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by (
3.214
). They observed for data sets of patients with severe heart failure that the
spectrum is essentially constant in the low-frequency regime, indicating that the
I
)
are not correlated over long times; see Figure
3.8
. The interpretation of this conclusion
in terms of random walks will be taken up in later chapters. For the time being we
note that for healthy individuals the data set yields 2
H
(
n
−
=−
.
≈
.
04,
indicating a long-time correlation in the interbeat interval differences. On comparing
this with classical diffusion we see that the time exponent is nearly zero. Peng
et al
.
use this result to point out that 0
1
0
93 so that
H
0
2 implies that the interbeat intervals are
anticorrelated, which is consistent with a nonlinear feedback web that “kicks” the heart
rate away from extremes. This tendency operates statistically on a wide range of time
scales, not on a beat-to-beat basis [
48
].
Note that the naturally evolved control mechanism for the heart is one that imposes
the inverse power-law on the long-time memory, anticipating when the next long delay
is going to occur and suppressing it. Consequently, this control web operates to reduce
the influence of extreme excursions and narrows the otherwise even broader range of
<
H
≤
1
/
(a)
10
-8
a
Normal
β
= 1
10
-9
10
-10
10
-11
10
-4
10
-3
10
-2
f [beat
-1
]
(b)
10
-8
Heart disease
b
10
-9
β
= 0
10
-10
10
-11
10
-4
10
-3
10
-2
f [beat
-1
]
The power spectrum
S
I
(
f
)
for the interbeat interval increment sequences over approximately 24
hours for the same subjects as in Figure
3.7
. (a) The best-line fit for the healthy adult has a slope
of
β
=
0
.
93. (b) The best-line fit for the patient with severe heart failure has an overall slope of
0.14 [
38
]. Reproduced with permission.
Figure 3.8.
