is out of the scope of this
review, I will summarize the most representative.
3.5.1. Study of transient alterations of heart rate
The need to study transient alterations of heart rate is
directly linked to the localization of specific events in the
spectral estimate. This need has to be studied under the
framework of the uncertainty principle, which states that
arbitrarily good time and frequency resolutions, at the
same location, cannot be achieved. Some methods that
can overcome this problem and be instrumental in
understanding the modulation of heart rate under timevarying conditions are described here. A more extensive
description of these methods can be found in the excellent
book by Akay [1].
During classical conditioning tests an animal learns
that a signal predicts the occurrence of a traumatic or
pleasing event. The signal itself elicits a complex, highly
dynamic sequence of changes, the so-called conditioned
response. To study these fast changes involved in the
conditioned response a complex demodulation algorithm
has been proposed [64]. Complex demodulation provides
a good solution to this problem because it provides time
local estimates of the properties of the process.
Joint time–frequency analysis (JTFA) is another alternative to balance spectral versus time resolution. It is
based on the recursive implementation of power spectrum estimation methods using the Short-time Fourier
transform, the Gabor spectrogram or the Wigner-Ville
distribution. It has been used to demonstrate that transient ischemic attacks in humans are preceded by an
453
activation of the sympathetic innervation of the heart
[21].
The newest methodology to study transient changes in
the HRVS is based on time–scale methods, also known
as wavelet transforms. Their utility in the understanding
of the physiology of HRV has recently been demonstrated during antistenotic surgery of the carotid artery.
In this case, the declamping of the carotid vessel after
surgery is followed by a significant increase of the power
of the high frequency spectral bands, suggesting a
recovery of the autonomic modulation of the heart [2].
Interestingly, the application of the STFT transform
rendered imprecise conclusions, suggesting that wavelet
transforms are more appropriately suited for the study
of transient alterations than time–frequency methods.
The wide application of wavelet transforms in other areas
of biomedical engineering such as the analysis of pulmonary hemodynamics [45] or ECG compression and
characterization [28,59] envisions an important role for
wavelet transforms in our future understanding of physiological processes.
3.5.2. Methods of non-linear and fractal analysis
The presence of self-similarity features in the HRVS
revealed by a non-flat 1/f spectra [43] opened up a new
area of study in the understanding of cardiac dynamics.
Self-similarity is indicative of the presence of aperiodic
but deterministic components also known as fractals.
These chaotic components are all embedded in the VLF
band described in Section 2.4, and are thought to be an
important part of the regulatory repertoire of the healthy
heart [36]. From a clinical point of view this suggestion
has been applied to the monitoring of sudden infant
death syndrome, sudden cardiac death and aging using
the approximate entropy measurement developed by
Pincus and co-workers (reviewed in [17]).
The physiological mechanisms responsible for the
genesis of fractal HRV, however, are largely unknown.
Blood pressure regulation through the baroreflex and
respiratory sinus arhythmia are poorly related to the
fractal HRV [24,71]. As to the effector mechanisms, the
sympathetic nervous system plays a minor role in modulating fractal HRV dynamics [73], and the parasympathetic nervous system seems to be largely responsible [74].
The physiological study of the fractal components of
the HRVS has greatly benefited from the coarse graining
spectral analysis method developed by Yamamoto and
Hughson [72], which permits the separation and quantification of fractal and periodic components.
4. The use of power spectrum estimation methods
requires the understanding of its limitations and a proper
application of solutions
The algorithms required in the analysis of SHRV via
the power spectrum are conceptually simple. However,
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J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
their practical implementation requires certain considerations of the processing of the cardiac-related
signal that will largely determine the quality of the
results.
In the next sections I will discuss some important
considerations to carry out the spectral analysis of iHR
series such as the type and the quality of the signal to
use, the signal processing steps and the length of the
recording period. As a corollary to this section, the
statistical reliability of the interval spectrum obtained
from the FFT algorithm will be discussed.
4.1. What cardiac-related signals are appropriate for
the analysis of SHRV?
The electrocardiogram (ECG) is the most appropriate signal to study SHRV because it offers the most
accurate representation of the electrical cardiac events.
In particular, the QRS complex of the ECG sharply
defines the onset of ventricular electrical depolarization
and is the closest approach to time the occurrence of
pacemaker potentials, which in turn are modulated by
the autonomic outflow. The simplicity and little invasivity of ECG recording have been exploited to study
SHRV in a wide variety of species, from fish [11] and
Fig. 5. Comparison of instantaneous heart rates obtained from ECG
and blood pressure signals. (A) Simultaneous recording of the ECG
and the blood pressure trace in a saltwater crocodile Crocodylus
porosus. (B) Relationship between heart rate and the relative difference in instantaneous rate as estimated from the two different signals.
Data as mean 9SD. Open symbols show the maximum and minimum error at each heart rate.
reptiles [38] to mammals ([4,39,54] among many
others).
If the ECG signal cannot be recorded, can other
signals be used? For example, average heart rates have
been routinely obtained from other signals like blood
pressure, blood flow, finger pulse pressure, heart sonography, plethysmography or Doppler ultrasound imaging among others. What determines if a cardiac-related
signal is suitable for the study of SHRV?
The main requirement is a good correspondence between the signal of choice and the standard ECG
signal. Commonly, the signal of choice will be delayed
in relation to the bioelectric signal. For instance,
the QRS complex precedes the onset of systolic
blood pressure in the cardiac cycle (Fig. 5A). If this
delay is relatively constant, we can conclude that blood
pressure is a reasonable estimator of instantaneous
heart rate.
This is what occurs in the example presented in Fig.
5, that compares the instantaneous heart rate obtained
simultaneously from the ECG and the femoral blood
pressure trace in the saltwater crocodile Crocodylus
porosus [10]. The results from eight animals (2000 heartbeats randomly picked from each animal) support several conclusions:
1. The relative difference between instantaneous HR
(iHR) obtained from ECG or BP signals is rate
dependent, i.e. a larger error is obtained at larger
iHR.
2. The distribution of relative differences is symmetrical. For a given iHR obtained from the ECG the
probability of overestimating or underestimating
iHR using the BP signal is the same.
3. The average maximum error is 9 2%.
The impact of this error on the spectral estimate will
be discussed in detail in the next section but taking into
account the low average heart rates and the high HRV,
the blood pressure signal is appropriate in this case to
analyze the SHRV.
Another example to discuss the suitability of cardiacrelated signals to estimate instantaneous heart rates is
the chicken embryo. The chicken embryo is an excellent
model for the study of the ontogeny of cardiovascular
regulation. A quick glance at the literature reveals
many different techniques directly or indirectly related
with different mechanical or electrical phenomena of
the cardiac cycle that have been used to measure heart
rate. These techniques are outlined in Fig. 6A in relation with the developmental window in which they can
be used.
Most of these signals can be immediately excluded in
order to estimate the instantaneous heart rate for
SHRV analysis. The acoustocardiogram, ballistocardiogram, pulse oximetry trace and obviously the visual
observation methods are unsuitable because the signal
under study reflects a complex interaction between car-
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
455
vessel. This procedure has little impact on the embryo
because it can be performed on a small circular opening
on the eggshell (5-mm diameter) and can be used
reliably from day 7 onwards.
In these cases we have to assume that vascular compliance does not change over time or that the time lag
between electrical cardiac systole and the maximum
speed or pressure in the vessel is constant. Although
these assumptions have not yet been verified, it is
feasible that even small deviations would not have a
large impact on the SHRV spectra. In Fig. 6B, an
example of the ECG, the impedance cardiogram (IP)
and the Doppler velocity (DOP) signals are shown to
compare the temporal resolution of the systolic events.
Note the different definition of the peak maxima,
clearly distinguished for the ECG trace but flattened
and more susceptible to noise contamination for DOP
and IP.
4.2. Which are the parameters during signal processing
that critically determine the quality of the heat rate
series?
Fig. 6. (A) Outline of the different techniques used in the literature to
measure heart rate in chicken embryos. Each method is displayed
against a developmental ruler to delimit the ontogenetic window
where it can be used. (B) Trace example of three different signals
obtained in the same chicken embryo (HH stage 20). Note the
different definition of the peak maxima, well defined for the ECG
trace and considerably flattened for the Doppler Flow signals and the
impedance cardiogram.
diac and embryonic movements, all of them buffered
and dampened by the viscosity of the egg albumen.
When obtained from electrodes inserted in the shell, the
impedance cardiogram has the same disadvantage.
None of these signals can guarantee a constant delay
between pacemaker potentials and the fiduciary point
detected in the signal of choice
More reliable impedance cardiograms can be obtained by inserting the electrodes close to the heart at
those embryonic stages where the embryo floats on top
of the yolk sack. We have recently employed this
technique to obtain noise-free 10-min recordings of
iHR from Hamburger Hamilton Stage 18 to HH Stage
30 chicks. However, this technique constraints the measurements to a very specific window in cardiovascular
development.
Methods based on direct measurements of Doppler
shifts or pressure in extraembryonic vessels are probably the most appropriate to derive precise iHR time
series when the ECG is not available. Blood pressure
recordings are intrinsically more invasive than blood
flow measurements because the shell needs to be penetrated in order to catheterize the vessel. However, a
Doppler crystal can be easily placed on top of the
external shell membrane overlying an extraembryonic
In order to time and detect each cardiac event the
digitalization of the cardiac signal is required, i.e. the
analog signal is converted to a sequence of numbers.
The key parameters governing this transformation are
the resolution of the analog-to-digital (AD) converter
and the sampling rate. The resolution of the AD converter is important for a proper reconstruction of the
signal but it is of little relevance in terms of event
timing. Nowadays, most commercially available signal
acquisition devices will have at least a 12-bit resolution,
which is sufficient for SHRV analysis.
More relevant is the choice of an appropriate sampling frequency. The quality of the iHR series is largely
dependent on it because low sampling frequencies introduce an error in the determination of the iHR, resulting
in a low signal-to-noise ratio. Although the Nyquist
theorem (a signal must be sampled at a rate at least
twice that of its highest frequency component) is commonly used as an indicator of an appropriate sampling
frequency, it is not sufficient to guarantee a good
signal-to-noise ratio.
The relationship between the average signal-to-noise
ratio (aSNR) and the sampling frequency can be described by the following equation (adapted from [51]):
aSNR= 6·Var·SF2 − 1
(1)
where Var is the total variance of the signal and SF is
the sampling frequency in Hz.
As the sampling frequency is reduced, aSNR decreases. Interestingly, the total variance of the signal
also plays a role in the aSNR, the lower the variance
the lower the ASNR for a given sampling frequency. In
human studies, sampling frequencies lower than 128 Hz
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
456
should be avoided, which has important implications
when using data from Holter recordings [51].
In comparative studies, sampling frequencies of 250
Hz can be safely applied in most cases where heart rates
range between 10 and 100 beats·min − 1 and the variance is large. However, at higher heart rates, particularly if lower variances are involved, care needs to be
taken to sample the signal with higher frequencies or to
apply correction routines that will be discussed below.
This can be shown by modeling the maximum error
(expressed in beats·min − 1) in the measurement of instantaneous heart rate as a function of the sampling
frequency:
Error=
2HR2
60SF+HR
(2)
Fig. 7 plots the maximum error incurred at different
sampling frequencies when average heart rate is 30, 60,
120 or 240 beats·min − 1. For example, for heart rates
below 120 beats·min − 1, a maximum sampling frequency of 500 Hz will suffice to estimate each instantaneous heart rate with an accuracy of 1 beat·min − 1.
However, due to the reciprocal relationship between
time and rate, much higher sampling frequencies are
required in order to maintain the same level of accuracy
when average heart rates are about 240 beats·min − 1.
An example where sampling frequencies are critical
in the determination of the SHRV estimation is the
embryonic chicken model. Two factors contribute to it:
(a) the high average heart rate (over 250 beats·min − 1
for the last half of incubation) and (b) the intrinsic low
variability of short-term heart rate changes. In this
case, a high sampling frequency is required if a reasonable aSNR is to be obtained. If practical reasons limit
the utilization of the optimum high sampling frequency,
alternative oversampling routines need to be applied.
Oversampling algorithms work ‘filling the gaps’ and
increasing the time resolution of the signal by various
interpolation procedures. A signal sampled at 500 Hz
can be easily converted to 1000 Hz by interpolating a
new point between each pair of truly acquired points.
A sinusoid interpolation procedure to reconstruct
acoustocardiograms sampled at 50 Hz from chicken
embryos has been recently reported [3]. In this example
the signal was oversampled at 4000 Hz (i.e. a ratio
SFoversampled:SFreal of 80:1) in order to achieve a proper
time resolution in the detection of the cardiac event.
The authors based their criteria on a comparison between signals sampled at 4kHz and the same signal
undersampled at their working sampling frequency of
50 Hz.
It is important to stress however, that a proper
oversampling ratio will directly depend on the type of
signal under study and that this procedure can never
restore the original signal with complete accuracy.
4.3. Which is the appropriate length of the heart rate
series for SHRV analysis?
The length of the iHR series is not a matter of
convenience but a fine balance between two important
issues: stationarity of the time series and resolution of
the spectral estimate. The longer the recording time, the
better will be the spectral resolution because it will be
based on more data points. However, by extending the
recording time it is also more likely to run into problems with non-stationary conditions. There is no fixed
rule to define how long the iHR series need to be. What
follows is an explanation of some examples with the
aim that the criteria discussed will be helpful to determine the best conditions for any new study.
Fig. 7. Effect of sampling frequency on the error in the accuracy in
the determination of heart rate. (A) Description of the empirical
model. (B) Plot of the error at four different average heart rates as a
function of the sampling frequency.
4.3.1. Stationarity conditions
Most algorithms of spectral analysis require that the
time series is stationary. This is particularly true for
non-parametric algorithms as described in Section 3. A
random process is stationary if its statistical characteristics are invariant under time shifts, that is, if they
remain the same when t is replaced by t+Dt, where Dt
is arbitrary. Although strict stationarity is unknown in
biological systems [48], partial stationarity is often sufficient to obtain reliable results.
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
457
series, the better the spectral resolution, but there will
also be a higher probability that the series is non-stationary. In practice, the FFT is usually computed in
fragments of 29 –211 points, which provide a sufficient
resolution to study the LF and HF spectral components
but is inefficient to resolve the VLF spectral component. This is not critical for the understanding of shortterm neural control of the heart because the VLF
component is determined by a complex set of neural
and humoral factors that requires the application of
non-linear techniques such as chaos analysis (see previous Section 2.3).
4.4. Statistical reliability of the power spectrum
Fig. 8. Examples of heart rate series in three different species to
illustrate the presence of non-stationarities. x-axis: number of beats.
Upper panel, data from the red eared slider Trachemys scripta (stars
show the start of ventilation episodes) [7]. Middle panel, data from
the Atlantic cod Gadus morhua [7]. Lower panel, data from the
Atlantic salmon Salmo salar [11].
Several examples of stationary and non-stationary
instantaneous heart rate series are shown in Fig. 8.
Long-term heart rate series in reptiles are always nonstationary due to the highly unpredictable episodic
nature of the respiratory events. Ventilation bouts are
always coupled to tachycardia in order to improve
oxygen uptake when the lungs are ventilated (cardiorespiratory synchrony, [70]). This is seen in Fig. 8 for the
red-eared slider turtle Trachemys scripta, where average
heart rate during apnea was increased at the onset of a
ventilatory episode (signaled by stars in the figure). In
fish, non-stationarities often occur as a result of external disturbances to the animal resulting in sudden
bradycardias or tachycardias (as seen in the Atlantic
cod Gadus morhua in the middle panel on the right of
Fig. 8), and special care needs to be taken to avoid
these external perturbations.
A common test to verify stationary conditions is the
use of a run test [18]. The run test assumes that any
non-stationarity of interest will be revealed by changes
in the standard deviation of the data. This is likely to
occur for HR series, where non-stationarities of biological origin due to tachycardic or bradycardic periods
are usually coupled with changes in the total variation
of the signal.
4.3.2. Resolution of the spectral estimate
The resolution of the spectra is the reciprocal of the
total recording time [34]. Thus, the longer the data
The periodogram that results of each single computation of the FFT algorithm is a poor estimator of the
power spectrum due to the limitation of non-parametric
FFT-based methods previously discussed [57]. In order
to obtain a better estimate, two different methods are
of common use: the Welch method and the Blackman–
Tukey method.
The Welch method improves the statistical likelihood
of the estimated power spectrum by averaging the
periodogram of consecutive segments of data. Using
this approach, the iHR series is divided in segments
short enough to be stationary and long enough not to
limit the spectral resolution.
The Blackman–Tukey method relies on smoothing
the periodogram via a moving average window.
Both methods are not mutually exclusive and are
usually combined. An extended discussion on these
methods and their basic statistical properties can be
found elsewhere [57].
5. Are we trying to describe noise?
It should be clear at this point that heart rate variations reflect the output of a complex system and include
harmonic and non-harmonic components of physiological origin. Aside, the processing of the cardiac-event
signal might introduce artifactual noise that is important to minimize in order to obtain meaningful results.
If the criteria discussed in Section 4 are taken into
account, the HRVS is a coherent representation of the
combined complexities of chronotropic cardiac regulation irrespective of the species and the stage of development. In adult individuals this complexity is channeled
through the autonomic innervation of the sinoatrial
node of the heart. However, during early embryonic
development, HRV might be uncoupled from the immature autonomic innervation and linked to the mechanical stresses and tensions of cardiac organogenesis,
and this is an interesting area of research that remains
largely unexplored.
458
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
The degree to which the different methods of power
spectrum estimation are able to uncover the periodic
components of heart rate variations is directly related
to the technique itself and to the physiological status of
the system under study. On one hand, each technique
has advantages and limitations such as the sensitivity to
non-stationarities or spectral leakage and the spectral
resolution achieved. They have been discussed in Sections 3 and 4.
On the other hand, all the components of the HRVS
are subjected to the fine balance of the sympathovagal
autonomic outflow, which in turn is very sensitive and
responds promptly to internal and external perturbations. Not surprisingly, some of the best results in
comparative studies have been obtained by using
telemetry equipment on undisturbed animals [11,31].
To conclude, the application of spectral analysis
techniques to unveil the intricacies of the autonomic
regulation of heart rate in non-mammalian species is
not only possible but also necessary to understand the
evolution of cardiac control under different environmental and internal perturbations. Thus, the variations
of instantaneous heart rate should not be seen as noise
but as a valuable resource providing new information
on the mechanisms of heart rate homeodynamics. The
utility of the power spectrum estimation methods is
now firmly established and with this background
knowledge it is then possible to approach cardiovascular regulation in a highly integrative manner without
denying the value and the need of other experimental
methods.
Acknowledgements
The Dan Charitable Trust Fund for Research in
Biological Sciences of the Nippon Trust Bank Limited
provided financial support for the presentation of this
work at the International Symposium on ‘‘Cardiac
Rhythms in Animals: regulation, development and environmental influences’’ held in Muroran, Japan. Support from Waxman International is also greatly
appreciated.
References
[1] Akay M. Detection and Estimation Methods for Biomedical
Signals. San Diego: Academic Press, 1996.
[2] Akay M, Landesberg G, Welkowitz W, Akay YM, Sapoznikov
D. Carotid – cardiac interaction: heart rate variability during the
unblocking of the carotid artery. In: Sideman S, Beyar R, editors.
Interactive Phenomena in the Cardiac System. New York: Plenum,
1993:365 – 72.
[3] Akiyama R, Ono H, Höchel J, Pearson JT, Tazawa H. Non-invasive determination of instantaneous heart rate in developing avian
embryos by means of acoustocardiogram. Med Biol Eng Comput
1997;35:323 – 7.
[4] Akselrod S, Gordon D, Madwed JB, Snidman NC, Shannon DC,
Cohen RJ. Hemodynamic regulation: investigation by spectral
analysis. Am J Physiol 1985;249:H867– 75.
[5] Akselrod S, Gordon D, Ubel FA, Shannon DC, Barger AC,
Cohen RJ. Power spectrum analysis of heart rate fluctuation: a
quantitative probe of beat-to-beat cardiovascular control. Science
1981;213:220 – 2.
[6] Allen AM, Adams JM, Guyenet PG. Role of the spinal cord in
generating the 2-Hz to 6-Hz rhythm in rat sympathetic outflow.
Am J Physiol 1993;264:R938– 45.
[7] Altimiras J. Heart Rate Variability. Its Significance in Lower
Vertebrates. Ph.D. Thesis. Barcelona: Department of Biochemistry and Physiology, University of Barcelona, 1995.
[8] Altimiras J, Aissaoui A, Tort L. Is the short-term modulation of
heart rate in teleost fish physiologically significant? Assessment by
spectral analysis techniques. Braz J Med Biol Res 1995;28:1197–
206.
[9] Altimiras J, Feliu M, Aissaoui A, Tort L. Computing heart rate
variability using spectral analysis techniques: HRVUAB, a readyto-use program. CABIOS 1994;10:559 – 62.
[10] Altimiras J, Franklin CE, Axelsson M. Relationships between
blood pressure and heart rate in the saltwater crocodile Crocodylus
porosus. J Exp Biol 1998;201:2235– 42.
[11] Altimiras J, Johnstone ADF, Lucas MC, Priede IG. Sex differences in the heart rate variability spectrum of free-swimming
Atlantic salmon (Salmo salar L.) during the spawning season. Phys
Zool 1996;69:770 – 84.
[12] Altman PL, Dittmer DS. Respiration and Circulation. Bethesda,
MD: Federation of American Societies for Experimental Biology,
1971.
[13] Axelsson M. The importance of nervous and humoral mechanisms
in the control of cardiac performance in the Atlantic cod Gadus
morhua at rest and during non-exhaustive exercise. J Exp Biol
1988;137:287 – 303.
[14] Baselli G, Cerutti S, Civardi S, Liberati D, Lombardi F, Malliani
A, Pagani M. Spectral and cross-spectral analysis of heart rate and
arterial blood pressure variability signals. Comput Biomed Res
1986;19:520 – 34.
[15] Baselli G, Cerutti S, Civardi S, Lombardi F, Malliani A, Merri
M, Pagani M, Rizzo G. Heart rate variability signal processing:
a quantitative approach as an aid to diagnosis in cardiovascular
pathologies. Int J Bio-Med Comput 1987;20:51 – 70.
[16] Baselli G, Cerutti S, Civardi S, Malliani A, Orsi G, Pagani M,
Rizzo G. Parameter extraction from heart rate and arterial blood
pressure variability signals in dogs for the validation of a physiological model. Comput Biol Med 1988;18:1 – 16.
[17] Bassingthwaighte JB, Liebovitch LS, West BJ. Fractal Physiology.
New York: Oxford University Press, 1994.
[18] Bendat JS, Piersol AG. Random Data: Analysis and Measurement
Procedures. New York: Wiley Interscience, 1971.
[19] Bennett AF. Interindividual variability: an underutilitzed resource. In: Feder ME, Bennett AF, Burggren WW, Huey RB,
editors. New Directions in Ecological Physiology. Cambridge:
Cambridge University Press, 1987:147 – 69.
[20] Berntson GG, Cacioppo JT, Quigley KS. Respiratory sinus arrhythmia-autonomic origins, physiological mechanisms, and psychophysiological implications. Psychophysiology 1993;30:183–
96.
[21] Bianchi AM, Mainardi L, Petrucci E, Signorini MG, Mainardi M,
Cerutti S. Time-variant power spectrum analysis for the detection
of transient episodes in HRV signal. IEEE Trans Biomed Eng
1993;40:136 – 44.
[22] Bootsma M, Swenne CA, Vanbolhuis HH, Chang PC, Cats VM,
Bruschke AVG. Heart rate and heart rate variability as indexes
of sympathovagal balance. Am J Physiol 1994;266:H1565–71.
[23] Burggren W, Tazawa H, Thompson D. Genetic and maternal
environmental influences on embryonic physiology: intraspecific
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
variability in avian embryonic heart rates. Isr J Zool 1994;40:351 –
62.
Butler GC, Yamamoto Y, Hughson RL. Fractal nature of short
term systolic BP and HR variability during lower body negative
pressure. Am J Physiol 1994;267:R26–33.
Cerutti C, Barres C, Paultre C. Baroreflex modulation of blood
pressure and heart rate variabilities in rats: assessment by spectral
analysis. Am J Physiol 1994;266:H1993–2000.
Cerutti C, Gustin MP, Paultre CZ, Lo M, Julien C, Vincent M,
Sassard J. Autonomic nervous system and cardiovascular variability in rats: a spectral analysis approach. Am J Pathol
1991;261:H1292– 9.
Cerutti C, Gustin MP, Paultre CZ, Lo M, Julien C, Vincent M,
Sassard J. Role of the autonomic nervous system in blood pressure
and heart rate variability in rats — a spectral analysis approach.
In: Dirienzo M, Mancia G, Parati G, Pedotti A, Zanchetti A,
editors. Blood Pressure and Heart Rate Variability. Amsterdam:
Ios Press, 1992:180 –91.
Crowe JA, Gibson NM, Woolfson MS, Someck MG. Wavelet
transform as a potential tool for ECG analysis and compression.
J Biomed Eng 1992;14:268–72.
De Boer RW, Karemaker JM, Strackee J. Comparing spectra of
a series of point events particularly for heart rate variability data.
IEEE Trans Biomed Eng 1984;31:384–7.
De Vera L, González J. Power spectral analysis of short-term RR
interval and arterial blood pressure oscillations in lizard (Gallotia
galloti ): effects of parasympathetic blockade. Comp Biochem
Physiol A 1997;118:671–8.
De Vera L, Priede IG. The heart rate variability signal in rainbow
trout (Oncorhynchus mykiss). J Exp Biol 1991;156:611–7.
De Vera L, Priede IG. Ultradian oscillation in the heart rate of
rainbow trout (Oncorrhynchus mykiss). Comp Biochem Physiol A
1993;106A:183– 6.
Delaney RG, Lahiri S, Fishman AP. Aestivation of the African
lungfish Protopterus aethiopicus: cardiovascular and respiratory
functions. J Exp Biol 1974;61:111–28.
Dempster J. Computer Analysis of Electrophysiological Signals.
London: Academic Press, 1993.
Elghozi J-L, Laude D, Girard A. Effects of respiration on blood
pressure and heart rate variability in humans. Clin Exp Pharmacol
Physiol 1991;18:735 –42.
Goldberger AL. Is the normal heartbeat chaotic or homeostatic?
NIPS 1991;6:87 – 91.
Goldberger JJ, Ahmed MW, Parker MA, Kadish AH. Dissociation of heart rate variability from parasympathetic tone — rapid
communication. Am J Physiol 1994;266:H2152–7.
González J, De Vera L. Spectral analysis of heart rate variability
of lizard, Gallotia galloti. Am J Physiol 1988;254:R242–8.
Hayano J, Sakakibara Y, Yamada A, Yamada M, Mukai S,
Fujinami T, Yokoyama K, Watanabe Y, Takata K. Accuracy of
assessment of cardiac vagal tone by heart rate variability in normal
subjects. Am J Cardiol 1991;15:199–204.
Hayano J, Mukai S, Sakakibara M, Okada A, Takata K, Fujinami
T. Effects of respiratory interval on vagal modulation of heart rate.
Am J Physiol 1994;267:H33–40.
Jaffe RS, Fung DL, Behrman KH. Optimal frequency ranges for
extracting information on autonomic activity from the heart rate
spectrogram. J Autonom Nerv Syst 1994;46:37–46.
Kingwell BA, Thompson JM, Kaye DM, McPherson GA, Jennings GL, Esler MD. Heart rate spectral analysis, cardiac norepinephrine spillover, and muscle sympathetic nerve activity during
human sympathetic nervous activation and failure. Circulation
1994;90:234 – 40.
Kobayashi M, Musha T. 1/f fluctuation of heartbeat period. IEEE
Trans Biomed Eng 1982;29:456–7.
Levy MN, Martin PJ. Neural control of the heart. In: Berne RM,
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[59]
[60]
[61]
[62]
[63]
[64]
459
Sperelakis N, editors. Handbook of Physiology. The Cardiovascular System. I. The heart. Bethesda, MD: American Physiological
Society, 1979:581 – 620.
Li Z, Grant BJB, Lieber BB. Time-varying pulmonary arterial
input impedance via wavelet decomposition. J Appl Physiol
1995;78:2309 – 19.
Livnat A, Zehr JE, Broten TP. Ultradian oscillations in blood
pressure and heart rate in free-running dogs. Am J Physiol
1984;246:R817– 24.
Madwed JB, Albretcht P, Mark RG, Cohen RJ. Low-frequency
oscillations in arterial pressure and heart rate: a simple computer
model. Am J Physiol 1989;256:H1573– 9.
Malliani A, Lombardi F, Pagani M. Power spectrum analysis of
heart rate variability — a tool to explore neural regulatory
mechanisms. Br Heart J 1994;71:1 – 2.
Malliani A, Pagani M, Lombardi F. Importance of appropriate
spectral methodology to assess heart rate variability in the
frequency domain. Hypertension 1994;24:140 – 1.
Malliani A, Pagani M, Lombardi F, Cerutti S. Cardiovascular
neural regulation explored in the frequency domain. Circulation
1991;84:482 – 92.
Merri M, Farden DC, Mottley JC, Titlebaum EL. Sampling
frequency of the electrocardiogram for spectral analysis of the
heart rate variability. IEEE Trans Biomed Eng 1990;17:99–106.
Milsom WK, Burlington RF, Burleson ML. Vagal influence on
heart rate in hibernating ground squirrels. J Exp Biol 1993;185:25–
32.
Moser M, Lehofer M, Sedminek A, Lux M, Zapotoczky HG,
Kenner T, Noordergraaf A. Heart rate variability as a prognostic
tool in cardiology — a contribution to the problem from a
theoretical point of view. Circulation 1994;90:1078 – 82.
Novak P, Novak V. Time/frequency mapping of the heart rate,
blood pressure and respiratory signals. Med Biol Eng Comput
1993;31:103 – 10.
Ong JJC, Sarma JSM, Venkataraman K, Levin SR, Singh BN.
Circadian rhythmicity of heart rate and QTc interval in diabetic
autonomic neuropathy — implications for the mechanism of
sudden death. Am Heart J 1993;125:744 – 52.
Pan J, Tompkins WJ. A real-time QRS detection algorithm. IEEE
Trans Biomed Eng 1985;32:230 – 6.
Proakis JG, Manolakis DG. Digital Signal Processing. Principles,
Algorithms and Applications. Singapore: Maxwell MacMillan
International, 1992.
Rompelman O, Coenen AJRM, Kitney RI. Measurement of
heart-rate variability. Part 1-Comparative study of heart-rate
variability analysis methods. Med Biol Eng Comput 1977;15:233–
9.
Sahambi JS, Tandon SN, Bhatt RKP. Using Wavelet transforms
for ECG characterization. IEEE Eng Med Biol Mag 1997;16:77–
83.
Sands KE, Appel ML, Lilly LS, Schoen FJ, Mudge GHJ, Cohen
RJ. Power spectrum analysis of heart rate variability in human
cardiac transplant recipients. Circulation 1989;79:76 – 82.
Sapoznikov D, Luria MH, Mahler Y, Gotsman MS. Computer
processing of artifact and arrhythmias in heart rate variability analysis. Comput Method Program Biomed 1992;39:75–
84.
Sarma JSM, Singh N, Schoenbaum MP, Venkataraman K, Singh
BN. Circadian and power spectral changes of RR and QT intervals
during treatment of patients with angina pectoris with nadolol
providing evidence for differential autonomic modulation of heart
rate and ventricular repolarization. Am J Cardiol 1994;74:131–
6.
Saul JP. Beat-to-beat variations of heart rate reflect modulation
of cardiac autonomic outflow. NIPS 1990;5:32 – 7.
Shin SJ, Tapp WN, Reisman SS, Natelson BH. Assessment of
autonomic regulation of heart rate variability by the method of
460
J. Altimiras / Comparati6e Biochemistry and Physiology, Part A 124 (1999) 447–460
complex demodulation. IEEE Trans Biomed Eng 1989;36:274 – 83.
[65] Smith JJ, Kampine JP. Circulatory Physiology — The Essentials.
Baltimore: Williams and Wilkins, 1990.
[66] Takalo R, Korhonen I, Turjanmaa V, Majahalme S, Tuomisto M,
Uusitalo A. Short-term variability of blood pressure and heart rate
in borderline and mildly hypertensive subjects. Hypertension
1994;23:18 – 24.
[67] Takalo R, Korhonen I, Turjanmaa V, Majahalme S, Uusitalo A.
Importance of appropriate spectral methodology to assess heart
rate variability in the frequency domain — response. Hypertension 1994;24:141 – 2.
[68] Tenvoorde BJ, Faes TJC, Rompelman O. Spectra of data sampled
at frequency-modulated rates in application to cardiovascular
signals. 1. Analytical derivation of the spectra. Med Biol Eng
Comput 1994;32:63 –70.
[69] Territo PR, Altimiras J. The ontogeny of cardio-respiratory
.
[70]
[71]
[72]
[73]
[74]
function under chronically altered gas compositions in Xenopus
lae6is. Resp Physiol 1998;111:311 – 23.
Wang T, Hicks JW. Cardiorespiratory synchrony in turtles. J Exp
Biol 1996;199:1791 – 800.
Yamamoto Y, Fortrat J-O, Hughson RL. On the fractal nature
of heart rate variability in humans: effects of respiratory sinus
arrhythmia. Am J Physiol 1995;269:H480– 6.
Yamamoto Y, Hughson RL. Coarse-graining spectral analysis:
new method for studying heart rate variability. J Appl Physiol
1991;71:1143 – 50.
Yamamoto Y, Hughson RL. On the fractal nature of heart rate
variability in humans: effects of data length and beta-adrenergic
blockade. Am J Physiol 1994;266:R40 – 9.
Yamamoto Y, Nakamura Y, Sato H, Yamamoto M, Kato K,
Hughson RL. On the fractal nature of heart rate variability in
humans: effects of vagal blockade. Am J Physiol 1995;269:R830–
7.