Biology Reference
In-Depth Information
(referred to as time series analyses) that take into account the order of
the RRIs.
Entropy, as it relates to dynamical systems, is the rate of information
production. There are two measures developed to account for the pattern
of the data and estimation of the entropy in time series that can be applied
to cardiovascular data. One is called approximate entropy (ApEn),
introduced by Pincus (1991), and the other is called sample entropy
(SampEn), introduced by Richman and Moorman (2000). Our analysis
uses SampEn.
The basic idea is that we want to measure the regularity of a sequence
of measurements. Consider, for example, two sequences of 0s
and 1s:
Sequence S1:
1,0,1,0,1,0,1,0,1,0
Sequence S2:
1,1,1,0,0,1,0,0,0,1
Both sequences have five 0s and five 1s, but sequence S1 seems to have
a pattern, and sequence S2 seems random. Sample entropy assigns
a non-negative number to each sequence. The more regular a sequence
is, the lower the sample entropy will be. Thus, SampEn for sequence
S1 will be lower than SampEn for sequence S2.
Intuitively, in a regular sequence, if we know two or three adjoining
terms, then we have a good idea of what the next term will be. In
sequence S1, there are nine adjoining two-term subsequences (only eight
with a following term). Each subsequence is either 1,0 or 0,1, and if it is
1,0, the following term is always 1; if it is 0,1, the following term is
always 0.
E
XERCISE
6-7
Determine all different types of two-term subsequences for the sequence
S2.
In sequence S1, the 1,0 subsequence appears five times. Two identical
subsequences are called matches. When considering RRI data, it would be
highly improbable to ever have an exact match, even in subsequences of
length 2, so instead we say there is a match when the subsequences
agree within a certain tolerance. The customary way to assign this
tolerance depends on the SD of the sample. Usually, the tolerance t is
chosen to be the product, t
ΒΌ
SD, where r is a number between 0.1 and
0.25 and SD is the standard deviation of the sample.
r
