Many variability indices, which have been proposed to quantitatively represent both short-term variability (=STV) and long-term variability (=LTV), were analyzed mathematically and the following static property was obtained.
All of the approximate expectations for indices developed by Tarlo, Kero, Dalton, Heilbron and Cabal assumed the same formula
k√1-ρσ (
k: constant, ρ: correlation coefficient between the beat-to-beat interval
Ti and the adjacent interval
Ti+1, σ: standard deviation of
Ti), and were indentical except for the constants. Those values for de Haan's and Yeh's indices were
k√1-ρσ/
T0 (
T0: mean of
Ti), while those for Modanlou's, Wade's, and Organ's indices were
k√1-ρσ/
T02 respectively.
Hence, all of these indices represented the same quantity in essence when the mean beat-to-beat interval was constant. The expected value for de Haan's and Heilbron's LTV indices was approximately
k√1+ρσ (
k: constant), while those for Yeh's, Organ's, and Cabal's LTV indices essentially showed standard deviation (=σ) of
Ti.
From these results, it can be concluded that measuring STV and LTV according to those formulae means evaluating ρ and σ at the same time.
Hence, there may be little significance in measuring them individually if ρ changes little. That is, it may suffice merely to measure the standard deviation (=σ) of
Ti as a quantity of variability.
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