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Results
The synthetic ECG (Fig. 5) illustrates
the modulation of the QRScomplex due to RSA.
Observational uncertainty is incorporated by adding normally
distributed measurement errors with mean zero
and standard deviation 0.025 mV (Fig. 6a),
yielding a similar signal to a segment of real ECG from a normal human
(Fig. 6b).
In order to illustrate the
dynamics of the RRintervals obtained from this synthetic ECG, peak detection
was used to identify the times of the Rpeaks.
In the noisefree case, a simple algorithm which looks for local maxima
within a small window is sufficient. For ECGs with noise and artefacts it
may be necessary to use more complicated methods [2,3].
A comparison between the continuous process with power spectrum
given by (3) and the piecewise constant
reconstruction of the RRprocess obtained from the Rpeak detection
(Fig. 7) illustrates the measurement errors that
arise when computing heart rate variability statistics from
RRintervals.
The RRintervals (Fig. 8a) and corresponding
instantaneous heart rate (Fig. 8b)
in units of beats per minute (bpm)
for a mean of 60 bpm and standard deviation of 5 bpm
display variability due to both RSA and Mayer waves.
A spectral estimation technique
for unevenly sampled time series, the Lomb periodogram
[15,16], was used to calculate the power
spectrum (Fig. 8c) from the RR tachogram,
derived from 5 minutes of data as recommended
by [7,10].
Despite the loss of information in going from the continuous process to the
piecewise constant reconstruction, a comparison between Fig. 4 and
Fig. 8c illustrates that it is still
possible to obtain a reasonable estimate of the power spectrum.
Figure 5:
ECG generated by dynamical model: (a) 10 seconds and (b) 50 seconds.

Figure 6:
Comparison between (a) synthetic ECG with additive normally
distributed measurement errors and (b) real ECG signal from a normal human.

Figure 7:
Reconstruction of RRprocess from Rpeak detection:
the underlying RRprocess generated using (3) (black line)
and the RRinterval time series obtained using Rpeak
detection of the synthetic ECG (grey line).

Figure 8:
Analysis of RRintervals from Rpeak detection of the ECG signal
generated by the dynamical model (1) with mean heart rate 60 bpm
and standard deviation 5 bpm: (a) RRintervals,
(b) instantaneous heart rate and (c) power spectrum of the RRintervals.
Note the two active frequencies belonging to RSA (0.25 Hz) and Mayer
waves (0.1 Hz).

An increase in the RRinterval implies that the trajectory has more time to
get pushed into the peak and trough given by the R and S events.
This is reflected by the strong correlation between the RRintervals and the
RSamplitude as shown in Fig. 9. A technique for deriving a measure
of the rate of respiration
from the ECG has been proposed [5,6].
This ECGderived respiratory signal (EDR) is of clinical use in
situations where the ECG, but not respiration, is recorded.
The synthetic ECG provides a means of testing the robustness of such
techniques against noise and the effects of different sampling frequencies.
Figure 9:
RSamplitudes versus RRintervals for the synthetic ECG.

As a consequence of constructing the model with a variable angular frequency
, the time taken to
move from the Q event to the T event, known as the QTinterval, varies with
the RRinterval on a beattobeat basis.
The relationship between the QTinterval and the
RRinterval is linear as shown in Fig. 10.
Such a linear relationship has been reported for real ECGs and
has been used to calculate a corrected QTinterval [4].
It is interesting that this relationship is a direct consequence of the
model. Furthermore it may be possible to use the model to assess how much of
the variation in the QTinterval is due to RRinterval variability so that
this effect can be factored out.
Figure 10:
QTintervals versus RRintervals for the synthetic ECG.

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