Vol. 283, Issue 3, H1142-H1149, September 2002
Scaling vs. nonscaling methods of assessing autonomic tone in
streptozotocin-induced diabetic rats
Itay
Perlstein1,
Nir
Sapir3,
Joshua
Backon1,
Dan
Sapoznikov2,
Roman
Karasik3,
Shlomo
Havlin3, and
Amnon
Hoffman1
1 Department of Pharmaceutics, School of Pharmacy,
Hebrew University of Jerusalem, Jerusalem 91120;
2 Department of Cardiology, Hadassah University
Hospital, Jerusalem 91120; and 3 Minerva Center and
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
 |
ABSTRACT |
We studied heart rate variability
in rats by power scaling spectral analysis (PSSA), autoregressive
modeling (AR), and detrended fluctuation analysis (DFA), assessed
stability by coefficient of variation between consecutive 6-h epochs,
and then compared cross-correlation among techniques. These same
parameters were checked from baseline conditions through acute and
chronic disease states (streptozotocin-induced diabetes) followed by
therapeutic intervention (insulin). Cross-correlation between methods
over the entire time period was r = 0.94 (DFA and
PSSA), r = 0.81 (DFA and AR), and r = 0.77 (AR and PSSA). Under baseline conditions the scaling parameter
measured by DFA and PSSA and the high-frequency (HF) component measured
by AR fluctuated around an average value, but these fluctuations were
different for the three methods. After diabetes induction, a
strong correlation was found between the HF power and the short-term
scaling parameter. Despite their differences in methodology, DFA and
PSSA assess changes in parasympathetic tone as detected by
autoregressive modeling.
heart rate variability; autoregressive modeling; detrended
fluctuation analysis; circasemiseptan rhythm; power scaling spectral
analysis
| |
INTRODUCTION |
ASSESSMENT OF
CARDIAC autonomic tone by analysis of heart rate
variability (HRV) has been used to investigate such conditions as
congestive heart failure, myocardial infarction, hypertension, neurological injury, diabetic neuropathy, prematurity of birth, pharmacodynamics, and mental stress and the effect of exercise. HRV has
been assessed by using parametric (autoregressive modeling, AR) methods
to determine the power spectral density (PSD) as well as by scaling
techniques. The advantages of parametric methods for calculating the
PSD are the following: smoother spectral components that can be
distinguished independently of preselected frequency, easy
postprocessing of the spectrum with an automatic calculation of low-
and high-frequency (HF) power components and easy identification of the
central frequency of each component, and an accurate estimation of PSD
even on a small number of samples on which the signal is supposed to
maintain stationarity (23). Nonstationarity in typical heart rate time series severely limits the range of frequencies that
can be studied by conventional frequency-domain analytic methods. The
frequency-domain analysis is used to measure the HF power to estimate
parasympathetic nervous system (PNS) activity. A scaling technique in
the frequency domain, power spectrum scaling analysis (PSSA), has also
been used (4). PSSA estimates the scaling parameter as the
slope of the linear regression of the log-log plot of the PSD. Only the
linear region of the plot is selected for regression. PSD is calculated
with a nonparametric method [fast Fourier transform (FFT)]. Because
the method cannot identify the underlying structure of physiological
fluctuations if there are trends due to external environmental
influences, a scaling technique called detrended fluctuation analysis
(DFA) was developed (25). DFA permits the detection of
correlations embedded in the seemingly nonstationary time series,
and this avoids the spurious detection of apparent long-term
correlations that are an artifact of nonstationarities
(17). In the present study, the scaling methods are used
to investigate short-term correlations in the heartbeat
expressing short-term memory between beats.
Although HRV has been studied in clinical and animal studies with a
variety of techniques [6 studies (Refs. 2,
7, 8, 13, 28,
29) compared FFT to autoregressive power spectral analysis
(AR) with a time period of 5-10 min; 2 studies (Refs. 1, 6) compared FFT to AR with a 24-h epoch],
there have been very few studies carrying out simultaneous comparisons.
One study (15) compared spectral powers and scaling
parameters with a 2-h epoch; two studies (17, 34) compared
the scaling parameters with spectral powers with a short-term epoch;
and two studies (22, 27) compared the two with a 24-h
epoch. Yet no multiple HRV measurement techniques have ever been
simultaneously investigated in instrumented rats under baseline
conditions, disease states, and therapeutic interventions comparing
spectral powers with scaling methods.
Cardiac autonomic neuropathy is a common complication in
insulin-dependent diabetes mellitus (IDDM) and is clearly displayed by
a decrease in HRV (3). Streptozotocin (STZ) is widely used to induce diabetes in animals as a model of IDDM (18). STZ
impairs cardiac vagal tone in rats within 5 days of injection
(21). There is a decrease in time-domain HRV
(9) as well as frequency-domain HRV (10) in
rats with chronic STZ-induced diabetes. This decrease in
frequency-domain HRV has also been found in chronic STZ-induced diabetic Yucatan pigs (24). However, insulin treatment
restores normal cardiovascular function during the early stages of
diabetes in rats as measured by baroreceptor reflex control
(5) and time-domain HRV (33).
Because longer-term physiological fluctuations may be due to endocrine
systems and metabolic processes (17), and no long-term sequential HRV studies comparing PNS activity and scaling measures have
ever been carried out using healthy rats made diabetic by STZ and then
checking for the effect of insulin on these HRV parameters, we
investigated the short- and long-term effect in healthy rats made
diabetic by STZ, the effect of insulin on the scaling parameter as well
as on the autonomic nervous system response, and the relations between
them. The main question to be investigated was whether in disease
states the short-term scaling parameter could serve as an index for
changes in parasympathetic vagal tone as detected by classic spectral analysis.
| |
METHODS |
Animals
Three male Sabra rats weighing 300-350 g were housed
separately in plastic cages and maintained on a 12:12-h light-dark
cycle with food and water available ad libitum. The project adhered to
the principles of laboratory animal care published by the National Institutes of Health (NIH Publication No. 85-23, Revised 1985).
Compounds
A solution of 0.2 mg/ml streptozotocin
(N-[methylnitrosocarbamoyl]-D-glucosamine;
Sigma, St. Louis, MO) in physiological solution (0.9% sodium chloride
injection USP; Teva Medical, Ashdod, Israel) was freshly prepared. Two
international units of injectable insulin (Actrapid HM-biosynthetic
human insulin; Novo Nordisk, Bagsvaerd, Denmark) were dissolved in 0.3 ml of physiological solution.
Drug Treatment Protocol
After 1 wk of baseline recording, rats were injected with STZ
solution. Three months after diabetic onset, the rats were treated with
insulin injections.
The diabetic state was confirmed by monitoring blood glucose levels
before and after diabetic onset and insulin treatment. Blood samples
were obtained by tail prick, and blood glucose concentration was
measured with a commercial monitor (Glucometer Elite XL; Bayer, Tarrytown, NY). Glucose concentrations were determined to be 100 mg/dl
for baseline ("healthy") condition, 
300 mg/dl for the diabetic state, and <170 mg/dl after insulin treatment.
Telemetry System
To minimize stress involved with data collection, a
telemetric monitoring system was implanted in the peritoneal cavity
under anesthesia (50 mg/kg ketamine and 10 mg/kg xylazine ip).
Preventive antibiotic treatment was given subcutaneously 30 min before
the operation. The telemetric device is a small (2 × 0.5") two-lead electrocardiogram (ECG) radio frequency transmitter (TCA-F40; DSI). The leads were tunneled subcutaneously to their positions at the right acrotrapezoidal muscle and the left gluteus muscle. Recording and experiments took place after a recovery period of 1 wk.
Signal Acquisition System
Data were acquired with a telemetry system that contained the
implantable radio frequency transmitter and a receiver (RCA-1020; DSI)
located below the cage. Analog signals were transmitted to a computer
(586 Pentium, 133 MHz) and digitized at a sampling rate of 600 Hz by an
analog-digital converter (PCL 818 HG; ICPC). The R-R interval data were
obtained online from the continuous ECG records by a threshold peak
algorithm. The R peak was identified by crossing a dynamic threshold
ranging between ±20% of the peak initially determined by the user.
The following R peak was determined after a specified (35 ms) lag time
to prevent a mistaken T peak identification. The threshold midrange was
then set with the new detected value. R-R interval data expressed in
milliseconds were recorded on continuous 1-h-length files.
Data Analysis
Autoregressive preprocessing.
artifact elimination.
Epochs of 120,000- or 1,200,000-ms duration were chosen for
calculation. Artifact elimination was performed by replacing an R-R
interval sample that exceeded both the previous sample R-R interval and
the epoch-average R-R interval by more than a prescribed value (50 and
80 ms, respectively) with the average R-R interval. Higher than 1%
correction of a single epoch was determined as the exclusion criterion.
In general, approximately <2% of the data were omitted
(26). To reduce the effect of a slow nonperiodic variation
of the parameters, detrending was performed by calculating a smoothed
moving polynomial and subtracting it from the original signal
(32).
AUTOREGRESSIVE POWER SPECTRUM ANALYSIS.
Autoregressive (AR) power spectrum analysis is based on time series
parametric modeling. Parametric modeling for power spectrum estimation
consists of an appropriate choice of a model, estimation of the
parameters of the model, and then substitution of these estimated
values into the theoretical power spectrum density (PSD) expressions.
An AR time series model is chosen, the parameters (a) of the
model are estimated, and PSD is calculated from these parameters. The
model output, which is the estimated R-R interval at a time point
n, is given by
where p is the order of the model and denotes the
number of terms in the time series model and
k is the kth coefficient of the
model. The input driving process is assumed to be a white noise
sequence of zero mean and variance of 
2. The
autocorrelation function, R(k), of the time series is first calculated. The Yule-Walker equations, which describe the relationship between the autocorrelation function and the AR parameters are then
derived.
where 2 is the variance of the white noise input
of the AR model and j is an order index. To solve
these equations for the AR parameters, the Levinson-Durbin algorithm is
implemented. The Levinson-Durbin algorithm is initialized by
and the recursion for k = 2,3, ...
p is given by
where i is an order index. The Levinson-Durbin
algorithm provides the coefficients of the autoregressive model of the
order p. The power spectrum of an output of a autoregressive
model with a white noise input of power spectrum of
2
t is related to the AR parameters by
where t is the sampling interval of the original
R-R signal calculated as the mean R-R interval during the epoch and
f is the frequency. The model order p selection
is generally chosen by several criteria such as the Akaike information
criterion or Parzen's criterion autoregressive transfer
function. The 16th-order AR model with a 301-point moving
polynomial was found to be the most suitable and serves as a good
compromise between a power spectrum that is too smooth and one with too
many peaks (19, 30, 31). The logarithmic values of the
distinct HF peak (range 1.35-2.65 Hz) served as markers (index)
for changes in PNS activity.
Detrended fluctuation analysis.
DFA is a modified root-mean-square analysis of a random walk. In DFA,
the numerical value of the scaling exponent is indicative of the
type and degree of correlation present in the heart rate data and can
be thought of as an indicator of the "roughness" of the time series
data (25).
The correlations in a time series between the steps
ui and
ui+n are defined by the autocorrelation function
|
(1)
|
where N is the length of the series and n
is the distance between the steps. In systems in which there are
long-range correlations, the nature of the correlations is of a power
law
|
(2)
|
where 
is the autocorrelation exponent. By integration of a
time series with long-range correlations, a self-affine process is
formed. The scaling properties of the integrated series are connected
to the long-range correlation properties of the original time series.
If we consider then the profile of the time series, the accumulated sum
Yn = 
ui, its fluctuations
F(n) as a function of different scales n are related to C(n) and increase by a power law
|
(3)
|
where is referred to as the scaling exponent or the
self-similar parameter and is equivalent to the Hurst exponent in the range 0 < < 1. However, the values can take are not
limited to that range.
The power spectrum of the original time series decreases by a
power law
|
(4)
|
The relation between and 
is
|
(5)
|
The case of = 1/2 still represents a fractal,
but one that has no correlation, like the steps of a random walker. The
fluctuations of a random walk (the standard deviation of its position)
acts as a scaling law, y ~ t1/2,
with = 1/2, so it is a fractal (11). When
the data are correlated > 1/2, and when the data are
anticorrelated < 1/2.
Calculations of short-time scale scaling exponent.
dfa.
The DFA is used to calculate the root mean square fluctuation of the
integrated and detrended time series for different time scales and is
actually a modified root-mean-square analysis of a random walk. The DFA
(order m) steps are as follows: 1) A profile is created
|
(6)
|
2) The profile is divided into nonoverlapping windows
of size l, and then the local polynomial trend of order
m in each window is calculated. This is achieved by the
least-squares fit method. 3) The variance is calculated
around the local trend in each window, to eliminate trends of order
m 
1 in the original time series; the variances
from all windows of size l are then averaged over number of
windows, and the square root of the result is the fluctuation function
F(l).
The fluctuation function is then plotted on a log-log scale, and
the scaling exponent is calculated from the slope of the line. In some
cases, there exists crossover from a short-scale scaling exponent to a
long-scale scaling exponent, meaning that the function has a certain
slope in the short-scale regime but a different slope in the long-scale
regime. Two separate scaling exponents are then considered. The
short-scale exponent, 1, is the slope up to the
crossover point, and the long-scale scaling exponent, 2,
is the slope from the crossover point (16). The scaling
exponents are used as monofractal measures of the heartbeat.
DFA of order m measures the scaling exponent accurately in
the range 0.5 < < m + 0.5. When a
scaling exponent < 1/2 is suspected, extra integration
is applied to the time series to increase the value of the scaling
exponent by 1. The fluctuations are then 
(l)
~l
+1. DFA can then reliably calculate the
new scaling exponent. We subtract 1 from the value of the new scaling
exponent to obtain the original scaling exponent. In such a way, values
of < 1/2 can now be estimated correctly, including
negative values.
We summed the data of each 20-min epoch and then applied the DFA of
order 2 on the summed series. We then plotted
(l)/l in log-log scale and calculated the
slope of the line up to a window of size 10, where there was the
crossover point. This scaling exponent is denoted as
.
PSSA.
The power spectrum S(f) is calculated with FFT of the time series
where
The square root of the power spectrum is then plotted into a
log-log scale, and again the crossover point is determined. The slopes
are then calculated and named for small frequencies and for high frequencies.
We plotted
in log-log scale and calculated 
from
f = 0.1 beat
1 to f = 0.3 beat1 to avoid the peak in the power spectrum associated
with breathing. corresponds with
as the high frequencies correspond with small
windows. was then calculated with Eq. 5.
Baseline and Disease State Measurements and Significance of
Analysis
The analysis was done for each rat independently of the others.
To compare between the methods, analysis of multiple observations was
performed for the same rats with the actual values of , , or HF
power for 20-min epochs. The values were cross-correlated between the
different measures of the same data for the same rat (over the entire
period of time), and therefore the sample size is considered not as the
number of animals but rather the number of epochs.
The stability of the short-term scaling parameter and of the HF power
was investigated during 24 consecutive 6-h epochs of HRV in healthy
instrumented rats. Coefficients of variation between consecutive 6-h
epochs were used to ascertain stability of measurement. Cross
correlations among the three techniques were also evaluated.
Because of the similarity of the results obtained with different
methods in different animals, an average value was used to describe the
values at each steady condition of the rats (healthy, acute, chronic,
insulin). The total epochs of the healthy state formed one average, to
which each daily epoch in the disease states was compared. Hence, each
state holds a distribution of values (corresponding to the 20-min epochs).
ANOVA tests were performed to distinguish the insulin treatment from
the healthy state as well as from the acute and chronic diabetic
states. Two-sample t-tests were performed for the baseline condition as well as all the diabetic days and the nadirs and peaks of oscillation.
| |
RESULTS |
After the initial week of the baseline period, the rats were given
STZ. After a 10-day waiting period, an acute effect of STZ-induced
diabetic neuropathy was observed with all three techniques. The
instrumented rats were kept in cages for another 3-mo period to
evaluate the effects of chronic diabetes. At the end of this 3-mo
period, HRV was investigated with the three techniques. After this
measurement, insulin was given and the three HRV techniques were again
applied. As parameters of measurement, we used only the HF power
associated with respiration and the short-term scaling parameter.
Figure 1A shows a typical
example of an R-R interval file, and its PSD calculated with the fast
Fourier transform is shown in Fig. 1B. Figure
2 shows the coefficient of variation of
the three methods in healthy rats during a 5-day period. The least amount of variation was in DFA. Thus, although DFA had the lowest amount of noise, it was the least sensitive, with the HF power having
>2.5 times higher levels. To investigate whether there were
differences in the use of 2-min epochs vs. 20-min epochs, we compared
AR plots of both epochs with a moving polynomial spline and found that
the two patterns were highly similar (not shown). DFA and PSSA were
performed over 20-min epochs only. In the healthy baseline stage, the
HRV exhibited uncorrelated behavior in the short time scales (averaged
scaling parameter close to 0.5), meaning that the heart beats were not
influenced by previous beats (i.e., no short-term memory).
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Fig. 1.
A: typical example of an R-R interval file.
B: its power spectral density (PSD) calculated with the fast
Fourier transform. f, Frequency; S(f), power
spectrum function.
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Fig. 2.
Coefficient of variation among 3 methods of heart rate
variability (HRV) analysis [power scaling spectral analysis (PSSA),
autoregressive modeling (AR), and detrended fluctuation analysis
(DFA)] obtained from healthy rats over a 5-day period. HF, high
frequency.
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Figure 3, A-C, shows the
correlation between measurements obtained by the three analysis methods
over the entire time period (healthy, acute/chronic diabetic state
induced by STZ, insulin). A comparison between the short-term scaling
parameters as obtained by the two different scaling techniques, PSSA
and DFA, produced the highest correlation (0.94, shared variance = 88%). High correlation was found between the short-term scaling
parameter and the logarithm of the HF power. The linear correlation of
the scaling parameter as measured by DFA and the logarithm of the HF
power yielded (0.85, shared variance = 72%), and between the
scaling parameter as measured by PSSA and the logarithm of the HF power
it yielded (0.8, shared variance = 64%). The DFA and PSSA
techniques are used to measure the same quantity (scaling parameter),
so we expect strong correlation between the results of the two.
However, the HF power is a different quantity that serves as a marker
for PNS activity. Our results show that the effect of the disease on
both quantities is correlated.
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Fig. 3.
Correlation between the 3 methods of HRV analysis over
the entire time period. A: vs.
. B: vs. HF
power by AR. C: vs. HF power by
AR.
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Figure 4 shows the percentage of change
of the logarithm of the HF power as detected by AR and of the
short-term scaling parameter by two different scaling techniques,
through the diabetic progression and after insulin treatment. Because
the measured parameters have both positive and negative values, a
change of the values from positive to negative results in >100%
decrease. From baseline to the STZ acute stage, the most sensitive
method was AR with 170% change, followed by PSSA with 163%; the
least sensitive method was DFA with 137% change (P < 0.0001 for all). From baseline to 13- to 23-day chronic STZ, the
most sensitive method was AR with 67% change, followed by DFA with
41%; the least sensitive method was PSSA with 33% change
(P < 0.0001 for all). From baseline to 3-mo chronic
STZ the most sensitive method was the AR with 46% change
(P < 0.0001). Although large differences were observed by the PSSA and DFA methods (85% and 65% change, respectively), the significance of these results was less profound (P > 0.1 for both). From baseline to insulin treatment, the most
sensitive method was PSSA with 47% increase, followed by DFA with 41%
(P < 0.0001 for both); the least sensitive method was
AR with 3% change (P < 0.05). After insulin
treatment a significant increase of values was observed by all the
three methods (P < 0.0001) from the far chronic
diabetic state. A full recovery to control values was detected
by both DFA and AR methods. More profound increase was detected by the
PSSA method, where the values were found to be significantly higher
than the control values (P < 0.05).
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Fig. 4.
HF power in healthy rats and the short-term scaling
parameter measured by DFA and PSSA through the diabetic progression and
after insulin treatment. Changes in the HF power log and in the scaling
parameter are presented as the percentage of change from the baseline
condition of healthy rats. Mean data are presented at 10 days after
diabetes induction (acute diabetic state), at 2-3 wk and 3 mo
after STZ diabetes induction (stable chronic diabetic state), and after
insulin administration to chronic (3-mo duration) diabetic rats.
Decreases of >100% are observed at the acute diabetic state, where
negative values are detected.
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Figure 5 shows the evolution of the
scaling parameter before and after STZ induction of diabetes. The
division for the different states of the disease was based on this type
of picture, which repeated itself for different rats. The -values at
the healthy state were not statistically different from 0.5, according
to the single distribution t-test, therefore representing
fractals that have no correlations. After the induction of STZ, HRV
showed an anticorrelated behavior (scaling parameter < 0.5) in
the short time scales. This shows that the following heartbeats act in
an inverse manner to the previous beats. Significant change from the
healthy condition (P < 0.05) was first observed by the
DFA method, 3 days after STZ administration. Such significant change was observed by the other methods (AR and PSSA) 1 day later.
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Fig. 5.
Mean ± SD scaling parameter calculated by DFA of
the second order on the integrated series over periods of
24 h. STZ administration was on the 10th day from the beginning of
the study. The acute phase was determined by the minimal value of the
scaling parameter and occurred 10 days after the STZ induction. On the
following day the scaling parameter increased rapidly toward normal
values. In the following 9-day period, the behavior of the scaling
parameter was found to be periodic (see Fig. 7). This period was
considered as chronic.
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Figure 6 shows strong correlation between
the daily averaged scaling parameters for different rats.
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Fig. 6.
Correlation between data sets of different rats. The
strong correlation indicates a strong resemblance. The rats were of the
same breed, and it manifests in the similar behavior of the scaling
parameter of the interbeat series.
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Figure 7 shows an interesting phenomenon
of an apparent 96-h cycle (circasemiseptan rhythm) in the scaling
parameter of the HRV starting ~10 days after STZ induction. The same
pattern was found with both scaling techniques and by the HF power.
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Fig. 7.
Periodicity in the scaling parameter, measured by DFA
found throughout the chronic diabetic phase. A representative 2-wk
period reveals an ~4-day periodicity (emphasized by regression).
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DISCUSSION |
This is the first study to investigate the stability and
cross-correlation of an indicator of PNS status and the short-term scaling parameter of HRV from baseline conditions through the evolution
of a disease, followed by therapeutic intervention. This study measures
and compares two different parameters, the HF power (1.5-2.65 Hz)
and the short-term scaling parameter. HF power has been established in
numerous investigations as an indirect marker related to
parasympathetic tone and respiratory sinus arrhythmia (23). Using conventional AR spectral analysis, we found
that in different stages of STZ-induced diabetes there were marked changes in PNS activity. This framework enabled us to assess the impact
of changes in PNS activity on the short-term memory of HRV. Despite
their differences in methodology and frequency, there was a high
correlation (0.85) between the parameters over the entire time period.
This suggests that a relationship exists between respiration and the
short-term correlations, a possibility also raised by Toweill et al.
(34). Because respiration is a periodic activity that
modulates the heart rate, it affects the short-term correlations between heartbeats and introduces a characteristic time scale. Surprisingly, the increased breathing activity was connected with a
stronger anticorrelation behavior of the short-term memory of the heartbeat.
The fractal measures of HRV complement the conventional measures
because they can uncover "hidden" information in the time series
data. DFA was developed in an attempt to distinguish between two
different classes of fluctuations in physiological data sets, those
that arise from changes in environmental conditions having little to do
with the intrinsic dynamics of the system itself and those that arise
from complex nonlinear dynamic interactions inherent to the system
(25). Whereas in a study using techniques of HRV to
predict imminent ventricular fibrillation DFA performed better than any
other measure of HRV in differentiating between patients with
ventricular fibrillation and controls (22), in another
study predicting survival in patients with congestive heart failure,
DFA was of borderline predictive significance when multivariate models
were used (15).
We found that the scaling parameter obtained by DFA had the least
amount of noise in baseline (having the lowest coefficient of
variation), and this scaling parameter was accordingly used to define
the status of the rat. The scaling parameters obtained by PSSA and DFA,
PSSA and DFA, are linearly related
(14). Indeed, our findings show a high correlation between
and .
We found that, after STZ administration, the scaling parameter
decreased for 10 days and then reached a minimal value. After that
acute chronic phase, a milder chronic state was obtained. Throughout
the chronic period, although the HF power and the scaling parameter
values fluctuated, they were significantly lower than the baseline
condition. Previously, such a significant decrease in the HF power was
recorded after 12-18 wk in STZ-induced diabetic rats
(10) and also at age 8-9 mo in the WBN/kob
spontaneous diabetic rat model (12).
Schaan et al. (33) showed that insulin infusion increased
time domain parameters of HRV in STZ diabetic rats during the early
stages of diabetes. We found that insulin administration (via the
intramuscular route) increased HF power in 3-mo chronic STZ diabetic
rats and restored it to baseline (healthy) levels. More profound
increase was detected by both the short-term scaling methods, where in
the case of PSSA values even significantly exceeded the control
(healthy) levels. In all three methods, however, remarkable changes
were detected before and after insulin administration. The effect of
insulin administration in the healthy state was not included in the
original design of the study.
Whether this study can be extrapolated to human studies remains to be
seen. The STZ model is not exactly analogous to human diabetes. A
common feature of STZ-induced diabetes is glucose insensitivity
(20), which does not occur in the human disease. Finally,
the intriguing phenomenon of a 96-h cycle (circasemiseptan rhythm) in
the HF power and scaling parameter (Fig. 7) may represent an infradian rhythm.
Our findings show that the short-term scaling parameter is related to
the HF power and is proportional to its logarithm. Therefore, we may
quantify the changes in the complex behavior of HRV in relation to the
disease state and as an index for autonomic nervous system functioning.
The changes in parasympathetic vagal tone can be assessed by changes in
the short-term scaling parameter.
| |
ACKNOWLEDGEMENTS |
A. Hoffman is affiliated with the David R. Bloom Center of
Pharmacy. This work is part of the PhD dissertation of I. Perlstein.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: A. Hoffman, Dept. of Pharmaceutics, School of Pharmacy, Hebrew Univ. of
Jerusalem, PO Box 12065, Jerusalem 91120, Israel (E-mail:
ahoffman{at}cc.huji.ac.il).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
May 30, 2002;10.1152/ajpheart.00519.2001
Received 14 June 2001; accepted in final form 1 May 2002.
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