Complexity Changes in Human Wrist Temperature Circadian Rhythms through Ageing - Foundations on Natural and Artificial Computation - page 407

Table 1. Analysis of LZHP , ApEnHP and ApEnWP correlation with age

Signal β 1 r p ρ ps
LZHP sfa4 − 0 . 644 · 10 − 3 0 . 492 0 . 182 · 10 − 3 − 0 . 465 0 . 454 · 10 − 3
LZHP PPS sfa4 − 0 . 203 · 10 − 3 0 . 278 0.044 − 0 . 259 0 . 062
LZHP sflp − 0 . 738 · 10 − 3 0 . 469 0 . 399 · 10 − 3 − 0 . 448 0 . 770 · 10 − 3
LZHP PPS sflp − 0 . 269 · 10 − 3 0 . 290 0.035 − 0 . 261 0 . 059
ApEnHP sfa4 − 1 . 016 · 10 − 3 0 . 492 0 . 182 · 10 − 3 − 0 . 473 0 . 354 · 10 − 3
ApEnHP PPS sfa4 − 0 . 514 · 10 − 3 0 . 344 0.012 − 0 . 317 0 . 021
ApEnHP sflp − 0 . 795 · 10 − 3 0 . 431 1 . 270 · 10 − 3 − 0 . 381 4 . 849 · 10 − 3
ApEnHP PPS sflp − 0 . 546 · 10 − 3 0 . 369 0.007 − 0 . 355 0 . 009
ApEnWP sfa4 − 0 . 288 · 10 − 3 0 . 389 3 . 982 · 10 − 3 − 0 . 440 0 . 980 · 10 − 3
ApEnWP PPS sfa4 − 0 . 054 · 10 − 3 0 . 363 0.008 − 0 . 368 0 . 007
ApEnWP sflp − 0 . 315 · 10 − 3 0 . 417 1 . 880 · 10 − 3 − 0 . 463 0 . 488 · 10 − 3
ApEnWP PPS sflp − 0 . 045 · 10 − 3 0 . 296 0.032 − 0 . 301 0 . 029

0.3

0.11

0.28

0.1

0.26

0.09

0.24

0.08

0.22

0.07

0.2

0.06

0.18

0.05

0.16

0.04

0.14

0.03

0.02

0.12

60 70 10 20 30 40 50 60 70

10 20 30 40 50

Age (Yrs) Age (Yrs)

(b) ApEnWP vs age ( sflp )

(a) LZHP γ vs age ( sfa4 )

Fig. 2. Correlation of some phase complexity measures with age

identical parameters for linear regression, although ApEnHP has a slightly better
Spearman's rank correlation. However, LZHP exhibits the smallest sensitivity
to the signal bandwidth and the largest differences with surrogates. In fact,
ApEnHP fails the surrogate test for the sflp signal, but not for sfa4 .Conversely,
ApEnWP fails the surrogate test for the sfa4 signal, but not for sflp . In summary,
LZHP might be considered a more robust index.
Our analysis suggests that the signal bandwidth is somewhat critical for the
ApEn based measures. PPS surrogates seem to be too similar to the original
signal, perhaps because they retain some feature of the periodic orbit in the
phase space that ApEn statistic can not discriminate solely based on linear
regression. Further studies are needed to assess the dependence on bandwidth
and different kinds of cyclic surrogates should be tested. It is worth to note that
the mean value of the LZHP index for sfa4 signals is γ =0 . 196 0 . 031, while for

a pure 1 c/d sinusoidal signal it is γ =0 . 050. This seems to reveal a relatively
high phase complexity level in healthy circadian temperature rhythms.

±