Biology Reference
In-Depth Information
matches of length m
24 (each template
101 or 010 has three matches). SampEn is then computed as
SampEn
¼
3isA
¼
3
þ
3
þ
3
þ
3
þ
3
þ
3
þ
3
þ
3
¼
¼
ln(A/B)
¼
ln(24/24)
¼
0, signifying complete order.
Now consider series S2, also having five 1s and five 0s, but in a more
random order: 1,1,1,0,0,1,0,0,0,1. The SD of this series is again 0.527
because SD does not depend on the order of observations. Thus, the
similarity tolerance would be again t
0.1054. All subsequences of
length 2 in the series are 11,11,10,00,01,10,00. Thus, the total number of
template matches of length m
¼
¼
2isB
¼
1
þ
1
þ
1
þ
2
þ
0
þ
1
þ
2
þ
2
¼
10. All
subsequences of length m
3 are 111,110,100,001,010,100,000,001, and
the total number of template matches of length m
þ
1
¼
¼
3isA
¼
0
þ
0
þ
1
þ
1
þ
0
þ
1
þ
0
þ
1
¼
4. Then, SampEn
¼
ln (4/10)
¼
0.9163,
signifying a certain degree of irregularity.
Thus, two time series that otherwise have identical distributions of 0s
and 1s (and therefore identical distribution-based characteristics) are
distinguished solely on the basis of the order of their observations. In the
first case, the series is periodic (i.e., there is apparent order), leading to
0 SampEn, while in the second there is no apparent order, and the
SampEn is substantially larger.
With regard to HRV, Griffin and Moorman (2001) and Lake et al. (2002)
have shown that SampEn is lower for RRI records with reduced variability
and transient decelerations. Thus, SampEn is another potential predictor
of sepsis and SIRS in prematurely born infants. Because a lower value
of SampEn indicates reduced complexity and more self-similarity in
the RRI time series, lower SampEn before sepsis would capture
decreased system complexity, disruption in the signal transduction
pathways controlling the HR, and increased system isolation.
SampEn has been validated in clinical studies recording HR in
premature infants. Figure 6-12 presents a plot of the changes in HR
SampEn of an infant during the 9 days before sepsis. There is an
apparent transient reduction in SampEn 4 to 5 days before sepsis,
indicating temporarily increasing HR regularity, and larger and more
sustained reduction in SampEn during the 24 hours before the
clinical manifestation of sepsis. As presented here, SampEn, combined
with the other measures of HRV discussed in this chapter, is a powerful
tool for predicting potentially deadly clinical situations.
E
XERCISE
6-9
For m
0.2, calculate SampEn for the sequences
0,0,1,0,0,1,0,0,1 and 1,0,0,0,1,0,1,0,0. What can you say about their SDs?
¼
2 and r
¼
